Problem 1. Stocks offer an expected rate of return of 18%, with a standard deviation of...

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Problem 1. Stocks offer an expected rate ofreturn of 18%, with a standard deviation of 22%. Gold offers anexpected return of 10% with a standard deviation of 30%.
a) In light of the apparent inferiority of gold with respect toboth mean return and volatility, would anyone hold gold? If so,demonstrate graphically why one would do so.
b) Given the data above, reanswer a) with the additionalassumption that the correlation coefficient between gold and stocksequals 1. Draw a graph illustrating why one would or would not holdgold in oneâ€™s portfolio. Could this set of assumptions for expectedreturns, standard deviations, and correlation represent anequilibrium for the security market?
Problem 2. Consider the following properties ofthe returns of stock 1, the returns of stock 2 and the returns ofthe market portfolio (m):
Standard deviation of stock 1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ïƒ1 = 0.30
Standard deviation of stock 2Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ïƒ2 = 0.30
Correlation between stock 1 and the market portfolioÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ï1, m = 0.2
Correlation between stock 2 and the market portfolioÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ï2, m = 0.5
Standard deviation of the market portfolioÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Ïƒm = 0.2
Expected return of stock 1Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â E (r1) = 0.08
Suppose further that the risk-free rate is 5%.
a) According to the Capital Asset Pricing Model, what should bethe expected return on the market portfolio and the expected returnof stock 2?
b) Suppose that the correlation between the return of stock 1and the return of stock 2 is 0.5. What is the expected return, thebeta, and the standard deviation of the return of a portfolio thathas a 50% investment in stock 1 and a 50% investment in stock2?
c) Is the portfolio you constructed in part b) an efficientportfolio? Assuming the CAPM is true, could you build a combinationof the market portfolio and the portfolio of part b) to increasethe expected return of the market portfolio without changing thevariance of the combined portfolio.

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Problem 1a Gold might seem dominated by stocks but it is still anattractive asset to hold as a part of the portfolio if not aloneIf the correlation between gold and stocks is very low it can behold as a part in portfolio In the above graph it can be seen thatthe graph for the portfolio of stocks and gold touch the optimalallocation line at the optimal tangency portfolio Pb if the correlation between gold and stocks equal one thenhold should not be held the set of risk and return combination ofstock and gold would plot as a straight line with a See Answer

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