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Sub: Finance Topic: Cost of Capital
Question:
Tangency Portfolio
Tangency Portfolio Problem. From finance.yahoo.com collect 10 years of monthly returns for four
stocks. Sample of 10 years of monthly data should be a pretty reasonable estimate of expected
returns, variances, and covariances.
Using this data, compute the tangency portfolio. You have to report
i. Weights of the individual stocks in the tangency portfolio;
ii. Expected returns and volatilities of the individual stocks;
iii. Variance-covariance matrix;
iv. Expected return and volatility of the tangency portfolio;
v. Sharpe ratio of the tangency portfolio;
Hint: using vector formulation, it is very easy to compute portfolio’s variance! If is the N 1 vector
of portfolio weights and is the N N variance-co variance matrix, then the portfolio variance is =
and portfolio volatility is = .
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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
submitting the same in lieu of their academic submissions for grades.
Sub: Finance Topic: Cost of Capital
Solution :
Date Walmart Microsoft Pfizer Starbucks
Share Share Share Share
price Returns price Returns price Returns price Returns
01-12-2008 55.14 0.75% 19.08 -3.83% 16.97 7.75% 9.46 5.94%
03-11-2008 54.73 0.13% 19.84 -8.87% 15.75 -5.58% 8.93 -31.99%
01-10-2008 54.66 -6.82% 21.77 -16.33% 16.68 -3.92% 13.13 -11.70%
02-09-2008 58.66 1.40% 26.02 -2.18% 17.36 -3.56% 14.87 -4.43%
01-08-2008 57.85 1.17% 26.6 6.53% 18 4.05% 15.56 5.92%
01-07-2008 57.18 4.30% 24.97 -6.51% 17.3 6.92% 14.69 -6.67%
02-06-2008 54.82 -2.66% 26.71 -2.87% 16.18 -9.81% 15.74 -13.47%
01-05-2008 56.32 0.00% 27.5 -0.33% 17.94 -2.18% 18.19 12.08%
01-04-2008 56.32 10.06% 27.59 0.51% 18.34 -3.93% 16.23 -7.26%
03-03-2008 51.17 6.74% 27.45 4.33% 19.09 -6.05% 17.5 -2.67%
01-02-2008 47.94 -2.26% 26.31 -16.24% 20.32 -3.24% 17.98 -4.92%
02-01-2008 49.05 6.75% 31.41 -8.43% 21 2.74% 18.91 -7.62%
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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
submitting the same in lieu of their academic submissions for grades.
Sub: Finance Topic: Cost of Capital
03-12-2007 45.95 -0.33% 34.3 5.93% 20.44 -4.31% 20.47 -12.48%
01-11-2007 46.1 5.95% 32.38 -8.40% 21.36 -2.29% 23.39 -12.33%
01-10-2007 43.51 3.57% 35.35 24.96% 21.86 0.74% 26.68 1.83%
04-09-2007 42.01 0.05% 28.29 2.54% 21.7 -1.63% 26.2 -4.90%
01-08-2007 41.99 -4.57% 27.59 -0.58% 22.06 6.93% 27.55 3.26%
02-07-2007 44 -4.49% 27.75 -1.63% 20.63 -8.07% 26.68 1.68%
01-06-2007 46.07 1.08% 28.21 -3.95% 22.44 -7.00% 26.24 -8.92%
01-05-2007 45.58 -0.22% 29.37 2.84% 24.13 5.00% 28.81 -7.12%
02-04-2007 45.68 2.08% 28.56 7.41% 22.98 4.74% 31.02 -1.08%
01-03-2007 44.75 -2.36% 26.59 -1.04% 21.94 1.25% 31.36 1.49%
01-02-2007 45.83 1.30% 26.87 -8.42% 21.67 -3.86% 30.9 -11.56%
03-01-2007 45.24 3.26% 29.34 3.35% 22.54 1.30% 34.94 -1.36%
01-12-2006 43.81 0.55% 28.39 1.72% 22.25 -5.76% 35.42 0.37%
01-11-2006 43.57 -6.46% 27.91 2.61% 23.61 4.05% 35.29 -6.52%
02-10-2006 46.58 -0.09% 27.2 4.98% 22.69 -6.05% 37.75 10.87%
01-09-2006 46.62 10.29% 25.91 6.41% 24.15 2.90% 34.05 9.80%
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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
submitting the same in lieu of their academic submissions for grades.
