There is one risk-free asset that pays a return of rF=0.005. There are 3 risky assets:...
There is one risk-free asset that pays a return of rF=0.005. There are 3 risky assets: A, B and C. The expected returns of the risky assets are: μA=0.01, μB=0.02, μC=0.03. The variances are: σ2A=0.00001, σ2B=0.0004, σ2C=0.0036. The covariances are: σAB=0.0002, σAC=0, σBC=-0.0002. Combining A,B and C, we create four risky portofolios, called 1,2,3 and 4. The shares of assets A, B and C in portfolio 1 are: w1A=0.6, w1B=0.2 and w1C=0.2. Similarly, the share in portfolio 2 are: w2A=0.2, w2B=0.4 and w2C=0.4. Porfolio 3 shares are: w3A=0.3, w3B=0.2 and w3C=0.5. Finally the shares in portfolio 4 are: w4A=0.2, w4B=0.6 and w4C=0.2.
Let the complete portfolio expected return be denoted by μ and its standard deviation by σ. If you have utility U=μ-500σ2 , what is the optimal share of risk-free asset, wF , in the complete portfolio?
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There is one risk-free asset that pays a return of
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