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# 675 95 or 56 513 95 expected variance of portfolio

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Unformatted text preview: 2.5-9.5)2 + .6(7.5-9.5)2 = 6, Std. Dev. = 2.45% Variance Std. Portfolio variance using covariances: Portfolio COV(A,B) = .4(30-6)(-5-13) + .6(-10-6)(25-13) = -288 COV(A,B) Variance of portfolio = (.5)2(384) + (.5)2(216) + 2(.5)(.5)(-288) = 6 Variance Standard deviation = 2.45% Standard Another Example Another Consider the following information State Probability X Z Boom .25 15% 10% Normal .60 10% 9% Recession .15 5% 10% a portfolio with an investment of \$6,000 in asset X and \$4,000 in asset Z Portfolio return in Boom: .6(15) + .4(10) = 13%, in Normal: .6(10) + .4(9) = Portfolio 9.6%, in Recession: .6(5) + .4(10) = 7% 9.6%, Expected return = .25(13) + .6(9.6) + .15(7) = 10.06% Variance = .25(13-10.06)2 + .6(9.6-10.06)2 + .15(7-10.06)2 = 3.6924, Std. dev. = 1.92% 1.92% Using covariances: COV(X,Z) = .25(15-10.5)(10-9.4) + .6(10-10.5)(9-9.4) + .15(5-10.5)(10-9.4) = .3 Portfolio variance = (.6*3.12)2 + (.4*.49)2 + 2(.6)(.4)(.3) = 3.6868 Expected versus Unexpected Returns Returns Realized returns are generally not equal to Realized expected returns expected There is the expected component and the There unexpected component unexpected At any point in time, the unexpected return can be At either positive or negative either Over time, the average of the unexpected Over component is zero component Announcements and News Announcements Announcements and news contain both an Announcements expected component and a surprise component expected It is the surprise component that affects a stock’s It price and therefore its return price This is very obvious when we watch how stock This prices move when an unexpected announcement is made or earnings are different than anticipated than Efficient Markets Efficient Efficient markets are a result of investors Efficient trading on the unexpected...
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