Risk Problem Set

1.You are given the following probabilities of payouts for three securities (A, B and C).For each security, calculate the expected payout and the standard deviation. Draw the histograms for the distributions of the payouts.

Probabilities

Payout	A	B	C
0	0.2	0.1	0.3
1	0.2	0.2	0.2
2	0.2	0.4	0.0
3	0.2	0.2	0.2
4	0.2	0.1	0.3

2. Plot the securities listed below on a riskreturn diagram. Which securities can we be sure that people would not want to hold if given the choice of picking one?

Security	Expected Return	Standard Deviation
A	3.1	3.1
B	2.5	2.7
C	1.7	1.4
D	4.2	5.5
E	2.6	1.3
F	3.7	2.9

3. There are two equallyprobable states of the world; call them good and bad. There are two securities: A and B.

State of the world	Return to A	Return to B
Good	6	4
Bad	4	8

Calculate the expected returns and standard deviations of three portfolios: one consisting of security A, one consisting of security B, and one consisting of security A plus security B. Compare the desirability of the portfolios. Calculate the covariance and correlation coefficient between A and B.