Question

Mutual Fund Inc. (MFI) serves two types of investors with two stock portfolios. Thebroad stock market index is expected to increase by 15% and Government of Canada T-bills is projected to earn a yield of 6%. The consensus among investors is that the stock market will remain as volatile as the past year with a standard deviation of 20%. The low-risk portfolio has a standard deviation of 10%, while the high-risk portfolio has a standard deviation of 25%. Both portfolios are on the efficient frontier. What are the expected returns on these two portfolios?

short answer question. please explain and provide more than just the number for an answer.

Answer 1

Sharpe ratio for Market = (Expected return of market - Risk free rate) / Standard deviation

= (15% - 6%) / 20%

= 9% / 20%

= 0.45.

Sharpe ratio that is return per unit of risk for market is 0.45.

If Both portfolios are on the efficient frontier then for both portfolio  return per unit of risk will be equal to market.

So,

For Low Risk portfolio

Sharpe ratio = (expected return of low risk - risk free) / Standard deviation

0.45 = (expected return of low risk - 6%) / 10%

4.50% =  (expected return of low risk - 6%)

Expected return of low risk = 6% + 4.50%

= 10.50%.

Expected return of low risk portfolio is 10.50%.

Now,

For High Risk portfolio

Sharpe ratio = (expected return of High risk - risk free) / Standard deviation

0.45 = (expected return of High risk - 6%) / 25%

11.25% =  (expected return of high risk - 6%)

Expected return of high risk = 6% + 11.25%

= 17.525.

Expected return of high risk portfolio is 17.25%.