MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e) 1 Ch’s 11 & 12: Risk & Return In...

MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e)

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Ch’s 11 & 12: Risk & Return In Capital Markets

Purpose of Ch’s 11 & 12: To understand financial risk and learn how to measure the risk associated with securities

Learning Objectives:Explain Systematic Risk and Unsystematic RiskDescribe the Causes of Systematic Risk and Unsystematic RiskExplain How Standard Deviation Quantifies the Riskiness of a Security or PortfolioExplain Coefficient of Variation and Use It To Make An Investment DecisionDescribe Diversification and How It Reduces the Riskiness of a PortfolioDescribe the Concept of Correlation and How It Affects DiversificationDescribe the Capital Asset Pricing Model (CAPM)Explain What Beta IsCompute the Required ROR of a Stock Using CAPMExplain the Difference Between Rqd ROR of a Stock Computed with CAPM and Rqd ROR Derived From the Average of Historical ReturnsExplain the Concept of Risk Aversion and Its Effects on Security Valuation and ReturnCompute The Expected and Realized Returns of a Portfolio Using CAPMCompute The Expected and Realized Returns of a Portfolio Using historical Returns

2e created Summer 11


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RiskDefinitions:

Webster’s: a hazard; a peril; exposure to loss or injury The chance that an outcome other than that which was expected will occur The chance that an outcome other than that which was desired (i.e. a negative return, negative future cash flows) will occur. This is financial risk

Uncertainty: the lack of knowledge of what will happen in the future→uncertainty = risk→the greater the uncertainty, the greater the risk

Average Annual Return (R): The arithmetic average of an investment’s realized annual stock returns over a certain period (usually 1 or 5 years)

R = 1/T(r1 + r2 + ……. + rT) (we learned how to compute r in Ch 7)

Example: The realized annual returns For Diamond Jim’s Inc. stock for the last five years were: 8.6782% (2004), 7.4203% (2005), 8.2501% (2006), 6.5925% (2007) and 1.5943% (2008). What is the average annual return for that period?

R = 1/5(8.6782% + 7.4203% + 8.2501% + 6.5925% + 1.5943%) = 1/5(32.5354%) = 6.5071%Using the main principle of statistics (past performance is a predictor of future performance) we estimate the expected return from the realized return:R = r (as discussed in Ch 7) Note: we will assume the individual realized annual returns are independent, i.e. the data is “normally distributed”

2e v1.1 created Fall 13


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Stand-alone RiskBig question from statistics: How reliable is the estimate for expected future return?Standard Deviation answers this question

Example: (continued) Compute the standard deviation of the realized annual returns For Diamond Jim’s Inc. stock for the last five years.

Note: since the probability (Pi) was the same for each stock return, it is computed simply as 1/n where n = total number of data points, which is 5 in this case

n

i = 1ri - r)2PiVariance =

Standard Deviation = n

i = 1ri - r)2Pi

ri r r - ri (ri - r)2 Pi(= 1/n) (ri - r)2Pi

8.6782% 6.5071% 2.1711% 0.0471% 0.20 0.009427%

7.4203% 6.5071% 0.9132% 0.0083% 0.20 0.001668%

8.2501% 6.5071% 1.7430% 0.0304% 0.20 0.006076%

6.5925% 6.5071% 0.0854% 0.0001% 0.20 0.000015%

1.5943% 6.5071% -4.9128% 0.2414% 0.20 0.048271%

Variance = 2 = 0.065457%

Standard Deviation = = 2.5585%

Quantifying the Risk of a Security – Standard DeviationTwo Basic Types of Risk: Stand-alone Risk :

The risk associated with an investment when it is held by itself or in isolation, and not in combination with other assets The stand-alone-risk of a particular security can be compared with that of other securities to assess relative riskiness

Portfolio Risk: The sum total risk of several securities held together in a single “portfolio”. Must account for the correlation of the securities to on another


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Stand-alone Risk (continued)Standard Deviation Using Sample Data:Since it is virtually impossible to find the true for any population, a sample of values is used:

Estimated Standard Deviation = S n

t = 1rt - rAVE)2

n-1Probability Distribution: the possible values of outcomes associated with the probability of their occurrenceExample: Probability distribution for the role of two 6-sided dice

Event Probability (P)2 2.78%3 5.56%4 8.33%5 11.11%6 13.89%7 16.67%8 13.89%9 11.11%

