Question

1. 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%.
   1. What would be the weight of your investment allocated to the risk-free asset if you want to have a portfolio standard deviation of 9%? (2 points)

2. How could you use these two investments to generate an expected return of 15% (please include quantitative as well as qualitative assessment) (3 points)

3. What is the slope of the capital allocation line with these two investments? (2 points)

Answer 1

ans a) we nee to invest (current standard deviation - desired standard deviation)/current standard deviation % into the risk free asset.

Investment in risk free asset = (10 - 9)/10

= 10%

Ans b) Since both the stock is generating less than 12% one has to short sell one stock which is giving less return and invest into the stock which is paying higher return in that way one can earn more return. So we need to short sell the risk free asset and investment that into the risky asset to earn 15% of return.

Thus one should invest 143% in risky asset and short sell 43% in risk free asset so that we can earn the return of 15%

return = 12% * 1.43 - .43*5%

= 15.01%

Ans c) Slope of the capital allocation line will be upward sloping since with the increase of risk, return is also increasing.

Slope = (return on risky asset - risk free asset)/standard deviation

= (12% - 5%)/10%

= .7