State of Economy Probability Stock PFE Stock GE Boom 0.3 12% 5% Normal 0.4 8% 4%

ID: 2766680 • Letter: S

Question

State of Economy Probability Stock PFE

Stock GE

Boom 0.3 12%

Normal 0.4 8%

Recession 0.3 6% 3%

Calculate expected returns of both stocks.

Calculate standard deviation of both stocks.

If you hold both stocks with equal weights, what is the expected return of your portfolio?

What is the expected variance of the portfolio?

State of Economy Probability Stock PFE

Stock GE

Boom 0.3 12%

Normal 0.4 8%

Recession 0.3 6% 3%

Calculate expected returns of both stocks.

Calculate standard deviation of both stocks.

If you hold both stocks with equal weights, what is the expected return of your portfolio?

What is the expected variance of the portfolio?

Expected Return of Stock PFE = .3*12% + .4*8% + .3*6% = 3.6 + 3.2 + 1.8 = 8.60%

Expected Return of Stock GE = .3*5% + .4*4% + .3*3% = 1.5 + 1.6 + .9 = 4%

Standard Deviation of PFE = Square root of [(12-8.60)^2 + (8-8.60)^2 + (6-8.6)^2]/ 3

= Square root of [11.56 + .36 + 6.76]/ 3 = 2.495%

Standard Deviation of GE = Square root of [(5-4)^2 + (4-4)^2 + (3-4)^2]/ 3

= Square root of [1 + 0 + 1]/ 3 = .82%

Expected return of your portfolio = 8.60% * 1/2 + 4% * 1/2 = 6.30%

Variance of portfolio = (Standard Deviation of portfolio)^2

= (2.495 * 1/2 + .82 * 1/2)^2 = 2.78

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