Question

4.      Suppose we have 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 J has an expected return of 20% and a beta of 0.8. The risk-free asset’s return is 5%.     

a. Calculate the expected returns and betas on portfolios with x% invested in Stock I and the rest invested in the risk-free asset, where x% = 0%, 50%, 100%, and 150%.                     

b. Using the four portfolio betas calculated in part (a), reverse engineer (i.e., derive mathematically) the portfolio weights for a portfolio consisting of only Stock J and the risk-free asset.    

Hint: For example, if we wished to obtain a portfolio beta of 0.5, then the weights on Stock J and the risk-free asset must be 62.5% and 37.5%, respectively, and the expected return for this portfolio must be 14.375%.              

1. Calculate the reward-to-risk ratios for Stock I and Stock J.        

2. Plot the portfolio betas against the portfolio expected returns for Stock I on a graph, and link all the points together with a line. Then plot the portfolio betas against the portfolio expected returns for Stock J on the same graph and link all these points together with another line. Ensure that the x-axis and y-axis are clearly labelled. (Hint: This can be done easily with the charting function in Microsoft Excel.)                                 
3. Using the graph in part (d) above, together with your answers in part (c) above, elaborate on the efficiency of the market containing Stock I and Stock J.                                                                    

Answer 1

d.Beta describes the activity of a security's returns responding to swings in the market. Risk free assets as the name suggests have no risk thus assumed to have zero beta. Individually looking Stock I has better return than Stock J, however we cannot look into returns blindly, because both these stock have different Beta. Thus one should look into reward to risk ratio to identify the best option to invest. Now looking at the reward risk ration we find that individually stock J has better reward risk ratio compared to Stock I. So eventhough stock I have higher return, when compared to the risk investor is exposed to, Stock J is the better option.The same is reflected in the graph plotted above. According to the graph stock J portfolio is giving higher return compared to Stock I portfolio as and when beta is increasing.