You are asked to examine two broad areas of investment opportunities: precious metals and crude oil....

 

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You are asked to examine two broad areas of investment opportunities: precious metals and crude oil. After a few days of data mining, you come up with an estimate of returns on one precious metals and one crude oil price indices. This estimate is summarized by the following expected (net) returns, E(R)=1, E(R)=.15 where k = 1 is the precious metals, while k = 2 is the crude oil index. Also, variances and covariances between these two indices are Var(R)=.01, Var(R)=.04, Cov(R. R) = Cov(R, R) = .01 An overall index portfolio (the "market" portfolio) is formed of 50% metals and 50% crude oil. i) Compute expected return expected return and variance for the index portfolio. [Hint: Var(a R+aR)=aVar(R)+aVar(R)+2a,a,Cov(R. R) where a, a, are real numbers.] ii) Assume that the CAPM holds true. Compute the proportion of wealth to be invested in precious metals and crude oil that gives you a zero beta portfolio. [Hint: the following formulas about the covariance from statistics are useful: Cov(R,R)=Var(R) and Cov(aR, R)=aCov(RR) = Cov(R,,aR,) for any real number a and any asset k = 1,2; Cov(aR +R, R) = Cov(aR, R) + Cov(aR. R).] iii) If there is a risk-free asset, what rate of return should this asset yield? Explain. iv) Graph the security market line for this 2-index market. You are asked to examine two broad areas of investment opportunities: precious metals and crude oil. After a few days of data mining, you come up with an estimate of returns on one precious metals and one crude oil price indices. This estimate is summarized by the following expected (net) returns, E(R)=1, E(R)=.15 where k = 1 is the precious metals, while k = 2 is the crude oil index. Also, variances and covariances between these two indices are Var(R)=.01, Var(R)=.04, Cov(R. R) = Cov(R, R) = .01 An overall index portfolio (the "market" portfolio) is formed of 50% metals and 50% crude oil. i) Compute expected return expected return and variance for the index portfolio. [Hint: Var(a R+aR)=aVar(R)+aVar(R)+2a,a,Cov(R. R) where a, a, are real numbers.] ii) Assume that the CAPM holds true. Compute the proportion of wealth to be invested in precious metals and crude oil that gives you a zero beta portfolio. [Hint: the following formulas about the covariance from statistics are useful: Cov(R,R)=Var(R) and Cov(aR, R)=aCov(RR) = Cov(R,,aR,) for any real number a and any asset k = 1,2; Cov(aR +R, R) = Cov(aR, R) + Cov(aR. R).] iii) If there is a risk-free asset, what rate of return should this asset yield? Explain. iv) Graph the security market line for this 2-index market.