10 8.33%11 5.56%12 2.78%

Sum: 100.00%

Chart Format Graph

Event

If there are is a vary large number of discrete random events (data points), the probability distribution looks more like this:

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Stand-alone Risk (continued)Normal Distribution:Random Sampling:

→if n elements are selected from a population in such a way that every set of n in a population has an equal probability of being selected, the n elements are said to be a random sample. (This is the definition of a simple random sample which is the most common technique)→The value of any element is not influenced by the value of any other element; i.e. the data is independent

Normal Distribution: The results of Random SamplingHistorical returns of securities are not truly independent (i.e. the closing price of a stock on any particular day may be influenced by the closing stock price on previous days) but they are close enough to being so that we usually treat them as being normally distributedThis means that the statistical methods for analyzing security returns is relatively simple

Empirical Rule: For normally distributed data

+1 +2 +3-2 -1-3 rs

99.74%

95.46%

68.26%


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Rate of Return (%)

Probability Density

Diamond Jim’s Inc.

Jihad Jim’s Military Surplus LLC

0.5 -

Expected Rate of Return (rs)

15%

Note: the area under each curve equals 1.00 (i.e. 100% probability)

Answer: Jihad Jim’s is riskierJihad Jim’s standard deviation is clearly much greater than that of Diamond Jim’sThe possible range of values for next years stock return for Jihad Jim’s is much greater than that for Diamond Jim’sJihad Jim’s expected stock return is much more uncertainThe estimate for expected return for Jihad Jim’s is much less reliableJihad Jim’s stock is much more risky than Diamond Jim’s stock

0%

Example: The probability distributions for two different stocks are shown below. Both stocks have an expected return (rs) of 15%. Which stock is riskier?

Stand-alone Risk (continued)How Standard Deviation Quantifies Risk:Standard deviation describes the degree of variation or the “range” of a probability distributionThe higher the , the greater the range of possible outcomes, the greater the uncertainty concerning the next possible outcome, thus greater riskA “tighter” or “narrower” probability distribution (as compared to other probability distributions) means a lower relative which means less uncertainty concerning the next possible outcomeThe smaller the , the more reliable the estimated expected return


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Stand-alone Risk (continued)

Most Common Way to Determine Rs, rs and

1) Find the monthly closing price of a stock for the last 61 months2) Compute the ROR for each month (New-Old)/Old3) Compute the average monthly ROR (use Excel function: AVERAGE)4) Convert the monthly average to an annual average. This is the average annual return Rs for the five year period5) As stated before: rs = Rs ≈ rs

5) Use the Excel function: STDEV to find of monthly returns6) Convert this to an annualized , multiply by SQRT(12)


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Excel Example: Apple Inc. (AAPL) = (B4-B3)/B3

Adjusted Monthly Average Average (Monthly Date Close Returns Monthly k Annual k Returns) (Annualized)

