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O945_1 x
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Problem 1: Estimating the Single Index Model [18 points]
On Blackboard, please find the data file data_PS.xlsx. In this tab you will find four worksheets, each containing historical monthly returns for individual stocks (XOM, AAPL, UTX, and TXN).
A. [12 points] Compute the excess returns for each stock and for the market. Use these excess returns to estimate the market model for each of the 4 stocks. Present the alpha, beta, and residual variance for each of the 4 stocks.
B. [6 points] Using the estimates from Part A, determine the alpha, beta, and residual variances of the following portfolios:
a. 20% XOM, 30% AAPL, 20% TXN, 30% UTX
b. 30% XOM, 20% AAPL, 25% TXN, 25% UTX
Problem 2: Consider the following three stocks and the provided information. Use this information to answer the following questions. [19 points]
Stock: alpha beta Residual
Variance
BIGA 1.50% 1.5 6.344%
NEGA 0.02% 1.2 3.312%
HIVOL 0.35% 1.8 12.222%
Market Excess Return 5.00%
Risk-free rate 1.00%
A. [3 points] Calculate the information ratio for each of the three stocks
B. [4 points] Assume the total return variance for the stock BIGA is 0.1141, or 11.41%. Using the given information, what is the market return variance?
C. [4 points] Determine the composition of the optimal active portfolio.
D. [4 points] Determine the composition of the optimal portfolio (i.e. the optimal allocation to the index portfolio and the portfolio from Part C.
E. [4 points] Compare the Sharpe ratio of the index to that of the portfolio in Part D.
O945_2.xlsx
XOM
date TICKER Stock Return Market Return Risk Free Return
20080131 XOM -7.78% -6.12% 0.21%
20080229 XOM 1.11% -3.48% 0.13%
20080331 XOM -2.79% -0.60% 0.17%
20080430 XOM 10.04% 4.75% 0.18%
20080530 XOM -4.20% 1.07% 0.18%
20080630 XOM -0.71% -8.60% 0.17%
20080731 XOM -8.74% -0.99% 0.15%
20080829 XOM -0.02% 1.22% 0.13%
20080930 XOM -2.94% -9.08% 0.15%
20081031 XOM -4.56% -16.94% 0.08%
20081128 XOM 8.68% -7.48% 0.03%
20081231 XOM -0.40% 0.78% 0.09%
20090130 XOM -4.20% -8.57% 0.00%
20090227 XOM -10.70% -10.99% 0.01%
20090331 XOM 0.29% 8.54% 0.02%
20090430 XOM -2.10% 9.39% 0.01%
20090529 XOM 4.65% 5.31% 0.00%
20090630 XOM 0.81% 0.02% 0.01%
20090731 XOM 0.69% 7.41% 0.01%
20090831 XOM -1.16% 3.36% 0.01%
20090930 XOM -0.78% 3.57% 0.01%
20091030 XOM 4.46% -1.98% 0.00%
