Visualisation of Risk Levelin Portfolio Management

Jonathan Mårtensson

U.U.D.M. Project Report 2005:12

Examensarbete i matematik, 10 poäng

Handledare och examinator: Maciej Klimek

Handledare: Jan Aronsson, Handelsbanken

November 2005

Department of Mathematics

Uppsala University

1

Abstract

In this dissertation a method of extracting raw market data in order to visualise portfolio risk is implemented. It concerns the risk in a Swedish stock portfolio, where the sample mean and the sample standard deviation are calculated from a 90 days interval. These numbers are then used in the Geometric Random Walk model in order to forecast a possible risk interval for the portfolio. A program called Forecast has been developed in Matlab in order to test if the implementation is possible. In Forecast six Swedish stocks are available and the forecast horizon ranges from one day to two years. A function called forecast within makes it possible to compare the real outcome of the portfolio to the forecasted interval and by using this function the forecast can be verified. The results show that it is only in special cases that the time series move outside the forecasted interval and thus the method seems reliable. The conclusion is that it is possible to create a risk visualisation for the end customer by extracting the portfolio data.

2

Contents 1 Introduction 4

1.1 Background...................................................................................4 1.2 Definition of the problem..............................................................4 1.3 The purpose of the project ............................................................5 1.4 Limitations ....................................................................................5

2 Theory 5

2.1 Assets ............................................................................................5 2.1.1 Stock .................................................................................5 2.1.2 Portfolio ............................................................................6 2.2 Mathematical background.............................................................7 2.2.1 Random variables..............................................................7 2.2.2 Expected value ..................................................................8 2.2.3 Variance – Standard deviation ..........................................9 2.2.4 Skewness – Kurtosis .........................................................9 2.2.5 Covariance ......................................................................10 2.2.6 Correlation ......................................................................10 2.2.7 Normal distribution.........................................................11 2.2.8 Lognormal distribution ...................................................11 2.3 Sampling .....................................................................................13 2.3.1 Sample mean and variance..............................................13 2.3.2 Confidence interval for the sample mean .......................14 2.3.3 Confidence interval for the sample variance ..................14 2.3.4 Sample covariance ..........................................................15 2.4 Stochastic processes....................................................................15 2.4.1 Autocovariance – Autocorrelation..................................15 2.4.2 Partial Autocorrelation function .....................................16 2.5 Time series ..................................................................................16 2.5.1 Stationary – non-stationary process ................................16 2.6 Forecasting..................................................................................20 2.6.1 Geometric Random Walk ...............................................20

3 Data 22

3.1 Data presentation ........................................................................22 3.2 Data analysis ...............................................................................22

4 Software for simulation 28

4.1 Important functions.....................................................................30

3

4.2 Implementation of the theory......................................................31 4.2.1 Create portfolio time series up to forecast date ..............31 4.2.2 Sampling .........................................................................32 4.2.3 Portfolio estimation.........................................................33 4.2.4 Portfolio recommendations.............................................34 4.2.5 Portfolio forecasting........................................................35

5 Simulation 36

6 Conclusions and suggestions to future studies 43

6.1 Conclusions.................................................................................44 6.2 Suggestions to future studies ......................................................44

7 Acknowledgements 45

A Appendix 47

4

1 Introduction The purpose of this dissertation is to show how risk in a customer portfolio can be visualised with the aid of the Geometric Random Walk model. The Geometric Random Walk is commonly used to model the behaviour of stocks and it will be described later in this paper. It will also include discussions regarding assumptions and requirements when implementing this model. Risk control has become an important factor for investors and when a group at J.P. Morgan released their RiskMetrics document in 1994 and publicly made available guidelines for evaluating portfolio risk, the awareness started to spread among initiated investors. The study of Geometric Random Walk is interesting since it captures the fundamental principles of the stock market behaviour which is essential in a risk model. With the aid of historic sampling and forecasting a visualisation of risk can be constructed and presented to end customers. This risk presentation will hopefully become an important factor for investors when analysing and constructing portfolios. With this paper the path from raw market data, through mathematics, to an understandable risk visualisation will be explained and analysed with the aid of a program called Forecast developed in Matlab for this sole purpose.

1.1 Background There is no perfect mathematical model for the behaviour of stocks. But during the 20th century mathematicians have developed different tools to model the behaviour reasonably well. Since the publication of RiskMetrics the field of risk analysis has risen in importance for regulatory bodies and large institutions. The widespread use of such factors has not yet been established among the public. Therefore it is interesting to analyse a possible way of visualising the portfolio risk for end customers.

1.2 Definition of the problem How can risk be visualised for the end customer with the aid of mathematics? And how can mathematics be used for recommendations concerning increasing or decreasing the portfolio risk for the end customer.

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1.3 The purpose of the project The main purpose is to find a technique to visualise risk for the end customer. In doing so it is necessary to find a way of extracting information from raw market data. With the aid of the extracted information it is possible to compute the characteristic values of the data. These values can then be used in the Geometric Random Walk model to create a forecasted interval that will visualise the portfolio risk for the end customer. The characteristic values of the data can also be used to recommend stocks that will increase or decrease the risk in the customer’s portfolio.

1.4 Limitations The main purpose of this paper is to find a way from raw market data to a risk visualisation of a customer’s portfolio. The limitations have been established by Handelsbanken and the instruments have been limited to Swedish stocks. Therefore bonds, options and the risk-free asset are excluded. All of these excluded instruments are of course possible in the real world and it would be interesting to see how they would affect the recommendations, which in itself could be a whole new paper. Despite these limitations the main purpose is still fulfilled since the risk level of Swedish stocks is an important parameter for the end customers.

2 Theory In this section the mathematical background of the problem will be introduced.

2.1 Assets This section will address stocks and portfolios and introduce the notations used in this paper.

2.1.1 Stock A stock is an instrument that is traded continuously throughout the opening hours of the stock exchange so that the price can change during the day. Therefore if an investor buys a stock i at day 1−t , which is the

6

time index of the previous day, for the price 1, −tip and sells the stock at day t , i.e. today for tip , the rate of return is

1,

1,,,

~−

−−=

ti

tititi p

ppr (1)

Since 1ln1,

,

1,

, −≈⎟⎟⎠

⎞⎜⎜⎝

⎛

−− ti

ti

ti

ti

pp

pp

when 1,

,

−ti

ti

pp

is close to 1, which is true for

stocks, the log-return

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−1,

,, ln

ti

titi p

pr (2)

can be used instead of (1). [1]

2.1.2 Portfolio There are many stocks available on the stock exchange and an investor can buy several to form a portfolio. The portfolio will then consist of multiple stocks with different returns tir ,

~ , where each stock will have a weight iw in the portfolio. For example if a portfolio consist of two stocks with a portfolio value of 40 SEK and 80 SEK respectively, the weights of each

stock in the portfolio are 31

1 =w and 32

2 =w . In general the return [1] of a

portfolio consisting of a stocks is

∑=

=a

itiit rwR

1,

~~ (3)

where the weights satisfy the condition

∑=

=a

iiw

11 (4)

7

2.2 Mathematical background In this section the mathematical background of the problem will be introduced. This paper is intended for readers with varying backgrounds and therefore some basic concepts will be discussed along with sections intended for more experienced readers.

2.2.1 Random variables In order to find a possible model for the behaviour of stocks, random variables are introduced. A random event is an outcome that cannot be predicted and in the case of stocks, the return as defined earlier is a random event since the sell price is unknown when the stock is bought. A random variable is a mathematical concept describing a quantity whose behaviour is non-deterministic. A full probabilistic description of a random variable X can be given in the form of its cumulative distribution function defined as ( ) =dFX Prob [ ]dX ≤ (5) for all real numbers d . A random variable is said to be discrete if the outcomes are values within a discrete set of numbers, which may be finite or not. For example stock prices or stock returns can be reasonably modelled by discrete random variables. In practice, however, it is more convenient to model these quantities by continuous random variables, i.e. random variables whose cumulative distribution functions are continuous. Such random variables can have outcomes of any value within an interval. A random variable X is said to have a probability density function Xf if, for some non-negative function Xf of one variable, it is true that the probability of all outcomes equal

( )∫∞

∞−

= 1dxxf X (6)

and

Prob [ ] ( )∫=<<c

bX dxxfcXb (7)

8

for all values b , c such that ∞≤<≤∞− cb . If this is the case then

( ) ( )dx

xdFxf XX = (8)

and

( ) ( )∫∞−

=x

XX dyyfxF (9)

for any real number x . This paper will use this type of random variables exclusively. Since the true characteristics of random variables are unknown, the data has to be analysed to find out if there is a model that approximately corresponds to the data. With the aid of a histogram the shape of the probability density function can be approximated. [2]

Figure 1: Histogram of the daily log-returns of Volvo B over 180 trading days.

2.2.2 Expected value A continuous random variable X has an expected value

( ) ∫∞

∞−

== dxxxfXE XX )(μ (10)

where Xf denotes the probability density function. [3]

9

2.2.3 Variance – Standard deviation The variance and the standard deviation are measures of dispersion around the expected value. If the value of the variance is low the probability of a number far from the expected value is low whereas if the variance is high a number far away has a higher probability. The formula for calculating the variance of X is [3] ( ) ( )[ ] ( ) 2222

XXX XEXEXVar μμσ −=−== (11) whereas the standard deviation of X is

( )XVarXX == 2σσ (12) which has the same units as the random variable. According to (11) the variance is always non-negative, i.e. 02 ≥Xσ (13) Furthermore if X is deterministic, the variance is 02 =Xσ (14)

2.2.4 Skewness – Kurtosis The skewness and kurtosis measures give a representation of the characteristics of the probability density function. The skewness value is a measure of how asymmetrical the function is, i.e. how much it leans to the left or to the right. The skewness measure is

( )[ ]3

3

X

XXESkewnessσ

μ−= (15)

The kurtosis value is a measure of how tall or flat the function is. The kurtosis measure is [4]

( )[ ]4

4

X

XXEKurtosisσ

μ−= (16)

10

2.2.5 Covariance The discussion so far has focused on the basic principles of a single random variable. It is also interesting to evaluate the dependence among two random variables. For instance if a portfolio consist of several stocks, i.e. several random variables, it is important to understand the characteristics of each random variable, but also how they relate to each other in order to fully understand the dynamics of the portfolio. The relationship between the outcomes of two random variables is called covariance, which is ( ) ( )( )[ ]221121, μμ −−= XXEXXCov (17) where 1μ and 2μ are the expected values of the respective random variables. The covariance thus measures the linear dependence among the random variables. A large covariance value indicates that the linear dependence among the variables is strong. If the covariance is positive the values of 1X and 2X increase at the same time whereas a negative value indicates that 1X decrease when 2X increase. If 1X and 2X are jointly normal and the covariance is zero, then the variables are independent. [2]

2.2.6 Correlation Since the covariance depend upon the scale of measurement it is hard to interpret if a high value indicates a strong covariance or not. Therefore correlation is introduced

( ) ( )21

2121

,,σσ

ρ XXCovXXCorr == (18)

where 1σ and 2σ are the standard deviations of 1X and 2X . The correlation coefficient standardises the value so that it is in the interval 11 ≤≤− ρ (19) The sign of the correlation is the same as the covariance but the scale has changed and hence 1 indicates perfect linear dependence among the variables. [2]

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2.2.7 Normal distribution The normal distribution has been studied thoroughly and therefore its characteristics are well known. In this paper it is said that a random variable X is normally distributed if, for some constants 0>Xσ and Xμ , the probability density function of X is

( )( )

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

=2

2

2

21 X

Xx

XX exf σ

μ

πσ (20)

In this paper this fact is denoted by writing ( )2,~ XXNX σμ . By necessity

Xμ is the expected value and Xσ is the standard deviation of X . The shape of the graph of Xf is similar to the curve shown in Figure 1. The normal distribution has a skewness of 0 and a kurtosis value of 3. For other probability distributions a positive or negative value of skewness describes how non-symmetrical those distributions are, whereas a high value of kurtosis indicates that the distribution is more peaked at the centre and has fatter tails than the normal distribution. The normal distribution gives a reasonable approximation of the distribution of the log-returns of Volvo B in Figure 1. There is however one outlier at -0.08 which means that the distribution has fat tails, i.e. higher probability of extreme outcomes. Thus if the log-returns of Volvo B are modelled with the normal distribution the extreme outcomes are unlikely in the model. They are however quite rare which will be shown in the data section later in this paper. But the extreme outcomes are movements in the stock that can affect the portfolio severely and thus it is important to realise that the model is not a complete representation of the behaviour of stocks. On the other hand both mathematical models as well as fundamental analysis cannot predict extreme outcomes like a market crash or an extreme rally. Therefore this approximation is reasonable and common among practitioners. If the number of returns is increased, the histogram will be smoother and an approximation will be more reliable.

2.2.8 Lognormal distribution The random variable Y is log-normally distributed if XeY = , where X is normally distributed. Furthermore

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( ) { }( ) }{( )( )

∫∞−

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

=≤=≤=y dxx

XY

X

X

eyXPyYPyFln

2 2

2

21ln σ

μ

σπ (21)

is its cumulative distribution function. Therefore the probability density function is

( ) ( )( )

⎟⎟⎠

⎞⎜⎜⎝

⎛ −−

==2

2

2ln

21 X

Xy

XYY e

yyF

dydyf σ

μ

σπ (22)

This gives the relationship between the normal and the lognormal probability distributions and therefore it is now possible to see how the means and variances correspond. The mean and variance of the normal distribution are denoted Xμ and 2

Xσ as previously stated and if the corresponding values of the lognormal distribution are denoted by m and

2s the relationships are [5]

( ) 2

2X

XeeEm Xσμ +

== (23) and

( ) ( ) ( )1122

2

222

2 −=−==⎟⎟⎠

⎞⎜⎜⎝

⎛+

XX

XX

emeeeVars X σσσμ

(24) This leads to the reverse relations

⎟⎟⎠

⎞⎜⎜⎝

⎛+= 1ln 2

22

ms

Xσ (25)

and

2

ln2X

X m σμ −= (26)

13

2.3 Sampling In order to forecast the risk of a portfolio the mean return, the variance and the covariance of stocks are important. Since the true values are not known there are different methods of approximating them. A common practice is to use historic sampling from the available portfolio data. Another method is to derive the necessary terms from options but this would not be suitable for this paper since options are not available on all Swedish stocks. There is also a problem with the forecast horizon when using the implied volatility from options, since a volatility derived from a six month option can only be used for a six month forecast. [6] Historic sampling is a method that is fairly reliable for the variance of a stock and the covariance between stocks but it is not as reliable for the mean return. It is therefore important to select a sampling interval that is sufficient and in this paper a 90 days interval will be used as recommended by [7]. That is equal to a period of about 4 months since there is no data for Saturdays and Sundays.

2.3.1 Sample mean and variance Given a set η,1, ,..., ii rr of independent observations of the random variable

ir the expected value and the variance are often estimated with the following unbiased estimators. The sample mean is

∑=

=η

η 1,

1ˆt

tii rr (27)

and the sample variance is

( ) ( )∑=

−−

=η

ησ

1

2, ˆ

11,ˆ

titiii rrrr (28)

These formulas can also be interpreted differently. Suppose that ( )tir , , where η,...,1=t , are observations from a sequence of independent identically distributed random variables. In this case (27) and (28) are estimates of the expected value

irμ and the variance 2

irσ common to all of

these random variables.

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2.3.2 Confidence interval for the sample mean Since the true mean is approximated by the derived sample mean there is an uncertainty in the value. Therefore the confidence interval, at a

( )%1100 α− confidence level, for the sample mean ir̂ as stated in (27) is

according to [5] equal to ( ) ( )

⎥⎥⎦

⎤

⎢⎢⎣

⎡+−

ησ

ησ

ααii

iii

i

rrtr

rrtr

,ˆˆ,

,ˆˆ . An

example from the program Forecast is Volvo B where the sample size is 90 days, the daily sample mean 00109.0ˆ =ir and the daily sample

standard deviation ( ) 01606.0,ˆ =ii rrσ . At a 95% confidence level, a two-sided t -Student distribution with ( )891 =−η -degrees of freedom has the value 987.1025.0;89 =t . This leads to a confidence interval for ir̂ that is

[ ]004454.0,002274.090

01606.0987.100109.0,90

01606.0987.100109.0 −=⎥⎥⎦

⎤

⎢⎢⎣

⎡+−

Thus with 95% confidence the sample mean is in the interval -0.23% to 0.45%. This demonstrates a problem called the mean blur since the interval around the sample mean %11.0ˆ =ir is quite broad. A daily percentage return ranging from -0.23% to 0.45% does make a difference in the long run when forecasting.

