4. Suppose wehave two risky assets, Stock I and Stock J, and a risk-free asset.Stock I has an expected return of 25% and a beta of 1.5. Stock Jhas an expected return of 20% and a beta of 0.8. The risk-freeasset’s return is 5%.
a. Calculate the expected returns andbetas on portfolios with x% invested in Stock I and the restinvested in the risk-free asset, where x% = 0%, 50%, 100%, and150%.
b. Using the four portfolio betascalculated in part (a), reverse engineer (i.e., derivemathematically) the portfolio weights for a portfolio consisting ofonly Stock J and the risk-free asset.
Hint: For example, ifwe wished to obtain a portfolio beta of 0.5, then the weights onStock J and the risk-free asset must be 62.5% and 37.5%,respectively, and the expected return for this portfolio must be14.375%.
- Calculate the reward-to-risk ratios for Stock I and StockJ.
- Plot the portfolio betas against the portfolio expected returnsfor Stock I on a graph, and link all the points together with aline. Then plot the portfolio betas against the portfolio expectedreturns for Stock J on the same graph and link all these pointstogether with another line. Ensure that the x-axis and y-axis areclearly labelled. (Hint: This can be done easilywith the charting function in Microsoft Excel.)
- Using the graph in part (d) above, together with your answersin part (c) above, elaborate on the efficiency of the marketcontaining Stock I and Stock J.
