There are three securities, A, B and C, which have the following payoffs under different states of the world:

State	Probability	Security A	Security B	Security C
Boom	0.2	0.20	0.15	-0.04
Moderate Growth	0.3	0.12	0.10	0.05
Slow Growth	0.3	0.06	0.05	0.06
Recession	0.2	-0.05	-0.02	0.11

1 Calculate the expected return and variance of the three securities.

2 Calculate the covariance between the three securities. Show the correlation matrix.

3 Construct a portfolio using the three securities that has the proportions 40:40:20 in the three securities. What is the portfolios expected return and portfolio risk?

4 If a portfolio is made up of securities A and C where the amount in A is 1 000 000 and in C 800 000, what will be the value at risk for the portfolio at 1.96 standard deviations?