Consider two possible investments whose payoffs are completely independent of on

Question

Consider two possible investments whose payoffs are completely independent of one another. Both investments have the same expected value and standard deviation. If you have $1,000 to invest, could you benefit from dividing your funds between these investments? Explain your answer.

a) Yes. By dividing your funds, you are adding combinations of possible payoffs that lie between the worst- and best-case scenarios and so the probability-weighted spread of the possible payoffs is smaller. The variance of the payoffs is halved.

b) Yes. Because one investment will always pay off when the other doesn't, your risk is reduced.

c) No. Because the payoffs from these investments are independent and not negatively correlated, there is no benefit.

d) No. Usually diversification helps to spread risk, but in this case, because the investments have the same expected value and standard deviation there is no benefit.

Explanation / Answer

a) Yes. By dividing your funds, you are adding combinations of possible payoffs that lie between the worst- and best-case scenarios and so the probability-weighted spread of the possible payoffs is smaller. The variance of the payoffs is halved.

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