11.1
Chapter
11Systematic Risk & Equity Risk Premium
11.2
Key Concepts and Skills
Know how to calculate expected returnsUnderstand the impact of diversificationUnderstand the systematic risk principleUnderstand the security market lineUnderstand the risk-return trade-off
11.3
Chapter Outline
Expected Returns and VariancesPortfoliosAnnouncements, Surprises, and Expected ReturnsRisk: Systematic and UnsystematicDiversification and Portfolio RiskSystematic Risk and BetaThe Security Market LineThe SML and the Cost of Capital: A Preview
11.4
Expected Returns
Expected returns are based on the probabilities of possible outcomes
In this context, “expected” means average if the process is repeated many times
The “expected” return does not even have to be a possible return
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11.5
Example: Expected Returns
You have predicted the following returns on Coke and Tyco stock in three possible economic states. What are the expected returns? State Probability Coke Tyco Boom 0.3 0.15 0.25 Normal 0.5 0.10 0.20 Recession ??? 0.02 0.01
RC =
RT =
11.6
Variance and Standard Deviation
Variance and standard deviation still measure the volatility of returns
Using unequal probabilities for the entire range of possibilities
Weighted average of squared deviations
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11.7Example: Variance and Standard Deviation Consider the previous example. What are the variance (2) and
standard deviation () for Coke and Tyco? Coke stock
State Prob. C Ret. Ave Diff Diff2 Wtd Diff2
Boom 0.3 0.15 Normal0.5 0.10 Recess.O.2 0.02
Tyco stock 2 = ? = .00741 = ? =
11.8
Another Example
Consider the following information:State Probability ABC, Inc.Boom .25 .15Normal .50 .08Slowdown .15 .04Recession .10 -.03
What is the expected return?What is the variance?What is the standard deviation?
11.9
Portfolios
A portfolio is a collection of assetsAn asset’s risk and return is important in how
it affects the risk and return of the portfolioThe risk-return trade-off for a portfolio is
measured by the portfolio’ expected return and standard deviation, just as with individual assets
11.10
Example: Portfolio Weights
Suppose you have invested money and have purchased securities in the following amounts. What are your portfolio weights in each security?$2000 of IBM$3000 of MCD$4000 of GE$6000 of HP
11.11
Portfolio Expected Returns
The expected return of a portfolio is the weighted average of the expected returns for each asset in the portfolio
You can also find the expected return by finding the portfolio return in each possible state and computing the expected value as we did with individual securities
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11.12
Example: Expected Portfolio ReturnsConsider the portfolio weights computed
previously. What is the expected return for the portfolio if the individual stocks have the following expected returns?IBM: 19.65%MCD: 8.96%GE: 9.67%HP: 8.13%
E(RP) =Portfolio Expected Return
11.13
Portfolio Variance
Compute the portfolio return for each state:RP = w1R1 + w2R2 + … + wmRm
Compute the expected portfolio return using the same formula as for an individual asset
Compute the portfolio variance and standard deviation using the same formulas as for an individual asset
11.14
Example: Portfolio VarianceWhat is the expected return and standard deviation
for each asset & portfolio considering the following?Invest 50% of your money in Asset AState Probability A B PortfolioBoom .4 30% -5% 12.5%Bust .6 -10% 25% 7.5%
11.15Example: Portfolio Variance #2: What is the expected return and standard deviation for a portfolio with an investment of $6000 in asset X and $4000 in asset Z?
Considering the following information State Probability X Z Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10%
11.16
Expected versus Unexpected ReturnsRealized returns are generally not equal to
expected returnsThere is the expected component and the
unexpected (surprise) component in total (realized) returnAt any point in time, the unexpected return can be
either positive or negativeOver time, the average of the unexpected component
is zero
11.17
Announcements and News
Announcements and news contain both an expected component and a surprise component
It is the surprise component that affects a stock’s price and therefore its return
This is very obvious when we watch how stock prices move when an unexpected announcement is made or earnings are different than anticipated
11.18
Efficient Markets
Efficient markets are a result of investors trading on the unexpected portion of announcements
The easier it is to trade on surprises, the more efficient markets should be
Efficient markets involve random price changes because we cannot predict surprises
11.19
Systematic Risk
Risk factors that affect a large number of assetsAlso known as non-diversifiable risk or market
riskIncludes such things as changes in GDP,
inflation, interest rates, etc.
11.20
Unsystematic Risk
Risk factors that affect a limited number of assets
Also known as unique risk, asset-specific risk, or firm-specific risk
Includes such things as labor strikes, part shortages, etc.