20091130 XOM 5.33% 5.74% 0.00%
20091231 XOM -9.16% 1.78% 0.01%
20100129 XOM -5.51% -3.70% 0.00%
20100226 XOM 1.54% 2.85% 0.00%
20100331 XOM 3.05% 5.88% 0.01%
20100430 XOM 1.18% 1.48% 0.00%
20100528 XOM -10.14% -8.20% 0.01%
20100630 XOM -5.61% -5.39% 0.01%
20100730 XOM 4.57% 6.88% 0.01%
20100831 XOM -0.22% -4.74% 0.01%
20100930 XOM 4.53% 8.76% 0.01%
20101029 XOM 7.61% 3.69% 0.01%
20101130 XOM 5.28% -0.23% 0.01%
20101231 XOM 5.12% 6.53% 0.01%
20110131 XOM 10.34% 2.26% 0.01%
20110228 XOM 6.56% 3.20% 0.01%
20110331 XOM -1.64% -0.10% 0.01%
20110429 XOM 4.58% 2.85% 0.00%
20110531 XOM -4.59% -1.35% 0.00%
20110630 XOM -2.50% -1.83% 0.00%
20110729 XOM -1.95% -2.15% 0.00%
20110831 XOM -6.64% -5.68% 0.01%
20110930 XOM -1.88% -7.18% 0.00%
20111031 XOM 7.52% 10.77% 0.00%
20111130 XOM 3.61% -0.51% 0.00%
20111230 XOM 5.37% 0.85% 0.00%
20120131 XOM -1.20% 4.36% 0.00%
20120229 XOM 3.86% 4.06% 0.00%
20120330 XOM 0.27% 3.13% 0.00%
20120430 XOM -0.45% -0.75% 0.00%
20120531 XOM -8.27% -6.27% 0.01%
20120629 XOM 8.83% 3.96% 0.00%
20120731 XOM 1.50% 1.26% 0.00%
20120831 XOM 1.17% 1.98% 0.01%
20120928 XOM 4.75% 2.42% 0.01%
20121031 XOM -0.31% -1.98% 0.01%
20121130 XOM -2.70% 0.28% 0.01%
20121231 XOM -1.80% 0.71% 0.01%
AAPL
date TICKER Stock Return Market Return Risk Free Return
20080131 AAPL -31.66% -6.12% 0.21%
20080229 AAPL -7.64% -3.48% 0.13%
20080331 AAPL 14.78% -0.60% 0.17%
20080430 AAPL 21.22% 4.75% 0.18%
20080530 AAPL 8.51% 1.07% 0.18%
20080630 AAPL -11.29% -8.60% 0.17%
20080731 AAPL -5.07% -0.99% 0.15%
20080829 AAPL 6.66% 1.22% 0.13%
20080930 AAPL -32.96% -9.08% 0.15%
20081031 AAPL -5.34% -16.94% 0.08%
20081128 AAPL -13.87% -7.48% 0.03%
20081231 AAPL -7.90% 0.78% 0.09%
20090130 AAPL 5.60% -8.57% 0.00%
20090227 AAPL -0.91% -10.99% 0.01%
20090331 AAPL 17.70% 8.54% 0.02%
20090430 AAPL 19.70% 9.39% 0.01%
20090529 AAPL 7.93% 5.31% 0.00%
20090630 AAPL 4.87% 0.02% 0.01%
20090731 AAPL 14.72% 7.41% 0.01%
20090831 AAPL 2.95% 3.36% 0.01%
20090930 AAPL 10.19% 3.57% 0.01%
20091030 AAPL 1.70% -1.98% 0.00%
20091130 AAPL 6.05% 5.74% 0.00%
20091231 AAPL 5.41% 1.78% 0.01%
20100129 AAPL -8.86% -3.70% 0.00%
20100226 AAPL 6.54% 2.85% 0.00%
20100331 AAPL 14.85% 5.88% 0.01%
20100430 AAPL 11.10% 1.48% 0.00%
20100528 AAPL -1.61% -8.20% 0.01%
20100630 AAPL -2.08% -5.39% 0.01%
20100730 AAPL 2.27% 6.88% 0.01%
20100831 AAPL -5.50% -4.74% 0.01%
20100930 AAPL 16.72% 8.76% 0.01%
20101029 AAPL 6.07% 3.69% 0.01%
