# Question

Consider an investor with $10,000 available to invest. He has the following options regarding the allocation of his available funds:

(1) He can invest in a risk-free savings account with a guaranteed 3% annual rate of return;

(2) He can invest in a fairly safe stock, where the possible annual rates of return are 6%, 8%, or 10%; or

(3) He can invest in a more risky stock, where the possible annual rates of return are 1%, 9%, or 17%. Note that the investor can place all of his available funds in any one of these options, or he can split his $10,000 into two $5000 investments in any two of these options. The joint probability distribution of the possible return rates for the two stocks is given in the file P06_41.xlsx.

a. Create a payoff table that specifies this investor’s return (in dollars) in one year for each possible decision and each outcome with respect to the two stock returns.

b. Use Precision Tree to identify the strategy that maximizes the investor’s expected earnings in one year from the given investment opportunities.

c. Perform a sensitivity analysis on the optimal decision, letting the amount available to invest and the risk-free return both vary, one at a time, plus or minus 100% from their base values, and summarize your findings.

(1) He can invest in a risk-free savings account with a guaranteed 3% annual rate of return;

(2) He can invest in a fairly safe stock, where the possible annual rates of return are 6%, 8%, or 10%; or

(3) He can invest in a more risky stock, where the possible annual rates of return are 1%, 9%, or 17%. Note that the investor can place all of his available funds in any one of these options, or he can split his $10,000 into two $5000 investments in any two of these options. The joint probability distribution of the possible return rates for the two stocks is given in the file P06_41.xlsx.

a. Create a payoff table that specifies this investor’s return (in dollars) in one year for each possible decision and each outcome with respect to the two stock returns.

b. Use Precision Tree to identify the strategy that maximizes the investor’s expected earnings in one year from the given investment opportunities.

c. Perform a sensitivity analysis on the optimal decision, letting the amount available to invest and the risk-free return both vary, one at a time, plus or minus 100% from their base values, and summarize your findings.

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