2.3.3 Confidence interval for the sample variance The confidence interval for the sample variance is derived from the fact

that ( )2

,ˆ

ir

ii rrσ

ση has a 2χ -distribution with ( )1−η -degrees of freedom. As

shown in [5] the confidence interval for a ( )%1100 α− confidence level is

( ) ( )⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

−2

2

2

21

,ˆ,,ˆ

αα χση

χση iiii rrrr which means that both the nominator and the

denominator depend on the sample size η . Thus in the Volvo B example with 05,0=α and ( ) 000258.0,ˆ =ii rrσ the confidence interval for the daily sample variance would be equal to

[ ]000197.0,000354.0136.118

000258.090,6466.65

000258.090 =⎥⎦

⎤⎢⎣

⎡. The confidence

interval for the sample variance is thus quite small. For the daily sample

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standard deviation the interval would be [ ]01402.0,018807.0 where ( ) 016062.0,ˆ =ii rrσ . Therefore it is possible to use sampling as a method

of deriving the mean and variance but one should bear in mind that the mean blur can affect the end result.

2.3.4 Sample covariance In order to calculate the sample covariance between two time series the samples from the second time series must have the same characteristics as the ones previously defined in 2.3.1, i.e. ( )tjr , which is drawn from an independent identically distributed sequence. tir , and tjr , are also assumed to have a joint normal distribution that does not depend on t . The sample covariance is

( ) ( )( )∑=

−−−

=η

ησ

1,, ˆˆ

11,ˆ

tjtjitiji rrrrrr (29)

The sample mean, sample variance and the sample covariance will be used in this paper as the input parameters to the forecast model.

2.4 Stochastic processes The Greek word stokhos which means a target or bull’s-eye is the originator of the word stochastic. A stochastic process is a time ordered sequence of random variables. With a dart board in mind one can understand that a game of darts is a stochastic process. The player aims to hit the bull’s-eye each time but often the result will be a hit outside of the midpoint. So each throw is a random variable which can result in a hit of the bull’s-eye or some other place around the centre. Comparing this to the development of the stock price tip , one can see that the price tomorrow is unknown and hence random. Since this will be true each future day the price process, similar to the dart game, is a stochastic process.

2.4.1 Autocovariance – Autocorrelation In order to describe the evolution of a stochastic process tX , the concepts of autocovariance and autocorrelation are used. The functions offer a measure of the degree of dependence between the values at different time

16

steps, for example ht + and t , i.e. lag ( ) htht =−+ , the autocovariance function of tX at lag h is ( ) ( )( )[ ]μμ −−= ++ thttht XXEXXCov , (30) Since the coefficient of the autocovariance depends on the unit of tX the autocorrelation function that normalise the autocovariance function is introduced

( ) ( )( ) ( )hthttt

thttht

XXCovXXCov

XXCovXXCorr++

++ =

,,

,, (31)

With the aid of the autocorrelation function it is possible to study if there is a trend in the data or if there is a seasonal component, i.e. the data is not random. These functions will be used in Section 3.2 to analyse if transformed time series have a trend or a seasonal component. [8]

2.4.2 Partial Autocorrelation function The partial autocorrelation function is another measure of dependence. The value of the autocorrelation function can be affected by intermediate variables. For example the autocorrelation function between 1+tX and

3+tX can be affected by the correlation they have with the variable in between, i.e. 2+tX . This problem is eliminated by the partial autocorrelation function since it removes the correlations with the intermediate variables. [4]

2.5 Time series In this section the basics of time series will be discussed as well as different tests for determining the characteristics of a time series. A time series, in this paper a known development of the stock price tip , , is a particular realisation of a stochastic process that develops in time.

2.5.1 Stationary – non-stationary process It is important to understand what a stationary time series is and how a non-stationary time series can be transformed so that it can be tested for stationarity. If samples from a non-stationary time series would be used

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they would not be valid for another time frame and thus not valid for a forecast model. [9] In order for a time series to be weakly stationary it must have constant mean and variance over time. The autocovariance must only depend on the lag between two time periods and not the time at which it is calculated. The weak form of stationarity is often enough and will therefore be used in this paper. The samples derived from a weakly stationary time series are suitable for the forecast model. An example of a non-stationary time series is the price process tp of Volvo B over the last 180 trading days.

Figure 2: Time series plot of the price process tp of Volvo B over 180 trading days. As seen in Figure 2 the positive trend in the time series is not constant and thus it is not stationary. In order to transform it into a stationary time series the first step is to use the return process instead of the price process. The result is seen in Figure 3.

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Figure 3: Time series plot of the return process 1−t

t

pp of Volvo B over 180

trading days. In Figure 3 the fluctuating trend that was visible in Figure 2 has diminished. The final step in the transformation is to take the logarithm of the return process which results in the time series in Figure 4.

Figure 4: Time series plot of the log-return process ⎟⎟⎠

⎞⎜⎜⎝

⎛

−1

lnt

t

pp over 180

trading days. The time series in Figure 4 is based on the same data used for the histogram in Figure 1. In order to analyse if a time series is stationary there are several tests available where graphical analysis and correlogram test are two. The graphical analysis is simply a matter of checking the graph of the time series to see if there is a trend present in the data, as was

19

the case in Figure 2. In the correlogram test the plots of the autocorrelation function and the partial autocorrelation function are used to see if there is a trend present. Two correlograms of Volvo B over 180 days are seen in Figure 5 and Figure 6.

Figure 5: The Autocorrelation function of the price process tp of Volvo B over 180 trading days.

Figure 6: The Autocorrelation function of the log-return process ⎟⎟⎠

⎞⎜⎜⎝

⎛

−1

lnt

t

pp

of Volvo B over 180 trading days. As seen in the correlograms above, in Figure 5 there is a clear trend and several observations are outside the significance limits whereas in Figure 6 there are no significant autocorrelations and no observable trend. Hence the log-return process of Volvo B over 180 trading days seem to be stationary according to the correlogram test in Figure 6.

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The unit root test is another method of analysing time series. The null hypothesis is that there is a unit root and thus the time series is non-stationary. The alternative hypothesis is that the time series is stationary. If the test rejects the null hypothesis the time series is stationary. In this paper the tests are performed with the statistical programs EViews and Minitab. The unit root tests used are the Augmented Dickey-Fuller test, that takes into account that the error terms can be correlated and the Phillips-Perron test that use nonparametric statistical methods to handle possible serial correlation in the error terms. [4] EViews is also used to test the transformed time series for normality. The tests used are Lilliefors, Cramer-von-Mises, Watson and Anderson-Darling where the null hypothesis is that the data is normally distributed.

2.6 Forecasting In order to forecast a time series the mean, variance and covariance of the time series is necessary. These statistics are derived by sampling from the transformed time series as discussed previously in this paper. The final step is to have a model for the behaviour of stock prices where the derived values will be used. Therefore the forecast model will be discussed in this section.

2.6.1 Geometric Random Walk There is a wide variety of models available to model the behaviour of stocks. Among popular volatility models are ARCH (Auto Regressive Conditional Heteroscedasticity), GARCH, IGARCH, EGARCH where the latter are versions of ARCH. These models are based on the notion that the volatility of time series is time dependent. There is however studies that have shown that over a longer time period these models do not outperform the geometric random walk [6]. Therefore this paper is based on the geometric random walk model which is a reasonable stock model. According to [5] a stochastic process tP , with discrete time

,...2,1,0=t , is called a geometric random walk with parameters 0>σ and ν if ( )t

tt ePP σεν ++ =1 (32)

where the random variables ( ) ( )1,0~ Ntε are independent. In order to have an interpretation of ν and σ it is observed that if

0≥> st , then

21

( ) ( )⎟⎟

⎠

⎞⎜⎜⎝

⎛+− ∑

=

−

=

1t

su

ust

st ePPεσν

(33)

and thus

( )stPPE

s

t −=⎟⎟⎠

⎞⎜⎜⎝

⎛νln (34)

and

( )stPPVar

s

t −=⎟⎟⎠

⎞⎜⎜⎝

⎛ 2ln σ (35)

In this case the ratio s

t

PP denotes the total return over the time period from

time s to time t and hence the quantities ν and σ are linked to the logarithmic return of portfolio P . Since the random variables ( )uε are independent, if 0P is deterministic and 0=s , then the relationship ( )ttPNPt

20 ,ln~ln σν+ (36)

is true. Which in turn means that tP is lognormal. If μ is defined as

2

2σνμ += (37)

the previous formulas leads to the final expressions for the expected value

( )st

s

t ePPE −=⎟⎟⎠

⎞⎜⎜⎝

⎛ μ (38)

and the variance

( ) ( )( )122 −=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −− stst

s

t eePPVar σμ (39)

22

which will be used as the forecasted mean and variance of the price series tP in this paper. Note also that ν and 2σ are approximated by the

weighted sample mean and the weighted sample variance as previously defined.

3 Data In this section the data used in this paper will be presented along with results from statistical tests performed on the data.

3.1 Data presentation The price processes of the Swedish stocks ABB LTD SDB, Axis, Ericsson B, Readsoft, SHB A and Volvo B constitute the data used in this paper. The data is based on daily price observations and adjusted for splits and issues.

Stock Start date End date Number of observations ABB LTD SDB

Axis Ericsson B Readsoft SHB A Volvo B

1999-06-22 2000-06-27 1982-01-04 1999-06-22 1982-01-04 1982-06-14

2005-08-23 2005-08-23 2005-08-23 2005-08-23 2005-08-23 2005-08-23

1550 1295 6095 1550 6095 5980

Table 1: The start date, end date and the number of observations of the stocks used in this paper. These stocks are intended to represent a selection of possible stocks in a private portfolio. The time series are extracted from the technical analysis program Vikingen and the longest time series dates back to 1982.

3.2 Data analysis Since the data in Table 1 is transformed as described in Section 2.5.1 the number of observations of each time series is decreased by one. The data used in the sampling is analysed in the statistical programs Minitab and Eviews. Tests and measures are explained in the theory chapter.

23

Stock Mean SE Mean St. Dev. Skewness Kurtosis ABB LTD SDB

Axis Ericsson B Readsoft SHB A Volvo B

-0.00067 0.00006360.000614 0.000712 0.000557 0.000585

0.0011 0.00112 0.00036 0.00118 0.000259 0.000242

0.043128 0.040373 0.028071 0.046476 0.020248 0.018708

-6.15 0.24 -0.25 0.38 0.58 0.13

141.59 4.5 8.1 5.37 13.91 3.57

Table 2: The daily mean, standard error of mean, standard deviation, skewness and kurtosis of each full length log-return series. The mean, the standard error of the mean and the standard deviation of each time series in Table 2 are small because they are daily values. The skewness and kurtosis measures are not equal to the values of the normal distribution. The tests for normality in the last column of Table 3 indicate that the distribution of the full length log-return series is not normally distributed. This show that the assumptions for the model are not fulfilled for the full length series.

Stock ACF PACF ADF P-P Normal ABB LTD SDB

Axis Ericsson B Readsoft SHB A Volvo B

Yes Yes Yes No Yes Yes

Yes No Yes Yes Yes Yes

No No No No No No

No No No No No No

No No No No No No

Table 3: Autocorrelation function, partial autocorrelation function, Augmented Dickey-Fuller test, Phillips-Perron test and tests for normality of each full length log-return series. The autocorrelation functions for all stocks except Readsoft indicate that there are several significant values for the autocorrelation coefficient at different lags. This is also true for the partial autocorrelation functions except in this case Axis’s values are non-significant. The Augmented Dickey-Fuller and Phillips-Perron tests for unit root indicate that all the time series are stationary since they reject the null hypothesis that there is a unit root in the time series. Finally the tests for normality all indicate that the null hypothesis that the time series are normally distributed is rejected, i.e. they are not normal.

24

If the data of the last 90 trading days, that is the data used in the program, is analysed the result is shown in Table 4 and Table 5.

Stock Mean SE Mean St. Dev. Skewness Kurtosis ABB LTD SDB

Axis Ericsson B Readsoft SHB A

Volvo B

0.00201 0.00418 0.00264 0.00212

-0.00006440.00109

0.00172 0.00321 0.00146 0.00341 0.0009850.00169

0.016279 0.03048 0.013856 0.032249 0.009349 0.016062

-0.96 1.1 0.21 -1.25 -1.38 -1.78

3.5 4.3 1.29 8.1 5.88 7.92

Table 4: The daily mean, standard error of mean, standard deviation, skewness and kurtosis of each 90 days log-return series. In the time span of 90 days, the mean, the standard error of the mean and the standard deviation of the time series in Table 4 are small since they are daily values. The skewness measures are not close to zero but the kurtosis measures are not as extreme as in Table 2. They do however indicate that they are not normally distributed.

Stock ACF PACF ADF P-P Normal ABB LTD SDB

Axis Ericsson B Readsoft SHB A Volvo B

No No No No No No

No No No No No No

No No No No No No

No No No No No No

Yes No No No No No

Table 5: Autocorrelation function, partial autocorrelation function, Augmented Dickey-Fuller test, Phillips-Perron test and tests for normality of each 90 days log-return series. In this case there are no significant values for the autocorrelation function or partial autocorrelation function and thus the data does not contain a trend or a seasonal pattern. The ADF and P-P tests for unit root indicate that the time series are stationary since they reject the null hypothesis that there is a unit root in the time series. In the case of the tests for normality ABB LTD SDB cannot be rejected as normally distributed whereas all the other indicate that they are not normal.

25

If these time series are visualised with a time series plot and a histogram, the result indicate that they are approximately normally distributed except for the extreme outliers that cause the data to have fat tails.

Figure 7: Time series plot and histogram of the log-return process of ABB LTD SDB over 90 trading days.

Figure 8: Time series plot and histogram of the log-return process of Axis over 90 trading days.

26

Figure 9: Time series plot and histogram of the log-return process of Ericsson B over 90 trading days.

Figure 10: Time series plot and histogram of the log-return process of Readsoft over 90 trading days.

Figure 11: Time series plot and histogram of the log-return process of SHB A over 90 trading days.

27

Figure 12: Time series plot and histogram of the log-return process of Volvo B over 90 trading days. An interesting result is obtained if the single most extreme value in each 90 days time series is set to zero. The Anderson-Darling normality test indicates that some of the time series cannot be rejected as normally distributed. The p-values of the test are seen in Table 6.

Stock Anderson-Darling Test p-value ABB LTD SDB

Axis Ericsson B Readsoft SHB A Volvo B

0.185 0.012

< 0.005 0.162 0.010 0.673

Table 6: P-values of the Anderson-Darling test for normality when the single most extreme value is set to zero. ABB LTD SDB, Readsoft and Volvo B cannot be rejected as normally distributed at 95% confidence level. The tests performed on the transformed data indicate that the data is stationary and approximately normally distributed. The approximations of the Geometric Random Walk model do not incorporate all aspects of the real behaviour of stocks. The extreme values are not incorporated into the model and hence as discussed earlier the forecast will fail in the case of extreme outcomes.

28

4 Software for simulation In order to find a method of extracting raw market data, transforming the data and then forecasting the time series a program called Forecast has been developed in Matlab.

Figure 13: Screenshot of Forecast developed in Matlab. A portfolio of ABB LTD, Ericsson B and Volvo B is forecasted 6 months and stocks for increasing or decreasing the portfolio risk are recommended. A flowchart of the sampling and forecast steps is seen in Figure 14.

29

Figure 14: Flowchart of the key steps of the sampling and forecast.

Sampling Stock prices tip , of all stocks. 6 stocks in paper or 270 on Stockholmsbörsen up to time 0t

Conversion of tip , to log-returns tir ,

Sample mean ir̂ and covariance ( )ji rr ,σ̂ of log-returns of all stocks based on the last

90=η days

Conversion to estimated mean im and covariance ( )ji rrs , of returns of all stocks

Calculation of estimated mean M and covariance 2S of returns of portfolio

Conversion to estimated mean R~ and covariance ( )RR,~σ of log-returns of portfolio

Accuracy of samples computed by confidence intervals of normal distribution in Section 2.3

All values are in daily form

Weights of each stock in portfolio

Forecast

Mean price prediction

( )( ) ( )0

0

2,~~ ttRRR

tt ePPE−⎟

⎠⎞

⎜⎝⎛ +

=σ

Lower bound of confidence interval ( ) ( ) ( ) ( )( )00

0

,~96.1~ ttRRttRtt ePPLCI −−−= σ

Upper bound of confidence interval

( ) ( ) ( ) ( )( )00

0

,~96.1~ ttRRttRtt ePPUCI −+−= σ

Time 0tt >

30

4.1 Important functions The complete code for the program is available in the appendix but a brief discussion about the important functions in the program will be presented here. The Forecast_OpeningFcn is a function that imports the data and initialises all the different variables. The function Normalbutton1 is a function that corresponds to the Normal button in the graphical user interface. When the button is pressed this function creates a portfolio of the stocks that the user has chosen in the portfolio part of the graphical user interface. Once the portfolio is created it plots the portfolio without any forecast. Forecastbutton1 is a function that creates a portfolio of the selected stocks. With the aid of the Sampling function it creates the necessary statistics for a forecast of the chosen length. This function is activated when the Forecast button is pressed and it plots the time series along with the forecasted interval. The Forecastwithinbutton1 function is activated by the Forecast within button and works in the same way as Forecastbutton1. The difference is that the forecast date is set to a date within the time series. If the forecast length for instance is set to six months, the forecast date will be six months into the time series counted from the end date. This means that they will be plotted in the same time frame and thus the forecast can be compared to the real outcome of the time series. Sampling is the function that samples the data so that the sample mean and sample standard deviation can be calculated. These values are then used to compute the forecasted mean series along with the upper and lower confidence series that creates the forecast interval. The Create_Portfolio function creates a weighted portfolio of the selected stocks. The start date is set to the start date of the shortest time series in the chosen portfolio. Current_Risk_Contributors is a function that extracts the stocks that contribute to the risk in the portfolio. This is done by checking the sample variance of each stock. The risk contributors are then organised with the highest risk contributor as number one. It also calculates what stocks the user should add to the portfolio in order to increase or decrease the portfolio risk. This is done by asking the user for the value of the stock to be bought. This value is then used to calculate which new stock will increase or decrease the portfolio risk the most. These are also displayed in the graphical user interface with the one that increases or decreases risk the most as number one.

