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Chapter 7

Risk, Return, and the Capital Asset Pricing Model

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Topics Covered

Measuring Market Risk Portfolio Betas Risk and Return CAPM and Expected Return Security Market Line CAPM and Stock Valuation

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Chapter 7 Objectives To be able to measure and interpret the

market risk, or beta of a security. Calculate a portfolio’s expected return

and its beta. To relate the market risk of a security to

the rate of return that investors demand and apply this rate to stock valuation.

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The Impact of Additional Assets on the Risk of a Portfolio

Port

folio

Sta

ndar

d D

evia

tion

Number of StocksNumber of Stocks

Systematic RiskSystematic Risk

1 2 3 111 2 3 11

Portfolio of 11 stocks

AMD

Unsystematic RiskUnsystematic Risk

AMD + American Airlines AMD + American Airlines + Wal-

Mart

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Diversification reduces portfolio volatility, but only up to a point. Portfolio of all stocks still

has a volatility of 21%.Systematic risk: the volatility of the portfolio

that cannot be eliminated through diversification.

Unsystematic risk: the proportion of risk of individual assets that can be eliminated

through diversification

What really matters is systematic risk….how a group of assets move together.

Systematic and Unsystematic Risk

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Systematic and Unsystematic Risk

The tradeoff between standard deviation and average returns that holds for asset classes

does not hold for individual stocks.

Because investors can eliminate unsystematic risk through diversification, market rewards

only systematic risk.

Standard deviation contains both systematic and unsystematic risk.

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Note:

The market compensates investors for accepting risk - but only for systematic risk. Unsystematic risk can and should be diversified away.

So - we need to be able to measure systematic risk. We use beta as a measure of systematic risk.

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The Concept of Beta Beta() measures how the return of an individual

asset (or even a portfolio) varies with the market portfolio (a stock index like the S&P 500).

= 1.0 : same risk as the market (average stock) < 1.0 : less risky than the market (defensive stock) > 1.0 : more risky than the market (aggressive

stock) Beta is the slope of the regression line (y = a + x)

between a stock’s return(y) and the market return(x) over time, from simple linear regression.

i = Covariancei,m/Mkt. Var. =imim/m2

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Relating Systematic Risk and Expected (or Required) Return: the CAPM Here’s the word story: a stock’s required

(expected) rate of return = risk-free rate + the (stock’s) risk premium.

The main assumption is investors hold well diversified portfolios = only concerned with systematic risk.

A stock’s risk premium = measure of systematic risk X market risk premium.

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CAPM Equation market risk premium = E(Rm) - Rf

risk premium = i (E(Rm) - Rf) E(Ri) = Rf + i (rm - rf )

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CAPM Example What is Intel’s expected (required) return

if its B = 1.35, the current 3-mo. T-bill rate is 4.6%, and the historical US market risk premium of 7.6% is expected?

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Portfolio Beta and Expected Return The for a portfolio of stocks is the weighted

average of the individual stock s. p = wjj

The expected return for a portfolio is the weighted average of the expected returns of the individual stocks.

RP = wjRj or use the portfolio beta in the CAPM to find the portfolio’s expected return.

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Portfolio Beta Example Example: What is the portfolio beta for a

portfolio consisting of 25% Best Buy with b = 2.0, 40% General Electric with b = 0.9, and 35% PepsiCo. with b = 0.5. What is this portfolio’s required (expected) return if the risk-free rate is 5% and the market expected return is 13%?

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The Security Market Line (SML) A graphical representation of the CAPM equation. Gives required (expected) returns for investments

with different betas. Y axis = expected return, X axis = beta Intercept = risk-free rate = 3-month T-bill rate (B =

0) Slope of SML = market risk premium For the following SML graph, let’s use a 3-month

T-bill rate of 5% and assume investors expect a market return of 13%.

Graph r = 5% + B(13%-5%) Market risk premium = 13% - 5% = 8%

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Our SML: Rf = 5%, E(Rm) = 13%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

0 0.5 1 1.5 2 2.5 3Beta

Return

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SML change, increase in inflation and Rf: Rf = 6%, E(Rm) = 14%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

0 0.5 1 1.5 2 2.5 3Beta

Return

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SML change in risk aversion (market risk premium: Rf = 5%, E(Rm) = 12%

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

0 0.5 1 1.5 2 2.5 3Beta

Return

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The Security Market Line

i

E(RP)

RF

SML

Slope = E(Rm) - RF = Market Risk Premium

•A - Undervalued

•

•

•RM

=1.0

•B

•A

• B - Overvalued

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Application of CAPM to Stock Valuation Can use CAPM to calculate a stock’s

required return for valuation purposes. Also, in equilibrium, our previous expected

return formulas should equal CAPM return. Expected Dividend Yield + Expected

Capital Gains Yield = CAPM required return (Div1 + P1 – P0)/P0 or Div1/P0 + g = CAPM

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Buy GE? GE’s recent stock price is $33.12 and the

expected next annual dividend is $1.00. GE’s MSN Money beta = 0.9. Also, analysts expect a constant growth rate of 9% for GE.

The 3-month T-bill rate is 4.6% and the market risk premium is the historical average of 7.6%.

Based on the above information, would you recommend buying GE?

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Buy GE?

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Buy GE? What is it’s value today?

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Efficient MarketsEfficient market hypothesis (EMH): in an

efficient market, prices rapidly incorporate all relevant information

Financial markets much larger, more competitive, more transparent, more homogeneous than product markets

Much harder to create value through financial activities

Changes in asset price respond only to new information. This implies that asset prices

move almost randomly.

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Efficient Markets

CAPM gives analyst a model to measure the systematic risk of any asset.

If asset prices unpredictable, then what is the use of CAPM?

On average, assets with high systematic risk should earn higher returns than assets with low

systematic risk.

CAPM offers a way to compare risk and return on investments alternatives.