Fill in the missing information in the following table. Assume that Portfolio AB
ID: 2751137 • Letter: F
Question
Fill in the missing information in the following table. Assume that Portfolio AB is 40 percent invested in Stock A. (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)
Annual Returns on Stocks A and B Year Stock A Stock B Portfolio AB 2009 13 % 23 % % 2010 36.2 % –36.8 % % 2011 –19.4 % 46.8 % % 2012 25.6 % 16.4 % % 2013 13.8 % 25.2 % % Average return % % % Standard deviation % % %Explanation / Answer
Actual reurns Year Stock A Stock B Portfolio AB (rA-Avg A)^2 (rb-AvgB)^2 (rAB-AvgAB)^2 (rA-AvgA)*(rb-AvgB) 2009 13% 23% 19.00% 0.00007056 0.0065286 0.002035814 -0.000679 2010 36.20% -36.80% -7.60% 0.04999696 0.2674958 0.048787974 -0.115646 2011 -19.40% 46.80% 20.32% 0.11048976 0.1016334 0.003401222 -0.105969 2012 25.60% 16.40% 20.08% 0.01382976 0.000219 0.003127046 0.001740 2013 13.80% 25.20% 20.64% 0.00000016 0.0105678 0.00378471 -0.000041 Average Return 13.84% 14.92% 14.49% Standard Deviation 18.68% 27.80% 11.06% Weight of stock A in portfolio AB 40% Weight of stock B in portfolio AB= 100-40% = 60% Return on Portfolio AB = Weight of stock A * return on Stock A + Weight of Stock B * return on Stock B Portfolio AB return in 2009 = 0.4 * 13% + 0.6 * 23% = 19.00% Portfolio AB return in 2010 = 0.4 * 36.2% + 0.6 * -36.80% = -7.60% Portfolio AB return in 2011 = 0.4 * -19.4% + 0.6 * 46.80% = 20.32% Portfolio AB return in 2012 = 0.4 * 25.60% + 0.6*16.40% = 20.08% Portfolio AB return in 2013 = 0.4 * 13.80% + 0.6*25.20% = 20.64% Average return of Stock A = (13%+36.2%-19.4%+25.6%+13.8%)/5 = 0.1384 or 13.84% AvgA Average return of Stock B = (23% -36.8%+46.8%+16.4%+25.2%)/5 = 0.1492 or 14.92% AvgB Average return of Portfolio AB = (19%-7.6%+20.32%+20.08%+20.64%)/5 = 0.14488 or 14.49% Avg AB Variance of returns = [Sum of [(return-Average return)^2] / Number of years Variance of Stock A = [(0.13-0.1384)^2 + (0.362-0.1384)^2 + (-0.194-0.1384)^2+(0.256-0.1384)^2+(0.1380-0.1384)^2]/5 = (0.00007056+0.049999696+0.11048976+0.01382976+0.00000016)/5 = 0.1743872 /5 = 0.034877 Standard Deviation of Stock A = (Square root of variance) = (0.03488)^(1/2) = 0.186755027 or 18.68% Variance of stock B = [(0.23-0.1492)^2+(-0.368-0.1492)^2 + (0.468-0.1492)^2 + (0.164-0.1492)^2+(0.252-0.1492)^2]/5 = (0.006529+0.267496+0.101633+0.000219+0.010568)/5 = 0.38644/5 = 0.077289 Standard Deviation of Stock B = Square root of Variance = (0.077288)^(1/2) = 0.278008921 or 27.80% Variance of Portfolio AB = [(0.19-0.1449)^2+(-0.076-0.1449)^2+(0.2032-0.1449)^2+(0.2008-0.1449)^2+(0.2064-0.1449)^2]/5 = (0.00204+0.04879+0.0034+0.00313+0.00378)/5 = 0.061136768/5 0.012227354 Standard Deviation of Portfolio AB = Square root of Variance = (0.012227354)^(1/2) = 0.110577365 or 11.06% Another way of Calculating Portfolio Standard deviation is Portfolio Variance = wA^2*Variance A + wB^2*Variance B + 2*wA*wB*Cov (A,B) Covariance of A,B can be calcualted as Covariance (A,B) = [Sum (rA-AvgA) * (rB - AvgB)] / 5 = [(0.13-0.1384)*(0.23-0.1492)+(0.362-0.1384)*(-0.368-0.1492)+(-0.194-0.1384)*(0.468-0.1492)+(0.256-0.1384)*(0.164-0.1492)+(0.138-0.1384)*(0.252-0.1492) = (-0.000679-0.0115646-0.105969+0.001740-0.000041)/5 = -0.220594/5 -0.044119 Variance of Portfolio = 0.4^2*0.03488+0.6^*0.07729 + 2 *0.4*0.6*-0.044119 = 0.16* 0.03488 + 0.36*0.07729 -0.02117712 = 0.0055808 + 0.0278244 - 0.02117712 = 0.01222808 Standard Deviation of Portfolio = Square root of variance = 0.01222808^(1/2) = 0.110580649 or 11.06% Which is the same as result for Portfolio given above
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