1-Feb-02 $10.85 4.0847% 49.0165% 11.2596% 39.0043%

1-Mar-02 $11.84 9.1244%

1-Apr-02 $12.14 2.5338%

1-May-02 $11.65 -4.0362%

3-Jun-02 $8.86 -23.9485%

1-Jul-02 $7.63 -13.8826%

1-Aug-02 $7.38 -3.2765%

3-Sep-02 $7.25 -1.7615%

1-Oct-02 $8.03 10.7586%

1-Nov-02 $7.75 -3.4869%

2-Dec-02 $7.16 -7.6129%

2-Jan-03 $7.18 0.2793%

3-Feb-03 $7.51 4.5961%

3-Mar-03 $7.07 -5.8589%

1-Apr-03 $7.11 0.5658%

1-May-03 $8.98 26.3010%

2-Jun-03 $9.53 6.1247%

1-Jul-03 $10.54 10.5981%

1-Aug-03 $11.31 7.3055%

2-Sep-03 $10.36 -8.3996%

1-Oct-03 $11.44 10.4247%

3-Nov-03 $10.45 -8.6538%

1-Dec-03 $10.69 2.2967%

2-Jan-04 $11.28 5.5192%

2-Feb-04 $11.96 6.0284%

1-Mar-04 $13.52 13.0435%

1-Apr-04 $12.89 -4.6598%

3-May-04 $14.03 8.8441%

1-Jun-04 $16.27 15.9658%

1-Jul-04 $16.17 -0.6146%

2-Aug-04 $17.25 6.6790%

1-Sep-04 $19.38 12.3478%

1-Oct-04 $26.20 35.1909%

1-Nov-04 $33.53 27.9771%

1-Dec-04 $32.20 -3.9666%

3-Jan-05 $38.45 19.4099%

1-Feb-05 $44.86 16.6710%

1-Mar-05 $41.67 -7.1110%

1-Apr-05 $36.06 -13.4629%

2-May-05 $39.76 10.2607%

1-Jun-05 $36.81 -7.4195%

1-Jul-05 $42.65 15.8653%

1-Aug-05 $46.89 9.9414%

1-Sep-05 $53.61 14.3314%

3-Oct-05 $57.59 7.4240%

1-Nov-05 $67.82 17.7635%

1-Dec-05 $71.89 6.0012%

3-Jan-06 $75.51 5.0355%

1-Feb-06 $68.49 -9.2968%

1-Mar-06 $62.72 -8.4246%

3-Apr-06 $70.39 12.2290%

1-May-06 $59.77 -15.0874%

1-Jun-06 $57.27 -4.1827%

3-Jul-06 $67.96 18.6660%

1-Aug-06 $67.85 -0.1619%

1-Sep-06 $76.98 13.4562%

2-Oct-06 $81.08 5.3261%

1-Nov-06 $91.66 13.0488%

1-Dec-06 $84.84 -7.4405%

3-Jan-07 $85.73 1.0490%

1-Feb-07 $84.74 -1.1548%

= AVERAGE(C4:C63)

= 4.0847%*12 or D3*12

= STDEV(C4:C63)

= 11.2596*SQRT(12)

R = 49.0165% per annum ≈ r = 39.043%

Note: monthly adjusted closing prices from Yahoo.com


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Risk Aversion: (Not covered in your text book)Concept: Given two securities with equal expected returns but different degrees of risk, the rational investor would choose the one with lower riskMost investors tend to choose less risky investments and accept commensurately lower returnsValuation Implications:

if two securities offer the same ROR, the riskier one is priced lower if the seller of that security wants anybody to buy it (the less riskier one is priced higher)if two securities are priced the same, the riskier one must offer higher expected returns if the seller of that security wants anybody to buy it

the difference between these expected returns is a risk premium

market forces (risk aversion influencing supply & demand) force the above to occur

How much higher does the ROR have to be or how much lower does the price have to be? Answer:ref. bonds (Ch 6): Consider 2 bonds with the same par value, maturity & coupon rate but different rd (one bond is AAA rated with rd of 4%, the other is B rated with rd of 6%). What’s the difference in value between two ?Example: FV=$1,000, rCPN = 5%, annual payment, 5-yr maturityAAA Bond: N=5, I/YR=4%, PMT=50, FV=1000; PV= $1044.52B Bond: N=5, I/YR=6%, PMT=50, FV=1000; PV= $957.88

ref. stocks (Ch 7): how does P0 change with different required ROR’s?


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Coefficient of Variation (CV) (Not covered in your text book)A way to quantify the relationship between risk and returnGiven two securities with equal expected returns but different degrees of risk, the rational investor would choose the one with lower riskThe CV….. is defined as: CV = / r S / r ; smaller is better shows the risk per unit of return; it provides a standardized measure of risk; the basis of comparison (per unit return) is the same provides a more meaningful basis for comparison when the expected returns of two alternatives are not the same

Using CV to measure risk/return characteristics of two stocks is like using miles per gallon (MPG) to measure fuel efficiency of two carsExample: Driver A travels 450 mi. in his ‘95 Geo Metro and consumes 12 gal. of gas. Driver B travels 890 mi. in his ’71 LS5 (454+cu) Corvette, stopping 3 times to fuel up and consumes 65 gal. of gas. What is the relative fuel efficiency of the two cars?

Geo: 450 mi./12 gal. = 37.5 mi. per gal‘Vette: 890 mi./65 gal. = 13.7 mi. per gal.

The standardized measure is one gallon of gas

~

Example: An investor wants to compare the risk/reward characteristics of two retail merchandising firms: Walmart and Target.

