1. Risk, Return, & the Capital Asset Pricing Model
CHAPTER 6
Risk, Return, & the Capital Asset Pricing Model

2. Topics in Chapter Basic return concepts Basic risk concepts
Stand-alone risk
Portfolio (market) risk
Risk and return: CAPM/SML 1

3. Determinants of Intrinsic Value: The Cost of Equity
Net operating
profit after taxes
Required investments
in operating capital −
Free cash flow
(FCF) =
FCF1
FCF2
FCF∞
Value =
...
(1 + WACC)1
(1 + WACC)2
(1 + WACC)∞
Weighted average
cost of capital
(WACC)
For value box in Ch 4 time value FM13.
Market interest rates
Firm’s debt/equity mix
Cost of debt
Cost of equity
Market risk aversion
Firm’s business risk

4. > Risk, > Return, (both + & -)
Stand – Alone Risk
Risk in Portfolio Context
b. Market Risk
Quantified by Beta & used in
CAPM: Capital Asset Pricing Model
Relationship b/w market risk & required return as depicted in SML
Req’d return =
Risk-free return + Mrkt risk Prem(Beta)
SML: ri = rRF + (RM - rRF )bi
a. Diversifiable

5. What are investment returns?
Investment returns measure financial results of an investment.
Returns may be historical or prospective (anticipated).
Returns can be expressed in:
($) dollar terms.
(%) percentage terms.

6. An investment costs $1,000 and is sold after 1 year for $1,100.
Dollar return:
$ Received - $ Invested
$1, $1, = $100
Percentage return:
$ Return/$ Invested
$100/$1, = 0.10 = 10% 2

7. What is investment risk?
Typically, investment returns are not known with certainty.
Investment risk pertains to the probability of earning a return less than expected.
Greater the chance of a return far below the expected return, greater the risk. 2

8. Risk & Return Student Sue Student Bob Exam 1 70% X weight X 50%
80%
X wt.
X 50%
Exam x wt
100% x
Final grade = 75 %
Final grade = 75 %

9. Probability Distribution: Which stock is riskier? Why?

10. WedTech Co Normal 40% Return 20% = .08 Bad 30% Return 5% = .015
Good 30% Return 35% = .105
=Expected ave return = 20%

11. WedTech Co Standard Deviation: Measure of stand-alone risk
Return-Exp Ret = Diff2 x Prob =
Variance:
SD:

12. Standard Deviation and Normal Distributions
1 SD = 68.26% likelihood
2 SD = 95.46%
3 SD = 99.74%

13. Stand-Alone Risk
Standard deviation measures the stand-alone risk of an investment.
The larger the standard deviation, the higher the probability that returns will be far below the expected return. 13

14. IBM Normal 80% Return 12% = .096 Bad 10% Return 4% = .004
Good 10% Return 20% = .02
=Expected ave return = 12%
Standard deviation = measure of dispersion= 3.58%

15. IBM Graph

16. WedTech Co vs. IBM

17. WedTech Co & IBM in 2 stock Portfolio
Ave Portfolio Return in 50%-50% split
Ave Return %split
Wedtech 20% x = 10%
IBM 12% x .5 = 6% Portf. Return = 16%
Portfolio Standard Deviation

18. Portfolio Standard Deviation
Consider returns of portfolio at various states of economy & associated probabilities
Will diversify away risk at higher rate than simple average of securities standard deviation

19. WedTech Co & IBM in 2 stock Risk Averse Portfolio
Ave Portfolio Return in 20%-80% split
Ave Return %split
Wedtech 20% x = 4%
IBM 12% x .8 = 9.6% Portf. Return = 13.6%
With even lower standard deviation

20. WedTech Co & IBM in 2 stock Risk Taker Portfolio
Ave Portfolio Return in 80%-20% split
Ave Return %split
Wedtech 20% x = 16%
IBM 12% x .2 = 2.4% Portf. Return = 18.4%
But have greater Portfolio S.D. than other scenarios

21. WedTech Co & IBM & adding other stocks to Portfolio
IBM WedTech
Coke Microsoft

22. Historical Risk vs. Return
Return: Hi – Lo
Risk: Hi - Lo
Small Co stock
Large Co Stock
LT Corp Bonds
LT Treasuries
ST T-Bills

23. Reward-to-Variabilty Ratio (Sharpe’s)
Portfolio’s average return in excess of risk-free rate divided by standard deviation
Rpf Rrf
S.D. Porftfolio

24. Comparing Different Stocks
Coefficient of Variation:
= S.D. / Return; or Risk / Return
WalMart vs Philip Morris
12% Return 12%
12 S.D. 24
= C.V. =

25. Expected Return versus Coefficient of Variation
Security
Expected
Return
Risk:  CV
Alta Inds
17.4%
20.0%
1.1
Market
15.0
15.3
1.0
Am. Foam
13.8
18.8
1.4
T-bills
8.0
0.0
Repo Men
1.7
13.4
7.9

26. Comparing Different Stocks
Correlation coefficient = r (rho):
Measures tendency of 2 variables to move together. Rho (r) = 1 = perfect + correlation & variables move together in unison.
Does not help with diversification

27. Two-Stock Portfolios
Two stocks can be combined to form a riskless portfolio if r = -1.0.
Risk is not reduced at all if the two stocks have r = +1.0.
In general, stocks have r ≈ 0.35, so risk is lowered but not eliminated.
Investors typically hold many stocks.
What happens when r = 0? 22

