Question

You invest $100 in a portfolio of stock JET and a risk-free asset with a return of 5%. JET has an expected return of 12% and a standard deviation of 10%. What is the percentage of your portfolio in the risk-free asset if your portfolio’s standard deviation is 9%?

A. 30%

B. 90%

C. 50%

D. 10%

Answer 1

Answer

% of investment in risk free asset is Option D : 10%

Calculation is done below

Let % of Investment in stock JET is a

Let % of Investment in risk free asset is b.

Standard deviation of stock JET is 10%

Standard deviation of risk free asset is always 0 %

Standard Deviation of portfolio = % of Investment in Stock JET * Standard deviation of stock JET +   % of Investment in risk free asset *Standard deviation of risk free asset

9 = 10*a + 0.00*b

9 = 10*a

a = 9/10 = 0.90 or 90%

it means investment instock JET is 90 % .

Investment in Risk free asset = 100 - investment instock JET

= 100-90 = 10%