Sub: Finance Topic: Cost of Capital
01-08-2006 42.27 0.88% 24.35 7.22% 23.47 7.02% 31.01 -9.41%
03-07-2006 41.9 -7.63% 22.71 3.27% 21.93 10.76% 34.23 -9.35%
01-06-2006 45.36 -0.57% 21.99 2.85% 19.8 -0.80% 37.76 5.92%
01-05-2006 45.62 7.98% 21.38 -5.86% 19.96 -5.72% 35.65 -4.35%
03-04-2006 42.25 -4.69% 22.71 -11.25% 21.17 1.63% 37.27 -0.96%
01-03-2006 44.33 4.55% 25.59 1.27% 20.83 -4.84% 37.63 3.61%
01-02-2006 42.4 -1.65% 25.27 -4.21% 21.89 2.96% 36.32 14.57%
03-01-2006 43.11 -1.46% 26.38 7.63% 21.26 10.16% 31.7 5.63%
01-12-2005 43.75 -3.34% 24.51 -5.51% 19.3 9.97% 30.01 -1.44%
01-11-2005 45.26 2.65% 25.94 8.04% 17.55 -1.63% 30.45 7.67%
03-10-2005 44.09 7.96% 24.01 -0.12% 17.84 -12.93% 28.28 12.89%
01-09-2005 40.84 -2.53% 24.04 -6.02% 20.49 -2.01% 25.05 2.20%
01-08-2005 41.9 -8.62% 25.58 7.21% 20.91 -3.15% 24.51 -6.70%
01-07-2005 45.85 2.39% 23.86 3.11% 21.59 -3.92% 26.27 1.70%
01-06-2005 44.78 2.05% 23.14 -3.74% 22.47 -1.14% 25.83 -5.73%
02-05-2005 43.88 0.50% 24.04 2.30% 22.73 3.37% 27.4 10.66%
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*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
submitting the same in lieu of their academic submissions for grades.
Sub: Finance Topic: Cost of Capital
01-04-2005 43.66 -5.93% 23.5 4.68% 21.99 3.43% 24.76 -4.14%
01-03-2005 46.41 -2.62% 22.45 -3.94% 21.26 -0.05% 25.83 -0.31%
01-02-2005 47.66 -1.51% 23.37 -3.95% 21.27 9.58% 25.91 -4.04%
03-01-2005 48.39 -0.78% 24.33 -1.66% 19.41 -10.14% 27 -13.41%
01-12-2004 48.77 1.71% 24.74 -0.32% 21.6 -3.18% 31.18 10.84%
01-11-2004 47.95 -3.46% 24.82 6.84% 22.31 -3.46% 28.13 6.39%
01-10-2004 49.67 1.37% 23.23 1.13% 23.11 -5.40% 26.44 16.32%
01-09-2004 49 0.99% 22.97 1.28% 24.43 -6.33% 22.73 5.13%
02-08-2004 48.52 -0.39% 22.68 -3.90% 26.08 2.76% 21.62 -8.00%
01-07-2004 48.71 0.95% 23.6 -0.21% 25.38 -6.76% 23.5 8.05%
01-06-2004 48.25 -5.78% 23.65 8.84% 27.22 -2.99% 21.75 7.14%
03-05-2004 51.21 -2.01% 21.73 0.42% 28.06 -0.71% 20.3 4.32%
01-04-2004 52.26 -4.50% 21.64 4.79% 28.26 2.02% 19.46 2.80%
01-03-2004 54.72 0.44% 20.65 -6.01% 27.7 -4.38% 18.93 1.23%
02-02-2004 54.48 10.60% 21.97 -4.06% 28.97 0.52% 18.7 2.13%
02-01-2004 49.26 1.50% 22.9 1.01% 28.82 3.67% 18.31 10.43%
www.classof1.com/homework-help/finance
*The Homework solutions from Classof1 are intended to help students understand the approach to solving the problem and not for
submitting the same in lieu of their academic submissions for grades.
Sub: Finance Topic: Cost of Capital
01-12-2003 48.53 -4.49% 22.67 6.48% 27.8 5.26% 16.58 3.11%
03-11-2003 50.81 -5.61% 21.29 -1.66% 26.41 6.71% 16.08 1.77%
01-10-2003 53.83 5.71% 21.65 -5.46% 24.75 4.04% 15.8 9.72%
02-09-2003 50.92 -5.62% 22.9 4.85% 23.79 1.54% 14.4 1.48%
01-08-2003 53.95 5.85% 21.84 0.41% 23.43 -9.88% 14.19 3.88%
01-07-2003 50.97 4.17% 21.75 2.98% 26 -2.33% 13.66 11.33%
02-06-2003 48.93 2.17% 21.12 4.19% 26.62 10.09% 12.27 -0.57%
01-05-2003 47.89 -6.57% 20.27 -3.75% 24.18 1.34% 12.34 4.93%
01-04-2003 51.26 8.23% 21.06 5.62% 23.86 -1.32% 11.76 -8.70%
03-03-2003