28. Adding Stocks to a Portfolio
What would happen to the risk of an average 1-stock portfolio as more randomly selected stocks were added?
sp would decrease because the added stocks would not be perfectly correlated, but the expected portfolio return would remain relatively constant. 25

29. s1 stock ≈ 35% sMany stocks ≈ 20%

30. Risk vs. Number of Stock in Portfolio
,000 stocks
Company Specific (Diversifiable) Risk
Market Risk
20%
Stand-Alone Risk, p p
35% 27

31. Stand-alone risk = Market risk + Diversifiable risk
Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.
Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification. 29

32. Conclusions
As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.
sp falls very slowly after about 40 stocks are included. The lower limit for sp is about 20% = sM .
By forming well-diversified portfolios, investors can eliminate about half the risk of owning a single stock. 31

33. No. Rational investors will minimize risk by holding portfolios.
Can an investor holding one stock earn a return commensurate with its risk?
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 less than that required by the risk. 32

34. How is market risk measured for individual securities?
Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio.
It is measured by a stock’s beta coefficient. For stock i, its beta is:
bi = (ri,M si) / sM 34

35. Beta Measurements
In addition to measuring a stock’s contribution of risk to a portfolio, beta also measures the stock’s volatility relative to the market.

36. How is beta interpreted
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 than average
Most stocks have betas in the range of 0.5 to 1.5

37. Using a Regression to Estimate Beta
Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.
The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b. 35

38. Use the historical stock returns to calculate the beta for PQU.
Year
Market
PQU 1
25.7%
40.0% 2
8.0%
-15.0% 3
-11.0% 4
15.0%
35.0% 5
32.5%
10.0% 6
13.7%
30.0% 7
42.0% 8
-10.0% 9
-10.8%
-25.0% 10
-13.1%
25.0%

39. Calculating Beta for PQU

40. Beta & PQU Co. Beta reflects slope of line via regression y = mx + b
m=slope + b= y intercept
Rpqu = rM
So, PQU’s beta is & 2.56%

41. Beta & PQU Co. & R2
R2 measures degree of dispersion about regression line (ie – measures % of variance explained by regression equation)
PQU’s R2 of means about 35% of PQU’s returns are explained by the market returns (32% for a typical stock)
R2 of .95 on portfolio of 40 randomly selected stocks would reflect a regression line with points tightly clustered to it.

42. Calculating Beta in Practice
Many analysts use the S7P 500 to find market return
Analysts typically use 4 or 5 years of monthly returns to establish regression line.
Some use 52 weeks of weekly returns.

43. Expected Return versus Market Risk: Which investment is best?
Security
Expected
Return (%)
Risk, b
Alta
17.4
1.29
Market
15.0
1.00
Am. Foam
13.8
0.68
T-bills
8.0
0.00
Repo Men
1.7
-0.86

44. Capital Asset Pricing Model
The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM).
Return = Risk Free + Beta (RetMrkt –Rf)
SML: ri = rRF + (RPM)bi . 43

45. Graph of Security Market Line

46. Use the SML to calculate each alternative’s required return.
The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM).
SML: return = risk-free return + Beta(Market risk premium) .
Assume T-Bill = 7% =rRF;
=Return on market =15%= rM
Then:
Market Risk premium =RPM = (rM - rRF) = 15% - 7% = 8%. 43

47. Use the SML to calculate each alternative’s required return.
If company’s Beta = 1.25
Then: R = Rrf + B ( Rm – Rf).
R = (.08) = 17%
Req’d return = 17% vs.
Expected return of 13%
Go / No Go ?
No Go, it’s overvalued! 43

48. Required Rates of Return
If t-bill =8%, & MRP = 7%
Then required rates of return are:
rAlta = 8.0% + (7%)(1.29) = 17%.
rM = 8.0% + (7%)(1.00) = 15.0%.
rAm. F. = 8.0% + (7%)(0.68) = 12.8%.
rT-bill = 8.0% + (7%)(0.00) = 8.0%.
rRepo = 8.0% + (7%)(-0.86) = 2.0%.

49. Expected versus Required Returns (%)
Alta
17.4
17.0
Undervalued
Market
15.0
Fairly valued
Am. Foam
13.8
12.8
T-bills
8.0
Repo
1.7
2.0
Overvalued

50. SML: ri = rRF + (RPM) bi ri = 8% + (7%) bi.
Repo
Alta
T-bills
Am. Foam
rM = 15
rRF = 8
ri (%)
Risk, bi
Market 46

51. Calculate beta for a portfolio with 50% Alta and 50% Repo
bp = Weighted average
= 0.5(bAlta) + 0.5(bRepo)
= 0.5(1.29) + 0.5(-0.86)
= 0.22. 47

52. Required Return on the Alta/Repo Portfolio?
rp = Weighted average r
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML:
rp = rRF + (RPM) bp
= 8.0% + 7%(0.22) = 9.5%. 48

53. Impact of Inflation Change on SML
Original situation
r (%)
SML2
Risk, bi 18 15 11 8
New SML
 I = 3% 50

54. Impact of Risk Aversion Change
SML1
Original situation
r (%)
SML2
After change
Risk, bi 18 15 8
1.0
 RPM = 3% 52

55. Has the CAPM been completely confirmed or refuted?
No. The statistical tests have problems that make empirical verification or rejection virtually impossible.
Investors’ required returns are based on future risk, but betas are calculated with historical data.
Investors may be concerned about both stand-alone and market risk. 53