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Excatly this one I need a good explanation : https://www.chegg.com/homework-help/questions-and-answers/portfolio-optimization-risk-free-asset-assume-addition-risky-assets-described-expected-ret-q91526373 Portfolio optimization with risk-free asset: Now assume that in addition to the risky assets described
Excatly this one I need a good explanation : https://www.chegg.com/homework-help/questions-and-answers/portfolio-optimization-risk-free-asset-assume-addition-risky-assets-described-expected-ret-q91526373
Portfolio optimization with risk-free asset: Now assume that in addition to the risky assets described above with expected return vector w and positive definite variance-covariance matrix E, there is a risk-free asset with deterministic return R > 0. We can think of this asset as a one-year treasury bond, or alternatively as a certificate of deposit (CD) in a bank. Consider a portfolio of her in the risky assets, and the remaining 1-h1 in the risk-free asset. You can verify that the expected return on this portfolio is R+h" ( R1), and that the variance is (as before) h?h. (9) The case when h?1 > 1 corresponds to a situation when money is borrowed from the bank to invest in the market. The case when h< 0 corresponds to short-selling assets in the market and depositing the money in the bank. Thus, h E RN is completely unconstrained in this case with a risk-free asset. The risk averse investor's optimization problem when the risky asset is present is then U(h) = max R+h" (p R1) - hEh, (10) with no restrictions on h ERN
(a) Show that there is so-called one-fund separation in the market in this case, in that all investors, regardless of their 7, will hold the same stock market portfolio 1 B-AR - (-R1), (11) and only differ in the amount of money they deposit in the bank. This is another classical result! w
(b) What is the relationship between an investor's 7 and the expected return (8) of the chosen portfolio (including the bond) in this case?
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