You have been given two different investments: Stock X and Stock Y. The Economist for your firm has given you the following expected returns given three different states of the economy for the next year.

State of the Economy Prob. Stock X Stock Y .25 X and .75 Y

Recession 0.2 -10% -5% -6.25%

Average 0.5 12 25.0 21.75

Boom 0.3 35 10.0 16.25

Mean % 14.50% %

Variance 137.25___ ______

Standard Deviation % 12.46%_ %

Covariance ______

Correlation ______

The mean, variance and standard deviation of returns for stock Y are given; however, calculate the mean, variance and standard deviation of returns for stock X. For a portfolio of 25% stock X and 75% stock Y, calculate the mean, variance and standard deviation of returns for the portfolio. Also, calculate the covariance and correlation between stocks X and Y.

E(R_X ) = %

Var (R_X ) = __________

Std. Dev(R_X ) = %

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E(R_Y ) = .2 (-5) + .5 (25) + .3 (10) = 14.50%

Var (R_Y ) =(-5-14.5)².2 + (25-14.5)².5 + (10-14.5)².3 =137.25

=76.05 + 55.125 + 6.075 = 137.25

Std. Dev(R_Y ) = 11.72%

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E(R_P ) = %

Var (R_P ) = __________

Std. Dev(R_P ) = %

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Cov(R_X, R_Y) = (-10-______)(-5-14.5).2 + (12-______)(25-14.5).5 + (35-________)(10-14.5).3 = _____________

_XY = Cov (R_X,R_Y)/_{X Y} = 0._________

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Calculate the Portfolio (P) expected return, variance and standard deviation using equations:

E(P) = .25E(R_X ) + .75E(R_Y ) = %

Var(P) = (.25)²Var (R_X ) + (.75)²Var (R_Y ) +2(.25)(.75)Cov(R_X,R_Y)

= (.25)²________ + (.75)²_________ +2(.25)(.75)_______ = _________

And

Stn Dev(P) = %