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# maximising returns in a portfolio

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1. 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)Ythe asset returns are random, with E(X) = μX = 0.05, E(Y) = μy = 0.01, and 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.

Is this kind of a trick question, as my thinking is you would allocate 100% of the portfolio to asset X as it has the highest expected returns?
2. (Original post by mikegmike)
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)Ythe asset returns are random, with E(X) = μX = 0.05, E(Y) = μy = 0.01, and 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.

Is this kind of a trick question, as my thinking is you would allocate 100% of the portfolio to asset X as it has the highest expected returns?
Agreed.

A variation on the question here has more meat, and I suspect is the original question on which yours is based.

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