Question

You invest $100 in a complete portfolio. The complete portfolio is composed of a risky asset

with an expected rate of return of 12% and a standard deviation of 10% and a treasury bill with a

rate of return of 5%.

__________ of your complete portfolio should be invested in the risk-free asset if you want your complete portfolio to have a standard deviation of 9%.

Answer 1

Standard deviation of a portfolio is

Oportfolio = wig+wo3 + 2wW2P1,20102 Where: W W 04 02 P12 = = = = = Proportion of the portfolio invested in Asset 1 Proportion of the portfolio invested in Asset 2 Asset 1 standard deviation of returns Asset 2 standard deviation of returns Correlation coefficient between the returns of Asset 1 and Asset 2

Now, the standard deviation of risk free asset and its correlation to any other asset is 0.

0 = V(w1*0.10)2 + (w2*0) + (2*w1* W2 * 0.10 *0*0)

0= V(W1*0.102

0.09 = (W1*0.10)

wl = 0.90

So if 0.90 (or 90%) is invested in risky asset, your should invest 1 - 90% = 10% in risk free asset.