Expected Return (Average Return)

Probability

Walmart

Target

6.5% 9.3%


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Example (continued)The average monthly returns for two firms over the last five years are: Walmart, 6.5%; Target, 9.3%. Based on the same data, the estimated standard of deviations (S) for the two firms are: Walmart, 10.3%; Target, 21.6%. Compute the coefficient of variation for the two firms. Which has the best risk/return characterisitcs?

CVWalmart = / r S / r = 10.3% / 6.5% = 1.58CVTarget = 21.6% / 9.3% = 2.32

The standardized measure is one unit of risk

Caution: CV doesn’t work if the expected returns are significantly differentExample: Consider the probability distributions of two the two firms shown below. CVKay-Mart is 1.93 while CVDiamond Jim’s is 3.76. CV analysis indicates that Kay-Mart has superior risk/return characteristics. However it would be more advantageous to invest in Diamond Jim’s. Why?

~

Expected Return (Average Return)

Probability

Kay-Mart

Diamond Jim’s Inc.

3.5% 14.3%


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Portfolio Investing

Investing in a portfolio of securities is less risky than investing in any single security. Why? Answer: the risks of the individual securities comprising the portfolio are averaged. How?

Answer:Diversification:

→the tendency for price movements of individual securities to counteract each other→This means that the price changes of the portfolio are usually less than the price changes of the individual securities→thus the price/return volatility () of the portfolio is less the price/return volatility () of the individual securities→Thus the risk of the portfolio is less than that of the securities comprising the portfolio

As more securities are added to a portfolio, the overall risk () of the portfolio decreasesThe securities should not be very correlatedSecurities (when combined in a portfolio) from companies in the same industry are (usually) highly positively correlated thus not much diversification effect


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Portfolio Returns

Portfolio Expected Returns (E[Rp] or rp): The weighted average of the expected returns of the individual securities held in a portfolio

E[Rp] = w1E[R1] + w2E[R2] + …… wnE[Rn]

rp = w1r1 + w2r2 + …… wnrn

Example: A portfolio consists of stocks from four companies and the expected returns (rs) for each stock are given. Find rp.

ATT&T 400 $43.67 $17,468.00 19.23% 5.65% 1.09%

GEE 450 $47.89 $21,550.50 23.72% 4.32% 1.02%

Microspongy 500 $34.23 $17,115.00 18.84% 4.87% 0.92%

Citigang 600 $57.86 $34,716.00 38.21% 3.87% 1.48%

Portfolio Value: $90,849.50 rP: 4.51%

Stock# of

Shares

Initial Stock Price Initial Value

Weight (by value)

Expected Return (r) Weighted r

0.1923 x 5.65%$17,468 / $90,849.50400 x $43.67

created Summer 09

OR


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Portfolio Returns (continued)

Portfolio Realized Rate of Return (Rp): The return that a portfolio actually earnedFor a portfolio, realized ROR (Rp) is the weighted average of the realized RORs of the individual securities held in a portfolio

Rp = w1R1 + w2R2 + …… wnRn

Example(continued): The portfolio is held for one year and the end of period price for each stock is indicated below. Find rp and the value of the portfolio at the end of the holding period.

ATT&T 400 $43.67 $45.67 $18,268.00 18.64% 4.58% 0.85%

GEE 450 $47.89 $51.89 $23,350.50 23.82% 8.35% 1.99%

Microspongy 500 $34.23 $39.56 $19,780.00 20.18% 15.57% 3.14%

Citigang 600 $57.86 $61.05 $36,630.00 37.37% 5.51% 2.06%

Portfolio Value: $98,028.50 rP: 8.05%

Stock# of

Shares

Initial Stock Price

Ending Stock Price

Ending Stock Value

Weight (by

value)

Realized Return

(r)Weighted

r

($45.67 - $43.67) / $43.67(New – Old) / Old

Note: 1. The weights have changed2. This example does not include dividend yield (Ch 9)

Another Way to Find rp:Premise of statistics: past performance is an indicator of future performancerp for an upcoming period = rp for the previous period


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Diversification of a Portfolio

Correlation: →the behavioral relationship between two or more variables (stocks in a portfolio)→a measure of the degree to which returns share common risk.→it is calculated as the covariance of returns divided by the standard deviation of each return