20101130 AAPL 3.38% -0.23% 0.01%
20101231 AAPL 3.67% 6.53% 0.01%
20110131 AAPL 5.20% 2.26% 0.01%
20110228 AAPL 4.09% 3.20% 0.01%
20110331 AAPL -1.33% -0.10% 0.01%
20110429 AAPL 0.47% 2.85% 0.00%
20110531 AAPL -0.66% -1.35% 0.00%
20110630 AAPL -3.50% -1.83% 0.00%
20110729 AAPL 16.33% -2.15% 0.00%
20110831 AAPL -1.45% -5.68% 0.01%
20110930 AAPL -0.91% -7.18% 0.00%
20111031 AAPL 6.15% 10.77% 0.00%
20111130 AAPL -5.58% -0.51% 0.00%
20111230 AAPL 5.97% 0.85% 0.00%
20120131 AAPL 12.71% 4.36% 0.00%
20120229 AAPL 18.83% 4.06% 0.00%
20120330 AAPL 10.53% 3.13% 0.00%
20120430 AAPL -2.60% -0.75% 0.00%
20120531 AAPL -1.07% -6.27% 0.01%
20120629 AAPL 1.09% 3.96% 0.00%
20120731 AAPL 4.58% 1.26% 0.00%
20120831 AAPL 9.35% 1.98% 0.01%
20120928 AAPL 0.28% 2.42% 0.01%
20121031 AAPL -10.76% -1.98% 0.01%
20121130 AAPL -1.24% 0.28% 0.01%
20121231 AAPL -9.07% 0.71% 0.01%
TXN
date TICKER Stock Return Market Return Risk Free Return
20080131 TXN -7.04% -6.12% 0.21%
20080229 TXN -3.20% -3.48% 0.13%
20080331 TXN -5.64% -0.60% 0.17%
20080430 TXN 3.50% 4.75% 0.18%
20080530 TXN 11.39% 1.07% 0.18%
20080630 TXN -13.30% -8.60% 0.17%
20080731 TXN -13.07% -0.99% 0.15%
20080829 TXN 0.53% 1.22% 0.13%
20080930 TXN -12.28% -9.08% 0.15%
20081031 TXN -8.51% -16.94% 0.08%
20081128 TXN -20.40% -7.48% 0.03%
20081231 TXN -0.32% 0.78% 0.09%
20090130 TXN -2.96% -8.57% 0.00%
20090227 TXN -4.01% -10.99% 0.01%
20090331 TXN 15.05% 8.54% 0.02%
20090430 TXN 10.05% 9.39% 0.01%
20090529 TXN 7.42% 5.31% 0.00%
20090630 TXN 9.79% 0.02% 0.01%
20090731 TXN 13.43% 7.41% 0.01%
20090831 TXN 2.25% 3.36% 0.01%
20090930 TXN -3.66% 3.57% 0.01%
20091030 TXN -0.51% -1.98% 0.00%
20091130 TXN 7.85% 5.74% 0.00%
20091231 TXN 3.04% 1.78% 0.01%
20100129 TXN -13.20% -3.70% 0.00%
20100226 TXN 8.36% 2.85% 0.00%
20100331 TXN 0.37% 5.88% 0.01%
20100430 TXN 6.78% 1.48% 0.00%
20100528 TXN -6.11% -8.20% 0.01%
20100630 TXN -4.67% -5.39% 0.01%
20100730 TXN 6.57% 6.88% 0.01%
20100831 TXN -6.76% -4.74% 0.01%
20100930 TXN 17.90% 8.76% 0.01%
20101029 TXN 9.43% 3.69% 0.01%
20101130 TXN 7.54% -0.23% 0.01%
20101231 TXN 2.20% 6.53% 0.01%
20110131 TXN 4.74% 2.26% 0.01%
20110228 TXN 5.01% 3.20% 0.01%
20110331 TXN -2.95% -0.10% 0.01%
20110429 TXN 3.18% 2.85% 0.00%
20110531 TXN -0.65% -1.35% 0.00%
20110630 TXN -7.00% -1.83% 0.00%
20110729 TXN -8.99% -2.15% 0.00%
20110831 TXN -11.90% -5.68% 0.01%
20110930 TXN 1.68% -7.18% 0.00%
20111031 TXN 15.95% 10.77% 0.00%
20111130 TXN -2.05% -0.51% 0.00%
