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Copyright 2002 by Harcourt, Inc All rights reserved.

CHAPTER 6Risk and Return: The Basics

Basic return concepts

Basic risk concepts

Stand-alone riskPortfolio (market) risk

Risk and return: CAPM/SML

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What are investment returns?

Investment returns measure thefinancial results of an investment.

Returns may be historical orprospective (anticipated).

Returns can be expressed in:Dollar terms.

Percentage terms.

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What is the return on an investmentthat costs $1,000 and is sold

after 1 year for $1,100?

Dollar return:

Percentage return:

$ Received - $ Invested$1,100 - $1,000 = $100.

$ Return/$ Invested$100/$1,000 = 0.10 = 10%.

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What is investment risk?

Typically, investment returns are not

known with certainty. Investment risk pertains to the

probability of earning a return lessthan that expected.

The greater the chance of a return farbelow the expected return, thegreater the risk.

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Probability distribution

Rate ofreturn (%)50150-20

Stock X

Stock Y

Which stock is riskier? Why?

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Assume the Following

Investment Alternatives

Economy Prob. T-Bill HT Coll USR MP

Recession 0.10 8.0% -22.0% 28.0% 10.0% -13.0%

Below avg. 0.20 8.0 -2.0 14.7 -10.0 1.0

Average 0.40 8.0 20.0 0.0 7.0 15.0

Above avg. 0.20 8.0 35.0 -10.0 45.0 29.0

Boom 0.10 8.0 50.0 -20.0 30.0 43.0

1.00

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What is unique about

the T-bill return?

The T-bill will return 8% regardlessof the state of the economy.

Is the T-bill riskless? Explain.

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Do the returns of HT and Collectionsmove with or counter to the economy?

HT moves with the economy, so itis positively correlated with theeconomy. This is the typicalsituation.

Collections moves counter to theeconomy. Such negativecorrelation is unusual.

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Calculate the expected rate of returnon each alternative.

.k = k Pi i

i=1

n

k = expected rate of return.

kHT = 0.10(-22%) + 0.20(-2%)+ 0.40(20%) + 0.20(35%)+ 0.10(50%) = 17.4%.

^

^

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HT has the highest rate of return. Does that make it best?

k

HT 17.4%

Market 15.0

USR 13.8T-bill 8.0

Collections 1.7

^

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What is the standard deviation

of returns for each alternative?

.

V ri

i tit r

iii

!!

W!!W

!W

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WT-bills = 0.0%.WHT = 20.0%.

WColl = 13.4%.WUSR= 18.8%.WM = 15.3%.

.1i i2

i!

!W

HT:

W = ((-22 - 17.4)20.10 + (-2 - 17.4)20.20+ (20 - 17.4)20.40 + (35 - 17.4)20.20+ (50 - 17.4)20.10)1/2 = 20.0%.

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Prob.

Rate of Return (%)

T-bill

USRHT

0 8 13.8 17.4

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Expected Return versus Risk

Which alternative is best?

Expected

Security return Risk, W

HT 17.4% 20.0%Market 15.0 15.3

USR 13.8 18.8

T-bills 8.0 0.0Collections 1.7 13.4

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Portfolio Risk and Return

Assume a two-stock portfolio with

$50,000 in HT and $50,000 inCollections.

Calculate kp and Wp.^

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Portfolio Return, kp

kp is a weighted average:

kp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.

kp is between kHT and kColl.

^

^

^

^

^ ^

^ ^

kp = 7wikin

i = 1

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Alternative Method

kp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40+ (12.5%)0.20 + (15.0%)0.10 = 9.6%.

^

Estimated Return

(More...)

Economy Prob. HT Coll. Port.

Recession 0.10 -22.0% 28.0% 3.0%

Below avg. 0.20 -2.0 14.7 6.4

Average 0.40 20.0 0.0 10.0

Above avg. 0.20 35.0 -10.0 12.5

Boom 0.10 50.0 -20.0 15.0

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Wp = ((3.0 - 9.6)20.10 + (6.4 - 9.6)20.20 +(10.0 - 9.6)20.40 + (12.5 - 9.6)20.20+ (15.0 - 9.6)20.10)1/2 = 3.3%.

Wp is much lower than:either stock (20% and 13.4%).

average of HT and Coll (16.7%).

The portfolio provides average returnbut much lower risk. The key here isnegative correlation.

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Two-Stock Portfolios

Two stocks can be combined to forma riskless portfolio if r = -1.0.

Risk is not reduced at all if the twostocks have r = +1.0.

In general, stocks have r} 0.65, so

risk is lowered but not eliminated. Investors typically hold many stocks.

What happens when r = 0?

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What would happen to the

risk of an average 1-stockportfolio as more randomly

selected stocks were added?

Wp would decrease because the

added stocks would not be

perfectly correlated, but kp would

remain relatively constant.

^

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Large

0 15

Prob.

2

1

W1 }35% ; WLarge }20%.

Return

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# Stocks in Portfolio

10 20 30 40 2,000+

Company Specific(Diversifiable) Risk

Market Risk

20

0

Stand-Alone Risk, Wp

Wp (%)35

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Stand-alone Market Diversifiable

Market risk is that part of a securitys

stand-alone risk that cannotbeeliminated by diversification.