Various conditions (i.e. the economy, security market forces & movements, financial performance of individual companies, political developments, etc.) will cause the securities held in a portfolio to change in valueThe direction and magnitude of how the value of securities held in a portfolio change with respect to each other can be described by correlation Positive Correlation: When external conditions cause the securities in a portfolio to change value in the same direction (i.e. they all increase in value or they all decrease in value)Negative Correlation: When external conditions cause the securities in a portfolio to change value in the opposite directions (one security increases in value, another decreases in value)No Correlation: The direction and magnitude of changes in value of one security are totally unrelated to those of another security


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Diversification of a Portfolio (continued)

Correlation Coefficient (): A measure of the degree of correlation between variables (stock securities, in this chapter)Perfectly negative correlation; = -1Perfectly positive correlation; = 1No correlation; = 0

How is correlation between two stocks determined?The returns from stocks that are highly correlated tend to move together

→they are affected by the same economic factors→stocks in the same industry tend to be highly correlated→they are exposed to similar risks

Academics have shown (after doing a whole lot of statistics) that:The returns for two randomly selected stocks have an r of about 0.6For most pairs of stock, lies between 0.5 and 0.7This means that that most stocks are partially positively correlated and partially negatively correlatedThis means that combining two stocks (in a portfolio) can reduce overall risk

Portfolio Standard Deviation:Unlike expected and realized portfolio returns, portfolio is not a weighted average of individual security ’sPortfolio risk is usually smaller than the weighted average of individual security ’sPortfolio risk is entirely dependent on the correlation among the securities held in the portfolioRead pp 370-374 for a discussion on how to compute portfolio


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0

-10

Stock G Stock H

Rat

e o

f R

etu

rn (

%)

2000999897

25

15

0

-10

Rat

e o

f R

etu

rn (

%)

2000999897

Portfolio GH

Perfectly Positively Correlated Stocks (Note: p = M = M’)

Perfectly Negatively Correlated Stocks (Note: p = 0)

Correlation & Diversification Effect on Portfolio Risk

-10

0

15

25

Portfolio LM

2000999897

25

15

0

-10

Stock LStock M

Rat

e o

f R

etu

rn (

%)

2000999897

Rat

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f R

etu

rn (

%)


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Portfolio Diversification

$20.00

$25.00

$30.00

$35.00

$40.00

$45.00

$50.00

$55.00

J F M A M J J A S O N D

Months

Pri

ce

Stock A

Stock B

Stock C

Stock D

Portfolio

Diversification is important, especially for corporate investors; they are very concerned about the liquidity of their investments

Partially Correlated Stocks (Note: p < W & Y)

Correlation & Diversification Effect on Portfolio Risk


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Systematic Risk versus Unsystematic Risk

The total risk of any security is due to a combination of Systematic Risk and Unsystematic RiskSystematic Risk (Market Risk, Undiversifiable Risk or Beta Risk)

this is the volatility of the an entire securities market (NYSE, NASDAQ, bond markets, etc)this volatility is due to changes in macro-economic, broad micro-economic conditions and geo-political eventsit applies to most of the firm’s that trade in a specific market (but not necessarily to the same extent)Because most stocks are somewhat partially correlated, most stocks do well when the economy is good and not so well when the economy is not so goodthere is no feasible way to eliminate the Systematic Risk of a particular market

Unsystematic Risk (Diversifiable Risk, Firm Specific-Risk or Unique Risk)

it is reflected in the volatility of the securities (stocks & bonds) of a specific firmit is that part of a security’s risk associated with factors generated by events, or behaviors, specific to the firm or the firm’s industryit is the result of the firm’s inherent management decisions, legal problems, product or service obsolescence, the firm’s market viability, etc. and that of their competitionthere is a way to reduce diversifiable (firm-specific) risk:

build a portfolio of securities from different industries or industry sectors (stocks that are not well correlated with each other)this will produce the diversification effect


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Unsystematic (Firm-Specific, Diversifiable) Risk

Portfolio Risk

Systematic (Market or Beta) Risk)

Minimum Attainable Risk in a Portfolio of Average Stocks

Number of Stocks in the Portfolio

Tot

al P

ortf

olio

Ris

k

market

1 10 20 30 40 1500+

Systematic Risk versus Unsystematic Risk (continued)

How Many Securities is Enough?18 securities provide about 90% complete diversification32 securities provide about 95% complete diversificationThe law of diminishing returns is in effect here

p falls very slowly after about 40 stocks are included in the portfolio.