31

The calculations of the sample mean, the sample variance and the sample covariance for a specific interval have also been verified in EViews since both programs returned the same result for these calculations. This means that the program can import time series data, extract the necessary variables and use the Geometric Random Walk model to construct a forecasted risk interval. It can also give recommendations concerning current risk contributors and new stocks that will increase or decrease the portfolio risk.

4.2 Implementation of the theory In this section the framework used in the program is introduced in order to show how the theory is implemented in practice.

4.2.1 Create portfolio time series up to forecast date When the Forecast button in the program is activated by the user a reset of the values of the portfolio is initiated. The next step is to check the forecast length and to set the time when the portfolio is to be valued, i.e.

0t . Thereafter the function Create_Portfolio creates a portfolio with the following steps. The program checks each stock and if it is chosen in the graphical user interface it calculates the number of shares the user will hold for the invested value.

0

0

,

,

ti

tii p

vn = (40)

where in denotes the number of shares of the chosen stock,

0,tiv the wealth invested in this stock at time 0t and

0,tip denotes the price of one share of the stock at time 0t . The time series of the current stock is then added to the time series of the other stocks in the portfolio in order to create the time series of the portfolio up to time 0t

∑=

=a

itiit pnP

1, 0ttts ≤≤ (41)

where tP is the time series of the portfolio from the start date st of the stock with the shortest time series up to 0t and a is the number of assets in the portfolio.

32

The function Current_Portfolio_Weights is then used to calculate each stock weight in the portfolio, i.e.

∑=

= a

iti

tii

v

vw

1,

,

0

0 (42)

4.2.2 Sampling The function Sampling estimates the mean and variance of each stock. It extracts each time series data to create a log-return series by taking the logarithm of each price at time t divided by the price at time 1−t .

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−1,

,, ln

ti

titi p

pr (43)

Then the daily sample mean, i.e. the average of the last 90=η days of daily log-returns, is calculated

⎟⎟⎠

⎞⎜⎜⎝

⎛=

−ηη0

0

,

,ln1ˆti

tii p

pr (44)

where η is the sample size and 0t is the end date of the time series. The program inserts the η elements from the log-return series of each stock into a matrix that is a a×η -matrix, where 6=a in the program since there are 6 stocks and the sample size is η . This matrix is used in the calculations of the variance and covariance of all the stocks. The daily sample variance - covariance matrix of the log-returns of all the stocks is calculated element by element

( ) ( ) ( )( )∑∑= =

−−−

=a

ji tjtjitiji rrrrrr

1, 1,, ˆˆ

11,ˆ

η

ησ (45)

where η is the sample size, i and j denote stock i and j , t denotes the time index. When ji = the result is the variance ( )ii rr ,σ̂ for stock i and when ji ≠ the result is the covariance ( )ji rr ,σ̂ between stock i and j .

33

In order to calculate the mean and variance – covariance values that can be used for a single stock or a portfolio, the samples are transformed from log-returns to returns, i.e. normally distributed to log-normally distributed. The transformation of the mean is

( )⎟

⎠⎞

⎜⎝⎛ +

=iii rrr

i em,ˆ

21ˆ σ

(46) where im denotes the estimated daily mean of stock i ’s returns. The transformation of the variance – covariance is

( ) ( ) ( ) ( ) ( )( )1,, ,ˆ,ˆ21ˆ,ˆ

21ˆ

−==⎟⎠⎞

⎜⎝⎛ +⎟⎠⎞

⎜⎝⎛ +

jijjjiii rrrrrrrr

jiji eerrCovrrs σσσ (47)

where ( )ji rrs , denotes the estimated daily variance – covariance of stock i ’s and j ’s returns. These transformed values can then be used when the portfolio is estimated.

4.2.3 Portfolio estimation The next step is to calculate the estimated daily mean and variance of returns of the chosen portfolio. These estimates are log-normally distributed. The estimated portfolio mean is

∑=

=a

iiimwM

1 (48)

where M denotes the estimated daily mean of the portfolio returns. The estimated variance of the portfolio is

( ) ( )∑∑= =

==a

i

a

jjiji rrswwRRVarS

1 1

2 ,, (49)

where 2S denotes the estimated daily variance of the portfolio returns. The derived estimates of mean and variance of the portfolio’s returns have to be transformed into estimates of log-returns in order to be utilised in the forecast. The transformation of the variance is

34

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛+= 1ln,~

2

2

MSRRσ (50)

where ( )RR,~σ denotes the daily estimated variance of log-returns of the portfolio. The transformation of the mean is

( ) ( )2,~

ln~ RRMR σ−= (51)

where R~ denotes the estimated daily mean of log-returns of the portfolio. These values are used in the forecasting of the portfolio. The estimated yearly mean M250 and yearly standard deviation 2250S of the portfolio are displayed in the plot.

4.2.4 Portfolio recommendations It is also possible to determine the current risk contributors which are derived from the weighted estimated variance of each stock return. The calculation for each stock is ( )iii rrsw ,2 (52) The stocks are ordered in descending order with the highest variance at number 1. In order to derive the stocks that will increase or decrease the portfolio risk, the user is prompted for the amount to be invested in the new stock, i.e.

0,thv . This value is used to calculate how many shares the user can buy of the stocks that are currently not in the portfolio.

0

0

,

,

th

thh p

vn = (53)

where hn is the number of stocks of each new stock h . In the program Forecast ah −= 6 , i.e. the number of stocks available to the user minus the number of stocks currently in the portfolio. In the real world, 6 is replaced by the stocks at the fundamental recommendation list from Handelsbanken with 40 to 50 stocks and not the whole Stockholm stock exchange with approximately 270 stocks.

35

The function Current_Portfolio_Weights is then used to calculate each new stock weight in the current portfolio, i.e.

00

0

,1

,

,

th

a

iti

tii

vv

vw

+=

∑=

(54)

It is also necessary to calculate the weights of the stocks that are currently not in the portfolio.

00

0

,1

,

,

th

a

iti

thh

vv

vw

+=

∑=

(55)

The weighted daily estimated mean of each possible portfolio is calculated

∑+

=

=1

1

a

iiimwM (56)

where the number of stocks in each possible portfolio is 1+a since a new stock is added to the current portfolio. The weighted daily estimated variance of each possible portfolio is calculated

( ) ( )∑∑+

=

+

=

==1

1

1

1

2 ,,a

i

a

jjiji rrswwRRVarS (57)

These variances are compared to the variance of the current portfolio so that they can be divided into a group of stocks that increase the portfolio risk and another group that decrease the portfolio risk. Finally these groups are ordered in descending order from the stock that increase or decrease risk the most at first place.

4.2.5 Portfolio forecasting In order to create a predicted interval of the portfolio, three data series are calculated. They are the mean data series, the upper confidence bound data series and the lower confidence bound data series. The first step is to calculate the portfolio value at 0t , i.e.

36

∑=

=a

itiit pnP

1, 00

(58)

The forecasted mean data series is

( )( ) ( )0

0

2,~~ ttRRR

tt ePPE−⎟

⎠⎞

⎜⎝⎛ +

=σ

fttt ≤≤0 (59) where f denotes the number of business days of the forecast. The sample mean and the sample standard deviation are daily values. The next step is to create the forecasted upper confidence bound data series

( ) ( ) ( ) ( )( )00

0

,~96.1~ ttRRttRtt ePPUCI −+−= σ fttt ≤≤0 (60)

Finally the forecasted lower confidence bound data series is ( ) ( ) ( ) ( )( )00

0

,~96.1~ ttRRttRtt ePPLCI −−−= σ fttt ≤≤0 (61)

These data series are added to time series objects with dates and thereafter visualised for the user along with the time series of the portfolio up to 0t . The end result is a time series plot of the portfolios historic trend up to 0t and the forecasted mean, upper confidence interval and lower confidence interval between 0t and the forecast end date ft .

5 Simulation In this section a selection of simulations performed in Forecast is discussed in order to evaluate if the program can achieve reasonable results and highlight some important topics. The Forecast within function is used to compare the forecast with the real outcome. The first forecast is a mixed portfolio with one third of the portfolio value in Axis, one sixth in Ericsson B and half in Volvo B.

37

Figure 15: Screenshot of Forecast with a portfolio of Axis, Ericsson B and Volvo B forecasted 6 months within the time series and the recommended stocks that will decrease the risk in the portfolio. In Figure 15 the portfolio consist of quite volatile stocks. The large movements are mainly due to movements in Axis which is a volatile stock that is one third of the portfolio. The development of the time series is inside the forecasted interval throughout the forecast period. The forecasted interval is widespread in august 2005, from 315 to 530, which gives the end customer a visualisation of the risk level in the portfolio. An example of a stock that moves outside the forecasted interval is seen in Figure 16.

38

Figure 16: Screenshot of Forecast with Axis forecasted 1 year within the time series and the recommended stocks that will decrease the risk in the portfolio. The true time series of Axis in Figure 16 moves outside the forecasted interval. When studying the time series over the forecasted period it is quite obvious that many models could not have forecasted an interval that would have covered the time series. There are two major movements in the stock over the forecasted period. The first move is so rapid that the time series moves outside of the interval. The second move occurs outside of the forecasted interval and thus the downward sloping forecast has definitely failed. These movements are triggered by the company’s interim reports and thus new information has been presented to the market that has definitely changed the markets view of the company. In this case it is quite probable that no model or fundamental analyst could have predicted the rapid upward movements in the stock. A period of one year is quite a long time for a forecast and a longer time frame must be considered quite unrealistic. If Axis is forecasted six months instead, the data is sampled from the first major movement. The result is seen in Figure 17.

39

Figure 17: Screenshot of Forecast with Axis forecasted six months within the time series and the recommended stocks that will decrease the risk in the portfolio. In Figure 17 it is obvious when studying the sample mean, which in this case is 2.3384, that the major movement in the stock previous to the forecast start date affected the sample mean. Since this value is used in the forecast, the prediction interval is quite upward trending. In this case the stock does continue upward due to the second interim report so the sample mean is relatively close to the real outcome. The interval forecasted in this case is broad, ranging from 58 to 150, which reflect the uncertainty in the stock due to the movement caused by the first interim report. This will hopefully give the end customer a picture of how risky a portfolio consisting of Axis alone is. If the end customer would instead hold a portfolio of Axis and Readsoft, as recommended by the program, the result is seen in Figure 18.

40

Figure 18: Screenshot of Forecast with Axis and Readsoft forecasted six months within the time series along with the recommended stocks that will decrease the risk in the portfolio. In Figure 18 the total portfolio value is still 50 SEK at the forecast date, but the portfolio consist of equal weights of Axis and Readsoft which lowers the sample mean to 2.247. The sample standard deviation is also lower with a value of 0.23512 instead of 0.34429. This leads to an interval six months later that range from 65 to 123 instead of 58 to 150. The end customer has thus created a portfolio that has a lower standard deviation and according to the program the downside risk is more upward trending than was the case for Axis alone. One should also bear in mind that the upside of the portfolio has decreased since the portfolio risk and the sample mean are lower. SHB A is the stock that has the lowest standard deviation out of the six stocks. An interesting example concerning the sample mean and the sample standard deviation is seen in Figure 19 and 20.

41

Figure 19: Screenshot of Forecast with SHB A forecasted six months within the time series and the recommended stocks that will increase or decrease the risk in the portfolio. As seen in Figure 19 SHB A has a low standard deviation of 0.15564 but Volvo B is recommended in order to decrease the risk even though it has a higher standard deviation. This is due to the fact that multiple stocks diversify away the risk of single stocks. In this case the covariance between SHB A and Volvo B is quite low. Increasing the number of stocks in a portfolio, as long as their covariance is relatively low, can decrease the risk in the portfolio as seen in Figure 20.

42

Figure 20: Screenshot of Forecast with SHB A and Volvo B forecasted six months along with the recommended stocks that will increase the risk in the portfolio. A portfolio consisting of SHB A and Volvo B will lead to a lower risk than a portfolio of SHB A alone, even though Volvo B has a sample standard deviation of 0.20827 compared to SHB A with 0.15564. This is due to the covariance between the two stocks and in this particular case the sample mean increase in the new portfolio. In the case of SHB A the sample mean is 1.2283 whereas in the new portfolio the sample mean is 1.375. The addition of Volvo B has thus created a portfolio with a lower risk but a higher expected return.

43

Figure 21: Screenshot of Forecast with ABB LTD SDB, Axis, Ericsson B and Volvo B forecasted six months along with the recommended stocks that will increase or decrease the risk in the portfolio. Figure 21 is an example of a forecast created for an end customer where the portfolios development is plotted to the forecast date. The interval in this case is relatively broad but the development of the portfolio during the year 2000 shows that the portfolio can perform rather large movements in a short time span.

6 Conclusions and suggestions to future studies In this section the conclusions of this paper will be discussed and areas of interest for future analysis will be suggested.

44

6.1 Conclusions The main purpose of this dissertation is to examine a way of extracting raw market data in order to present a visualisation of risk for the end customer. The program Forecast developed in Matlab confirm that it is possible to construct a program that will perform the necessary calculations in order to obtain the desired risk representation. This visualisation of risk is a method of transforming a number into something understandable. The numbers derived from the program can also be used to visualise risk in other ways, i.e. different graphs or compared to a risk index. A specific sample calculation has been verified with EViews which showed that the sample calculations performed in the program are correct. The sample mean, sample variance and sample covariance calculations can if implemented in a real system be executed each night. Therefore it is no problem if the heavy calculations with approximately 270 Swedish stocks requires a lot of time. The recommendation function that suggests stocks that will increase or decrease the risk has to be executed when the forecast is activated by the user. These calculations would however be considerably limited since the program will only suggests stocks that are recommended by the bank. This means that the program only suggests stocks based on mathematical calculations as well as fundamental analysis.

6.2 Suggestions to future studies This dissertation has shown that it is possible to go from market data to a risk representation of a customer portfolio. There are however some areas that would be interesting to study further. The first area of interest is of course to see how well it will perform if implemented in a real system where all the stocks on Stockholmsbörsen is available. It would also be interesting to compare the variance and covariance numbers derived for the stocks to the numbers derived from a professional system. Another topic of interest would be to see if other methods of calculating the sample variance and the sample covariance values would improve the obtained results. An interesting evaluation would be to compare this forecast method to other methods such as the RiskMetrics. It would also be interesting to study different methods of deriving the mean value. Finally it would be very interesting to utilise the derived values for mean – variance optimisation of portfolios.

45

7 Acknowledgements I would like to thank Professor Maciej Klimek at the Department of Mathematics at Uppsala University for his excellent support and dedication. I would also like to thank Jan Aronsson and Mikael Forssén at Handelsbanken for their ideas and enthusiasm throughout the process.

46

References [1] Luenberger David G. Investment Science. Oxford university press,

New York, 1998. [2] Wackerly Dennis D., Mendenhall III William, Scheaffer Richard L.

Mathematical Statistics with Applications. Duxbury, Pacific Grove, 2002.

[3] Yates Roy D, Goodman David J. Probability and Stochastic

Processes. John Wiley & Sons, New York, 1999. [4] Gujarati Damodar N. Basic Econometrics. McGraw-Hill/Irwin, New

York, 2003. [5] Klimek Maciej, Lecture Notes on Mathematics of Financial

Modeling. Uppsala University. 2002. [6] Morgan Guaranty Trust Company. Risk Metrics – Technical

document, 4th edition. J.P. Morgan/Reuters, New York, 1996. [7] Hull John C. Options, Futures, and Other Derivatives. Prentice-

Hall, New Jersey, 2003. [8] Brockwell Peter J., Davis Richard A. Introduction to Time Series

and Forecasting. Springer-Verlag, New York, 2002. [9] Chatfield Chris. The analysis of Time Series An Introduction.

Chapman & Hall/CRC, Boca Raton, 1996.

47

A Appendix The Matlab code for the Forecast program.

end

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= a

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xis.

txt')

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ndle

s.er

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onb

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ndle

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i2fts

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les.

shba

= a

scii2

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ndle

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ndle

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is);

info

eric

sson

b =

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es.e

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ft =

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andl

es.re

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shba

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les.

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ob);

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- %

--- F

orec

ast

func

tion

vara

rgou

t = fo

reca

st(v

arar

gin)

%

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Beg

in in

itial

izat

ion

code

- D

O N

OT

ED

IT

gui_

Sing

leto

n =

1;

gui_

Sta

te =

stru

ct('g

ui_N

ame'

,

mfil

enam

e, ..

.

'g

ui_S

ingl

eton

', g

ui_S

ingl

eton

, ...