Can be diversified away
11.21
Returns
Total Return = expected return + unexpected return
Unexpected return = systematic portion + unsystematic portion
Therefore, total return can be expressed as follows:
Total Return = expected return + systematic portion + unsystematic portion
11.22
Diversification
Portfolio diversification =investing in several different asset classes or sectors
Diversification is not just holding a lot of assets
For example, if you own 50 internet stocks, you are not diversified
However, if you own 50 stocks that span 20 different industries, then you are diversified
11.23
The Principle of Diversification
Diversification can substantially reduce the riskiness (variability) of returns with a smaller reduction in expected returns
This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another
However, there is a minimum level of risk that cannot be diversified away and that is the systematic portion
11.24
Table 11.7
1 49.24 1.00
2 37.36 .76
4 29.69 .60
6 26.64 .54
8 24.98 .51
10 23.93 .49
20 21.68 .44
30 20.87 .42
40 20.46 .42
50 20.20 .41
100 19.69 .40
200 19.42 .39
300 19.34 .39
400 19.29 .39
500 19.27 .39
1,000 19.21 .39
(2)Average Standard
Deviation of AnnualPortfolio Returns
(3)Ratio of Portfolio
Standard Deviation toStandard Deviationof a Single Stock
(1)Number of Stocks
in Portfolio
%
11.25
Figure 11.1Average annualstandard deviation (%)
Diversifiable risk
Nondiversifiablerisk
Number of stocksin portfolio
49.2
23.9
19.2
1 10 20 30 40 1,000
11.26
Diversifiable Risk
The risk that can be eliminated by combining assets into a portfolio
Often considered the same as unsystematic, unique or asset-specific risk
If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away
11.27
Total Risk
Total risk = systematic risk + unsystematic riskThe standard deviation of returns is a measure
of total riskFor well diversified portfolios, unsystematic
risk is very smallConsequently, the total risk for a diversified
portfolio is essentially equivalent to the systematic risk
11.28
Systematic Risk Principle
There is a reward for bearing riskThere is not a reward for bearing risk
unnecessarilyThe expected return on a risky asset depends
only on that asset’s systematic risk since unsystematic risk can be diversified away
11.29
Measuring Systematic Risk
How do we measure systematic risk?We use the beta coefficient to measure
systematic riskWhat does beta tell us?
A beta of 1 implies the asset has the same systematic risk as the overall market
A beta < 1 implies the asset has less systematic risk than the overall market
A beta > 1 implies the asset has more systematic risk than the overall market
11.30
Table 11.8
Company Beta Coefficient
McDonalds .85
Gillette .90
IBM 1.00
General Motors 1.05
Microsoft 1.10
Harley-Davidson 1.20
Dell Computer 1.35
America Online 1.75
(I)
11.31
Total versus Systematic Risk
Consider the following information: Standard Deviation BetaSecurity C 20% 1.25Security K 30% 0.95
Which security has more total risk?Which security has more systematic risk?Which security should have the higher
expected return?
11.32
Example: Portfolio Betas
Consider the previous example with the following four securitiesSecurity Weight BetaIBM .133 4.03MCD .2 0.84GE .267 1.05HP .4 0.59
What is the portfolio beta?
11.33
Beta and the Risk Premium
Remember that the risk premium = expected return – risk-free rate
The higher the beta, the greater the risk premium should be
Can we define the relationship between the risk premium and beta so that we can estimate the expected return?YES!
11.34
Example: Portfolio Expected Returns and Betas
0%
5%
10%
15%
20%
25%
30%
0 0.5 1 1.5 2 2.5 3
Beta
Exp
ecte
d R
etur
n
Rf
E(RA)
A
11.35Reward-to-Risk Ratio: Definition and Example The reward-to-risk ratio is the slope of the line illustrated in the
previous example Slope = (E(RA) – Rf) / (A – 0) Where: E(RA)= expected return on stock A
Rf=risk-free rate of return on T-bills
A= Beta for stock A (a measure of the stock’s riskiness)
SO: (E(RA) – Rf)= return on the risk premium for stock A Reward-to-risk ratio for previous example =
(20 – 8) / (1.6 – 0) = 7.5 What if an asset has a reward-to-risk ratio of 8 (implying that
the asset plots above the line)? What if an asset has a reward-to-risk ratio of 7 (implying that
the asset plots below the line)?
11.36
Market Equilibrium
In equilibrium, all assets and portfolios must have the same reward-to-risk ratio and they all must equal the reward-to-risk ratio for the market
“A’s ”Reward-to- Market’s Reward-to-
Risk Ratio Risk Ratio
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fA RRERRE
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11.37
Security Market LineThe security market line (SML) is the
representation of market equilibriumThe slope of the SML is the reward-to-risk
ratio: (E(RM) – Rf) / M
But since the Beta for the market is ALWAYS equal to one, M=1, the slope can be rewritten:
Slope = Return on the Market (E(RM)) – Risk-free rate of return (Rf) = market risk premium
OR: Market risk premium = E(RM) - Rf
11.38Capital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the
relationship between risk and returnExpected return on stock A = Risk-free return +
Beta of stock A(Return on Mrkt -- Risk free return) Where: Return on the market – risk free return
= Market risk premium
E(RA) = Rf + A(E(RM) – Rf)If we know an asset’s systematic risk, we can use the
CAPM to determine its expected returnThis is true whether we are talking about financial assets
or physical assets
11.39
Factors Affecting Expected Return
Pure time value of money – measured by the risk-free rate
Reward for bearing systematic risk – measured by the market risk premium
Amount of systematic risk – measured by beta
11.40Example - CAPMConsider the betas for each of the assets given
earlier. If the risk-free rate is 6.15% and the market risk premium is 9.5%, what is the expected return for each?
Security Beta Expected ReturnIBM 4.03MCD 0.84GE 1.05HP 0.59
11.41
Figure 11.4
= E(RM) - Rf
E(R
M)
R
f
M=1.0
Asset beta (I)
Asset expectedreturn (E(Ri))
The slope of the security market line is equal to themarket risk premium, i.e., the reward for bearing anaverage amount of systematic risk. The equation describing the SML can be written:
E(Ri) = Rf + [E(RM) - Rf] X I
which is the capital asset pricing model, or CAPM.
11.42
Figure 11.4
Risk, or Beta
ExpectedReturn
11.43
Chapter 11 Quick Quiz
How do you compute the expected return and standard deviation for an individual asset? For a portfolio?
What is the difference between systematic and unsystematic risk?
What type of risk is relevant for determining the expected return?
Consider an asset with a beta of 1.2, a risk-free rate of 5% and a market return of 13%. What is the reward-to-risk ratio in equilibrium? What is the expected return on the asset?