AP Lecture 6-What is Risk

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ASSET PRICING

Lecture 6

What is Risk?

Bristol Business School, UWE

Dr. Jesus G. Garza-Garcia



1. WHAT IS (FINANCIAL) RISK?

´ Some preliminary questions

´ Assume that you want to invest $100,000.

What do you want from this investment?

´ What dangers to your investment could you

see?




´ Definition of risk:

´ Actual outcome (return) is different from theexpected outcome (return). This means a gain or

a loss. So, the definition of risk is symmetric.

´ However, people·s attitude towards risk isasymmetric. People are more concerned about a

possible loss than a possible gain. People are riskaverse.

´ The same amount added to wealth is valued lessthan the same amount lost.




´ It follows: If people are risk averse, they will be less

willing to hold a risky asset than they will be to hold anasset with little or no risk. Thus, agents only hold riskyassets if they receive a higher reward.




´ What is the reward? (Recall!)

´ Reward = return

´ Eg. A share: the current return is: (Recall: HPR!)

´ Again, risk is the deviation of the actual returnfrom the average return.

1 1 0

0

( ) D P P return

P

!

sumof returnaveragereturn

T

!§




´ Exercise 1:

´ An investor has the choice between assets with

the following return-risk combinations:A

(8,15);B(6,12); C(11,15); D(16,21).

´ Which asset will the risk averse investor reject?




´ Daily returns of McDonald·s stock price 2nd Jan 1990 to31st Jan 1990

´

Looking at the graph, is it risky to invest in

McDonald·s?




´ Daily data from 29th Dec 1989 until 31st Dec1999 (2531 returns): Graph:

´ What do you see?

McDonald's--Daily Returns, 29 Dec 89 - 31 Dec 99

-11.0%

-10.0%

-9.0%

-8.0%

-7.0%

-6.0%

-5.0%

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

11.0%

02- J an

- 9 0

0 9- S e p- 9 0

17-M a

y- 91

22- J an

- 92

2 8- S e p- 92

0 5- J un

- 9 3

1 0-F e b- 94

1 8- O c t - 94

2 5- J un

- 9 5

01-M a

r - 9 6

0 6-N ov- 9 6

14- J ul - 97

21-M a

r - 9 8

2 6-N ov- 9 8

0 3-A u g- 9 9

8 September 1998

31 August 1998




´ Y ou get a bit more when you look at a frequency distribution:

´ Highest daily return = 10.86%´ Lowest daily return= -10.07%

´ What do you see now?



WHAT DOES AN INVESTOR WANT FROM

THE INVESTMENT?

´ High average rate of return and low risk

´ How do we measure both?

´ For ease of calculation (and daily averagereturn is close to zero), we use annual data

now.




THE INVESTMENT?

Date

McDonald's

return

Return minus

average,

squared

31-Dec-90 -15.65% 11.908%31-Dec-91 30.54% 1.365%

31-Dec-92 28.31% 0.893%

31-Dec-93 16.90% 0.038%

30-Dec-94 2.64% 2.633%

29-Dec-95 54.27% 12.536%

31-Dec-96 0.54% 3.357%

31-Dec-97 5.23% 1.857%

31-Dec-98 60.88% 17.659%

31-Dec-99 4.94% 1.938%




THE INVESTMENT?

´ Calculate expected return:

´ On average, an investor in McDonald·s stocksreceives about 19% p.a.

´ Calculating the variance:

´ (Since risk is defined as the difference of actualreturns from expected returns, variance andstandard deviations seem to be good measures.)

1

1 1( ) 15.65 30.54 ... 4.94 18.86%

10

T

t

t

E r r T !

! ! !§




THE INVESTMENT?

´ The average variation around the expected

return of 18.86% is 24.56%.

´ Anything striking?



AVERAGE RETURN VERSUS STANDARD

DEVIATION OF RETURNS

Average

return

Standard

deviation

Average

return

Standard

deviation

Abbott 17.12% 19.27% Marriott 7.15% 39.81%

Alcoa 19.03% 27.59% Micr osoft 62.72% 37.99%

American

Air lines 9.26% 29.34% NASDAQ 23.00% 20.17%

ATT 6.76% 27.96% Nicor 9.15% 16.50%

Boeing 7.57% 25.57% Nordstr om 5.44% 38.21%

Cisco 67.31% 38.80% Nor thr op 14.76% 34.40%

Coke 10.18% 24.29%

Vanguard

Long-Ter m

Tr easury

Fund 2.43% 7.94%

Dell 69.86% 55.48%

Pr octer &

Gamble 19.41% 20.91%

Duke 11.07% 15.43%

Standard &

Poor's 500

Index 15.09% 13.18%




THE INVESTMENT?

´ What do you see on the graph (relate to table)?

´ What does the straight line indicate to you?



VALUE AT RISK (VAR)

´ What is VaR?

´ VaR estimates the capital loss on a portfolio over agiven period (e.g.1 day) that will be exceeded with

a given percentage (e.g. 1%).

´ Capital loss can be in £ or, as we will define ithere, it can be a percentage of our portfolio.

´ VaR is calculated on the basis of the probabilitydistribution of returns.



VALUE AT RISK (VAR)

´ Figure 1: Histogram of daily returns of FTSE All

Shares between 3rd May 2004 and 2nd May 2008.

0

50

100

150

200

250

F

r

e

u

e

n

c

y

Return %

p=1%

(1-p)=99%



VALUE AT RISK (VAR)

´ Here: the daily VaR (99% confidence level) = -

2.61%. This means that if the portfolio value

were £100 million, the VaR would simply be:

´ VaR = £100 million x 2.61% = £2.61 million

´ The VaR value of £2.61 million tells us that

there is a 1% chance that next day we will lose

£2.61 million or more.



2. USING EXCEL

´ NOTE: HPR (which we should calculate) include

dividends. When we look for data on stock

prices or stock indices, we need to be careful to

choose prices marked as ¶adj close· (adjusted

prices at the close of the day: adjusted for

dividends, splits etc).

´ Calculation of daily return (assuming adjustedprices):

Arithmetic:



2. USING EXCEL

´ To calculate frequency distribution:

´ Use frequency function in EXCEL:

´ Construct classes (called BINS)´ Use frequency command



2. USING EXCEL

A B C D E F

1 Date Price Return Frequency

Distribution

EXEL

Instruction

2 29-Jan-90 8.50 -10% =frequency

(c3:c102,

e3:e12)

3 30-Jan-90 8.59 1.05% -8%

4 31-Jan-90 8.50 -1.053% -6%

5 1-Feb-90 8.34 -1.900% -4%

6 2-Feb-90 8.19 -1.815% -2%

7 « « «. 0%

.. « « «. «

102

AP Lecture 6-What is Risk

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