'gui

_Ope

ning

Fcn'

, @Fo

reca

st_O

peni

ngFc

n, ..

.

'g

ui_O

utpu

tFcn

', @

Fore

cast

_Out

putF

cn, .

..

'g

ui_L

ayou

tFcn

', []

, ...

'g

ui_C

allb

ack'

, []

); if

narg

in &

& is

char

(var

argi

n{1}

)

gui

_Sta

te.g

ui_C

allb

ack

= st

r2fu

nc(v

arar

gin{

1});

end

if na

rgou

t

[var

argo

ut{1

:nar

gout

}] =

gui_

mai

nfcn

(gui

_Sta

te, v

arar

gin{

:});

else

gui

_mai

nfcn

(gui

_Sta

te, v

arar

gin{

:});

48

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,1))

, ...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

axes

(han

dles

.Val

ue_o

f_A

xis)

; cl

a;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,2))

, ...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

axes

(han

dles

.Val

ue_o

f_E

ricss

on);

cla;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,3

)), .

..

'Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; ax

es(h

andl

es.V

alue

_of_

Rea

dsof

t);

cla;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,4

)), .

..

'Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; ax

es(h

andl

es.V

alue

_of_

SHB

); cl

a;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,5))

, ...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

axes

(han

dles

.Val

ue_o

f_Vo

lvo)

; cl

a;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,6))

, ...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

%S

et th

e nu

mbe

r of s

tock

s in

the

curre

nt p

ortfo

lio

hand

les.

num

ber_

of_s

tock

s =

1;

%S

et th

e st

artd

ate

of th

e po

rtfol

io

hand

les.

portf

olio

_sta

rt_da

te =

0;

%S

et th

e po

rtfoi

o sa

mpl

e m

ean

hand

les.

portf

olio

_sam

ple_

mea

n =

0;

%C

reat

e a

vect

or w

ith th

e di

ffere

nt ti

mes

erie

s st

artd

ates

ha

ndle

s.st

ocks

_sta

rt_da

te =

[dat

enum

(info

abb.

star

tdat

e), .

..

dat

enum

(info

axis

.sta

rtdat

e), d

aten

um(in

foer

icss

onb.

star

tdat

e), .

..

dat

enum

(info

read

soft.

star

tdat

e), d

aten

um(in

fosh

ba.s

tartd

ate)

, ...

d

aten

um(in

fovo

lvob

.sta

rtdat

e)];

%C

reat

e a

vect

or w

ith th

e tim

eser

ies

endd

ates

ha

ndle

s.st

ocks

_end

_dat

e =

date

num

(info

abb.

endd

ate)

; %

Cre

ate

a ve

ctor

with

the

diffe

rent

num

ber o

f dat

es

hand

les.

stoc

ks_n

data

= [i

nfoa

bb.n

data

, inf

oaxi

s.nd

ata,

...

in

foer

icss

onb.

ndat

a, in

fore

adso

ft.nd

ata,

info

shba

.nda

ta, .

..

info

volv

ob.n

data

]; %

Set

cur

rent

dat

a to

AB

B

hand

les.

curre

nt_d

ata

= ha

ndle

s.ab

b;

%C

reat

e a

vect

or to

kee

p tra

ck o

f the

cur

rent

sto

ck in

the

portf

olio

(AB

B

%ch

oose

n as

def

ault)

ha

ndle

s.cu

rrent

_por

tfolio

= [1

,0,0

,0,0

,0];

%C

reat

e a

vect

or w

ith th

e cu

rren

t num

ber o

f sha

res

boug

ht

hand

les.

curre

nt_s

tock

_sha

res

= [0

,0,0

,0,0

,0];

%S

et th

e cu

rrent

sto

ck p

rice

vect

or to

zer

o ha

ndle

s.cu

rrent

_sto

ck_p

rice

= [0

,0,0

,0,0

,0];

%S

et th

e po

rtfol

io v

alue

to 5

0 fo

r AB

B (w

here

the

last

0 is

use

d by

the

%C

urre

nt_R

isk_

Con

tribu

tors

func

tion

hand

les.

curre

nt_p

ortfo

lio_v

alue

= [5

0,0,

0,0,

0,0,

0];

%S

et th

e te

xt in

all

the

Val

ue_o

f_ fi

gure

s ax

es(h

andl

es.V

alue

_of_

AB

B);

cla;

49

%S

et th

e co

varia

nce

retu

rn m

atrix

ha

ndle

s.co

varia

nce_

retu

rn_m

atrix

= 0

; %

Set

act

ive

chec

kbox

to c

heck

box1

se

t(han

dles

.che

ckbo

x1,'V

alue

',1);

set(h

andl

es.c

heck

box2

,'Val

ue',0

); se

t(han

dles

.che

ckbo

x3,'V

alue

',0);

set(h

andl

es.c

heck

box4

,'Val

ue',0

); se

t(han

dles

.che

ckbo

x5,'V

alue

',0);

set(h

andl

es.c

heck

box6

,'Val

ue',0

); %

Set

che

ckbo

x7 to

no

reco

mm

enda

tion

set(h

andl

es.c

heck

box7

,'Val

ue',0

); %

Set

cur

rent

fore

cast

leng

th to

6 M

onth

s se

t(han

dles

.For

ecas

tbut

ton6

m,'V

alue

',1);

%S

et th

e fo

reca

st_b

utto

n to

sho

w th

at th

e ca

ll do

es n

ot c

ome

from

%

Nor

mal

butto

n1

hand

les.

fore

cast

_but

ton

= 0;

%

Set

the

sam

ple

size

ha

ndle

s.sa

mpl

e_si

ze =

90;

%

Plo

t the

cur

rent

dat

a ax

es(h

andl

es.G

raph

); zo

om o

ut;

cla;

pl

ot(h

andl

es.c

urre

nt_d

ata)

; tit

le('N

orm

al p

lot')

; le

gend

('AB

B L

TD S

DB

');

xlab

el('D

ate'

); yl

abel

('Val

ue (S

EK

)');

zoom

on;

%S

et th

e po

rtfol

io s

ampl

e st

anda

rd d

evia

tion

hand

les.

portf

olio

_sam

ple_

stan

dard

_dev

iatio

n =

0;

%S

et th

e nu

mbe

r of d

ates

in th

e po

rtfol

io

hand

les.

portf

olio

_nda

ta =

0;

%S

et th

e cu

rrent

sto

ck w

eigh

ts

hand

les.

curre

nt_s

tock

_wei

ghts

= [0

,0,0

,0,0

,0];

%S

et th

e cu

rrent

por

tfolio

val

ue d

ate

hand

les.

curre

nt_p

ortfo

lio_v

alue

_dat

e =

0;

%S

et th

e m

ean

vect

or

hand

les.

mea

n_ve

ctor

= 0

; %

Set

the

cova

rianc

e ve

ctor

ha

ndle

s.co

varia

nce_

vect

or =

0;

%S

et th

e co

varia

nce

mat

rix

hand

les.

cova

rianc

e_m

atrix

= 0

; %

Set

the

wei

ghte

d co

varia

nce

vect

or

hand

les.

wei

ghte

d_co

varia

nce_

vect

or =

0;

%S

et th

e w

eigh

ted

cova

rianc

e m

atrix

ha

ndle

s.w

eigh

ted_

cova

rianc

e_m

atrix

= 0

; %

Set

the

wei

ghte

d m

ean

vect

or

hand

les.

wei

ghte

d_m

ean_

vect

or =

0;

%S

et th

e m

ean

retu

rn v

ecto

r ha

ndle

s.m

ean_

retu

rn_v

ecto

r = 0

;

50

%R

otat

e th

e fig

ure

to fi

ll th

e pa

per

orie

nt ro

tate

d;

%S

et th

e pa

pers

ize

to A

4 se

t(gcf

, 'P

aper

Pos

ition

Mod

e', '

man

ual')

; se

t(gcf

, 'P

aper

Uni

ts',

'cen

timet

ers'

); se

t(gcf

, 'P

aper

Pos

ition

', [1

1 2

5 19

]);

%P

rint

prin

tdlg

(han

dles

.figu

re1)

%

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r the

Exi

t men

u ch

oice

fu

nctio

n E

xitM

enuI

tem

_Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Use

a q

uest

ion

dial

og to

ask

if th

e us

er w

ants

to e

xit

sele

ctio

n =

ques

tdlg

(['D

o yo

u w

ant t

o ex

it ' g

et(h

andl

es.fi

gure

1,'N

ame'

)...

'?

'],['E

xit '

get

(han

dles

.figu

re1,

'Nam

e') '

...'],

...

'Yes

','No'

,'Yes

');

%If

the

user

ans

wer

s N

o re

turn

to th

e pr

ogra

m

if st

rcm

p(se

lect

ion,

'No'

)

retu

rn;

end

%O

ther

wis

e en

d th

e pr

ogra

m

dele

te(h

andl

es.fi

gure

1)

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

-

% C

hoos

e de

faul

t com

man

d lin

e ou

tput

for F

orec

ast

hand

les.

outp

ut =

hO

bjec

t; %

Upd

ate

hand

les

stru

ctur

e gu

idat

a(hO

bjec

t, ha

ndle

s);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- O

utpu

ts fr

om th

is fu

nctio

n ar

e re

turn

ed to

the

com

man

d lin

e.

func

tion

vara

rgou

t = F

orec

ast_

Out

putF

cn(h

Obj

ect,

even

tdat

a, h

andl

es)

% v

arar

gout

cel

l arra

y fo

r ret

urni

ng o

utpu

t arg

s (s

ee V

AR

AR

GO

UT)

; %

Get

def

ault

com

man

d lin

e ou

tput

from

han

dles

stru

ctur

e va

rarg

out{1

} = h

andl

es.o

utpu

t; %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r the

File

men

u fu

nctio

n Fi

leM

enu_

Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r the

Prin

t men

u ch

oice

fu

nctio

n P

rintM

enuI

tem

_Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

51

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,1

)),..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; en

d %

Set

fore

cast

_but

ton

to 2

so

that

Cre

ate

Por

tfolio

set

s th

e co

rrect

%

curre

nt_p

ortfo

lio_v

alue

_dat

e ha

ndle

s.fo

reca

st_b

utto

n =

2;

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,h

andl

es);

% --

----

----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

---

% C

all t

he C

reat

Por

tfolio

Fun

ctio

n to

set

the

hand

les.

curre

nt_d

ata

%

fiel

d to

the

valu

e of

the

choo

sen

portf

olio

C

reat

e_P

ortfo

lio(h

andl

es.fi

gure

1,[],

hand

les)

; %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

-----

----

----

- %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

%P

lot t

he c

urre

nt p

ortfo

lio

axes

(han

dles

.Gra

ph);

zoom

out

; cl

a;

plot

(han

dles

.cur

rent

_dat

a);

tit

le('N

orm

al p

lot')

; xl

abel

('Dat

e');

ylab

el('V

alue

(SE

K)')

; %

Set

the

lege

nd to

the

nam

e of

the

stoc

k if

only

one

sto

ck is

cho

osen

if(

1 ==

sum

(han

dles

.cur

rent

_por

tfolio

))

lege

nd(C

urre

nt_L

egen

d(ha

ndle

s.fig

ure1

,[],h

andl

es))

; el

se

le

gend

('off'

)

% --

- Fun

ctio

n fo

r the

Hel

p m

enu

func

tion

Hel

pMen

u_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es)

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- F

unct

ion

for t

he A

bout

men

u ch

oice

fu

nctio

n A

bout

Fore

cast

_Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Use

a h

elp

dial

og to

pre

sent

the

info

rmat

ion

help

dlg(

'For

ecas

t Ver

sion

1.0

Cop

yrig

ht 2

005,

Jon

atha

n M

årte

nsso

n', .

..

'

Abo

ut F

orec

ast')

%

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Exe

cute

s on

but

ton

pres

s in

Nor

mal

butto

n1.

func

tion

Nor

mal

butto

n1_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es, v

arar

gin)

%

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

%If

no s

tock

s ar

e se

lect

ed a

utom

atic

ally

sel

ect A

BB

if

(0 =

= su

m(h

andl

es.c

urre

nt_p

ortfo

lio))

%

Set

act

ive

chec

kbox

to c

heck

box1

set

(han

dles

.che

ckbo

x1,'V

alue

',1);

%

Cre

ate

a ve

ctor

to k

eep

track

of t

he c

urre

nt s

tock

in th

e po

rtfol

io

h

andl

es.c

urre

nt_p

ortfo

lio =

[1,0

,0,0

,0,0

];

%S

et th

e po

rtfol

io v

alue

to 5

0 fo

r AB

B

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

= [5

0,0,

0,0,

0,0,

0];

%

Set

the

text

in V

alue

_of_

AB

B to

50

a

xes(

hand

les.

Val

ue_o

f_A

BB

);

52

%

Set

act

ive

chec

kbox

to c

heck

box1

set

(han

dles

.che

ckbo

x1,'V

alue

',1);

%

Cre

ate

a ve

ctor

to k

eep

track

of t

he c

urre

nt s

tock

in th

e po

rtfol

io

h

andl

es.c

urre

nt_p

ortfo

lio =

[1,0

,0,0

,0,0

];

%S

et th

e po

rtfol

io v

alue

to 5

0 fo

r AB

B

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

= [5

0,0,

0,0,

0,0,

0];

%

Set

the

text

in V

alue

_of_

AB

B to

50

a

xes(

hand

les.

Val

ue_o

f_A

BB

);

cla

;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,1)),

...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

end

%S

et to

zer

o so

that

the

func

tion

Sam

plin

g kn

ows

that

the

call

%co

mes

from

For

ecas

tbut

ton1

ha

ndle

s.fo

reca

st_b

utto

n =

0;

% --

- Che

ck th

e le

ngth

of t

he fo

reca

st

n =

Fore

cast

_Len

gth(

hand

les.

figur

e1,[]

,han

dles

); %

Set

the

curre

nt p

ortfo

lio v

alue

dat

e te

mp_

date

num

bers

= g

etfie

ld(h

andl

es.a

bb,'d

ates

');

hand

les.

curre

nt_p

ortfo

lio_v

alue

_dat

e =

tem

p_da

tenu

mbe

rs(e

nd);

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

-----

----

----

- %

Cal

l the

Cre

at P

ortfo

lio F

unct

ion

to s

et th

e ha

ndle

s.cu

rrent

_dat

a

% fi

eld

to th

e va

lue

of th

e ch

oose

n po

rtfol

io

Cre

ate_

Por

tfolio

(han

dles

.figu

re1,

[],ha

ndle

s);

% --

----

----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

---

end

%S

et th

e tic

ks o

n th

e x-

axis

to th

e co

rrec

t dat

es

curre

nt_d

ate_

leng

th =

han

dles

.sto

cks_

end_

date

-ha

ndle

s.po

rtfol

io_s

tart_

date

; t1

= h

andl

es.p

ortfo

lio_s

tart_

date

; t2

= h

andl

es.p

ortfo

lio_s

tart_

date

+(cu

rrent

_dat

e_le

ngth

)/8;

t3 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/4

; t4

= h

andl

es.p

ortfo

lio_s

tart_

date

+(cu

rrent

_dat

e_le

ngth

)*3/

8;

t5 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/2

; t6

= h

andl

es.s

tock

s_en

d_da

te-(c

urre

nt_d

ate_

leng

th)*

3/8;

t7

= h

andl

es.s

tock

s_en

d_da

te-(c

urre

nt_d

ate_

leng

th)/4

; t8

= h

andl

es.s

tock

s_en

d_da

te-(c

urre

nt_d

ate_

leng

th)/8

; t9

= h

andl

es.s

tock

s_en

d_da

te;

set(g

ca,'X

Tick

Labe

l',{d

ates

tr(t1

,1);d

ates

tr(t2

,1);d

ates

tr(t3

,1);

...

d

ates

tr(t4

,1);d

ates

tr(t5

,1);d

ates

tr(t6

,1);d

ates

tr(t7

,1);

...

d

ates

tr(t8

,1);d

ates

tr(t9

,1)}

); se

t(gca

,'XTi

ck',[

t1 t2

t3 t4

t5 t6

t7 t8

t9]);

zo

om o

n;

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,h

andl

es);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- E

xecu

tes

on b

utto

n pr

ess

in F

orec

astb

utto

n1.

func

tion

Fore

cast

butto

n1_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es, v

arar

gin)

%

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

%If

no s

tock

s ar

e se

lect

ed a

utom

atic

ally

sel

ect A

BB

if

(0 =

= su

m(h

andl

es.c

urre

nt_p

ortfo

lio))

53

title

('For

ecas

t plo

t');

xlab

el('D

ate'

); yl

abel

('Val

ue (S

EK

)');

%S

et th

e le

gend

to th

e na

me

of th

e st

ock

if on

ly o

ne s

tock

is c

hoos

en

if(1

== s

um(h

andl

es.c

urre

nt_p

ortfo

lio))

le

gend

(Cur

rent

_Leg

end(

hand

les.

figur

e1,[]

,han

dles

));

else

lege

nd('o

ff')

end

text

(0.3

4,0.

97,'S

ampl

e M

ean:

','U

nits

','Nor

mal

ized

', ...

