Capital Allocation
Between the Risky Asset
and the Risk-Free Asset
Allocating Capital Between 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)
Allocating Capital Between
Risky & Risk Free Assets (cont.)
Issues
Examine risk/return tradeoff.
Demonstrate how different degrees of
risk aversion will affect allocations
between risky and risk free assets.
Example
rf = 7%
rf = 0%
E(rp) = 15%
p = 22%
w = % in p
(1-w) = % in rf
Expected Returns for Combinations
E(rc) = wE(rp) + (1 - w)rf
rc = complete or combined portfolio
For example, w = .75
E(rc) = .75(.15) + .25(.07)
= .13 or 13%
Possible Combinations
E(r)
E(rp) = 15%
E(rc) = 13%
P
C
rf = 7%
F
0
c
22%

Variance on
the Possible Combined Portfolios
Since
 r = 0, then
f
 c = w p*
Combinations Without Leverage
If w = .75, then

c
= .75(.22) = .165 or 16.5%
If w = 1

c
= 1(.22) = .22 or 22%
If w = 0
 c = (.22) = .00 or 0%
Using Leverage with
Capital Allocation Line
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
CAL (Capital Allocation Line)
E(r)
P
E(rp) = 15%
E(rp) - rf = 8%
) S = 8/22
rf = 7%
F
0
p = 22%

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.
Example
rf = 7%
rf = 0%
E(rp) = 15%
p =
22%
(1-w) = % in r
w = % in p
f
 1. Given the above data, suppose you want to
achieve 10% of rate of return, how much do you
want to invest in the risky asset p?
 2. Again, suppose you want to maintain your risk
level with standard deviation at 11%, what’s the
maximum return you can achieve?