1. Professor XXX Course Name / #

2. Efficient Risky Portfolios
Variance of return - a poor measure of risk
Investors can only expect compensation for systematic risk
Asset pricing models aim to define and quantify systematic risk
Begin developing pricing model by asking: Are some portfolios better than others?

3. Expanding The Feasible Set On The Efficient Frontier
EF including domestic & foreign assets
E(RP)
EF including domestic stocks, bonds, and real estate
EF for portfolios of domestic stocks P

4. What happens when we add a risk-free asset to the picture?
Are Some Portfolios Better Than Others?
Efficient portfolios achieve the highest possible return for any level of volatility
Two – Asset Portfolios D F • E
N – Asset Portfolios
E(RP)
MVP (75%A, 25%B)
C (50%A, 50%B)
inefficient portfolios
efficient portfolios •
Stock A •
Stock B
efficient portfolios •
MVP P
What happens when we add a risk-free asset to the picture?

5. Expected Return (per month) and Standard Deviation for Various Portfolios

6. Riskless Borrowing And Lending
Three possible returns: -10%; 10%; 30%
Risky asset X
Expected return = 10%
Standard deviation =16.3%
Return: 6%
Risk-free asset Y
Buying asset Y = Lending money at 6% interest
How would a portfolio with $100 (50%) in asset X and $100 (50%) in asset Y perform?
$100 Asset X
$100 Asset Y
Three possible returns: -2%; 8%; 18%
Expected return = 8%
Standard deviation =8.16%
Portfolio has lower return but also less volatility than 100% in X
Portfolio has higher return and higher volatility than 100% in risk-free

7. Original $200 investment plus $100 in borrowed funds
Riskless Borrowing And Lending (Continued)
What if we sell short asset Y instead of buying it? Borrow $100 at 6% Must repay $106
Invest $300 in X
Original $200 investment plus $100 in borrowed funds
When X Pays –10%
When X Pays 10%
When X Pays 30%
Expected return on the portfolio is 12%. Higher expected return comes at the expense of greater volatility

8. Riskless Borrowing And Lending (Continued)
The more we invest in X, the higher the expected return
The expected return is higher, but so is the volatility
This relationship is linear
Portfolio
Expected Return
Standard Deviation
50% risky, 50% risk-free 8%
8.16%
100% risky, 0% risk free
10%
16.33%
150% risky, -50% risk free
12%
24.49%

9. Portfolios Of Risky & Risk-Free Assets
E(RP)
borrowing •
16.5% B •
12%
lending MF • 9% A •
RF=6% P
15%
30%
52%

10. New Efficient Frontier

11. Only one risky portfolio is efficient
The Market Portfolio
Only one risky portfolio is efficient
Equilibrium requires this to be the Market Portfolio
Suppose investors agree on which portfolio is efficient
Market Portfolio: value weighted portfolio of all available risky assets
The line connecting Rf to the market portfolio - called the Capital Market Line

12. Finding the Optimal Risky Portfolio
If investors can borrow and lend at the risk-free rate, then from the entire feasible set of risky portfolios, one portfolio will emerge that maximizes the return investors can expect for a given standard deviation.
To determine the composition of the optimal portfolio, you need to know the expected return and standard deviation for every risky asset, as well as the covariance between every pair of assets.

13. Finding the Optimal Portfolio

14. The Capital Market Line
The line connecting Rf to the market portfolio is called the Capital Market Line (CML)
CML quantifies the relationship between the expected return and standard deviation for portfolios consisting of the risk-free asset and the market portfolio, using

15. Capital Asset Pricing Model (CAPM)
Only beta changes from one security to the next. For that reason, analysts
classify the CAPM as a single-factor model, meaning that just one variable explains differences in returns across securities.

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

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

18. In the CAPM, a stock’s systematic risk is captured by beta
The numerator is the covariance of the stock with the market
The denominator is the market’s variance
In the CAPM, a stock’s systematic risk is captured by beta
The higher the beta, the higher the expected return on the stock

19. Beta And Expected Return
Beta measures a stock’s exposure to market risk
The market risk premium is the reward for bearing market risk:
Rm - Rf
E(Ri) = Rf + ß [E(Rm) – Rf]
Return for bearing no market risk
Stock’s exposure to market risk
Reward for bearing market risk

20. Calculating Expected Returns
E(Ri) = Rf + ß [E(Rm) – Rf]
Assume
Risk–free rate = 2%
Expected return on the market = 8%
If Stock’s Beta Is
Then Expected Return Is 2%
0.5 5% 1 8% 2
14%
When Beta = 0, The Return Equals The Risk-Free Return
When Beta = 1, The Return Equals The Expected Market Return

24. Using The Security Market Line
The SML and where P&G and GE place on it r%
SML 15
12.4%
slope = E(Rm) – RF =
MRP = 10% - 2% = 8%
= Y ÷ X • 10
6.8% 5
Rf = 2% 
P&G 1 GE 2

25. Shifts In The SML Due To A Shift In Required Market Return15
SML2
11.1% •
Shift due to change in market risk premium from 8% to 7% 10 •
6.2% 5
Rf = 2% 
P&G 1 GE 2

26. Shifts In The SML Due To A Shift In The Risk-Free Rate15
14.4%
Shift due to change in risk-free rate from 2% to 4%, with market risk premium remaining at 8%. Note all returns increase by 2% • 10
8.8% 5
Rf = 4% 
P&G 1 GE 2

27. Alternatives To CAPM Arbitrage Pricing Theory Fama-French Model
Betas represent sensitivities to each source of risk
Terms in parentheses are the rewards for bearing each type of risk.

28. The Current State of APT
Investors demand compensation for taking risk because they are risk averse.
There is widespread agreement that systematic risk drives returns.
You can measure systematic risk in several different ways depending on the asset pricing model you choose.
The CAPM is still widely used in practice in both corporate finance and investment-oriented professions.