1. Capital Asset Pricing Model
Chapter 7

2. Learning Objectives
Explain the theory behind the Capital Asset Pricing Model
Construct the security market line and use it to estimate cost of capital
Understand the practical applications of the CAPM

3. Asset Pricing Models Capital Asset Pricing Model (CAPM )
Expected returns are proportional to an investment’s systematic risk
A stock’s expected risk premium varies in proportion to it’s β
CAPM has issues, but is widely used in both corporate and investment settings

4. Capital Asset Pricing Model (CAPM)
It is the equilibrium model that underlies all modern financial theory
Derived using Markowitz’s principles of diversification with simplified assumptions
Sharpe (1964), Lintner (1965), and Mossin (1966) are researchers credited with its development 4

5. Assumptions of the CAPM
Individuals
All have the same (Homogeneous) expectations
Only care about mean and variance (Mean-variance optimizers)
Single-period investment horizon
Everyone can borrow or lend at the risk-free rate
Markets are Perfect
All assets are publicly held and publicly traded
All information is costless and available to all investors
No taxes or transaction costs

6. Assumption Results
All investors will hold the same portfolio of risky assets – market portfolio
Optimal Risky Portfolio
Market portfolio will contains all securities
Each security will be held in proportion to its market value as a percentage of total market value

7. The Efficient Frontier and the CML

8. Passivity is Efficient
CAPM implies that passively investing in the market portfolio is efficient
Mutual fund theorem: A single mutual fund composed of the market will satisfy the desires of all investors
Active investors holding anything other than the market are holding an inefficient portfolio
Conundrum: if everyone is passive, because it is costless and efficient, what makes the market portfolio efficient?

9. βD = D,M / M2 or βD = (ρDMD)/M
Security’s Risk
The only risk we are concerned with is systematic which we measure with β
A function of a security’s returns covariance with the market
βD = D,M / M2 or βD = (ρDMD)/M

10. βD = (ρDMD)/M D – Measures asset ‘D’ total risk
ρDM – Measures the proportion of D’s total risk that is systematic
ρDMD– Measures the systematic risk of asset ‘D’
M – Measures the total market risk
Which is???
So βD:

11. Notes on β β – tells us how sensitive a stock is to market movements
“Average Stock” has a β of 1
Stocks with β > 1?
Stocks with 0 < β < 1?
Stocks with negative β?
What is the β of the market?
What is the β of the risk free asset?

12. CAPM and β
CAPM states that expected returns are proportional to an investment’s systematic risk
A stock’s expected risk premium varies in proportion to it’s β
E(Ri) = Rf + βi (RM - Rf)
Stock’s risk premium

13. CAPM Example
What is the expected return for a stock with a beta of 1.7, if the expected market risk premium is 12% and the risk free rate is 3%?
What is the expected return for a stock with a beta of 1.7, if the stock’s expected risk premium is 12% and the risk free rate is 3%?
What is the expected return for a stock with a beta of 1.7, if the expected return on the market is 12% and the risk free rate is 3%?

14. Market Risk Premium: RM - Rf
The market risk premium depends on the risk aversion of the average investor
It will be a function of the risk of the market and the average investor’s risk aversion:
E(RM)-rf = Ᾱσ2M
Ᾱ is the average degree of risk aversion across investors
σ2M is the variance of the market portfolio
What happens as the average risk aversion increases? Decreases? Why?
What happens to the SML?

15. How Risk Averse is the Market?
The variance of the return on the market portfolio is .04 and the expected return on the market portfolio is 20%. If the risk-free rate of return is 10%, the market’s degree of risk aversion, A, is _________

16. Market Risk Premium Is the risk pricing benchmark
How much must investor be compensated to bear systematic risk
The risk premium is the price that investors earn on their investment in the market portfolio
When investors are scared the risk premium rises to induce people into the market
When investors are confident the risk premium falls as investors are less concerned with risk

17. Risk Premium Example
A stock is currently selling at $56. Its expected rate of return is 12%, the risk free rate is 4%, and the market risk premium is 6%. If the stock’s β triples? Assume a constant dividend
What is the stock’s new risk premium?
What is the new fair rate of return?
What is the new price of the stock?

