Given the following information:

State Probability Stock 1 Stock 2

Boom .25 5% 30%

Normal .40 7% 18%

Recession .35 11% -17%

a. Calculate the expected return and the standard deviation for Stock 1 and Stock 2 respectively. (6 pts)

b. What is the expected return for a portfolio with an investment of $7,000 in Stock 1 and $3,000 in Stock 2? [Hint: Calculate portfolio weights, W₁ and W₂ , first.] (2 pts)

c. Calculate the standard deviation for this portfolio using three methods: (12 pts)

Use Formulas (5) and (6).

Use Formula (7) and (10)

Use Formula (8) and (11). Formulas are listed below in the screenshot

Remember that you need to show the calculation procedures for all questions listed here.

For each state of economy (s =1,2,n), get E(Rp,s)=i=1mwiE(Ri,s) p=s=1n[ps(E(Rp,s)E(Rp)2] Covariance of two securities, 1 and 2: Cov(R1,R2)=s=1nps[E(R1,s)E(R1)][E(R2,s)E(R2)] Correlation coefficient of two securities, 1 and 2: Corr(R1,R2)=12=12Cov(R1,R2) Two-Risky-Assets Portfolio with two securities 1 and 2: E(RP)=w1E(R1)+w2E(R2)p=(w11)2+(w22)2+2w1w2Cov(R1,R2)p=(w11)2+(w22)2+2w1w212Corr(R1,R2)w1(min)=12+2221212221212w1(optimal)=[E(R1)rf]22+[E(R2)rf]12[E(R1)rf+E(R2)rf]1212[E(R1)rf]22[E(R2)rf]1212