1. Risk Aversion and Capital Allocation to Risky Assets
Investments
Cover image
CHAPTER 6
Risk Aversion and Capital Allocation to Risky Assets
Slides by
Richard D. Johnson
McGraw-Hill/Irwin
Copyright © 2008 by The McGraw-Hill Companies, Inc. All rights reserved

2. Table 6.1 Available Risky Portfolios (Risk-free Rate = 5%)

3. Utility Function
U = E ( r ) – 1/2 A s2
Where
U = utility
E ( r ) = expected return on the asset or portfolio
A = coefficient of risk aversion
s2 = variance of returns

4. Table 6. 2 Utility Scores of Alter
Table 6.2 Utility Scores of Alter. Portfolios for Investors with Varying Risk Aversion

5. Figure 6.1 The Trade-off Between Risk and Returns of a Potential Investment Portfolio

6. Figure 6.2 The Indifference Curve

7. Table 6.3 Utility Values of Possible Portfolios for an Investor with Risk Aversion, A = 4

8. Table 6.4 Investor’s Willingness to Pay for Catastrophe Insurance

9. Figure 6.3 Spread Between 3-Month CD and T-bill Rates

10. Allocating Capital: Risky & Risk Free Assets
It’s possible to split investment funds between safe and risky assets.
Risk free asset: proxy; T-bills
Risky asset: stock (or a portfolio)

11. Example Using Chapter 6.4 Numbers
rf = 7%
rf = 0%
E(rp) = 15%
p = 22%
y = % in p
(1-y) = % in rf

12. Expected Returns for Combinations
E(rc) = yE(rp) + (1 - y)rf
rc = complete or combined portfolio
For example, y = .75
E(rc) = .75(.15) + .25(.07)
= .13 or 13%

13. Combinations Without Leverage
= .75(.22) = .165 or 16.5%
If y = .75, then
= 1(.22) = .22 or 22%
If y = 1
= (.22) = .00 or 0%
If y = 0   

14. Capital Allocation Line with Leverage
Borrow at the Risk-Free Rate and invest in stock.
Using 50% Leverage,
rc = (-.5) (.07) + (1.5) (.15) = .19
c = (1.5) (.22) = .33

15. Figure 6.4 The Investment Opportunity Set with a Risky Asset and a Risk-free Asset in the Expected Return-Standard Deviation Plane

16. Figure 6.5 The Opportunity Set with Differential Borrowing and Lending Rates

17. Table 6.5 Utility Levels for Positions in Risky Assets for an Investor with Risk Aversion A = 4

18. Figure 6.6 Utility as a Function of Allocation to the Risky Asset, y

19. Table 6.6 Spreadsheet Calculations of Indifference Curves

20. Figure 6. 7 Indifference Curves for U =. 05 and U =
Figure 6.7 Indifference Curves for U = .05 and U = .09 with A = 2 and A = 4

21. Figure 6.8 Finding the Optimal Complete Portfolio Using Indifference Curves

22. Table 6.7 Expected Returns on Four Indifference Curves and the CAL

23. Table 6. 8 Average Annual Return on Stocks and 1-Month T-bills; S. Dev
Table 6.8 Average Annual Return on Stocks and 1-Month T-bills; S. Dev. and Reward to Variability of Stocks Over Time