<p>Quippy Inc (“Quippy”) and Whippy Inc (“Whippy”) have
ID: 2670579 • Letter: #
Question
<p>Quippy Inc (“Quippy”) and Whippy Inc (“Whippy”) have common shares listed on the New York Exchange. Assume that the S&P 500 Index represents the market portfolio.<br /><br />An equal-weighted portfolio of Quippy’s shares and a risk-free asset has an annual variance of 0.04.<br /><br />An equal-weighted portfolio of the S&P 500 Index and a risk-free asset has an annual variance of 0.01.<br /><br />An equal-weighted portfolio of Quippy’s shares and the S&P 500 Index has an annual variance of 0.08.<br /><br />The risk-free asset has an expected annual return of 3%, and the S&P 500 Index has an expected annual return of 7%.<br /><br /><br />(a) Calculate the beta of Quippy’s shares.<br />(b) Suppose you want to put together an equal-weighted portfolio of Quippy’s and Whippy’s shares. Whippy’s shares have the same beta as the S&P 500 Index. What is the required annual return of this portfolio? <br /><br />(c) Suppose you can change the weights in the portfolio in (b) above. What percentage of the portfolio must be invested in the shares of Quippy in order to achieve a required annual portfolio return of 12%?</p><p> </p>
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<p>I know we should first calculate convarriance.. but how??</p>
Explanation / Answer
A bit hard to understand, but it looks like you need to solve for the covariance. Here's how to do it: 1.) Decide which formula to use. While both formulas are correct, the shortcut formula is generally easier to use as it requires less calculations. The following steps assume you are using the shortcut formula. 2.) Calculate the sum of x. Add together all values of x. 3.) Calculate the sum of y. Add together all values of y. 4.) Calculate the sum of xy. Multiply each x by the corresponding y value, and then add together the answers. 5.) Substitute the values into the equation (n = number of variable sets) and solve the equation. 6.) Interpret the results: *Sign of covariance - nature of relationship. If positive then x and y move in the same direction. If negative then x and y move in opposite directions. Size of covariance - strength of relationship. If large, then there is a strong relationship. If small, there is a weak or no relationship.
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