# Expected return and standard deviation of securities

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

Probability Return on Return on Return on

States of Outcome Security 1 (%) Security 2 (%) Security 3 (%)

1 0.1 0.25 0.25 0.10

2 0.4 0.20 0.15 0.15

3 0.4 0.15 0.20 0.20

4 0.1 0.10 0.10 0.25

a. what is the expected return and standard deviation of each security?

b. what are the covariances and correlations between the pairs of securities?

c. what is 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 is 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 is 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, and e imply about diversification?

https://brainmass.com/math/probability/120810

#### Solution Summary

The solution calculates the expected return and standard deviation of securities, covariances and correlations between the pairs of securities and the expected return and standard deviation of portfolios with different combinations of securities given the probability distribution of return on securities.