Question

Suppose you are currently invested 100% in U.S. stocks and you CANNOT short: a.Find the portfolio that maximizes expected return if you want the same risk of U.S. stocks. b.What is the expected return of this portfolio and what are the portfolio weights

Answer 1

Answer:

Part a: The portfolio which maximizes the expected return is in the attached file.

Part b:The portfolio's expected rate of return is 11.20% and the weight is 100% for US only.

Explanation:

As the question is incomplete and the data is not available, thus the complete question is found as attached with the solution.

The Sharpe rate is given as

$S_a=\frac{E_a-E_r}{\sigma}$

Where

1. E_a is the estimated rate of return for a value
2. E_r is the risk free rate of return
3. σ is the standard deviation of the investment.

The portfolio variance is given as

$\sigma^2_{portfolio}=\sum_{i}^{n}{\sigma_i^2w_i^2}+\sum_{i}^{n(n-1)/2}{cv_i}$

Where

1. σ is the standard deviation of the investment.
2. w is the weighted value of the investment
3. cv is the covariance term

Portfolio standard deviation is given as

$\sigma_{portfolio}=\sqrt{\sigma^2_{portfolio}}$

Expected rate is given as

$E_{rate of return}=\sum_{i=1}^{n}{E_a_i\times w_i}$

Now the Sharp value is calculated as above.

Now the values as given in the excel sheet are added in the attached excel sheet,  following formulas are used to calculate various values

Sharpe ratio is calculated using =(B6-J3)/C6

Portfolio variance is calculated using (=B13^2*C6^2+B14^2*C7^2+B15^2*C8^2+B16^2*C9^2+2*B13*B14*C6*C7*D7+2*B13*B15*C6*C8*D8+2*B13*B16*C6*C9*D9+2*B14*B15*C7*C8*E8+2*B14*B16*C7*C9*E9+2*B15*B16*C8*C9*F9)

Portfolio standard deviation is SQRT(Variance)

Expected return is calculated using =B13*B6+B14*B7+B15*B8+B16*B9

Sharpe is calculated using =(B23-$J$3)/B22

Part a:

The portfolio which maximizes the expected return is in the attached file.

Part b:

The portfolio's expected rate of return is 11.20% and the weight is 100% for US only.