By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stockDiversification does not reduce Firm-Specific Risk; it reduces the effects of Firm-Specific Risk on a portfolio

total

Vo

lati

lity

(Ris

k)

created Summer 09


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Portfolio standard deviation measures total riskThe book says only systematic risk is related to required return (i.e. systematic risk is all that matters since unsystematic risk can be diversified away)

→Prof. Jim has strong reservations concerning this statement→it is true only if the stocks are truly randomly chosen and there are at least 40 stocks (thus the portfolio is well diversified)→it is not true if stocks in the portfolio are not randomly chosen

If systematic risk is the only one that matters, then we need a way to quantify just the systematic risk

Market Portfolio & Market (Systematic) Risk:A market portfolio is a portfolio of all risky investments, held in proportion to their valueA market portfolio is a portfolio of all the stock in a particular market (i.e. NYSE, NASDAQ, AMEXthe standard deviation of the market portfolio quantifies the volatility of the entire system; it is the amount of systematic risk that particular market has

Capital Asset Pricing Model (CAPM):A theory that quantifies the market risk of an stock by comparing the behavior of that stock to the behavior of the market portfolioThis behavioral relationship is expressed by a variable called Beta (Definition: is a measure of the extent to which the returns of a particular security move with respect to the returns of the securities market as a whole

measure a stock’s sensitivity to the market portfolio (the rest of the market) quantifies a stock’s market risk tells us how risky a particular stock is compared to a market portfolio (the rest of the market)

Measuring Systematic Risk


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Measuring Systematic RiskCapital Asset Pricing Model (CAPM): (continued)

the market portfolio has = 1 (by definition)if a stock has = 1, it’s returns will tend to move in the same direction and magnitude as the market portfolio; the stock is just as risky as the marketif a stock has = 2, it’s returns will tend to move in the same direction but twice the magnitude as the market portfolio; the stock is twice as risky as the marketif a stock has = -1, it’s returns will tend to move the same magnitude but in the opposite direction as the market portfolioif a stock has = 0, the direction and magnitude of it’s returns movements will be totally unrelated to the market portfolioHow to calculate

plot the stock’s historical returns against historical returns of the market portfoliouse regression (line fit techniques) to form a line is the slope of the fitted lineAnalysts typically use five years’ of monthly returns to establish the regression line. Some use 52 weeks of weekly returns

10

20

30

-10

40

-20

-30

-40

-10-20-30-40 10 20 30 40Market Portfolio Return

Individual Stock Return


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10

20

30

-10

40

-20

-30

-40

-10-20-30-40 10 20 30 40Market Portfolio Return

Individual Stock Return

= 0.5

= 1 = 2

= -1

You don’t have to calculate ’s on your own; you can find them online (yahoo/finance; Hoover’s, WSJ, etc.)Very few stocks have negative ’s quantifies a firm’s Market Risk; it doesn’t say anything about Firm-Specific Risk

CAPM assumes the stock in question is part of a well diversified portfolio thus the Firm-Specific Risk of an individual stock should have a negligible effect on portfolio returns

450


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More on Risk versus Return:Recall the concept of risk premiums (DRP, LP, MRP)30-day T-bills (which are considered riskless) compensate lenders only for opportunity costs and inflation (i.e. rT-bill = r* + IP = rRF)Individual stocks as well as entire stock markets must compensate investors at least for opportunity costs, inflation and risk or nobody would invest in them (r = r* + IP + RP from Ch 5)Market Risk Premium:

We identified DRP, LP and MRP which we discussed in the context of lending moneythe same concepts behind the above premiums apply to stocksbut there are an unbelievably long and complex list of additional factors that also apply to stocks which can’t easily be broken down into individual componentstherefore we lump them all together and just refer to the “risk premium” (RP) for individual stocks and stock markets as a whole

Any securities market has a required rate of return (rM)rM for any market is simply the current average return for that market (this assumes that market forces and risk aversion have already been at work to “force” the required ROR to equal average return) The rM for any market is composed, in part, of some sort of compensation for opportunity cost and inflation. This is the nominal risk-free rate (rRF) (sound familiar?) The rest must be compensation for risk.Thus rM = rRF + Market Risk Premium(RPm)

Market Risk Premium: RPm = (rM - rRF) (by definition)


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Example: If the NASDAQ has had an average ROR of 6.5% over the last five years and 30-day T-bills have had an average return of 1.9% for the last five years, what is the NASDAQ market risk premium?

