k B State of Economy Probability 008 0.20 0.12 0.09 0.50 0.04 Work for Mean of S
ID: 2802049 • Letter: K
Question
k B State of Economy Probability 008 0.20 0.12 0.09 0.50 0.04 Work for Mean of Stock B (5 points) b. Suppose you know that the standard deviation of Stock A is 0 0319531, and the standard Compute the mean, variance, and standard deviation of a portfolio of these 2 slocks assuming you put 70% of your funds in A and 30% in B Cempue the state returns and then compute the portfolie mean, variance, and treating the portiolio as if it is a single stock). 10 points deviation for stock B is 0.0608276 and sandard deviation (hy Show work belowExplanation / Answer
Prob. Stock A Variance Stock B Variance Boom 0.20 13% 4.42 8% 0.20 Normal 0.50 9% 0.24 12% 12.50 Bust 0.30 4% 5.55 -2% 24.30 Expected Return 8.30% 10.21 7.00% 37.00 Sd 3.19531% 6.08276% Expected Return Stock A=.2*13%+.5*9%+.3*4% 70% 8.3% Stock B=.2*8%+.5*12%+.3*-2% 30% 7.0% Mean Return =.7*8.3%+.3*7% 7.91% Variance in the protfolio invested 70% in Stock A and 30% in Stock B State of economy Prob A B Boom 0.20 0.13 0.08 Normal 0.50 0.09 0.12 Bust 0.30 0.04 (0.02) Weight 0.7 0.3 Expected return from boom =.13*.7+.08*.3 0.1150 Expected return from Normal =.09*.7+.12*.3 0.0990 Expected return from bust =.04*.7-.02*.3 0.0220 So Expected return from both boom & bust Probability of boomX expected return from boom+ probabiltiy of bustXexpected return from bust =.2*.115+.5*.099+.3*.022 0.0791 Scenario Probability Deviation from Expected Value Squared Boom 0.20 .115-.0791 0.0359 0.1289% Normal 0.50 .099-.0791 0.02 0.0396% Bust 0.30 .022-.0791 -0.0571 0.3260% Variance then weights each squared deviation by its probability, giving us the following calculation: =(0.2)*(.1289%)+(0.5)*(0.0396%)+.3*(.3260%) 0.001434
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