Question

Assume you are a financial adviser, and one of your clients needs your help. The client wishes to invest part of her capital in a risky fund with an expected return of 16% and standard deviation of 15%, and the rest of her capital in the risk-free rate, which is 3%. If the client wants the expected return of her total investments to be 7%, what percentage of her capital must be invested in the risky fund?

Answer 1

Capital allocation, is the apportionment of funds between risk-free investments, such as T-bills, and risky assets, such as stocks. The simplest case of capital allocation is the allocation of funds between a risky asset and a risk-free asset. The risk-return profile of this 2-asset portfolio is determined by the proportion of the risky asset to the risk-free asset. If this portfolio consists of a risky asset with a proportion of x, then the proportion of the risk-free asset must be 1 – x.

Portfolio Return = x × Risky Asset Return + (1 – x) × Risk-free Return

Variance is Zero when a risk free asset and Risky asset is combined.Hence in this case :

(.16x+.03(1-x))/1 = .07

.16x+.03-.03x =.07

.13x =.04

x = .3076 and 1-x =.6924

Hence proportion of investment = 30.76%and 69.24%