The following is a probability distribution for returns on two securities A and M:

State Probability R_A R_M

1 10% 15% 12%

2 40% 8% 6%

3 40% 4% 1%

4 10% -6% -2%

1. Calculate the expected returns on securities A and M.

2. Calculate the variances and the standard deviations of securities A and M.

3. Calculate the coefficient of variation (CV) for securities A and M. Does A initially seem to be more or less attractive than M? Why? What other consideration might affect your answer and how?

4. i) What is the probability that the actualized return on security A will be equal or less than zero in the coming investment period?

ii) What is the probability of actually losing 5% or more on security M in the coming investment period?

5. Calculate the covariance between A and M.

6. Calculate the correlation coefficient between securities A and M. Verify that the covariance given in part (e) above is equal to the product of the standard deviation of A, standard deviation of M and the correlation coefficient between A and M.