20111230 TXN -3.29% 0.85% 0.00%
20120131 TXN 11.82% 4.36% 0.00%
20120229 TXN 3.00% 4.06% 0.00%
20120330 TXN 0.78% 3.13% 0.00%
20120430 TXN -4.46% -0.75% 0.00%
20120531 TXN -10.83% -6.27% 0.01%
20120629 TXN 0.74% 3.96% 0.00%
20120731 TXN -4.46% 1.26% 0.00%
20120831 TXN 6.61% 1.98% 0.01%
20120928 TXN -5.11% 2.42% 0.01%
20121031 TXN 2.70% -1.98% 0.01%
20121130 TXN 4.91% 0.28% 0.01%
20121231 TXN 4.82% 0.71% 0.01%
UTX
date TICKER Stock Return Market Return Risk Free Return
20080131 UTX -4.27% -6.12% 0.21%
20080229 UTX -3.33% -3.48% 0.13%
20080331 UTX -2.40% -0.60% 0.17%
20080430 UTX 5.30% 4.75% 0.18%
20080530 UTX -1.53% 1.07% 0.18%
20080630 UTX -13.15% -8.60% 0.17%
20080731 UTX 3.70% -0.99% 0.15%
20080829 UTX 3.02% 1.22% 0.13%
20080930 UTX -8.43% -9.08% 0.15%
20081031 UTX -8.49% -16.94% 0.08%
20081128 UTX -11.00% -7.48% 0.03%
20081231 UTX 10.45% 0.78% 0.09%
20090130 UTX -10.47% -8.57% 0.00%
20090227 UTX -14.12% -10.99% 0.01%
20090331 UTX 5.27% 8.54% 0.02%
20090430 UTX 13.63% 9.39% 0.01%
20090529 UTX 8.51% 5.31% 0.00%
20090630 UTX -1.24% 0.02% 0.01%
20090731 UTX 4.83% 7.41% 0.01%
20090831 UTX 9.68% 3.36% 0.01%
20090930 UTX 2.64% 3.57% 0.01%
20091030 UTX 0.85% -1.98% 0.00%
20091130 UTX 10.05% 5.74% 0.00%
20091231 UTX 3.23% 1.78% 0.01%
20100129 UTX -2.78% -3.70% 0.00%
20100226 UTX 2.36% 2.85% 0.00%
20100331 UTX 7.23% 5.88% 0.01%
20100430 UTX 1.82% 1.48% 0.00%
20100528 UTX -9.53% -8.20% 0.01%
20100630 UTX -3.67% -5.39% 0.01%
20100730 UTX 9.54% 6.88% 0.01%
20100831 UTX -7.69% -4.74% 0.01%
20100930 UTX 9.23% 8.76% 0.01%
20101029 UTX 4.97% 3.69% 0.01%
20101130 UTX 1.24% -0.23% 0.01%
20101231 UTX 4.58% 6.53% 0.01%
20110131 UTX 3.28% 2.26% 0.01%
20110228 UTX 3.28% 3.20% 0.01%
20110331 UTX 1.33% -0.10% 0.01%
20110429 UTX 5.82% 2.85% 0.00%
20110531 UTX -1.48% -1.35% 0.00%
20110630 UTX 0.84% -1.83% 0.00%
20110729 UTX -6.41% -2.15% 0.00%
20110831 UTX -9.79% -5.68% 0.01%
20110930 UTX -5.24% -7.18% 0.00%
20111031 UTX 10.83% 10.77% 0.00%
20111130 UTX -1.15% -0.51% 0.00%
20111230 UTX -4.58% 0.85% 0.00%
20120131 UTX 7.20% 4.36% 0.00%
20120229 UTX 7.66% 4.06% 0.00%
20120330 UTX -1.11% 3.13% 0.00%
20120430 UTX -1.57% -0.75% 0.00%
20120531 UTX -8.64% -6.27% 0.01%
20120629 UTX 1.92% 3.96% 0.00%
20120731 UTX -1.44% 1.26% 0.00%
20120831 UTX 7.99% 1.98% 0.01%
20120928 UTX -1.95% 2.42% 0.01%
20121031 UTX -0.17% -1.98% 0.01%
20121130 UTX 3.18% 0.28% 0.01%
20121231 UTX 2.37% 0.71% 0.01%
