Question

Determine whether the following statements are true or false and in either case briefly explain why.

Answers must be three sentences or less. Answers longer than three sentences will receive an automatic zero.

1. (b) Assume that a risk-free asset as well as two risky securities exist in the economy. If the risky securities are perfectly positively correlated with each other, diversifying among the two will not make a greedy risk-averse investor better off. Hint: it may be worth drawing a diagram to clarify your point.

Answer 1

The statement is True.

Diversification benefits arises, when assets are added in the portfolio and they are not perfectly correlated with each, infact the assets have a negative correlation with each other. The risk of a portfolio consisting of two risky assets is measured by:

standard deviation of portfolio = root over of [ (W1)^VARIANCE OF ASSET A + (W2)^2*VARIANCE OF ASSET B + 2*WA*WB *COVARIANCE OF A AND B.

covariance = correlation between A and B *standard deviation of A *standard deviation of B.

The lower, the correlation between the assets, the lower is the risk of the portfolio. Add an asset, which is not perfectly positively but perfectly negatively correlated and this will solve the problem of the greedy risk averse investor.