Question
You are considering investing in a risk-free asset that pays 5% per annum and a risky portfolio, P, consisting of two risky securities, X and
You are considering investing in a risk-free asset that pays 5% per annum and a risky portfolio, P, consisting of two risky securities, X and Y. The weights of X and Y in P are 0.60 and 0.40, respectively. X has an expected rate of return of 14% and variance of 0.01, and Y has an expected rate of return of 10% and a variance of 0.0081. Suppose the correlation coefficient between X and Y is 0.5.
(1) What is the expected return for the risky portfolio P? Please express your final answer in % and keep two decimal places, for example 9.70%.
(2) What is the variance of the risky portfolio P? Please express variance as it is (NOT as %) and keep four decimal places.
(3) If you want to form a complete portfolio with an expected rate of return of 10%, what percentages should you invest in the risk-free asset, X, and Y, respectively, if you keep X and Y in the same proportions to each other as in portfolio P? To put it another way, you will consider the risky portfolio as a whole when you make your investment decision. Please express your final answer in % and keep two decimal places, for example 30.55%.
(4) If you want to form a complete portfolio with a standard deviation of 0.07, what percentages should you invest in the risk-free asset, X, and Y, respectively, if you keep X and Y in the same proportions to each other as in portfolio P? To put it another way, you will consider the risky portfolio as a whole when you make your investment decision. Please express your final answer in % and keep two decimal places, for example 30.55%.
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