(p) An investor must choose what proportion of wealth to spend on each of two risky...

 

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(p) 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 proportion of wealth spent on X (so 1- w is spent on Y). So the return to the chosen portfolio is R=WX + (1-w)Y The asset returns are random, with E(X) = a, E(Y) = 0.01, and the vari- ances are V(X) = y and V(Y) = 0.004. The values a and y can be found using the final digit of your Student ID number and the following table Final digit 0 of ID 1 0.06 0.02 Y 0.001 0.002 α 9 2 3 4 5 6 7 8 0.03 0.04 0.05 0.04 0.03 0.06 0.02 0.06 0.003 0.005 0.006 0.005 0.003 0.002 0.001 0.002 For instance if your ID number is 20556897, the final digit is 7 and so from the table a = 0.06 and y = 0.002 i. Find the fraction of the portfolio to be invested in asset X if the investor wishes to maximise the expected return to the portfolio. Explain your answer. ii. Find the fraction of the portfolio to be invested in asset X if the investor wishes to minimise the variance of the return to the portfolio. Explain your answer. iii. If the investor minimises the portfolio variance, find the expected return for the portfolio. (p) 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 proportion of wealth spent on X (so 1- w is spent on Y). So the return to the chosen portfolio is R=WX + (1-w)Y The asset returns are random, with E(X) = a, E(Y) = 0.01, and the vari- ances are V(X) = y and V(Y) = 0.004. The values a and y can be found using the final digit of your Student ID number and the following table Final digit 0 of ID 1 0.06 0.02 Y 0.001 0.002 α 9 2 3 4 5 6 7 8 0.03 0.04 0.05 0.04 0.03 0.06 0.02 0.06 0.003 0.005 0.006 0.005 0.003 0.002 0.001 0.002 For instance if your ID number is 20556897, the final digit is 7 and so from the table a = 0.06 and y = 0.002 i. Find the fraction of the portfolio to be invested in asset X if the investor wishes to maximise the expected return to the portfolio. Explain your answer. ii. Find the fraction of the portfolio to be invested in asset X if the investor wishes to minimise the variance of the return to the portfolio. Explain your answer. iii. If the investor minimises the portfolio variance, find the expected return for the portfolio.

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