1. Capital Allocation Between The Risky And The Risk-Free Asset
Chapter 7

2. 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)

3. Allocating Capital: Risky & Risk Free Assets
Issues
Examine risk/return tradeoff.
Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets.

4. Example Using Chapter 7.3 Numbers
rf = 7%
rf = 0%
E(rp) = 15%
p = 22%
y = % in p
(1-y) = % in rf

5. 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%

6. Possible Combinations
E(r)
E(rp) = 15% P
E(rc) = 13% C
rf = 7% F  c
22%

7. Variance For Possible Combined Portfolios=
Since rf y
= 0, then  *  
* Rule 4 in Chapter 6

8. 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   

9. 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

10. CAL (Capital Allocation Line)
E(r) P
E(rp) = 15%
E(rp) -
rf = 8%
) S = 8/22
rf = 7% F 
p = 22%

11. CAL with Higher Borrowing RateP
) S = .27 9% 7%
) S = .36 
p = 22%

12. Risk Aversion and Allocation
Greater levels of risk aversion lead to larger proportions of the risk free rate.
Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets.
Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations.

13. Utility Function U = E ( r ) - .005 A s2 Where U = utility
E ( r ) = expected return on the asset or portfolio
A = coefficient of risk aversion
s2 = variance of returns

14. CAL with Risk Preferences
The lender has a larger A when
compared to the borrower P
Borrower 7%
Lender 
p = 22%