18. Portfolios
Portfolio β is a weighted average of the component stocks’ β
Because the portfolio return is a weighted average of the component stocks return
Returns are a function of β
For the Market:

19. Portfolio β Example
You invested 40% of your money in asset A, βA is 1.5 and the balance in asset B, βB is 0.5. What is the portfolio beta?
If the risk free rate is 3% and the market risk premium is 11%, what are Stock A & B’s expected return?
What is the portfolio’s expected return?

20. Security Market Line The graphical representation of the CAPM equation
Graphs individual asset’s returns as a function of their systematic risk
Alpha: is the deviation from fair return

21. The SML and a Positive-Alpha Stockrf
What is the slope of the SML?

22. α Example Risk free is 5% & the market risk premium is 7%
If a stock has a β of 1.6, what is its fair return?
If the stocks expected return is 19%, what is α?

23. Dis-Equilibrium SML
E(ri)
SML C B A β

24. Applications of CAPM
Use SML as benchmark for fair return on risky asset
SML provides “hurdle rate” for internal projects

25. Example 1 What is the fair return for each company?
The T-bill rate is 1% and the market risk premium is 6%.
What is the fair return for each company?
Which stocks are overvalued and which are undervalued?
Stock
Forecast Return
Beta
Fair Return GS
9.5%
1.38 ? C
18%
2.59
JPM
8.0%
1.33

26. Example 2
The T-bill rate is 1% and the market risk premium is __%.
Assume that all stocks are fairly priced, fill in the missing blanks
Stock
Forecast Return
Beta
Fair Return GS
9.5% ? C
18.0%
JPM
8.0%
1.33

27. Example 3
A stock is selling for $125, its β is 1.1, and is expected to pay a $5.50 dividend next year. At what price does the investor expect to sell the stock for after the dividend, if the risk free rate is 4% and the expected return on the market is 18%?

28. Example 4
The market price of a security is $56. Its expected rate of return is 16%. The risk-free rate is 5%, and the market risk premium is 9%. What will the market price of the security be if its beta increase by 50%?
Assume the stock is expected to pay a constant dividend in perpetuity

29. Example 5
Consider two stocks, A and B. Stock A has an expected return of 10% and a beta of 1.2. Stock B has an expected return of 14% and a beta of 1.8. The market expected return is 9% and the risk-free rate is 5%. Which stock is a better buy? Why?

30. CAPM in practice CAPM deals with expectations and the “market”
We CANNOT observe expectation so we have to use realized returns
We CANNOT observe the market so we have to use an index → Have to cast CAPM as an Index Model

31. Expect versus Realized Returns
E(ri) ri
Actual return = Expected return + the effect of surprises
ri = Actual return earn on the security
E(ri )= Expected return on the security
βi= Market Beta
F = Surprise in the market return (+/-)
ei = Firm specific events

32. Expect v Actual Return Example
If the market is expected to return 15% over the next year, what is the expected return for a stock with a β of 0.9? The risk free is expected to be 3%.
If the actual market return was 21%:
What is the market surprise?
What was the actual return earned over the year?

33. CAPM as an Index Model rit - rft = αi + βi (rMt – rft) + eit
rit: Asset i’s HPR
i: Asset
t: Time
αi: SCL intercept
βi: SCL slope
rMt: Index return at time t
eit: Firm-specific return

34. Google, 01/06-12/10

35. Google vs. S&P 500, 01/06-12/10

36. CAPM and the Real World
CAPM is based on fundamentally false assumption, and has some issues empirically
The principals underlying CAPM are VALID
Investors should diversify
We should only care about systematic risk
A well-diversified risky portfolio is suitable for the majority of investors