Market Risk Premium: RPm = (rM - rRF) = 6.5% - 1.9% = 4.6%

Individual Stock Risk Premium: RPs = (rM - rRF)s = RPmsThe risk of an individual stock as portrayed by its is incorporated in computing that stock’s risk premium

Finding Required ROR (rs) for an Individual Stock:

It should be apparent by now that rs for a stock should be related to the riskiness of the firm that issues that stock. Thus:

rs = rRF + (rM - rRF)s = rRF + RPms

The above formula is call the “Capital Asset Pricing Model” (CAPM) formulaAnother way to look at the CAPM formula:

Mkt Risk Premium Quantity of Risk (Cost of Risk)

rs = rRF + (rM - rRF)s

Compensation for Opp. Cost & Inflation Stock Risk Premium


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Measuring Systematic RiskFinding Required ROR (rs) for an Individual Stock

Example: Jamaica Jim’s Caribbean Pirate Adventures Inc. stock trades on the NASDAQ and has a of 1.96. If the NASDAQ has had an average ROR of 5.3% for the last 5 years and 30-day T-bills are currently returning 1.4%, what is the required ROR for this stock?

rs = rRF + (rM - rRF)s

= 1.4% + (5.3% - 1.4%)1.96 = 9.04%

Required ROR (rs) vs Expected ROR ( rs)As discussed in Ch 9, rs for a rational investor is at least equal to rs

Thus rs > rs; for all practical purposes, rs = rs

Important Point Regarding Market Risk & Firm Specific Risk:

rs produced by the CAPM formula and rs produced using statistical averaging of historical returns (as discussed in Ch 10) won’t be equal to each other. Why?Answer:The statistical rs incorporates both market risk and firm specific riskThe CAPM rs incorporates market risk only

is a measure of market risk only CAPM assumes all stocks under consideration will be part of a well diversified portfolio, thus firm specific risk is negligible and can be ignored


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Measuring Systematic Risk

Beta of a Portfolio:p is the weighted average of the ’s of the stocks that comprise the portfolio

p = w11 + w22 + w33 + …... wnn

Example: A portfolio is comprised of the stocks indicated below. Find the portfolio’s .

Required ROR for a Portfolio (rp) using p: This is the main advantage of the CAPM

rp = rRF + (rM - rRF)p

rp for a rational investor is at least equal to rp

Thus rp > rp; for all practical purposes, rp = rp

rp produced using CAPM (as shown above) and rp (as discussed earlier) should be fairly close. Why?Answer: Both methods incorporate diversification and thus minimize firm specific risk. If the portfolio is well diversified, all that’s left is market risk and it’s pretty much equal regardless of which method you use to measure it

Stock Weight Wt x ATT&T 20% 0.87 0.174GEE 15% 0.75 0.1125

Microspongy 15% 1.67 0.2505Citigang 25% 1.30 0.325Pfazer 10% 0.14 0.014

Northrap 15% 0.87 0.1305

portf olio 1.0065


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Security Market Line (SML):

The CAPM equation is also the algebraic equation for a linerRF is the y-interceptThe slope of this line is rM - rRF (i.e. RPM)

This slope will change only when rM or rRF changej is the x-axis valueThis line can be used to find k for any security, if you know for that security

Required ROR (%)

Risk-Free Rate: 6%

0 0.5 1.0 1.5 2.0

Risk, (j)

rhigh = 22

rM = rA = 14

rRF = 6

Safe Stock Risk Premium: 4%

Market (Average Stock) Risk Premium: 8%

jRFMRFj rr r r:SML

Relatively Risky Stock’s Risk Premium: 16%rLOW = 10


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What’s the point of all this stuff in Chapters 10 & 11?

Answer:Security value & ROR are influenced by riskIf you know rs or rp…. And if you know rs or rp…… You should be able to determine if your investments are performing as well as they should with respect to their theoretical riskiness

Key Point: is a tool to assess risk/reward potential of a security, it is not (by itself) a predictor of how the security will perform in the future

MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e) 1 Ch’s 11 & 12: Risk & Return In...

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Transcript of MGT 326 Ch 11 & 12: Risk & Return in Capital Markets (bdh2e) 1 Ch’s 11 & 12: Risk & Return In...