1. Professor XXXXX Course Name / Number
Risk, Return, and CAPM
Professor XXXXX
Course Name / Number

2. Expected Returns Decisions must be based on expected returns
Methods used to estimate expected return
Historical approach
Probabilistic approach
Risk-based approach

3. Historical Approach for Estimating Expected Returns
Assume that distribution of expected returns will be similar to historical distribution of returns.
Using annual returns, the average risk premium for U.S. stocks relative to Treasury bills is 7.6%. Treasury bills currently offer a 2% yield to maturity
Expected return on U.S. stocks: 7.6% + 2% = 9.6%
Can historical approach be used to estimate the expected return of an individual stock?

4. Historical Approach for Estimating Expected Returns
Assume General Motors long-run average return is 17.0%. Treasury bills average return over same period was 4.1%
GM historical risk premium: 17.0% - 4.1% = 12.9%
GM expected return = Current Tbill rate + GM historical risk premium = 2% % = 14.9%
Limitations of historical approach for individual stocks
May reflect GM’s past more than its future
Many stocks have a long history to forecast expected return

5. Probabilistic Approach for Estimating Expected Returns
Identify all possible outcomes of returns and assign a probability to each possible outcome:
For example, assign probabilities for possible states of economy: boom, expansion, recession and project the returns of GM stock for the three states
55%
10%
Boom
15%
70%
Expansion
-30%
20%
Recession
GM Return
Probability
Outcome
GM Expected Return = 0.20(-30%) (15%) +0.10(55%) = 10%

6. Risk-Based Approach for Estimating Expected Returns
1. Measure the risk of the asset
2. Use the risk measure to estimate the expected return
1. Measure the risk of the asset
Systematic risks simultaneously affect many different assets
Investors can diversify away the unsystematic risk
Market rewards only the systematic risk: only systematic risk should be related to the expected return
How can we capture the systematic risk component of a stock’s volatility?

7. Risk-Based Approach for Estimating Expected Returns
Collect data on a stock’s returns and returns on a market index
Plot the points on a scatter plot graph
Y–axis measures stock’s return
X-axis measures market’s return
Plot a line (using linear regression) through the points
Slope of line equals beta, the sensitivity of a stock’s returns relative to changes in overall market returns
Beta is a measure of systematic risk for a particular security.

8. Sharper Image weekly returns
Scatter Plot for Returns on Sharper Image and S&P 500
Sharper Image weekly returns
S&P 500 weekly returns

9. ConAgra weekly returns
Scatter Plot for Returns on ConAgra and S&P 500
ConAgra weekly returns
S&P 500 weekly returns

10. Risk-Based Approach for Estimating Expected Returns
2. Use the risk measure to estimate the expected return:
Plot beta against expected return for two assets:
A risk-free asset that pays 4% with certainty, with zero systematic risk and
An “average stock”, with beta equal to 1, with an expected return of 10%.
Draw a straight line connecting the two points.
Investors holding a stock with beta of 0.5 or 1.5, for example, can find the expected return on the line.
Beta measures systematic risk and links the risk and expected return of an asset.

11. Risk and Expected Returns•
18% •
14%
ß = 1.5 • • •
10%
“average” stock • 4%
Risk-free asset • • • • • • • • • •
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6
1.8 2
Beta
What is the expected return for stock with beta = 1.5?

12. Portfolio Expected Returns
How does the expected return of a portfolio relate to the expected returns of the securities in the portfolio?
The portfolio expected return equals the weighted average of the portfolio assets’ expected returns
E(Rp) = w1E(R1)+ w2E(R2)+…+wnE(Rn)
w1, w2 , … , wn : portfolio weights
E(R1), E(R2), …, E(RN): expected returns of securities
Expected return of a portfolio with N securities

13. Portfolio Expected Returns
E(R)
$ Invested
Weights
IBM
10%
$2,500
0.125 GE
12%
$5,000
0.25
Sears 8%
Pfizer
14%
$10,000
0.5
E(Rp) = (0.125)(10%) + (0.25)(12%) + (0.125)(8%) + (0.5)(14%) = 12.25%
E(Rp) = w1E(R1)+ w2E(R2)+…+wnE(Rn)

14. Portfolio Risk
Portfolio risk is the weighted average of systematic risk (beta) of the portfolio constituent securities.
Portfolio
Beta
$ Invested
Weights
IBM
1.00
$2,500
0.125 GE
1.33
$5,000
0.25
Sears
0.67
Pfizer
1.67
$10,000
0.5
ß P = (0.125)(1.00) + (0.25)(1.33) + (0.125)(0.67) (0.50)(1.67) = 1.38
But portfolio volatility is not the same as the weighted average of all portfolio security volatilities

15. Portfolio composed of the following two assets:
Security Market Line
Portfolio composed of the following two assets:
An asset that pays a risk-free return Rf, , and
A market portfolio that contains some of every risky asset in the market.
Portfolio
E(R)
Beta
Risk-free asset Rf
Market portfolio
E(Rm) 1
Security market line: the line connecting the risk-free asset and the market portfolio

16. Security Market Line and CAPM
The two-asset portfolio lies on security market line
Given two points (risk-free asset and market portfolio asset) on the security market line, the equation of the line:
E(Ri) = Rf + ß [E(Rm) – Rf]
Return for bearing no market risk
Portfolio’s exposure to market risk
Reward for bearing market risk
The equation represents the risk and return relationship predicted by the Capital Asset Pricing Model (CAPM)

17. The Security Market Line
Plots relationship between expected return and betas
In equilibrium, all assets lie on this line.
If individual stock or portfolio lies above the line:
Expected return is too high.
Investors bid up price until expected return falls.
If individual stock or portfolio lies below SML:
Expected return is too low.
Investors sell stock driving down price until expected return rises.

18. The Security Market Line
E(RP)
SML •
A - Undervalued • A
Slope = E(Rm) - RF = Market Risk Premium RM • • • B RF •
B - Overvalued •
 =1.0 i

19. Much harder to create value through financial activities
Efficient Markets
Efficient 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.

20. If asset prices unpredictable, then what is the use of CAPM?
Efficient Markets
If asset prices unpredictable, then what is the use of CAPM?
CAPM gives analyst a model to measure the systematic risk of any asset.
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.

21. Decisions should be made based on expected returns.
Risk, Return, and CAPM
Decisions should be made based on expected returns.
Expected returns can be estimated using historical, probabilistic, or risk approaches.
Portfolio expected return/beta equals weighted average of the expected returns/beta of the assets in the portfolio.
CAPM predicts that the expected return on a stock depends on the stock’s beta, the risk-free rate and the market premium.