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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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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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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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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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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%

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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

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