Question

You are currently only invested in the Natasha Fund (aside from risk­free securities). It has an expected return of 14% with a volatility of 20%. Currently, the risk­free rate of interest is 3.5%. Your broker suggests that you add Hannah Corporation to your portfolio. Hannah Corporation has an expected return of 20%, a volatility of 60%, and a correlation of 0 (zero) with the Natasha Fund. You follow your broker's advice and make a substantial investment in Hannah stock so that, considering only your risky investments, 40.0% is invested in Hannah stock and the rest is invested in the Natasha Fund.

Your finance professor suggests that you should calculate the optimal amount of Hannah stock in the portfolio assuming a risk­free rate of 2%. (Hint: use Excel's solver, the portfolio's Sharpe ratio shall be maximized. Consider the risk­free rate in the Sharpe ratio formula.)

1.The optimal weight of Hannah stock in the portfolio is? %. (Round to one decimal place.) 2.This optimal portfolio has a Sharpe ratio of

just need some steps to show how to do with excel solver, thank you.

Answer 1

Solution:

You now have two assets in risky portfolio:

Natasha Fund with return of 14% and standard deviation of 20%

Hannah Stock with return of 20% and standard deviation of 60%

For the Risky portoflio, let w1 and w2 be the weights of funds invested in the Natasha Fund and Hannah Stock.

w2 = 1- w1

Portfolio return = w1 * 14% + w2 * 20%

Portfolio variance = w1^2 * 20%^2 + w2^2 * 60%^2 ...........Note correlation between then is zero

Portfolio Standard deviaton = square root of protfolio variance.

Risk free rate = 2%

Sharpe ratio of the portfolio = (Portfolio return - Risk free rate)/Standard deviation of the portfolio

We have to maximise the Sharpe ratio.

See the solution and the solver condition below.

Optimal weight of the Hannah stock in the portfolio is .14.

Maximum sharpe ratio is 0.67

-x-