Firm-specific, ordiversifiable, risk is

that part of a securitys stand-alone riskthat can be eliminated bydiversification.

risk risk risk= + .

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Conclusions

As more stocks are added, each newstock has a smaller risk-reducing

impact on the portfolio.Wp falls very slowly after about 40

stocks are included. The lower limitforWp is about 20% = WM .

By forming well-diversified portfolios,investors can eliminate about half theriskiness of owning a single stock.

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No. Rational investors will minimize

risk by holding portfolios.They bear only market risk, so prices

and returns reflect this lower risk.

The one-stock investor bears higher(stand-alone) risk, so the return is lessthan that required by the risk.

Can an investor holding one stock earn

a return commensurate with its risk?

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Market risk, which is relevant for stocksheld in well-diversified portfolios, is

defined as the contribution of a securityto the overall riskiness of the portfolio.

It is measured by a stocks betacoefficient, which measures the stocksvolatility relative to the market.

What is the relevant risk for a stock heldin isolation?

How is market risk measured for

individual securities?

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How are betas calculated?

Run a regression with returns on

the stock in question plotted on theY axis and returns on the marketportfolio plotted on the X axis.

The slope of the regression line,which measures relative volatility,is defined as the stocks betacoefficient, orb.

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Use the historical stock returns tocalculate the beta for KWE.

Year Market KWE1 25.7% 40.0%2 8.0% -15.0%

3 -11.0% -15.0%4 15.0% 35.0%5 32.5% 10.0%6 13.7% 30.0%

7 40.0% 42.0%8 10.0% -10.0%9 -10.8% -25.0%

10 -13.1% 25.0%

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Calculating Beta for KWE

KWE 0. 0.02

0.0%

20%

0%

20%

0%

0% 20% 0% 20% 0%

KWE

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How is beta calculated?

The regression line, and hencebeta, can be found using acalculator with a regression

function or a spreadsheet program.In this example, b = 0.83.

Analysts typically use four or five

years of monthly returns toestablish the regression line.Some use 52 weeks of weeklyreturns.

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If b = 1.0, stock has average risk.

If b > 1.0, stock is riskier than average.

If b < 1.0, stock is less risky thanaverage.

Most stocks have betas in the range of

0.5 to 1.5.

Can a stock have a negative beta?

How is beta interpreted?

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Expected Return versus Market Risk

Which of the alternatives is best?

Expected

Security return Risk, b

HT 17.4% 1.29Market 15.0 1.00

USR 13.8 0.68

T-bills 8.0 0.00Collections 1.7 -0.86

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Use the SML to calculate each

alternatives required return.

The Security Market Line (SML) ispart of the Capital Asset PricingModel (CAPM).

SML: ki = kRF + (RPM)bi .

Assume kRF = 8%; kM = kM = 15%.

RPM = (kM - kRF) = 15% - 8% = 7%.

^

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Required Rates of Return

kHT = 8.0% + (7%)(1.29)

= 8.0% + 9.0% = 17.0%.kM = 8.0% + (7%)(1.00) =15.0%.

kUSR = 8.0% + (7%)(0.68) =12.8%.

kT-bill = 8.0% + (7%)(0.00) = 8.0%.

kColl = 8.0% + (7%)(-0.86) = 2.0%.

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Expected versus Required Returns

k k

HT 17.4% 17.0% Undervalued

Market 15.0 15.0 Fairly valued

USR 13.8 12.8 Undervalued

T-bills 8.0 8.0 Fairly valued

Coll 1.7 2.0 Overvalued

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.

.Coll.

.HT

T-bills

.USR

kM = 15

kRF = 8

-1 0 1 2

.

SML: ki = kRF + (RPM) biki = 8% + (7%) bi

ki (%)

Risk, bi

SML and Investment Alternatives

Market

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Calculate beta for a portfolio with 50%

HT and 50% Collections

bp = Weighted average= 0.5(bHT) + 0.5(bColl)= 0.5(1.29) + 0.5(-0.86)= 0.22.

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What is the required rate of return

on the HT/Collections portfolio?

kp = Weighted average k

= 0.5(17%) + 0.5(2%) = 9.5%.

Or use SML:

kp = kRF + (RPM) bp= 8.0% + 7%(0.22) = 9.5%.

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SML1

Original situation

Required Rateof Return k (%)

SML2

0 0.5 1.0 1.5 2.0

18

15

11

8

New SML( I = 3%

Impact of Inflation Change on SML

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kM = 18%

kM = 15%SML1

Original situation

Required Rateof Return (%)

SML2

After increasein risk aversion

Risk, bi

18

15

8

1.0

( RPM = 3%

Impact of Risk Aversion Change

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Has the CAPM been verified through

empirical tests?

No. The statistical tests have

problems that make empiricalverification virtually impossible.

Investors may be concerned aboutboth stand-alone risk and market risk.

Furthermore, investors requiredreturns are based on future risk, butbetas are based on historical data.

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