Case Study: Adding The Risk-Free Government Finance

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Register to read the introduction… Adding the risk-free government securities would result in a lower beta for the new portfolio. The new portfolio beta will be a weighted average of the individual security betas in the portfolio; the presence of the risk-free securities would lower that weighted average.

q. The comment is not correct. Although the respective standard deviations and expected returns for the two securities under consideration are equal, the covariances between each security and the original portfolio are unknown, making it impossible to draw the conclusion stated. For instance, if the covariances are different, selecting one security over the other may result in a lower standard deviation for the portfolio as a whole. In such a case, that security would be the preferred investment, assuming all other factors are equal.

r. Grace clearly expressed the sentiment that the risk of loss was more important to her than the opportunity for return. Using variance (or standard deviation) as a measure of risk in her case has a serious limitation because standard deviation does not distinguish between positive and negative price movements.

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The SML is determined by the following: T-bill rate = 8% with a beta equal to zero, beta for the market is 1.0, and the expected rate of return for the market is:

0.5 ( (20% + 5%) = 12.5% See the following graph. [pic] The equation for the security market line is: E(r) = 8% + β(12.5% – 8%) y. The aggressive stock has a fair expected rate of return of: E(rA) = 8% + 2.0(12.5% – 8%) = 17% The security analyst’s estimate of the expected rate of return is also 17%. Thus the alpha for the aggressive stock is zero. Similarly, the required return for the defensive stock is:

E(rD) = 8% + 0.7(12.5% – 8%) = 11.15% The security analyst’s estimate of the expected return for D is only 8.75%, and hence: αD = actual expected return – required return predicted by CAPM = 8.75% – 11.15% = –2.4% The points for each stock are plotted on the graph above. z. The hurdle rate is determined by the project beta (i.e., 0.7), not by the firm’s beta. The correct discount rate is therefore 11.15%, the fair rate of return on stock

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