Question

Adrienne has $1,000.00 to invest in a portfolio. She will build the portfolio from three assets: - Stock X with an expected return of 16.0% and a standard deviation of 40% - Stock Y with an expected return of 10.0% and a standard deviation of 30% - T-Bills with an expected return of 3.00% and a standard deviation of 0%. Assume she can short sell assets (or borrow at the risk-free rate). Assume also that she will invest the same amount in Stock X and Stock Y. How much money will she invest in Stock X if her goal is to create a portfolio with an expected return of 20.00%. (to nearest $0.01 )

Answer 1

Adrienne will invest $700.00 in Stock X to create a portfolio with an expected return of 20.00%, assuming equal investment in Stock X and Stock Y and the ability to short sell or borrow at the risk-free rate.

Step-by-step explanation:

To achieve a portfolio expected return of 20.00%, we need to find the weight of Stock X in the portfolio. Since Stock X and Stock Y will have equal weights and the T-Bills will balance the return to reach the desired 20.00%, we can set up an equation based on the expected returns of the investments. Let w denote the weight of Stock X (which will be the same as Stock Y), and (1 - 2w) will be the weight of T-Bills.

The expected return for the portfolio (Rp) would be the weighted average of the returns:
Rp = w * RX + w * RY + (1 - 2w) * RT-Bills, where RX = 16.0%, RY = 10.0%, and RT-Bills = 3.00%.

Substituting the expected return of the portfolio and the returns of the investments, we get:
20% = w * 16% + w * 10% + (1 - 2w) * 3%. Solving for w gives us w = 0.7 or 70% of the portfolio. Since Stock X and Stock Y have equal weights, Adrienne will invest $700.00 in Stock X.

Note that a portfolio expected return of 20% is not achievable with the given assets without allowing for short selling or leveraging (borrowing at the risk-free rate).