# Finance_SL2

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```					                 Finance

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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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