'Bac

kgro

undC

olor

',[1

1 1]

); te

xt(0

.58,

0.97

,num

2str(

(han

dles

.por

tfolio

_sam

ple_

mea

n-1)

*250

+1),

...

'U

nits

','N

orm

aliz

ed','

Bac

kgro

undC

olor

',[1

1 1]

); te

xt(0

.34,

0.93

,'Sam

ple

Sta

ndar

d D

evia

tion:

','Uni

ts','N

orm

aliz

ed',

...

'B

ackg

roun

dCol

or',[

1 1

1]);

text

(0.5

8,0.

93,n

um2s

tr(ha

ndle

s.po

rtfol

io_s

ampl

e_st

anda

rd_d

evia

tion

* ...

sqr

t(250

)),'U

nits

','N

orm

aliz

ed','

Bac

kgro

undC

olor

',[1

1 1]

); %

Set

the

ticks

on

the

x-ax

is to

the

corr

ect d

ates

cu

rrent

_dat

e_le

ngth

= d

ates

(end

)-ha

ndle

s.po

rtfol

io_s

tart_

date

; t1

= h

andl

es.p

ortfo

lio_s

tart_

date

; t2

= h

andl

es.p

ortfo

lio_s

tart_

date

+(cu

rrent

_dat

e_le

ngth

)/8;

t3 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/4

; t4

= h

andl

es.p

ortfo

lio_s

tart_

date

+(cu

rrent

_dat

e_le

ngth

)*3/

8;

t5 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/2

; t6

= d

ates

(end

)-(c

urre

nt_d

ate_

leng

th)*

3/8;

t7

= d

ates

(end

)-(c

urre

nt_d

ate_

leng

th)/4

; t8

= d

ates

(end

)-(c

urre

nt_d

ate_

leng

th)/8

; t9

= d

ates

(end

); se

t(gca

,'XTi

ckLa

bel',

{dat

estr(

t1,1

);dat

estr(

t2,1

);dat

estr(

t3,1

); ...

dat

estr(

t4,1

);dat

estr(

t5,1

);dat

estr(

t6,1

);dat

estr(

t7,1

); ...

dat

estr(

t8,1

);dat

estr(

t9,1

)});

set(g

ca,'X

Tick

',[t1

t2 t3

t4 t5

t6 t7

t8 t9

]);

zoom

on;

%C

alcu

late

the

fore

cast

ed lo

wer

con

fiden

ce d

ata

serie

s fo

r t =

1:n

+1

fo

reca

st_l

ower

_con

fiden

ce_d

ata(

t,1) =

...

su

m(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

) * ..

.

exp(

sam

ple_

mea

n *

(t-1)

- 1.

96 *

...

sq

rt(sa

mpl

e_va

rianc

e) *

sqr

t(t-1

));

end

%C

reat

e th

e fo

reca

st lo

wer

con

fiden

ce ti

mes

erie

s fo

reca

st_l

ower

_con

fiden

ce_v

ecto

r = fi

nts(

date

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fore

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er_c

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ence

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eset

the

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%C

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the

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ata

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r t =

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reca

st_u

pper

_con

fiden

ce_d

ata(

t,1) =

...

su

m(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

) * ..

.

exp(

sam

ple_

mea

n *

(t-1)

+ 1

.96

* ...

sqrt(

sam

ple_

varia

nce)

* s

qrt(t

-1))

; en

d %

Cre

ate

the

fore

cast

upp

er c

onfid

ence

tim

eser

ies

fore

cast

_upp

er_c

onfid

ence

_vec

tor =

fint

s(da

tes,

...

fo

reca

st_u

pper

_con

fiden

ce_d

ata)

; %

--- P

lot t

he d

ata

axes

(han

dles

.Gra

ph);

zoom

out

; cl

a;

plot

(fore

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er_c

onfid

ence

_vec

tor);

pl

ot(fo

reca

st_u

pper

_con

fiden

ce_v

ecto

r);

plot

(plo

t_da

ta);

54

%S

et th

e cu

rrent

por

tfolio

val

ue d

ate

to th

e la

st d

ate

min

us th

e le

ngth

of

%th

e fo

reca

st

tem

p_da

tenu

mbe

rs =

get

field

(han

dles

.abb

,'dat

es');

ha

ndle

s.cu

rrent

_por

tfolio

_val

ue_d

ate

= te

mp_

date

num

bers

(end

-n);

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

-----

----

----

- %

Cal

l the

Cre

at P

ortfo

lio F

unct

ion

to s

et th

e ha

ndle

s.cu

rrent

_dat

a

% fi

eld

to th

e va

lue

of th

e ch

oose

n po

rtfol

io

Cre

ate_

Por

tfolio

(han

dles

.figu

re1,

[],ha

ndle

s);

% --

----

----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

---

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

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----

----

- %

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l the

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rent

Por

tfolio

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ghts

to s

et th

e

% h

andl

es.c

urre

nt_p

ortfo

lio_w

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ts fi

eld

to th

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e ch

oose

n %

por

tfolio

C

urre

nt_P

ortfo

lio_W

eigh

ts(h

andl

es.fi

gure

1,[],

hand

les)

; %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

-----

----

----

- %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

% --

----

----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

---

% C

all t

he S

ampl

ing

func

tion

to c

alcu

late

the

sam

ple

mea

n

% a

nd s

ampl

e st

anda

rd d

evia

tion

Sam

plin

g(ha

ndle

s.fig

ure1

,[],h

andl

es);

% --

----

----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

---

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Exe

cute

s on

but

ton

pres

s in

For

ecas

twith

inbu

tton1

. fu

nctio

n Fo

reca

stw

ithin

butto

n1_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es)

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); %

If no

sto

cks

are

sele

cted

aut

omat

ical

ly s

elec

t AB

B

if (0

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sum

(han

dles

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rent

_por

tfolio

))

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et a

ctiv

e ch

eckb

ox to

che

ckbo

x1

s

et(h

andl

es.c

heck

box1

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ue',1

);

%C

reat

e a

vect

or to

kee

p tra

ck o

f the

cur

rent

sto

ck in

the

portf

olio

han

dles

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rent

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tfolio

= [1

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,0,0

,0];

%

Set

the

portf

olio

val

ue to

50

for A

BB

han

dles

.cur

rent

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ue =

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0,0,

0,0,

0,0]

;

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et th

e te

xt in

Val

ue_o

f_A

BB

to 5

0

axe

s(ha

ndle

s.V

alue

_of_

AB

B);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,1

)), ..

.

'

Uni

ts','

Nor

mal

ized

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oriz

onta

lAlig

nmen

t','ri

ght')

; En

d %

Set

han

dles

.fore

cast

_but

ton

to o

ne s

o th

at th

e fu

nctio

n

%S

ampl

ing

know

s th

at th

e ca

ll co

mes

from

For

ecas

twith

inbu

tton1

ha

ndle

s.fo

reca

st_b

utto

n =

1;

% --

- Che

ck th

e le

ngth

of t

he fo

reca

st

n =

Fore

cast

_Len

gth(

hand

les.

figur

e1,[]

,han

dles

);

55

% E

xtra

ct th

e da

tes

with

in th

e cu

rrent

tim

eser

ies

to u

se th

em fo

r the

%

fore

cast

vec

tors

da

te_m

atrix

= g

etfie

ld(h

andl

es.c

urre

nt_d

ata,

'dat

es');

da

tes

= da

te_m

atrix

(end

-n:e

nd);

%C

reat

e th

e fo

reca

st m

ean

vect

or

fore

cast

_mea

n_ve

ctor

= fi

nts(

date

s, fo

reca

st_m

ean_

data

); %

Res

et th

e fo

reca

st_l

ower

_con

fiden

ce_d

ata

vect

or

fore

cast

_low

er_c

onfid

ence

_dat

a(1:

n+1,

1)=0

; %

Cal

cula

te th

e fo

reca

sted

low

er c

onfid

ence

dat

a se

ries

for t

= 1

:n+1

fore

cast

_low

er_c

onfid

ence

_dat

a(t,1

) = ..

.

sum

(han

dles

.cur

rent

_por

tfolio

_val

ue) *

...

ex

p(sa

mpl

e_m

ean

* (t-

1) -

1.96

* ..

.

sqrt(

sam

ple_

varia

nce)

* s

qrt(t

-1))

; en

d %

Cre

ate

the

fore

cast

low

er c

onfid

ence

tim

eser

ies

fore

cast

_low

er_c

onfid

ence

_vec

tor =

fint

s(da

tes,

...

f

orec

ast_

low

er_c

onfid

ence

_dat

a);

%R

eset

the

fore

cast

_upp

er_c

onfid

ence

_dat

a ve

ctor

fo

reca

st_u

pper

_con

fiden

ce_d

ata(

1:n+

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=0;

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alcu

late

the

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ed u

pper

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fiden

ce d

ata

serie

s fo

r t =

1:n

+1

fo

reca

st_u

pper

_con

fiden

ce_d

ata(

t,1) =

...

su

m(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

) * ..

.

exp(

sam

ple_

mea

n *

(t-1)

+ 1

.96

* ...

sqrt(

sam

ple_

varia

nce)

* s

qrt(t

-1))

; en

d

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); %

Res

et s

ampl

e_va

rianc

e sa

mpl

e_va

rianc

e =

0;

%Tr

ansf

orm

the

daily

sam

ple

stan

dard

dev

iatio

n of

the

portf

olio

retu

rns

%

into

the

daily

sam

ple

varia

nce

of lo

g-re

turn

s of

the

portf

olio

sa

mpl

e_va

rianc

e =

log(

...

(h

andl

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lio_s

ampl

e_st

anda

rd_d

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* ...

han

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(h

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ampl

e_m

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han

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tfolio

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ple_

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1);

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eset

sam

ple_

mea

n sa

mpl

e_m

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= 0;

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Tran

sfor

m th

e da

ily s

ampl

e m

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of th

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s in

to th

e da

ily

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mpl

e m

ean

of lo

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s.po

rtfol

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ampl

e_m

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sam

ple_

varia

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/ 2;

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eset

the

fore

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data

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+1,1

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%

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cula

te th

e fo

reca

sted

mea

n da

ta s

erie

s fo

r t =

1:n

+1

fo

reca

st_m

ean_

data

(t,1)

= s

um(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

) * ..

.

exp

((sam

ple_

mea

n +

0.5

* sa

mpl

e_va

rianc

e) *

(t-1

));

end

56

t3 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/4

; t4

= h

andl

es.p

ortfo

lio_s

tart_

date

+(cu

rrent

_dat

e_le

ngth

)*3/

8;

t5 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/2

; t6

= h

andl

es.s

tock

s_en

d_da

te-(c

urre

nt_d

ate_

leng

th)*

3/8;

t7

= h

andl

es.s

tock

s_en

d_da

te-(c

urre

nt_d

ate_

leng

th)/4

; t8

= h

andl

es.s

tock

s_en

d_da

te-(c

urre

nt_d

ate_

leng

th)/8

; t9

= h

andl

es.s

tock

s_en

d_da

te;

set(g

ca,'X

Tick

Labe

l',{d

ates

tr(t1

,1);d

ates

tr(t2

,1);d

ates

tr(t3

,1);

...

d

ates

tr(t4

,1);d

ates

tr(t5

,1);d

ates

tr(t6

,1);d

ates

tr(t7

,1);

...

d

ates

tr(t8

,1);d

ates

tr(t9

,1)}

); se

t(gca

,'XTi

ck',[

t1 t2

t3 t4

t5 t6

t7 t8

t9]);

zo

om o

n;

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r the

For

ecas

tpan

el1

func

tion

Fore

cast

pane

l1_B

utto

nDow

nFcn

(hO

bjec

t, ev

entd

ata,

han

dles

) %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Exe

cute

s on

but

ton

pres

s in

che

ckbo

x1.

func

tion

chec

kbox

1_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es)

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

);

%C

reat

e th

e fo

reca

st u

pper

con

fiden

ce ti

mes

erie

s fo

reca

st_u

pper

_con

fiden

ce_v

ecto

r = fi

nts(

date

s, ..

.

for

ecas

t_up

per_

conf

iden

ce_d

ata)

; %

--- P

lot t

he d

ata

axes

(han

dles

.Gra

ph);

zoom

out

; cl

a;

plot

(fore

cast

_low

er_c

onfid

ence

_vec

tor);

pl

ot(fo

reca

st_u

pper

_con

fiden

ce_v

ecto

r);

plot

(fore

cast

_mea

n_ve

ctor

); pl

ot(h

andl

es.c

urre

nt_d

ata)

; tit

le('F

orec

ast p

lot')

; xl

abel

('Dat

e');

ylab

el('V

alue

(SE

K)')

; %

Set

the

lege

nd to

the

nam

e of

the

stoc

k if

only

one

sto

ck is

cho

osen

if(

1 ==

sum

(han

dles

.cur

rent

_por

tfolio

))

lege

nd(C

urre

nt_L

egen

d(ha

ndle

s.fig

ure1

,[],h

andl

es))

; el

se

le

gend

('off'

) en

d te

xt(0

.34,

0.97

,'Sam

ple

Mea

n:','

Uni

ts','N

orm

aliz

ed',

...

'B

ackg

roun

dCol

or',[

1 1

1]);

text

(0.5

8,0.

97,n

um2s

tr((h

andl

es.p

ortfo

lio_s

ampl

e_m

ean-

1)*2

50+1

), ...

'Uni

ts','

Nor

mal

ized

','B

ackg

roun

dCol

or',[

1 1

1]);

text

(0.3

4,0.

93,'S

ampl

e S

tand

ard

Dev

iatio

n:','U

nits

','Nor

mal

ized

', ...

'Bac

kgro

undC

olor

',[1

1 1]

); te

xt(0

.58,

0.93

,num

2str(

hand

les.

portf

olio

_sam

ple_

stan

dard

_dev

iatio

n *

...

s

qrt(2

50))

,'Uni

ts','N

orm

aliz

ed','

Bac

kgro

undC

olor

',[1

1 1]

); %

Set

the

ticks

on

the

x-ax

is to

the

corr

ect d

ates

cu

rrent

_dat

e_le

ngth

= h

andl

es.s

tock

s_en

d_da

te-

hand

les.

portf

olio

_sta

rt_da

te;

t1 =

han

dles

.por

tfolio

_sta

rt_da

te;

t2 =

han

dles

.por

tfolio

_sta

rt_da

te+(

curre

nt_d

ate_

leng

th)/8

;

57

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,h

andl

es);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- E

xecu

tes

on b

utto

n pr

ess

in c

heck

box2

. fu

nctio

n ch

eckb

ox2_

Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

if (g

et(h

Obj

ect,'

Val

ue')

== g

et(h

Obj

ect,'

Max

'))

h

andl

es.c

urre

nt_p

ortfo

lio(1

,2) =

1;

te

mp

= in

putd

lg('E

nter

the

valu

e of

Axi

s at

the

Fore

cast

dat

e', .

..

'

Val

ue o

f Axi

s',1

,cel

lstr(

'50'

),'of

f');

w

hile

(0 =

= is

scal

ar(s

tr2nu

m(te

mp{

1,1}

)))

tem

p =

inpu

tdlg

('Ent

er th

e va

lue

of A

xis

at th

e Fo

reca

st d

ate'

, ...

'

Val

ue o

f Axi

s',1

,cel

lstr(

'50'

),'of

f');

e

nd

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,2

) = s

tr2nu

m(te

mp{

1,1}

);

axe

s(ha

ndle

s.V

alue

_of_

Axi

s);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,2

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; el

se

h

andl

es.c

urre

nt_p

ortfo

lio(1

,2) =

0;

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,2

) = 0

;

axe

s(ha

ndle

s.V

alue

_of_

Axi

s);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,2

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; en

d

% If

the

chec

kbox

is m

arke

d if

(get

(hO

bjec

t,'V

alue

') ==

get

(hO

bjec

t,'M

ax'))

% S

et th

e ha

ndle

s.cu

rrent

_por

tfolio

(1,1

) to

1 to

incl

ude

AB

B in

% p

ortfo

lio

h

andl

es.c

urre

nt_p

ortfo

lio(1

,1) =

1;

%

Use

an

inpu

t dia

log

to a

sk th

e va

lue

of th

e st

ock

at fo

reca

st d

ate,

if

%

the

inpu

t is

not a

num

ber a

sk a

gain

unt

il it

is a

num

ber

te

mp=

inpu

tdlg

('Ent

er th

e va

lue

of A

BB

LTD

SD

B a

t the

For

ecas

t dat

e',..

.

'

Val

ue o

f AB

B L

TD S

DB

',1,c

ells

tr('5

0'),'

off')

;

whi

le (0

==

issc

alar

(str2

num

(tem

p{1,

1}))

)

te

mp

= in

putd

lg( .

..

'E

nter

the

valu

e of

AB

B L

TD S

DB

at t

he F

orec

ast d

ate'

, ...

