Question

Consider two possible investments whose payoffs are completely independent of one another. Both investments have the same expected value and standard deviation. You have $1,000 to invest between the two investments. Now suppose that 10 independent investments are available rather than just two. Would it matter if you spread your $1,000 across these 10 investments rather than two? Select the correct response below

A) Yes. The gains from spreading your investments would be larger if you spread the $1,000 across 10 investments. The risk, as measured by the variance of the payoffs, is inversely related to the number of independent investments.

B) Yes. Because the payoffs from these investments are negatively correlated with one another, spreading your $1,000 across a larger number of investments reduces your risk.

C) No. Because in this case diversification does not help to spread risk, so it doesn't matter how many investments you spread your $1,000 across.

D) No. Because the payoffs from these investments are independent, it doesn't matter how many investments you spread your $1,000 across, as there is no benefit in terms of reduced risk.

Answer 1

Answer:  (A) Yes. The gains from spreading your investments would be larger if you spread the $1,000 across 10 investments. The risk, as measured by the variance of the payoffs, is inversely related to the number of independent investments.

Explanation: Irrespective of the fact that all the investment has same expected value and standard deviation ,their overall value benefits goes increases. Since with all the independent investment we made different possible combination of worst and best case scenario to payoff from the investment. It results in short down the variation between payoffs and leads to higher gains. That is the reason risk of variation associated with the investment is inversely related to the number of investment which are independent.