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CHAPTER 10: Risk and Return, The Capital Asset Pricing Model

Stand-alone versus Portfolio risk Firm-specific versus systematic (market

or economic) risk The Capital Asset Pricing Model (CAPM)

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What drives security or investment values

The price and/or intrinsic value of any security or investment should be the Present Value of all future expected cash flows.

The value of any security, e.g., a common stock, should change whenever: The forecast of future cash flows changes. The perceived risk of the future cash flows changes.

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Introduction to Risk and Return

Every investment has some required rate of return, based on its level of perceived risk. Of course, your realized return from an investment may

differ substantially from what you had originally expected or required – uncertainty concerning the final outcome is unavoidable.

People tend to be averse to risk, therefore they demand higher rates of return (additional compensation) for investments of increasing risk.

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Risk and return of a two stock portfolio

Stock A’s future return depends on next year’s’ state of the economy.

Good economy, probability=25%

Average economy, probability=50%

Bad economy, probability=25%

20%

10%

0%

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Risk and return of a two stock portfolio

Stock B’s future return also depends on next year’s state of the economy.

Good economy, probability=25%

Average economy, probability=50%

Bad economy, probability=25%

5%

10%

15%

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Risk and return of a two stock portfolio (with two stocks that are perfectly negatively correlated)

Suppose that we invest $100 in stock A and $200 in stock B. The performance of investing $300 in this two stock portfolio is shown below.

We have two risky stocks. Yet, when we combine them here, we produce a portfolio which is riskless, in that it earns a 10% return in each future economic state.

Outcomes Prob. (ps) CF on $100 in A

CF on $100 in A

Total CF % Return on $300 in A&B

Boom 0.25 $120 $210 $330 10%

Normal 0.50 $110 $220 $330 10%

Bust 0.25 $100 $230 $330 10%

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The two types of investment risk

Stand-alone risk: The total risk of any single investment, such as Intel Corp.

stock, without regard or reference to any other investments, usually measured as that security’s standard deviation of returns.

Portfolio risk: The total risk of a portfolio of different securities. Often

measured as the standard deviation of an entire portfolio. How a portfolio’s total risk will change if a particular security is added or deleted?

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Risk-free rates and risk premiums

The interest rate or yield on a short-term U.S. government bill or bond, e.g., a Treasury Bill, is usually considered to be a proxy for the risk-free rate of return or rRF. rRF = real interest rate + inflation premium

The required rate of return on any risky investment i is defined the risk-free rate plus some extra compensation or premium for the risk: ri = rRF + Risk Premium

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Average annual returns for selected investment categories, 1926 – 2002

Average Standard Return Deviation

Small-company stocks 16.9% 33.2%Large-company stocks 12.2 20.5L-T corporate bonds 6.2 8.7L-T government bonds 5.8 9.4U.S. Treasury bills 3.8 3.2Inflation 3.1 4.4

Does a risk premium seem to have been realized or earned over the 1926-2002 period when investment categories of differing perceived levels of risk are compared?

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Capital Market Equilibrium and CAPM Model

E(r)

rF

M

Market portfolio “M”

Capital Market Line or CML

individual securities

Opportunity set of risky assets, the bullet E(rM)

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Decomposition of the total risk of a typical common stock

Assume that Boeing common stock is typical. The total risk of this stock consists of: Firm specific risk – the risk that is unique to Boeing, e.g.,

competitiveness, managerial effectiveness, lawsuits, labor disputes, winning or losing a contract, etc. These events impact Boeing, but do not affect DuPont, IBM, Coca-Cola, Disney, etc.

Systematic (market or macroeconomic) risk – the risk that affects all firms to some degree: external events such as recessions, expansion, interest rates, world events, etc.

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Firm Specific versus Systematic Risks

Systematic (market or macroeconomic) risk usually accounts for about 25% of a typical stock’s total risk.

Firm-specific risk usually accounts for about 75% of a typical firm’s total risk.

You can eliminate almost all the firm-specific risk by holding a well-diversified portfolio of stocks. The random bad and good firm-specific events are then largely offset within the portfolio.

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Firm Specific versus Systematic Risk

Most people would never put all of their wealth in one common stock. Too much exposure to firm-specific risk

However, many people would put a large amount of their wealth in a mutual fund that invests in a diversified portfolio of common stocks. The relevant risk here is the systematic risk, as the firm-

specific risk has been diversified away. You can never diversify away systematic risk, as all

stocks have exposure to this risk.

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Illustrating diversification effects of a stock portfolio, standard deviation versus the number of stocks

30 No. of securities

p

50%

20%

Diversifiable risk

Market risk

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Which risk should be relevant in the determination of market prices?

Which investors drive stock prices? Most trading (and analysis) is conducted by financial institutions: mutual funds, pension funds, insurance companies, hedge funds, etc.

We thus must assume that stock prices are mostly driven by investors that are reasonably or well-diversified. Most investors manage portfolios.

Thus we should only expect a risk premium or extra compensation for the exposure to systematic (market or macroeconomic) risk. No compensation should exist for firm-specific risk.

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Capital Asset Pricing Model or CAPM

The CAPM (introduced circa 1965) is used to estimate a stock’s risk premium and required rate of return. We will use IBM stock as an example. CAPM→ rIBM = rRF + βIBM[rM - rRF]

rRF is the riskless rate, βIBM is the Beta of IBM, and rM is the required return on some well-diversified or market portfolio of assets (call it the market portfolio). The term [rM - rRF] is the market risk premium βIBM[rM - rRF] is IBM’s risk premium

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What is the market risk premium, given as [rM - rRF] in the CAPM?