'

Val

ue o

f AB

B L

TD S

DB

',1,c

ells

tr('5

0'),'

off')

;

end

%S

et th

e cu

rrent

_por

tfolio

_val

ue(1

,1) t

o th

e ch

oose

n va

lue

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,1

) = s

tr2nu

m(te

mp{

1,1}

);

%U

pdat

e th

e ha

ndle

s.Va

lue_

of_A

BB fi

gure

with

the

choo

sen

valu

e

axe

s(ha

ndle

s.V

alue

_of_

AB

B);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,1

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; %

If th

e ch

eckb

ox is

unm

arke

d el

se

%

Set

the

hand

les.

curre

nt_p

ortfo

lio(1

,1) t

o 0

to e

xclu

de A

BB

from

the

%

por

tfolio

han

dles

.cur

rent

_por

tfolio

(1,1

) = 0

;

%S

et th

e cu

rrent

_por

tfolio

_val

ue(1

,1) t

o ze

ro

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,1

) = 0

;

%U

pdat

e th

e ha

ndle

s.Va

lue_

of_A

BB

figu

re w

ith th

e va

lue

zero

axe

s(ha

ndle

s.V

alue

_of_

AB

B);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,1

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; en

d

58

end

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,h

andl

es);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- E

xecu

tes

on b

utto

n pr

ess

in c

heck

box4

. fu

nctio

n ch

eckb

ox4_

Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

if (g

et(h

Obj

ect,'

Val

ue')

== g

et(h

Obj

ect,'

Max

'))

h

andl

es.c

urre

nt_p

ortfo

lio(1

,4) =

1;

te

mp

= in

putd

lg('E

nter

the

valu

e of

Rea

dsof

t at t

he F

orec

ast d

ate'

, ...

'V

alue

of R

eads

oft',

1,ce

llstr(

'50'

),'of

f');

w

hile

(0 =

= is

scal

ar(s

tr2nu

m(te

mp{

1,1}

)))

tem

p =

inpu

tdlg

( ...

'

Ent

er th

e va

lue

of R

eads

oft a

t the

For

ecas

t dat

e', .

..

'V

alue

of R

eads

oft',

1,ce

llstr(

'50'

),'of

f');

e

nd

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,4

) = s

tr2nu

m(te

mp{

1,1}

);

axe

s(ha

ndle

s.V

alue

_of_

Rea

dsof

t);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,4

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; el

se

h

andl

es.c

urre

nt_p

ortfo

lio(1

,4) =

0;

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,4

) = 0

;

axe

s(ha

ndle

s.V

alue

_of_

Rea

dsof

t);

c

la;

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,h

andl

es);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- E

xecu

tes

on b

utto

n pr

ess

in c

heck

box3

. fu

nctio

n ch

eckb

ox3_

Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

if (g

et(h

Obj

ect,'

Val

ue')

== g

et(h

Obj

ect,'

Max

'))

h

andl

es.c

urre

nt_p

ortfo

lio(1

,3) =

1;

te

mp=

inpu

tdlg

('Ent

er th

e va

lue

of E

ricss

on B

at t

he F

orec

ast d

ate'

, ...

'V

alue

of E

ricss

on B

',1,c

ells

tr('5

0'),'

off')

;

whi

le (0

==

issc

alar

(str2

num

(tem

p{1,

1}))

)

te

mp

= in

putd

lg( .

..

'E

nter

the

valu

e of

Eric

sson

B a

t the

For

ecas

t dat

e', .

..

'V

alue

of E

ricss

on B

',1,c

ells

tr('5

0'),'

off')

;

end

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,3) =

str2

num

(tem

p{1,

1});

a

xes(

hand

les.

Val

ue_o

f_E

ricss

on);

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,3

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; el

se

h

andl

es.c

urre

nt_p

ortfo

lio(1

,3) =

0;

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,3

) = 0

;

axe

s(ha

ndle

s.V

alue

_of_

Eric

sson

);

cla

;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,3)),

...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

59

c

la;

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,5

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; en

d %

Upd

ate

hand

les

stru

ctur

e gu

idat

a(hO

bjec

t,han

dles

); %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Exe

cute

s on

but

ton

pres

s in

che

ckbo

x6.

func

tion

chec

kbox

6_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es)

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); if

(get

(hO

bjec

t,'V

alue

') ==

get

(hO

bjec

t,'M

ax'))

han

dles

.cur

rent

_por

tfolio

(1,6

) = 1

;

tem

p =

inpu

tdlg

('Ent

er th

e va

lue

of V

olvo

B a

t the

For

ecas

t dat

e', .

..

'

Val

ue o

f Vol

vo B

',1,c

ells

tr('5

0'),'

off')

;

whi

le (0

==

issc

alar

(str2

num

(tem

p{1,

1}))

)

te

mp

= in

putd

lg( .

..

'E

nter

the

valu

e of

Vol

vo B

at t

he F

orec

ast d

ate'

, ...

'

Val

ue o

f Vol

vo B

',1,c

ells

tr('5

0'),'

off')

;

End

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,6) =

str2

num

(tem

p{1,

1});

a

xes(

hand

les.

Val

ue_o

f_V

olvo

);

cla

;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,6)),

...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

te

xt(0

.95,

0.5,

num

2str(

hand

les.

curre

nt_p

ortfo

lio_v

alue

(1,4

)), ..

.

'

Uni

ts','

Nor

mal

ized

','H

oriz

onta

lAlig

nmen

t','ri

ght')

; en

d %

Upd

ate

hand

les

stru

ctur

e gu

idat

a(hO

bjec

t,han

dles

); %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Exe

cute

s on

but

ton

pres

s in

che

ckbo

x5.

func

tion

chec

kbox

5_C

allb

ack(

hObj

ect,

even

tdat

a, h

andl

es)

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); if

(get

(hO

bjec

t,'V

alue

') ==

get

(hO

bjec

t,'M

ax'))

han

dles

.cur

rent

_por

tfolio

(1,5

) = 1

;

tem

p =

inpu

tdlg

('Ent

er th

e va

lue

of S

HB

A a

t the

For

ecas

t dat

e', .

..

'

Val

ue o

f SH

B A

',1,c

ells

tr('5

0'),'

off')

;

whi

le (0

==

issc

alar

(str2

num

(tem

p{1,

1}))

)

te

mp

= in

putd

lg('E

nter

the

valu

e of

SH

B A

at t

he F

orec

ast d

ate'

, ...

'

Val

ue o

f SH

B A

',1,c

ells

tr('5

0'),'

off')

;

end

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,5) =

str2

num

(tem

p{1,

1});

a

xes(

hand

les.

Val

ue_o

f_S

HB

);

cla

;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,5)),

...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

else

han

dles

.cur

rent

_por

tfolio

(1,5

) = 0

;

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,5) =

0;

a

xes(

hand

les.

Val

ue_o

f_S

HB

);

60

%C

heck

whi

ch s

tock

is c

hoos

en a

nd s

et l

to th

e na

me

of th

e st

ock

if (1

==

get(h

andl

es.c

heck

box1

,'Val

ue'))

l =

'AB

B LT

D S

DB

'; el

seif

(1 =

= ge

t(han

dles

.che

ckbo

x2,'V

alue

'))

l

= 'A

xis'

; el

seif

(1 =

= ge

t(han

dles

.che

ckbo

x3,'V

alue

'))

l

= 'E

ricss

on B

'; el

seif

(1 =

= ge

t(han

dles

.che

ckbo

x4,'V

alue

'))

l

= 'R

eads

oft';

el

seif

(1 =

= ge

t(han

dles

.che

ckbo

x5,'V

alue

'))

l

= 'S

HB

A';

else

if (1

==

get(h

andl

es.c

heck

box6

,'Val

ue'))

l =

'Vol

vo B

'; en

d %

Upd

ate

hand

les

stru

ctur

e gu

idat

a(hO

bjec

t,han

dles

); %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r det

erm

inin

g fo

reca

st le

ngth

dep

endi

ng o

n us

er c

hoic

e.

func

tion

n =

Fore

cast

_Len

gth(

hObj

ect,

even

tdat

a, h

andl

es, v

arar

gin)

%

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

%C

heck

the

choo

sen

leng

th a

nd s

et it

to th

e co

rrect

val

ue

if (1

==

get(h

andl

es.F

orec

astb

utto

n1d,

'Val

ue'))

n =

1;

else

if (1

==

get(h

andl

es.F

orec

astb

utto

n1w

,'Val

ue'))

n =

5;

else

han

dles

.cur

rent

_por

tfolio

(1,6

) = 0

;

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,6) =

0;

a

xes(

hand

les.

Val

ue_o

f_V

olvo

);

cla

;

text

(0.9

5,0.

5,nu

m2s

tr(ha

ndle

s.cu

rrent

_por

tfolio

_val

ue(1

,6)),

...

'U

nits

','N

orm

aliz

ed','

Hor

izon

talA

lignm

ent',

'righ

t');

end

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,h

andl

es);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- E

xecu

tes

on b

utto

n pr

ess

in c

heck

box7

. fu

nctio

n ch

eckb

ox7_

Cal

lbac

k(hO

bjec

t, ev

entd

ata,

han

dles

) %

Use

d to

che

ck if

use

r wan

ts re

com

men

datio

ns a

bout

new

sto

cks

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- F

unct

ion

for s

ettin

g th

e co

rrect

lege

nd in

the

figur

e.

func

tion

l = C

urre

nt_L

egen

d(hO

bjec

t, ev

entd

ata,

han

dles

, var

argi

n)

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); l =

0;

61

%C

heck

the

star

tdat

e of

the

curre

nt p

ortfo

lio

hand

les.

portf

olio

_sta

rt_da

te =

max

(han

dles

.cur

rent

_por

tfolio

.* ..

.

han

dles

.sto

cks_

star

t_da

te);

%C

heck

the

num

ber o

f dat

es in

the

portf

olio

j =

1;

for i

= 1

:6

if

(0 =

= ha

ndle

s.cu

rrent

_por

tfolio

(1,i)

)

els

e

t

emp_

ndat

a(1,

j) =

hand

les.

stoc

ks_n

data

(1,i)

;

j

= j

+ 1;

end

en

d %

Set

the

num

ber o

f dat

es to

the

low

est v

alue

of t

emp_

ndat

a ha

ndle

s.po

rtfol

io_n

data

= m

in(te

mp_

ndat

a);

%C

hang

e th

e cu

rrent

por

tfolio

val

ue d

ate

if th

e ca

ll co

mes

from

%

Nor

mal

butto

n1

if(2

== h

andl

es.fo

reca

st_b

utto

n)

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

_dat

e =

hand

les.

portf

olio

_sta

rt_da

te;

end

%S

et th

e cu

rrent

sto

ck s

hare

s to

zer

o ha

ndle

s.cu

rrent

_sto

ck_s

hare

s =

[0,0

,0,0

,0,0

]; %

Set

the

curre

nt s

tock

pric

e to

zer

o ha

ndle

s.cu

rrent

_sto

ck_p

rice

= [0

,0,0

,0,0

,0];

%C

reat

e th

e po

rtfol

io

%S

et th

e fla

g to

zer

o is

data

= 0

;

else

if (1

==

get(h

andl

es.F

orec

astb

utto

n1m

,'Val

ue'))

n =

20;

el

seif

(1 =

= ge

t(han

dles

.For

ecas

tbut

ton3

m,'V

alue

'))

n

= 6

0;

else

if (1

==

get(h

andl

es.F

orec

astb

utto

n6m

,'Val

ue'))

n =

120

; el

seif

(1 =

= ge

t(han

dles

.For

ecas

tbut

ton1

y,'V

alue

'))

n

= 2

50;

else

if (1

==

get(h

andl

es.F

orec

astb

utto

n2y,

'Val

ue'))

n =

500

; en

d %

Upd

ate

hand

les

stru

ctur

e gu

idat

a(hO

bjec

t, ha

ndle

s);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- F

unct

ion

for c

reat

ing

a po

rtfol

io.

func

tion

Cre

ate_

Por

tfolio

(hO

bjec

t, ev

entd

ata,

han

dles

, var

argi

n)

%Lo

ad th

e cu

rren

t han

dles

ha

ndle

s =

guid

ata(

gcbo

); %

Res

et c

urre

nt p

ortfo

lio

hand

les.

curre

nt_d

ata

= 0;

%

Res

et th

e cu

rrent

sto

ck s

hare

s ha

ndle

s.cu

rrent

_sto

ck_s

hare

s =

[0 0

0 0

0 0

]; %

Num

ber o

f sto

cks

in p

ortfo

lio

hand

les.

num

ber_

of_s

tock

s =

sum

(han

dles

.cur

rent

_por

tfolio

);

62

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,3))

h

andl

es.c

urre

nt_s

tock

_pric

e(1,

3) =

get

field

(han

dles

.eric

sson

b, ..

.

's

erie

s1',h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

_dat

e);

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,3)

= ..

.

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,3)/h

andl

es.c

urre

nt_s

tock

_pric

e(1,

3);

if

(0 =

= is

data

)

h

andl

es.c

urre

nt_d

ata

= ha

ndle

s.er

icss

onb.

* ...

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,3)

;

i

sdat

a =

1;

e

lse

han

dles

.cur

rent

_dat

a =

...

hand

les.

eric

sson

b(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd).*

...

hand

les.

curr

ent_

stoc

k_sh

ares

(1,3

) + ..

.

ha

ndle

s.cu

rrent

_dat

a(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd);

e

nd

end

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,4))

h

andl

es.c

urre

nt_s

tock

_pric

e(1,

4) =

get

field

(han

dles

.read

soft,

...

'ser

ies1

',han

dles

.cur

rent

_por

tfolio

_val

ue_d

ate)

;

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,4)

= ..

.

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,4)/h

andl

es.c

urre

nt_s

tock

_pric

e(1,

4);

if

(0 =

= is

data

)

h

andl

es.c

urre

nt_d

ata

= ha

ndle

s.re

adso

ft.*

...

han

dles

.cur

rent

_sto

ck_s

hare

s(1,

4);

isd

ata

= 1;

els

e

h

andl

es.c

urre

nt_d

ata

= ...

ha

ndle

s.re

adso

ft(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd).*

...

hand

les.

curr

ent_

stoc

k_sh

ares

(1,4

) + ..

.

ha

ndle

s.cu

rrent

_dat

a(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd);

e

nd

end

%If

AB

B L

TD S

DB

is c

hoos

en a

dd it

to th

e cu

rrent

_dat

a m

atrix

if

(1 =

= ha

ndle

s.cu

rrent

_por

tfolio

(1,1

))

%E

xtra

ct th

e cu

rrent

sto

ck p

rice

of A

BB

han

dles

.cur

rent

_sto

ck_p

rice(

1,1)

= g

etfie

ld(h

andl

es.a

bb, .

..

's

erie

s1',h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

_dat

e);

%

Cal

cula

te th

e nu

mbe

r of s

hare

s of

AB

B b

ough

t at t

he fo

reca

st d

ate

in

%

orde

r to

have

the

choo

sen

valu

e of

AB

B

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,1)

= ..

.

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,1)/h

andl

es.c

urre

nt_s

tock

_pric

e(1,

1);

%

Sca

le th

e A

BB

tim

eser

ies

with

the

num

ber o

f sto

ck s

hare

s

han

dles

.cur

rent

_dat

a =

hand

les.

abb.

*han

dles

.cur

rent

_sto

ck_s

hare

s(1,

1);

%

Set

the

flag

to o

ne s

o th

at th

e ne

xt s

tep

know

s th

at it

sha

ll ad

d th

e

%ne

w ti

mes

erie

s

isda

ta =

1;

end

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,2))

h

andl

es.c

urre

nt_s

tock

_pric

e(1,

2) =

get

field

(han

dles

.axi

s, ..

.

's

erie

s1',h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

_dat

e);

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,2)

= ..

.

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,2)/h

andl

es.c

urre

nt_s

tock

_pric

e(1,

2);

%

Che

ck if

the

times

erie

s sh

ould

be

a ne

w o

r add

ed to

a c

urre

nt

if

(0 =

= is

data

)

h

andl

es.c

urre

nt_d

ata

= ha

ndle

s.ax

is.*

...

han

dles

.cur

rent

_sto

ck_s

hare

s(1,

2);

isd

ata

= 1;

els

e

h

andl

es.c

urre

nt_d

ata

= ...

ha

ndle

s.ax

is(e

nd-h

andl

es.p

ortfo

lio_n

data

+1:e

nd).*

...

hand

les.

curr

ent_

stoc

k_sh

ares

(1,2

) + ..

.

ha

ndle

s.cu

rrent

_dat

a(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd);

e

nd

end

63

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r exe

cutin

g th

e S

ampl

ing.

fu

nctio

n S

ampl

ing(

hObj

ect,

even

tdat

a, h

andl

es, v

arar

gin)

%

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

%C

heck

if c

all c

omes

from

For

cast

or F

orec

astw

ithin

f =

han

dles

.fore

cast

_but

ton;

%

--- C

heck

the

leng

th o

f the

fore

cast

n

= Fo

reca

st_L

engt

h(ha

ndle

s.fig

ure1

,[],h

andl

es);

%S

et th

e va

lues

to z

ero

colu

mn

= 1;

ha

ndle

s.m

ean_

vect

or =

0;

hand

les.

cova

rianc

e_ve

ctor

= 0

; ha

ndle

s.co

varia

nce_

mat

rix =

0;

hand

les.

wei

ghte

d_m

ean_

vect

or =

0;

hand

les.

wei

ghte

d_co

varia

nce_

vect

or =

0;

hand

les.

wei

ghte

d_co

varia

nce_

mat

rix =

0;

portf

olio

_log

_ret

urn_

mat

rix =

0;

portf

olio

_wei

ghts

_mat

rix =

0;

%E

xtra

ct th

e da

ta fr

om th

e A

BB

tim

eser

ies

abb_

data

_vec

tor =

get

field

(han

dles

.abb

, 'se

ries1

');

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,5))

h

andl

es.c

urre

nt_s

tock

_pric

e(1,

5) =

get

field

(han

dles

.shb

a, ..

