1. Ch. 11: Risk and Return Expected Returns & Variances
Relevant Risk & Portfolio Diversification
Beta
Security Market Line, CAPM

2. Expected Returns & Variances
Expected return: historic versus projected
Expected risk premium =
Expected return - Risk-free rate
Expected return of a portfolio
Portfolio variance and standard deviation

3. Example Returns for Stock W, Stock X, & Portfolio (25%X + 75%W)
Year W X Portfolio Excel Formula
% 33% 38%
% 2% -7%
% -20% 21%
% 10% -1%
% 15% 15% =0.75*B *C29
mean 15.0% 8.0% 13.2% =SUM(D25:D29)/5
stdev 22.6% 19.4% 18.1% =STDEV(D25:D29)
correlation W&X = =CORREL(B25:B29,C25:C29)

4. Surprise & Risk R = E(R) + U
Return = Expected return + Unexpected return
R = E(R) + U
Announcement = Expected part + Surprise
Systematic (market) risk
Unsystematic (unique, diversifiable) risk
R = E(R) + Systematic portion + Unsystematic portion

5. Portfolio Diversification & Beta
See Fig. 11.1, p. 319
Some individual asset risk can be eliminated by portfolio diversification and some cannot
Unsystematic risk can be
Systematic risk cannot be
The reward for bearing risk depends on the systematic risk of the investment
Beta () measures the systematic risk of an asset relative to the average asset’s systematic risk. Beta for the average asset = 1
Portfolio beta is weighted average of asset betas

6. Beta
 measures a stock’s contribution to the riskiness of a well-diversified portfolio
 = slope coefficient from regressing stock’s returns on market portfolio’s returns.
The regression equation is
y = a + x + e,
where y is the dependent variable (stock return), a
is the intercept, x is the market return, and e is the
error

7. Example (A) (B) (C) (D) Year Stock X Stock Y Market 1994 14 13 12
a. Find betas: Use Function Wizard's LINEST
function to regress stock returns on market returns:
beta for X = =LINEST(B70:B74,D70:D74)
beta for Y = =LINEST(C70:C74,D70:D74)

8. Security Market Line (SML)
Beta of a risk-free asset = 0 Why?
Beta of market portfolio = 1 Why?
Derive SML graphically (p. 330)
SML: E(Ri) = Rf + (E(RM) - Rf) * i
Slope = E(RM) - Rf = “market risk premium,” measures risk aversion, how much return over the risk-free rate is required to get investors to bear the market portfolio’s risk
Intercept: Rf
Reward-to-risk ratio is same for all assets in market

9. Example continued Part b):
Assume risk-free rate = 6%, market risk premium = 5%
Find required rates of return, using Security Market Line:
SML: E(Ri) = Rf + (E(RM) - Rf) * i
We know E(RM) - Rf is the market risk premium, 5%
Therefore, according to the SML,
for X, kX = 6 + 5* =
for Y, kY = 6 + 5* =
The betas were calculated earlier

10. CAPM Capital Asset Pricing Model (CAPM): definition
E(Ri) = Rf + (E(RM) - Rf) * i
Expected return depends on pure time value of money, reward for bearing systematic risk, and amount of systematic risk
Out-of-equilibrium:
An undervalued stock will graph above the SML
How does it reach equilibrium?
An overvalued stock will graph below the SML
Why do stocks (assets) get out-of-equilibrium?

11. Example finished
Portfolio’s beta = weighted average of individual betas
Part c):
Find the required rate of return for the portfolio of 80% X and 20% Y
Beta for Portfolio = .8* *.651 =
Using the SML, the expected return on the portfolio
is E(RP) = * =
Also E(RP) is the weighted average of E(Rx) & E(Ry) from above:
E(RP) = .8(12.736) + .2(9.254)

12. Recommended Practice Self-Test Problems 11.3 & 11.4, pp. 333-4
Questions 2, 6, 7, p. 335
Problems on pp : 3, 11, 13, 15, 19, 37, 39 (answers are on p. 549)