1. Today Risk and Return Reading Portfolio Theory
Capital Asset Pricing Model
Reading
Brealey, Myers, and Allen, Chapters 7 and 8

2. Measuring Risk
Variance - Average value of squared deviations from mean. A measure of volatility.
Standard Deviation - Average value of squared deviations from mean. A measure of volatility.
Variance measures ‘Total Risk’

3. Measuring Risk
Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”
Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”
Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments. 18

4. Measuring Risk 21

5. Portfolio Risk
The variance of a two stock portfolio is the sum of these four boxes 19

6. Portfolio Risk Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The expected return on your portfolio is: 19

7. Portfolio Risk Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

8. Portfolio Risk Example
Suppose you invest 60% of your portfolio in Exxon Mobil and 40% in Coca Cola. The expected dollar return on your Exxon Mobil stock is 10% and on Coca Cola is 15%. The standard deviation of their annualized daily returns are 18.2% and 27.3%, respectively. Assume a correlation coefficient of 1.0 and calculate the portfolio variance. 19

9. Portfolio Return and Risk19

10. Portfolio Risk To calculate portfolio variance add up the boxes
The shaded boxes contain variance terms; the remainder contain covariance terms. 1 2 3 4 5 6 N
To calculate portfolio variance add up the boxes
STOCK
STOCK

11. Copyright 1996 by The McGraw-Hill Companies, Inc
Beta and Unique Risk
1. Total risk = diversifiable risk + market risk
2. Market risk is measured by beta, the sensitivity to market changes
beta
Expected
return
market
10% - +
+10%
stock
Copyright 1996 by The McGraw-Hill Companies, Inc
-10%

12. Beta and Unique Risk
Market Portfolio - Portfolio of all assets in the economy. In practice a broad stock market index, such as the S&P Composite, is used to represent the market.
Beta - Sensitivity of a stock’s return to the return on the market portfolio.

13. Beta and Unique Risk
Covariance with the market
Variance of the market

14. Markowitz Portfolio Theory
Combining stocks into portfolios can reduce standard deviation, below the level obtained from a simple weighted average calculation.
Correlation coefficients make this possible.
The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.

15. Markowitz Portfolio Theory
Price changes vs. Normal distribution
Coca Cola - Daily % change
Proportion of Days
Daily % Change

16. Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment A
% probability
% return

17. Markowitz Portfolio Theory
Standard Deviation VS. Expected Return
Investment B
% probability
% return

18. Markowitz Portfolio Theory
Expected Returns and Standard Deviations vary given different weighted combinations of the stocks
Expected Return (%)
Coca Cola
40% in Coca Cola
Exxon Mobil
Standard Deviation

19. Efficient Frontier
Each half egg shell represents the possible weighted combinations for two stocks.
The composite of all stock sets constitutes the efficient frontier
Expected Return (%)
Standard Deviation

20. Efficient Frontier T rf S
Lending or Borrowing at the risk free rate (rf) allows us to exist outside the efficient frontier.
Expected Return (%) T
Lending Borrowing rf S
Standard Deviation

21. Efficient Frontier Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp % %
Big Corp % %
Standard Deviation = weighted avg =
Standard Deviation = Portfolio =
Return = weighted avg = Portfolio =

22. Efficient Frontier Let’s Add stock New Corp to the portfolio
Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp % %
Big Corp % %
Standard Deviation = weighted avg =
Standard Deviation = Portfolio =
Return = weighted avg = Portfolio =
Let’s Add stock New Corp to the portfolio

23. Efficient Frontier NOTE: Higher return & Lower risk
Example Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio % %
New Corp % %
NEW Standard Deviation = weighted avg =
NEW Standard Deviation = Portfolio =
NEW Return = weighted avg = Portfolio =
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION

24. Efficient Frontier
Return B A
Risk (measured as s)

25. Efficient Frontier
Return B AB A
Risk

26. Efficient Frontier
Return B N AB A
Risk

27. Efficient Frontier
Return B
ABN N AB A
Risk

28. Efficient Frontier Goal is to move up and left. Return WHY? B ABN N AB
Risk

29. Efficient Frontier Return Low Risk High Return High Risk High Return
Low Return
High Risk
Low Return
Risk

30. Efficient Frontier Return Low Risk High Return High Risk High Return
Low Return
High Risk
Low Return
Risk

31. Efficient Frontier
Return B
ABN N AB A
Risk

32. . Security Market Line rf Return Market Return = rm
Efficient Portfolio
Risk Free
Return = rf
Risk

33. . Security Market Line rf Return Market Return = rm
Efficient Portfolio
Risk Free
Return = rf
1.0
BETA

34. . Security Market Line rf Return Risk Free Return =
Security Market Line (SML) rf
BETA

35. Security Market Line rf SML Equation = rf + β ( rm - rf ) Return SML
BETA
1.0
SML Equation = rf + β ( rm - rf )

36. Capital Asset Pricing Model
R = rf + β ( rm - rf )
CAPM

37. Beta vs. Average Risk Premium
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium 30 20 10
SML
Investors
Market Portfolio
Portfolio Beta
1.0

38. Beta vs. Average Risk Premium
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium
SML 30 20 10
Investors
Market Portfolio
Portfolio Beta
1.0

39. Beta vs. Average Risk Premium
Testing the CAPM
Beta vs. Average Risk Premium
Avg Risk Premium 30 20 10
SML
Investors
Market Portfolio
Portfolio Beta
1.0

40. Arbitrage Pricing Theory
Alternative to CAPM
Expected Risk
Premium = r - rf
= Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + …
Return = a + bfactor1(rfactor1) + bf2(rf2) + …

41. Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors
( )