.

'

serie

s1',h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

_dat

e);

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,5)

= ..

.

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,5)/h

andl

es.c

urre

nt_s

tock

_pric

e(1,

5);

if

(0 =

= is

data

)

h

andl

es.c

urre

nt_d

ata

= ha

ndle

s.sh

ba.*

...

han

dles

.cur

rent

_sto

ck_s

hare

s(1,

5);

isd

ata

= 1;

els

e

h

andl

es.c

urre

nt_d

ata

= ...

ha

ndle

s.sh

ba(e

nd-h

andl

es.p

ortfo

lio_n

data

+1:e

nd).*

...

hand

les.

curr

ent_

stoc

k_sh

ares

(1,5

) + ..

.

ha

ndle

s.cu

rrent

_dat

a(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd);

e

nd

end

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,6))

h

andl

es.c

urre

nt_s

tock

_pric

e(1,

6) =

get

field

(han

dles

.vol

vob,

...

'se

ries1

',han

dles

.cur

rent

_por

tfolio

_val

ue_d

ate)

;

h

andl

es.c

urre

nt_s

tock

_sha

res(

1,6)

= ..

.

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,6)/h

andl

es.c

urre

nt_s

tock

_pric

e(1,

6);

if

(0 =

= is

data

)

h

andl

es.c

urre

nt_d

ata

= ...

h

andl

es.v

olvo

b.*h

andl

es.c

urre

nt_s

tock

_sha

res(

1,6)

;

i

sdat

a =

1;

e

lse

han

dles

.cur

rent

_dat

a =

...

hand

les.

volv

ob(e

nd-h

andl

es.p

ortfo

lio_n

data

+1:e

nd).*

...

hand

les.

curr

ent_

stoc

k_sh

ares

(1,6

) + ..

.

ha

ndle

s.cu

rrent

_dat

a(en

d-ha

ndle

s.po

rtfol

io_n

data

+1:e

nd);

end

en

d

64

read

soft_

sam

ple_

mea

n =

1/ha

ndle

s.sa

mpl

e_si

ze *

...

l

og(r

eads

oft_

data

_vec

tor(

end-

n*f)

/ ...

r

eads

oft_

data

_vec

tor(e

nd-h

andl

es.s

ampl

e_si

ze-n

*f));

hand

les.

mea

n_ve

ctor

(1,c

olum

n) =

read

soft_

sam

ple_

mea

n;

colu

mn

= co

lum

n +

1;

shba

_dat

a_ve

ctor

= g

etfie

ld(h

andl

es.s

hba,

'ser

ies1

');

shba

_log

_ret

urn_

vect

or =

log(

shba

_dat

a_ve

ctor

(2:e

nd)./

...

shb

a_da

ta_v

ecto

r(1:e

nd-1

));

shba

_sam

ple_

mea

n =

1/ha

ndle

s.sa

mpl

e_si

ze*lo

g(sh

ba_d

ata_

vect

or(e

nd-

n*f)

/...

shb

a_da

ta_v

ecto

r(end

-han

dles

.sam

ple_

size

-n*f)

); ha

ndle

s.m

ean_

vect

or(1

,col

umn)

= s

hba_

sam

ple_

mea

n;

colu

mn

= co

lum

n +

1;

volv

ob_d

ata_

vect

or =

get

field

(han

dles

.vol

vob,

'ser

ies1

');

volv

ob_l

og_r

etur

n_ve

ctor

= lo

g(vo

lvob

_dat

a_ve

ctor

(2:e

nd)./

...

vo

lvob

_dat

a_ve

ctor

(1:e

nd-1

));

volv

ob_s

ampl

e_m

ean

= 1/

hand

les.

sam

ple_

size

* ..

.

log(

volv

ob_d

ata_

vect

or(e

nd-n

*f) /

...

vo

lvob

_dat

a_ve

ctor

(end

-han

dles

.sam

ple_

size

-n*f)

); ha

ndle

s.m

ean_

vect

or(1

,col

umn)

= v

olvo

b_sa

mpl

e_m

ean;

co

lum

n =

colu

mn

+ 1;

%

Cre

ate

a po

rtfol

io lo

g re

turn

mat

rix fo

r the

var

ianc

e - c

ovar

ianc

e %

calc

ulat

ions

po

rtfol

io_l

og_r

etur

n_m

atrix

= [

...

a

bb_l

og_r

etur

n_ve

ctor

(end

-han

dles

.sam

ple_

size

-n*f

+1:e

nd-n

*f) .

..

axi

s_lo

g_re

turn

_vec

tor(

end-

hand

les.

sam

ple_

size

-n*f

+1:e

nd-n

*f) .

..

eric

sson

b_lo

g_re

turn

_vec

tor(e

nd-h

andl

es.s

ampl

e_si

ze-n

*f+1:

end-

n*f)

...

r

eads

oft_

log_

retu

rn_v

ecto

r(end

-han

dles

.sam

ple_

size

-n*f+

1:en

d-n*

f) ...

shb

a_lo

g_re

turn

_vec

tor(e

nd-h

andl

es.s

ampl

e_si

ze-n

*f+1

:end

-n*f

) ...

v

olvo

b_lo

g_re

turn

_vec

tor(e

nd-h

andl

es.s

ampl

e_si

ze-n

*f+1:

end-

n*f)]

;

%C

reat

e th

e A

BB

log

retu

rn m

atrix

ab

b_lo

g_re

turn

_vec

tor =

log(

abb_

data

_vec

tor(

2:en

d)./

...

abb_

data

_vec

tor(

1:en

d-1)

); %

Cal

cula

te th

e da

ily A

BB

sam

ple

mea

n ab

b_sa

mpl

e_m

ean

= 1/

hand

les.

sam

ple_

size

*log(

abb_

data

_vec

tor(e

nd-

n*f)/

...

abb_

data

_vec

tor(

end-

hand

les.

sam

ple_

size

-n*f)

); %

Set

the

mea

n ve

ctor

s fir

st e

lem

ent t

o da

ily A

BB

sam

ple

mea

n ha

ndle

s.m

ean_

vect

or(1

,col

umn)

= a

bb_s

ampl

e_m

ean;

%

Set

the

colu

mn

inde

x to

2

colu

mn

= co

lum

n +

1;

axis

_dat

a_ve

ctor

= g

etfie

ld(h

andl

es.a

xis,

'ser

ies1

');

axis

_log

_ret

urn_

vect

or =

log(

axis

_dat

a_ve

ctor

(2:e

nd)./

...

axi

s_da

ta_v

ecto

r(1:e

nd-1

));

axis

_sam

ple_

mea

n =

1/ha

ndle

s.sa

mpl

e_si

ze*lo

g(ax

is_d

ata_

vect

or(e

nd-

n*f)/

...

axi

s_da

ta_v

ecto

r(en

d-ha

ndle

s.sa

mpl

e_si

ze-n

*f));

ha

ndle

s.m

ean_

vect

or(1

,col

umn)

= a

xis_

sam

ple_

mea

n;

colu

mn

= co

lum

n +

1;

eric

sson

b_da

ta_v

ecto

r = g

etfie

ld(h

andl

es.e

ricss

onb,

'ser

ies1

');

eric

sson

b_lo

g_re

turn

_vec

tor =

log(

eric

sson

b_da

ta_v

ecto

r(2:e

nd)./

...

eric

sson

b_da

ta_v

ecto

r(1:e

nd-1

));

eric

sson

b_sa

mpl

e_m

ean

= 1/

hand

les.

sam

ple_

size

* ..

.

log

(eric

sson

b_da

ta_v

ecto

r(en

d-n*

f) / .

..

eric

sson

b_da

ta_v

ecto

r(en

d-ha

ndle

s.sa

mpl

e_si

ze-n

*f));

ha

ndle

s.m

ean_

vect

or(1

,col

umn)

= e

ricss

onb_

sam

ple_

mea

n;

colu

mn

= co

lum

n +

1;

read

soft_

data

_vec

tor =

get

field

(han

dles

.read

soft,

'ser

ies1

');

read

soft_

log_

retu

rn_v

ecto

r = lo

g(re

adso

ft_da

ta_v

ecto

r(2:

end)

./ ...

rea

dsof

t_da

ta_v

ecto

r(1:e

nd-1

));

65

h

andl

es.w

eigh

ted_

mea

n_ve

ctor

(1,i)

= ..

.

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,i) *

...

h

andl

es.m

ean_

retu

rn_v

ecto

r(1,i)

; en

d %

Cal

cula

te th

e to

tal w

eigh

ted

daily

por

tfolio

sam

ple

mea

n ha

ndle

s.po

rtfol

io_s

ampl

e_m

ean

= su

m(h

andl

es.w

eigh

ted_

mea

n_ve

ctor

); %

Cre

ate

a po

rtfol

io w

eigh

ts m

atrix

so

that

it c

an e

xtra

ct th

e w

eigh

ted

%co

varia

nces

from

the

hand

les.

cova

rianc

e_re

turn

_mat

rix

for i

= 1

:6

f

or j

= 1:

6

if(i =

= j)

por

tfolio

_wei

ghts

_mat

rix(i,

j) =

...

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,i)

;

else

p

ortfo

lio_w

eigh

ts_m

atrix

(i,j)

= 0;

end

e

nd

end

%C

reat

e a

wei

ghte

d co

varia

nce

mat

rix fr

om th

e ha

ndle

s.co

varia

nce_

retu

rn

%_m

atrix

whe

re p

ortfo

lio w

eigh

ts m

atrix

is u

sed

in o

rder

to e

xtra

ct th

e %

curre

nt p

ortfo

lio e

lem

ents

and

set

the

othe

r to

zero

ha

ndle

s.w

eigh

ted_

cova

rianc

e_m

atrix

= p

ortfo

lio_w

eigh

ts_m

atrix

* ..

.

han

dles

.cov

aria

nce_

retu

rn_m

atrix

*por

tfolio

_wei

ghts

_mat

rix;

%

Cal

cula

te th

e da

ily p

ortfo

lio s

ampl

e st

anda

rd d

evia

tion

by ta

king

the

%sq

uare

root

of t

he s

um o

f all

varia

nce

cova

rianc

e el

emen

ts

hand

les.

portf

olio

_sam

ple_

stan

dard

_dev

iatio

n =

...

sqr

t(sum

(sum

(han

dles

.wei

ghte

d_co

varia

nce_

mat

rix)))

;

%C

alcu

late

the

varia

nce

- cov

aria

nce

mat

rix fo

r all

the

stoc

ks

for i

= 1

:6

fo

r j =

1:6

h

andl

es.c

ovar

ianc

e_m

atrix

(i,j)

= 1/

(han

dles

.sam

ple_

size

-1) *

...

sum

((por

tfolio

_log

_ret

urn_

mat

rix(1

:end

,i) -

...

han

dles

.mea

n_ve

ctor

(1,i)

).* ..

.

(p

ortfo

lio_l

og_r

etur

n_m

atrix

(1:e

nd,j)

- ...

h

andl

es.m

ean_

vect

or(1

,j)));

end

en

d %

Cal

cula

te th

e da

ily s

ampl

e m

ean

vect

or o

f the

sto

ck re

turn

s fo

r i =

1:6

han

dles

.mea

n_re

turn

_vec

tor(1

,i) =

exp

(han

dles

.mea

n_ve

ctor

(1,i)

+ ...

0

.5 *

han

dles

.cov

aria

nce_

mat

rix(i,

i));

end

%C

alcu

late

the

daily

sam

ple

varia

nce

- cov

aria

nce

mat

rix o

f the

sto

ck

%re

turn

s of

all

the

stoc

ks

for i

= 1

:6

fo

r j =

1:6

h

andl

es.c

ovar

ianc

e_re

turn

_mat

rix(i,

j) =

(exp

( ...

(han

dles

.mea

n_ve

ctor

(1,i)

+ 0

.5 *

...

hand

les.

cova

rianc

e_m

atrix

(i,i))

* ..

.

(h

andl

es.m

ean_

vect

or(1

,j) +

0.5

* ..

.

ha

ndle

s.co

varia

nce_

mat

rix(j,

j))))

* ...

(e

xp(h

andl

es.c

ovar

ianc

e_m

atrix

(i,j))

- 1)

;

end

en

d %

Cal

cula

te th

e w

eigh

ted

daily

sam

ple

mea

n ve

ctor

of t

he s

tock

retu

rns

for i

= 1

:6

66

else

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,1) =

0;

end

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,2))

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,2

) = ..

.

(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,2

)) /

...

(sum

(han

dles

.cur

rent

_por

tfolio

_val

ue));

el

se

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,2

) = 0

; en

d if

(1 =

= ha

ndle

s.cu

rrent

_por

tfolio

(1,3

))

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,3) =

...

(han

dles

.cur

rent

_por

tfolio

_val

ue(1

,3))

/ ...

(s

um(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

));

else

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,3) =

0;

end

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,4))

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,4

) = ..

.

(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,4

)) /

...

(sum

(han

dles

.cur

rent

_por

tfolio

_val

ue));

el

se

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,4

) = 0

; en

d if

(1 =

= ha

ndle

s.cu

rrent

_por

tfolio

(1,5

))

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,5) =

...

(han

dles

.cur

rent

_por

tfolio

_val

ue(1

,5))

/ ...

(s

um(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

));

else

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,5) =

0;

end

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

-----

----

----

- %

Cal

l the

Cur

rent

Ris

k C

ontri

buto

rs to

upd

ate

the

hand

les.

Por

tfolio

_ris

k

% fi

gure

, han

dles

.Ris

k_in

crea

se a

nd h

andl

es.R

isk_

decr

ease

fiel

ds

Cur

rent

_Ris

k_C

ontri

buto

rs(h

andl

es.fi

gure

1,[],

hand

les)

; %

----

----

----

-----

----

----

----

----

-----

----

----

----

----

-----

----

----

- %

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r cal

cula

ting

the

Cur

rent

Por

tfolio

Wei

ghts

. fu

nctio

n C

urre

nt_P

ortfo

lio_W

eigh

ts(h

Obj

ect,

even

tdat

a, h

andl

es, v

arar

gin)

%

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

hand

les.

curre

nt_s

tock

_wei

ghts

= [0

0 0

0 0

0];

%C

alcu

late

the

portf

olio

wei

ghts

at t

he c

urre

nt d

ate

(the

pric

es a

t the

%

day

of h

andl

es.p

ortfo

lio_v

alue

_dat

e if

(1 =

= ha

ndle

s.cu

rrent

_por

tfolio

(1,1

))

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,1) =

...

(han

dles

.cur

rent

_por

tfolio

_val

ue(1

,1))

/ ...

(s

um(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

));

67

%S

et th

e en

d_in

dex

in th

e fo

r loo

p to

cur

rent

num

ber o

f sto

cks

end_

inde

x =

sum

(han

dles

.cur

rent

_por

tfolio

); %

Che

ck w

hich

sto

ck c

ontri

bute

s m

ost t

o th

e ris

k an

d pl

ace

them

in o

rder

of

%

the

high

est c

ontri

buto

r firs

t fo

r i =

1:e

nd_i

ndex

[C,I]

= m

ax(te

mp_

vect

or);

te

mp_

orde

r_ve

ctor

(1,i)

= I;

tem

p_ve

ctor

(1,I)

= 0

; en

d %

Plo

t the

text

in th

e P

ortfo

lio_r

isk

figur

e ax

es(h

andl

es.P

ortfo

lio_r

isk)

; cl

a;

text

(0.0

5,0.

75,'1

.','U

nits

','Nor

mal

ized

');

text

(0.0

5,0.

5,'2

.','U

nits

','Nor

mal

ized

');

text

(0.0

5,0.

25,'3

.','U

nits

','Nor

mal

ized

');

%S

et th

e en

d_in

dex

of th

e fo

r loo

p to

3 o

r if t

here

are

less

sto

cks

%in

the

portf

olio

set

it to

the

num

ber o

f sto

cks

in th

e po

rtfol

io

end_

inde

x =

0;

end_

inde

x =

min

(3,s

um(h

andl

es.c

urre

nt_p

ortfo

lio));

%

Set

the

stoc

ks in

the

corre

ct o

rder

in th

e P

ortfo

lio_r

isk

figur

e fo

r i =

1:e

nd_i

ndex

if(1

==

tem

p_or

der_

vect

or(1

,i))

tex

t(0.1

8,(1

-0.2

5*i),

'AB

B L

TD S

DB

','Uni

ts','N

orm

aliz

ed');

els

eif(2

==

tem

p_or

der_

vect

or(1

,i))

tex

t(0.1

8,(1

-0.2

5*i),

'Axi

s','U

nits

','Nor

mal

ized

');

e

lsei

f(3 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

t

ext(0

.18,

(1-0

.25*

i),'E

ricss

on B

','Uni

ts','N

orm

aliz

ed');

els

eif(4

==

tem

p_or

der_

vect

or(1

,i))

tex

t(0.1

8,(1

-0.2

5*i),

'Rea

dsof

t','U

nits

','Nor

mal

ized

');

if (1

==

hand

les.

curre

nt_p

ortfo

lio(1

,6))

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,6

) = ..

