Assignment:
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?
Provide complete and step by step solution for the question and show calculations and use formulas.