Capital Allocation Between the Risky Asset and the Risk-Free Asset
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Transcript Capital Allocation Between the Risky Asset and the Risk-Free Asset
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?