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Estimating expected return and standard deviation

There are three securities in the market. The following chart shows their possible payoffs:

State Probability of Return on Return on Return on

Outcome Security1 security2 Security3

1 .15 .25 .25 .10

2 .35 .20 .15 .15

3 .35 .15 .20 .20

4 .15 .10 .10 .25

a) What are the expected return and standard deviation of each security?

b) What are the covariances and correlations between the pairs of securities?

c) What are the expected return and standard deviation of a portfolio with half of its funds invested in security 1 and half in security 2?

d) What are the expected return and standard deviation of a portfolio with half of its funds invested in security 1 and half in security 3?

e) What are the expected return and standard deviation of a portfolio with half of its funds invested in security 2 and half in security 3?

f) What do your answers in parts (a), (c), (d), (e) imply about diversification?

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