Question

Midas is considering two stocks. The expected return on LAN is 15% with a standard deviation of 32%. The expected return on GBT is 9% with a standard deviation of 23%. The correlation between the returns on LAN and GBT is 0.15. The betas of LAN and GBT are 1.2 and 0.8 respectively.
a. Assume that Midas would like to have a portfolio with a beta of 0.9. Recommend how he can invest in two stocks to achieve his objective. Determine the expected return and standard deviation on this portfolio.
b, Now suppose the T-bill rate is 4.5%. Recommend how Midas can construct a new portfolio with a beta of 0.6 by investing in both the portfolio in (a) and the T-bills. Determine the expected return and standard deviation on the new portfolio.

Anyone can help me to answer question b?

Answer 1

Part a ) First of all we need to find the portfolio weights which gives the beta of 0.9, this can be done by solving the following equation:

W_LAN is the weight of LAN in the portfolio and W_GBT is the weight of GBT in the portfolio. As the entire portfolio is invested in just these two assets, therefore the W_GBT = 1- W_LAN

So the weights of both the assets should be LAN = 25% and GBT = 25%

Expected return of the portfolio is calculated through the following equation:

So portfolio return is 10.5%

standard deviation of LAN, standard deviation of GBT, correlation, portfolio standard deviation

Part b) Next we combine the portfolio with the risk free asst to achieve a beta of 0.6. The within the portfolio weight will remain in the ratio of 0.27:0.75 while we determine the weight of the portfolio and the riskfree asset

beta of risk free asset is 0

So new portfolio return is 8.52%

Risk free asset has 0 standard deviation

so ultimately above formula is reduced to :