Consider three securities with the following payoffs for different states of the economy:

Economic State Probability R1 R2 R3

Recession 0.4 30% 30% 10%

Normal 0.4 10% 30% 15%

Expansion 0.1 10% 50% 25%

Boom 0.1 0% 120% 45%

(a) What is the expected return and standard deviation on each security?

(b) What is Cov(R1, R2), Cov(R1, R3), and Cov(R2, R3)? What is Corr(R1, R2),Corr(R1, R3), and Corr(R2, R3)?

(c) What is the expected return, p, and standard deviation, p, of a portfolio which has its funds invested equally in (i) securities #1 and #2, or (ii) securities #1 and #3,or (iii) securities #2 and #3?

(d) What is p and p, of a portfolio which has its funds invested equally in securities#1 to #3?

(e) What is the correlation of the return of the portfolio in part (d) with the return of an equally weighted portfolio of securities #1 and #2?