Assume that an individual can either invest all of his resources in one of the two securities, A or B; or, alternatively, he can diversify his investment between the two. The distributions of the returns are as follows: Security A Security B

Return Probability Return Probability

-10 1/2 -20 1/2

50 1/2 60 1/2

Assume that the correlation between the returns from the two securities is zero, and answer the following questions:

1) Calculate each security's expected return, variance and standard deviation.

2) Calculate the probability distribution of the returns on a mixed portfolio comprised of equal proportions of securities A and B, i. e. calculate all possible returns on this portfolio and the probability of each one.[1]

3) Also calculate the portfolio's expected return, variance and standard deviation.

4) Calculate the expected return and the variance of a mixed portfolio comprised of 75% of security A and 25% of security B.

Please show formulas

[1] In the case of the two independently distributed returns the joint probability that the return on A is x% and the return on B is y% at the same time is the product of marginal probabilities. That is .