ASSET ALLOCATION ACROSS RISKY AND RISK-FREE PORTFOLIOS

Allocating Capital
1. Possible to split investment funds between safe and risky assets
2. Risk free asset: proxy; T-bills
3. Risky asset:  stock (or a portfolio)


Issues to consider
1. Examine risk/ return tradeoff
2. Demonstrate how different degrees of risk aversion will affect allocations between risky and risk free assets

Example

Total portfolio value                  = $300,000
Risk-free value                         =     90,000
Risky (Vanguard  and Fidelity) =   210,000
Vanguard (V) = 54%           
Fidelity (F)     = 46%

CALCULATING EXPECTED RETURN

rf = 7%
srf = 0% (std. dev of risk free)
E(rp) = 15%
sp = 22% (std. dev of portfolio)
y = % in p (risky)
(1-y) = % in rf


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%

Investment Opportunity Set with a Risk-Free Investment

Variance on the Possible Combined Portfolios: Since srf = 0 then sc = y*sp
What it means is that standard deviation of risk free asset = 0. So only variance/std deviation that we should be concerned is risky asset/portfolio. Multiply std deviation of risky asset by the asset's allocation % to get total std. deviation.

Combinations Without Leverage

If y = .75, then
sc = .75(.22) = .165 or 16.5%
If y = 1
sc = 1(.22) = .22 or 22%
If y = 0
sc = 0(.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

sc = (1.5) (.22) = .33


Risk Aversion and Allocation

1. Greater levels of risk aversion lead to larger proportions of the risk free rate
2. Lower levels of risk aversion lead to larger proportions of the portfolio of risky assets
3. Willingness to accept high levels of risk for high levels of returns would result in leveraged combinations