The additional return over the risk-free rate needed to compensate investors for assuming an average amount of risk.

Its size depends on the perceived risk of the overall stock market and investors’ degree of risk aversion.

Varies across time, but most estimates suggest it has ranged between 4% and 8% per year; 5 to 6% seems to be a good current estimate.

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CAPM and required return for IBM’s common stock

Let rRF=6%, rM=12%, and the Beta of IBM common stock is βIBM=1.3

rIBM = rRF + βIBM[rM - rRF]

rIBM = 0.06 + 1.3[0.12 – 0.06]

rIBM = 0.06 + 1.3[0.06]

rIBM = 0.06 + 0.078 =0.138 or 13.8% Note the following items:

The market risk premium is [12% - 6%] = 6% IBM’s risk premium is 1.3[12% – 6%] = 7.8%.

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How to interpret Betas (β) Beta measures a stock’s degree of systematic or

market risk. It can also be thought of as the stock’s contribution to the risk of a well-diversified portfolio. β = 1: the stock has average market risk. The stock

generally tends to go up (down) by the same percentage amount as the market.

β = 1.5: The stock generally tends to go up (down) by 50% (1.5x) more than the market.

β = 0.5: The stock generally tends to go up (down) by half as much as the market.

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How to interpret Betas (β), continued β = 0: the stock has no correlation with movements in the

overall stock market. All of this firm’s risk would actually be firm-specific risk.

β < 0: The stock generally tends move in a direction opposite that of the market (very rare).

Firms that supply basic consumer goods (Proctor & Gamble) and utilities (phone, cable, gas, or electric) tend to have low Betas (lower than 1.0, often around 0.4 to 0.6).

Firms that are in economically cyclical industries would have higher Betas (greater then 1.0).

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Expected return and Beta of a portfolio of stocks

Both portfolio expected returns and portfolio Betas are always a weighted average of the stocks that comprise the portfolio.

You invest $10,000: $6000 in Apple Computer and $4000 in Proctor & Gamble (PG). Let rRF=5% and rM=10%. Let βAPPLE=1.3 and βPG=0.6 The investment weights are (6000/10000)=0.6 for Apple

and (4000/10000)=0.4 for PG. The weights must always sum up to 1.

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Expected return and Beta of a portfolio of stocks, continued

The portfolio Beta is always the weighted average of each of the stock’s betas.

βP = wappleβapple + wpgβpg

βP = 0.6(1.30) + 0.4(0.6)

βP = 1.02 Now find the portfolio required return.

rP = 0.05 + 1.02[0.10 – 0.05] = 0.101 or 10.1%

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The Security Market Line or SML

The SML is basically just a graph of the CAPM equation. For our example, let rRF=5%, rM=10%, and therefore the

market risk premium is 5%. In this case the CAPM is represented as:

ri = rRF + βi[rM - rRF], putting in the numbers we have:

ri = 0.05 + 0.05βi The required return on any security here is solely

a function of the Beta and SML.

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The Security Market Line or SML, continued

Below, we plot the SML from the last slide: ri = 0.05 + 0.05βi

SML

ri (%)

0 0.5 1.0 1.5

10

5

Risk, βi

Mkt. risk prem. = 5%

rRF=5%

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What if the SML changes?

Two possible SML changes can definitely occur. Each has important effects. (1) Risk-free rates rRF can change. This can be due to the

Inflation Premium (IP) or the real rate of interest changing. Note that in this case, the kM must also increase by the same amount so that the market risk premium [rM-rRF] is unchanged.

(2) The market risk premium [rM-rRF] can change. This would typically be due to changing attitudes toward risk aversion by investors.

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What if the SML changes? Following slides allow for two separate SML

changes: In the first case, we let the risk-free rate rRF increase by

2% (from 5% to 7%). The market required return rM must increase by the same amount (from 10% to 12%), so that the market risk premium [rM-rRF] remains at 5%.

In the second case, we allow for a 2% increase in the market risk premium (from 5% to 7%). The risk-free rate remains the same at 5%, however, rM must increase by 2% (from 10% to 12%) so that the market risk premium can now be [rM-rRF] = 7%.

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The Security Market Line or SML, continued

Risk-free rate increases from 5% to 7%. The new SML is ri = 0.07 + 0.05βi

SML, old

ri (%)

0 0.5 1.0 1.5

1210

7 5

Risk, βi

Mkt. risk prem. = 5%

rRF=7%

SML, new

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The Security Market Line or SML, continued

The market risk premium increases from 5 to 7%. The new SML is ri = 0.05 + 0.07βi

SML, old

ri (%)

0 0.5 1.0 1.5

1210

5

Risk, βi

Mkt. risk prem. = 7%

rRF=5%

SML, new

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Pros and Cons of the CAPM The CAPM is relatively simple. Firm specific risk is

diversifiable and irrelevant. Market (macroeconomic) risk is not diversifiable and is therefore relevant.

Required returns are a function of the risk-free rate, market risk premium, and the Beta.

The CAPM is very difficult to test empirically. It’s impossible to measure the true market portfolio. Early results were in support, in early 1990s there was some doubt, and more (sophisticated) recent tests are more in support of the CAPM.