You have ten million dollars to allocate across two projects, code named 'Wombat' and 'Marmot.' Both projects are somewhat scalable, in that you could potentially invest as much (up to your budget) or as little (bounded below by zero) as you wish. Both projects are risky, in the sense that you can estimate an internal rate of return for each, but depending on how things go; the returns could be higher or lower.

You have estimated that Project Wombat has an expected IRR of20%, but that the standard deviation of that IRR is 30%. Project Marmot has an expected IRR of 10%,with a standard deviation of 12%.

a. Compute the expected return of taking:

(i) 1/4 Wombat and 3/4 Marmot.

(ii) 1/2 Wombat and 1/2 Marmot.

(iii) 3/4Wombat and 1/4 Marmot.

b. If you go half and half, what is the standard deviation of returns of the combination, assuming that the returns on the projects are uncorrelated?

c. If you can choose any pair of weights (bounded by 0% and 100%), exactly what weights maximize the expected return of the combination?

Express the weights as percentages of the total budget.

d. If you can choose any pair of weights (bounded by 0% and 100%), exactly what weights minimize the standard deviation of the combination, and how low can the standard deviation go (to two decimal places, e. g., 3.45%)?

Express the weights as percentages of the total budget.

e. Assume that you want the optimal expected return to risk trade off (i.e., the maximum Sharpe ratio). What weights do you put in each project if the risk free rate is 2%?

Express the weights as percentages of the total budget.