.

(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,6

)) /

...

(sum

(han

dles

.cur

rent

_por

tfolio

_val

ue));

el

se

h

andl

es.c

urre

nt_s

tock

_wei

ghts

(1,6

) = 0

; en

d %

Upd

ate

hand

les

stru

ctur

e gu

idat

a(hO

bjec

t, ha

ndle

s);

%--

----

----

----

----

----

----

----

----

-----

----

----

----

----

-----

----

----

----

- %

--- F

unct

ion

for u

pdat

ing

the

Por

tfolio

_ris

k fie

ld.

func

tion

Cur

rent

_Ris

k_C

ontri

buto

rs(h

Obj

ect,

even

tdat

a, h

andl

es, v

arar

gin)

%

Load

the

curr

ent h

andl

es

hand

les

= gu

idat

a(gc

bo);

%R

eset

dat

a te

mp_

vect

or =

0;

tem

p_or

der_

vect

or =

0;

end_

inde

x =

0;

C =

0;

I = 0

; %

Cre

ate

a te

mpo

rary

wei

ghte

d ve

ctor

from

the

cova

rianc

e_re

turn

_mat

rix

for i

= 1

:6

te

mp_

vect

or(1

,i) =

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,i) *

...

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,i) *

...

han

dles

.cov

aria

nce_

retu

rn_m

atrix

(i,i);

en

d

68

C

urre

nt_P

ortfo

lio_W

eigh

ts(h

andl

es.fi

gure

1,[],

hand

les)

;

% --

-----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

----

--

%

Load

the

curre

nt h

andl

es

h

andl

es =

gui

data

(gcb

o);

%

Cre

ate

a po

rtfol

io w

eigh

ts m

atrix

so

that

it c

an e

xtra

ct th

e w

eigh

ted

%

cova

rianc

es fr

om th

e ha

ndle

s.co

varia

nce_

mat

rix

por

tfolio

_wei

ghts

_mat

rix =

0;

%

Cre

ate

an in

vers

e po

rtfol

io w

eigh

ts m

atrix

so

that

it c

an e

xtra

ct th

e

%w

eigh

ted

cova

rianc

es fr

om th

e ha

ndle

s.co

varia

nce_

mat

rix o

f the

st

ocks

%th

at a

re n

ot in

the

portf

olio

inve

rse_

portf

olio

_wei

ghts

_mat

rix =

0;

%

Cre

ate

a w

eigh

ted

diag

onal

mat

rix fo

r the

add

ition

al c

ovar

ianc

e

%ca

lcul

atio

n

wei

ghte

d_di

agon

al_m

atrix

= 0

;

%S

et th

e w

eigh

t for

the

new

sto

ck

n

ew_s

tock

_wei

ght =

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,7) /

...

s

um(h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

);

for i

= 1

:6

fo

r j =

1:6

if

(i ==

j)

p

ortfo

lio_w

eigh

ts_m

atrix

(i,j)

= ...

han

dles

.cur

rent

_sto

ck_w

eigh

ts(1

,i);

i

nver

se_p

ortfo

lio_w

eigh

ts_m

atrix

(i,j)

= ...

ab

s((h

andl

es.c

urre

nt_p

ortfo

lio(1

,i)-1

))*ne

w_s

tock

_wei

ght;

w

eigh

ted_

diag

onal

_mat

rix(i,

j) =

...

n

ew_s

tock

_wei

ght*

new

_sto

ck_w

eigh

t * ..

.

han

dles

.cov

aria

nce_

retu

rn_m

atrix

(i,j)*

...

a

bs((h

andl

es.c

urre

nt_p

ortfo

lio(1

,i)-1

));

els

e

e

lsei

f(5 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

t

ext(0

.18,

(1-0

.25*

i),'S

HB

A','U

nits

','Nor

mal

ized

');

e

lsei

f(6 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

t

ext(0

.18,

(1-0

.25*

i),'V

olvo

B','U

nits

','Nor

mal

ized

');

e

nd

end

%If

the

Rec

omm

end

chec

kbox

is m

arke

d an

d no

t all

stoc

ks a

re c

hoos

en

%ca

lcul

ate

wha

t sto

cks

will

incr

ease

or d

ecre

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the

portf

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risk

if(

(1 =

= ge

t(han

dles

.che

ckbo

x7,'V

alue

')) &

...

(su

m(h

andl

es.c

urre

nt_p

ortfo

lio) <

6))

%

Use

an

inpu

t dia

log

to a

sk th

e va

lue

of th

e ne

w s

tock

at f

orec

ast

%

date

, if t

he in

put i

s no

t a n

umbe

r ask

aga

in u

ntil

it is

a n

umbe

r

tem

p =

inpu

tdlg

( ...

'Ent

er th

e va

lue

of th

e ne

w s

tock

you

wan

t to

buy

at th

e Fo

reca

st d

ate'

...

,'

Val

ue o

f new

sto

ck',1

,cel

lstr(

'50'

),'of

f');

w

hile

(0 =

= is

scal

ar(s

tr2nu

m(te

mp{

1,1}

)))

tem

p =

inpu

tdlg

( ...

'Ent

er th

e va

lue

of th

e ne

w s

tock

you

wan

t to

buy

at th

e Fo

reca

st d

ate'

...

,'

Val

ue o

f new

sto

ck',1

,cel

lstr(

'50'

),'of

f');

e

nd

%

Set

the

curre

nt_p

ortfo

lio_v

alue

(1,7

) to

the

choo

sen

valu

e in

ord

er to

%ge

t the

cor

rect

wei

ghts

in C

urre

nt_P

ortfo

lio_W

eigh

ts

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,7

) = s

tr2nu

m(te

mp{

1,1}

);

% U

pdat

e ha

ndle

s st

ruct

ure

g

uida

ta(h

Obj

ect,

hand

les)

;

% --

-----

----

-----

----

----

----

----

-----

----

----

----

-----

----

----

----

--

%

Cal

l the

Cur

rent

Por

tfolio

Wei

ghts

to s

et th

e

%

han

dles

.cur

rent

_por

tfolio

_wei

ghts

fiel

d to

the

valu

e of

the

choo

sen

% p

ortfo

lio

69

%

Cal

cula

te th

e da

ily s

tand

ard

devi

atio

n fo

r the

pos

sibl

e po

rtfol

ios

w

eigh

ted_

stan

dard

_dev

iatio

n_ve

ctor

= ..

.

s

qrt(w

eigh

ted_

cova

rianc

e_ve

ctor

);

%R

eset

dat

a

tem

p_ve

ctor

= 0

;

tem

p_or

der_

vect

or =

0;

e

nd_i

ndex

= 0

;

C =

0;

I

= 0;

%

Set

the

end_

inde

x of

the

for l

oop

to th

e nu

mbe

r of s

tock

s no

t in

the

%

curre

nt p

ortfo

lio

e

nd_i

ndex

= 6

-sum

(han

dles

.cur

rent

_por

tfolio

);

%C

heck

wha

t sto

cks

incr

ease

the

risk

and

plac

e th

em in

ord

er o

f

%th

e hi

ghes

t con

tribu

tor f

irst

te

mp_

vect

or =

wei

ghte

d_st

anda

rd_d

evia

tion_

vect

or;

te

mp_

orde

r_ve

ctor

_len

gth

= 0;

for i

= 1

:end

_ind

ex

[C

,I] =

max

(tem

p_ve

ctor

);

i

f(C >

han

dles

.por

tfolio

_sam

ple_

stan

dard

_dev

iatio

n)

tem

p_or

der_

vect

or(1

,i) =

I;

tem

p_or

der_

vect

or_l

engt

h =

tem

p_or

der_

vect

or_l

engt

h +

1;

els

e

e

nd

tem

p_ve

ctor

(1,I)

= 0

;

end

%P

lot t

he te

xt in

the

Ris

k_in

crea

se fi

gure

axe

s(ha

ndle

s.R

isk_

incr

ease

);

cla

;

por

tfolio

_wei

ghts

_mat

rix(i,

j) =

0;

inve

rse_

portf

olio

_wei

ghts

_mat

rix(i,

j) =

0;

wei

ghte

d_di

agon

al_m

atrix

(i,j)

= 0;

e

nd

en

d

end

%C

reat

e a

wei

ghte

d co

varia

nce

mat

rix fr

om th

e ha

ndle

s.co

varia

nce_

retu

rn

%

_mat

rix w

here

por

tfolio

wei

ghts

mat

rix is

use

d in

ord

er to

ext

ract

the

%

cur

rent

por

tfolio

ele

men

ts a

nd s

et th

e ot

her t

o ze

ro

w

eigh

ted_

cova

rianc

e_m

atrix

= p

ortfo

lio_w

eigh

ts_m

atrix

* ..

.

han

dles

.cov

aria

nce_

retu

rn_m

atrix

*por

tfolio

_wei

ghts

_mat

rix;

%

Sum

the

wei

ghte

d co

varia

nce

mat

rix to

kno

w th

e cu

rren

t sum

wei

ghte

d_co

varia

nce_

sum

= s

um(s

um(w

eigh

ted_

cova

rianc

e_m

atrix

));

%

Set

the

wei

ghte

d_ad

ditio

nal_

cova

rianc

e_m

atrix

to z

ero

w

eigh

ted_

addi

tiona

l_co

varia

nce_

mat

rix =

0;

%

Con

stru

ct th

e w

eigh

ted_

addi

tiona

l_co

varia

nce_

mat

rix b

y ta

king

the

%co

varia

nces

from

eac

h st

ock

colu

mn

not i

n th

e po

rtfol

io a

nd

%

mul

tiply

ing

them

by

two

for t

he c

orre

ct c

alcu

latio

n an

d by

add

ing

%

the

varia

nces

for t

hose

sto

cks

w

eigh

ted_

addi

tiona

l_co

varia

nce_

mat

rix =

(por

tfolio

_wei

ghts

_mat

rix *

...

han

dles

.cov

aria

nce_

retu

rn_m

atrix

* ..

.

i

nver

se_p

ortfo

lio_w

eigh

ts_m

atrix

).*2

+...

wei

ghte

d_di

agon

al_m

atrix

;

%C

reat

e a

vect

or w

ith th

e su

ms

of th

e co

lum

ns

w

eigh

ted_

addi

tiona

l_co

varia

nce_

vect

or =

...

sum

(wei

ghte

d_ad

ditio

nal_

cova

rianc

e_m

atrix

);

%C

reat

e a

vect

or w

ith th

e to

tal p

ortfo

lio c

ovar

ianc

es

wei

ghte

d_co

varia

nce_

vect

or =

wei

ghte

d_ad

ditio

nal_

cova

rianc

e_ve

ctor

+...

((ab

s(ha

ndle

s.cu

rrent

_por

tfolio

-1)).

*wei

ghte

d_co

varia

nce_

sum

);

70

%

Res

et d

ata

te

mp_

vect

or =

0;

in

vers

e_te

mp_

orde

r_ve

ctor

= 0

;

tem

p_or

der_

vect

or =

0;

e

nd_i

ndex

= 0

;

C =

0;

I

= 0;

%S

et th

e en

d_in

dex

of th

e fo

r loo

p to

the

num

ber o

f sto

cks

not i

n th

e

%cu

rrent

por

tfolio

end

_ind

ex =

6-s

um(h

andl

es.c

urre

nt_p

ortfo

lio);

%

Che

ck w

hat s

tock

s de

crea

se th

e ris

k an

d pl

ace

them

in o

rder

of

%

the

low

est c

ontri

buto

r firs

t so

that

the

vect

or e

nds

up w

ith th

e

%

corre

ct le

ngth

tem

p_or

der_

vect

or_l

engt

h =

0;

te

mp_

vect

or =

wei

ghte

d_st

anda

rd_d

evia

tion_

vect

or;

j

= 1;

for i

= 1

:end

_ind

ex

[C

,I] =

max

(tem

p_ve

ctor

);

i

f(C <

han

dles

.por

tfolio

_sam

ple_

stan

dard

_dev

iatio

n)

inve

rse_

tem

p_or

der_

vect

or(1

,j) =

I;

tem

p_or

der_

vect

or_l

engt

h =

tem

p_or

der_

vect

or_l

engt

h +

1;

j = j

+ 1;

e

lse

end

t

emp_

vect

or(1

,I) =

0;

e

nd

%

Rea

rrang

e th

e or

der s

o th

at th

e st

ock

that

will

decr

ease

the

risk

the

%

mos

t is

plac

ed fi

rst i

n te

mp_

orde

r_ve

ctor

te

xt(0

.05,

0.75

,'1.',

'Uni

ts','N

orm

aliz

ed');

text

(0.0

5,0.

5,'2

.','U

nits

','Nor

mal

ized

');

te

xt(0

.05,

0.25

,'3.',

'Uni

ts','N

orm

aliz

ed');

%S

et th

e en

d_in

dex

to th

e m

inim

um o

f 3 o

r the

num

ber o

f sto

cks

not i

n

%

the

portf

olio

or t

he n

umbe

r of s

tock

s th

at w

ill in

crea

se th

e ris

k

end

_ind

ex =

0;

e

nd_i

ndex

= m

in(m

in(3

,sum

(6-h

andl

es.c

urre

nt_p

ortfo

lio)),

...

te

mp_

orde

r_ve

ctor

_len

gth)

;

%S

et th

e st

ocks

in th

e co

rrec

t ord

er in

the

Ris

k_in

crea

se fi

gure

for i

= 1

:end

_ind

ex

if(1

==

tem

p_or

der_

vect

or(1

,i))

text

(0.1

8,(1

-0.2

5*i),

'AB

B L

TD S

DB

','Uni

ts','N

orm

aliz

ed');

e

lsei

f(2 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

te

xt(0

.18,

(1-0

.25*

i),'A

xis'

,'Uni

ts','N

orm

aliz

ed');

e

lsei

f(3 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

te

xt(0

.18,

(1-0

.25*

i),'E

ricss

on B

','Uni

ts','N

orm

aliz

ed');

e

lsei

f(4 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

te

xt(0

.18,

(1-0

.25*

i),'R

eads

oft',

'Uni

ts','N

orm

aliz

ed');

e

lsei

f(5 =

= te

mp_

orde

r_ve

ctor

(1,i)

)

te

xt(0

.18,

(1-0

.25*

i),'S

HB

A','U

nits

','Nor

mal

ized

');

els

eif(6

==

tem

p_or

der_

vect

or(1

,i))

text

(0.1

8,(1

-0.2

5*i),

'Vol

vo B

','Uni

ts','N

orm

aliz

ed');

e

nd

e

nd

%

Res

et th

e va

lue

of th

e re

com

men

ded

stoc

k

han

dles

.cur

rent

_por

tfolio

_val

ue(1

,7) =

0;

%

Set

che

ckbo

x7 to

no

reco

mm

enda

tion

s

et(h

andl

es.c

heck

box7

,'Val

ue',0

);

71

else

if((

1 ==

get

(han

dles

.che

ckbo

x7,'V

alue

')) &

...

(6 =

= (s

um(h

andl

es.c

urre

nt_p

ortfo

lio)))

)

%

Use

a h

elp

dial

og to

pre

sent

the

info

rmat

ion

hel

pdlg

( ...

'The

re a

re n

o ne

w s

tock

s le

ft to

reco

mm

end.

Loo

k at

the

Cur

rent

risk

co

ntrib

utor

s in

ord

er to

low

er th

e po

rtfol

io ri

sk '.

..

,'All

avai

labl

e st

ocks

are

alre

ady

in th

e po

rtfol

io');

%

Res

et th

e va

lue

of th

e re

com

men

ded

stoc

k

h

andl

es.c

urre

nt_p

ortfo

lio_v

alue

(1,7

) = 0

;

%

Set

che

ckbo

x7 to

no

reco

mm

enda

tion

set

(han

dles

.che

ckbo

x7,'V

alue

',0);

e

nd

%

Cle

ar th

e te

xt in

the

Ris

k_in

crea

se fi

gure

axe

s(ha

ndle

s.R

isk_

incr

ease

);

cla

;

%C

lear

the

text

in th

e R

isk_

decr

ease

figu

re

a

xes(

hand

les.

Ris

k_de

crea

se);

c

la;

end

% U

pdat

e ha

ndle

s st

ruct

ure

guid

ata(

hObj

ect,

hand

les)

; %

----

----

----

----

----

----

----

----

----

-----

----

----

----

-----

----

----

----

---

% --

- Fun

ctio

n fo

r the

For

ecas

t Hel

p m

enu

choi

ce

func

tion

Fore

cast

Hel

p_C

allb

ack(

hObj

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How

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Go

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enu

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choo

se P

rint.

The

who

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cree

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ill be

prin

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', ...

'

Fore

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Hel

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