11. If you want to have a return for your Final Portfolio (that is invested between Optimal Risky portfolio and Risk Free Security) of 1.10%, what would be your allocation between Optimal 2-stock risky portfolio and risk free security

Answer is explained in the explanation section.

Explanation:

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Solution:

SD = Standard Deviation

Using utility function, E(R) = Rp - 0.005 x A x = 1.34 - 0.005 x 3x

Using utility function, E(R) = 1.093%

If the weight in the risky portfolio is let's say, "a" then,

weight in the risk-free asset = 1 - a

So,

E(R) = a x Rp + (1 - a) x Rf

1.093% = a x 1.34% + (1 - a) x 0.50%

Solving for "a"

a = 70.56% - weight in risky portfolio

and 1 - a = 29.44% - weight in risk-free asset.

Similarly, if you want a return of 1.10%,

we can follow the above steps and get

1.1% = a x 1.34% + (1 - a) x 0.5%

Weight in risky portfolio,

a = 71.43%

weight in risk-free asset,

1 - a = 28.57%

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