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 belowA) 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

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.

Step-by-step explanation:

Statement A is correct.

As it is provided both investments are completely independent and that the risk associated with these investments are also same as standard deviation is same.

Now if the investment is spread into a number of investments providing multiple returns, some negative and some positive will accumulate to provide the best return as the relationship between number of investments made and the risk associated is inversely proportional. That is with increase in number the risk will decrease in order to provide maximum return.