Question

There are two risky securities A and B that are perfect negatively correlated. The expected return and standard deviation of A and B are E(rA), E(rB), , . How much is the standard deviation of the minimum variance portfolio that includes these two securities?

Answer 1

Answer:

The expected return of two perfectly negatively correlated securities will be ZERO.

Suppose the return of one security is 10%

Then the return of the other will be -10%

If the weights are equal, i.e I invest 50% of my money in the first security and 50% in the second, the net return I will get is zero

Return = 0.5 * 0.10 + 0.5 * (-0.10)

Return = 0%

If two securities are perfectly negatively correlated , the standard deviation of the minimum variance portfolio of those two securities will be always ZERO.

The correlation coefficient will be -1.

The weights will be calcuated

And standard deviationw will be zero for the minmum variance portfolio.