maximising returns in a portfolio, with E(X) = μX = 0.05, E(Y) = μy = 0.01

[stm93]

3. An investor must choose what proportion of wealth to spend on each of two risky assets.
Let the return to these two assets be X and Y respectively, and let w be the proportionof wealth spent on X (so 1 − w is spent on Y).
So the return to the chosen portfolio isR = wX + (1 − w)Y
The asset returns are random, with E(X) = μX = 0.05, E(Y) = μy = 0.01,
The variancesare σ2X= 0.002 and σ2Y= 0.004

(a) [30%] Find the fraction of the portfolio to be invested in asset X if the investor wishesto maximise the expected return to the portfolio. Explain your answer.

Can someone please explain how to answer this question?

Many thanks

 

[Deleted member 4993]

3. An investor must choose what proportion of wealth to spend on each of two risky assets.
Let the return to these two assets be X and Y respectively, and let w be the proportionof wealth spent on X (so 1 − w is spent on Y).
So the return to the chosen portfolio isR = wX + (1 − w)Y
The asset returns are random, with E(X) = μX = 0.05, E(Y) = μy = 0.01,
The variancesare σ2X= 0.002 and σ2Y= 0.004

(a) [30%] Find the fraction of the portfolio to be invested in asset X if the investor wishesto maximise the expected return to the portfolio. Explain your answer.

Can someone please explain how to answer this question?

Many thanks

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