If two assets have zero covariance, can they still be used to diversify each other even if the CAPM holds?

Assume N securities. The expected returns on all the securities are equal to 0.01 and the variances of their returns are all equal to 0.01. The covariances of the returns between two securities are all equal to 0.005.

1.What are the expected return and the variance of the return on an equally weighted portfolio of all N securities?

2.What value will the variance approach as N gets large?

3.What characteristic of the securities is most important when determining the variance of a well-diversified portfolio?

This is a table about possible rates of return on Stock A and B:

The following data have been calculated:

SD(A) = 9.34%, SD(B) = 13.68%, Covariance between Stock A & B = 124.38%, Correlation between Stock A & B = 0.9735

(a) Would it be advisable to form a portfolio of both Stock A and B to diversify risk? Explain reasons in words.

(b) Short-selling either stock is allowed (ie. weights need not be all positive), find the minimun variance one can get by forming a portfolio of Stock A and B.

Assume N securities. The expected returns on all the securities are equal to 0.01 and the variances of their returns are all equal to 0.01. The covariances of the returns between two securities are all equal to 0.005.

i.What are the expected return and the variance of the return on an equally weighted portfolio of all N securities? Please, note that the variance is presented by the formula, which depends on N.

ii.What value will the variance approach as N gets large?

iii.From parts (i) and (ii): Can you conclude what characteristic of the securities is most important when determining the variance of a well-diversified portfolio?