Consider the following classic portfolio choice problem. Two assets are available to an investor

at time t$.$ One is riskless, with simple return Rf from time t to t$+1,$ and the other is risky. The

risky asset has simple return R from time t to t$+1.$ The investor puts a share w of his portfolio

into the risky asset. We assume that the investor trades off mean and variance in a linear fashion.

That is$,$ investor maximizes a linear combination of mean and variance, with a positive weight on

mean and a negative weight on variance:

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$2$

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a$)(7$ marks$)$ What is the proportion of wealth invested in risky asset?