1. Introduction to Risk and Return
Principles of
Corporate Finance
Tenth Edition
Chapter 7
Introduction to Risk and Return
Slides by
Matthew Will
McGraw-Hill/Irwin
Copyright © 2011 by the McGraw-Hill Companies, Inc. All rights reserved. 1 1 1 1 1 2

2. Topics Covered Over a Century of Capital Market History
Measuring Portfolio Risk
Calculating Portfolio Risk
How Individual Securities Affect Portfolio Risk
Diversification & Value Additivity 2 2 2 2 3 2

3. The Value of an Investment of $1 in 190013

4. The Value of an Investment of $1 in 1900
Real Returns 13

5. Average Market Risk Premia (by country)
Risk premium, %
Country

6. Dividend Yield
Dividend yields in the U.S.A. 1900–2008

7. Stock Market Index Returns
Rates of Return
Stock Market Index Returns
Percentage Return
Year
Source: Ibbotson Associates 14

8. Histogram of Annual Stock Market Returns
Measuring Risk
Histogram of Annual Stock Market Returns
( )
# of Years
Return %

9. Measuring Risk Variance - Average of squared deviations from mean.
Standard Deviation – Square root of the variance. A measure of volatility.

10. Measuring Risk
Coin Toss Game-calculating variance and standard deviation

11. Measuring Risk 19

12. Equity Market Risk (by country)
Average Risk ( )
Standard Deviation of Annual Returns, %

13. Annualized Standard Deviation of the DJIA over the preceding 52 weeks
Dow Jones Risk
Annualized Standard Deviation of the DJIA over the preceding 52 weeks
(1900 – 2008)
Standard Deviation (%)
Years

14. Measuring Risk
Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.
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.” 18

15. Comparing Returns

16. Measuring Risk 20

17. Measuring Risk 21

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

19. 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

20. Portfolio Risk Another 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

21. Portfolio Risk Another 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

22. Portfolio Risk 19

23. Portfolio Risk Example Correlation Coefficient = .4
Stocks s % of Portfolio Avg Return
ABC Corp % %
Big Corp % %
Standard Deviation = weighted avg = 33.6
Standard Deviation = Portfolio = 28.1
Real Standard Deviation:
= (282)(.62) + (422)(.42) + 2(.4)(.6)(28)(42)(.4)
= CORRECT
Return : r = (15%)(.60) + (21%)(.4) = 17.4%

24. Portfolio Risk 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 = 33.6
Standard Deviation = Portfolio = 28.1
Return = weighted avg = Portfolio = 17.4%
Let’s Add stock New Corp to the portfolio

25. Portfolio Risk NOTE: Higher return & Lower risk
Example Correlation Coefficient = .3
Stocks s % of Portfolio Avg Return
Portfolio % %
New Corp % %
NEW Standard Deviation = weighted avg = 31.80
NEW Standard Deviation = Portfolio =
NEW Return = weighted avg = Portfolio = 18.20%
NOTE: Higher return & Lower risk
How did we do that? DIVERSIFICATION

26. 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

27. Portfolio 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.

28. Portfolio Risk The return on Dell stock changes on average
by 1.41% for each
additional 1% change in
the market return. Beta
is therefore 1.41.

29. Portfolio Risk The middle line shows that a well
Diversified portfolio of randomly
selected stocks ends up with 1
and a standard deviation equal to
the market’s—in this case 20%.
The upper line shows that a
well-diversified portfolio with 1.5
has a standard deviation of about
30%—1.5 times that of the market.
The lower line shows that a
well-diversified portfolio with .5
10%—half that of the market.

30. Portfolio Risk

31. Portfolio Risk
Covariance with the market
Variance of the market

32. Beta