Description
Analysis of risk and return, portfolio diversification
Here you will apply what you have learned about portfolio theory. Use the monthly-adjusted closing prices for IBM, MSFT, And the S&P500 during the five-year period from January 2013 – December 2017 in the file “Stock Project Stock Prices” posted on Canvas. Calculate returns for each month for each of these three assets (Stock 1; Stock 2; S&P 500).
Exercise 1:Calculate the following for each asset (in Excel, using the statistical functions given in parentheses): average return (AVERAGE), standard deviation of returns (STDEV.S), and variance of returns (VAR.S). What is the covariance (COVAR.S) and correlation (CORREL) between the returns of stock 1 and stock 2?
Exercise 2:Calculate the return and standard deviation of a portfolio that holds these two stocks in the following weights: 0%-100%; 10%-90%; 20%-80%; 30%-70%; 40%-60%; 50%-50%; 60%-40%; 70%-30%; 80%-20%; 90%-10%, 100%-0%. Plot these portfolio return / standard deviation combinations. Make sure return is on the vertical axis and standard deviation is on the horizontal axis. (Important: use a scatterplot) (You may use excel for this part)
Exercise 31. Which specific combination would deliver the least amount of risk? Use the formula for the minimum variance portfolio (show your work by hand) to get the exact weights, calculate its return, standard deviation and Sharpe ratio (show your work by hand), and mark it by hand on your plot printout.
2. Calculate the optimal risky portfolio’s weights (show your work by hand) in the two stocks. For this optimal portfolio, calculate the average return, standard deviation, and Sharpe ratio (show your work). Mark the ORP on the plot printout by hand. Draw in the CAL (by hand) that gives you the best risk-return combinations, given that the monthly risk free rate is 0.15%.
3. Mark the spot on your return / standard deviation plot where the market index (i.e. S&P 500) falls.
4. For a moment, assume the correlation between the two stocks equals exactly +1. Graph the investment opportunity set. (Hint: This does not require any additional excel work or calculations)
5. Now assume the correlation between the two stocks equals exactly –1. Again, graph the investment opportunity set. If you would like, you can perform steps 4 and 5 on the same graph.
you should clearly show all of your work! Write out all equations that you use, with the exception of those that are functions in excel such as AVG, COVAR, VAR, etc. For example, you need to write out the equations for portfolio weights, returns, standard deviations, and sharpe ratios for your calculations in determining the MVP and ORP.
Unformatted Attachment Preview
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Explanation & Answer
If you will need to draw the graph by Hand you will print out separately and follow what I have done in microsoft word file. If you need anything else let me know.
1
Analysis of risk and return, portfolio diversification
Student’s Name
Department, University
Course Name
Professor’s Name
November 18, 2020
2
Analysis of risk and return, portfolio diversification
Exercise 1
Exercise 1
Average
Standard deviation of returns
Variance of returns
Covariance (IBM & MSFT)
Correlation (IBM & MSFT)
IBM
MSFT
S&P500
-0.00062 0.02349 0.01023
0.051085 0.060527 0.027149
0.00261 0.003664 0.000737
0.00074
0.239186
Exercise 2
Exercise 2
Portfolio composition
IBM
MSFT
Average
Variance of portfolio returns
Standard deviation of Portfolio
returns
0%
100%
2.35%
0.003664
0.060527
% in
Portfolio Portfolio
IBM
SD
Er
0%
6.1%
2.3%
10%
5.6%
2.1%
20%
5.2%
1.9%
30%
4.8%
1.6%
40%
4.6%
1.4%
50%
60%
70%
80%
90%
100%
4.4%
4.3%
4.4%
4.5%
4.8%
5.1%
CML
2.5%
Expected return
2.0%
1.5%
1.0%
0.5%
0.0%
4.0%
-0.5%
4.5%
5.0%
5.5%
Standard deviation
6.0%
6.5%
1.1%
0.9%
0.7%
0.4%
0.2%
-0.1%
3
Exercise 31
Minimum Variance portfolio
𝑊1 =
𝜎22 − 𝜌1𝑥𝜎1𝜎2
𝜎12 + 𝜎22 − 2𝜎1𝜎2
0.0605272 − 0.239186𝑥 0.051085 ∗ 0.060527
𝑊1 =
0.0510852 + 0.0605272 − 2𝑥0.051085𝑥0.060527
𝑊1 = 32.8%
𝑊2 = 1 − 𝑊1
𝑊2 = 67.2%
The specific combination that will deliver minimal risk is 32.8% of IBM stock and 67.2% of
MSFT stock.
Returns
IBM stock: -0.0620%
MSFT stock: 2.3495%
𝑅𝑒𝑡𝑢𝑟𝑛𝑠 = (32.8% ∗ −0.0620%) + (67.2% ∗ 2.3495%) = 1.56%
The return on IBM and MSFT stock under minimal risk is 1.56%
Standard deviation: 4.7554%
Variance of portfolio: 0.0061%
Sharper ratio
Risk free rate (2013-2017) 0.28%
Standard deviation of excess return: 4.7554%
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =
(1.56% − 0.28%)
= 0.27
4.7554%
Optimal risky portfolio weights
𝑊1 =
(𝐸(𝑅1) − 𝑅𝑓)𝜎22 − (𝐸(𝑅2) − 𝑅𝑓)𝜎12
[𝐸(𝑅1) − 𝑅𝑓]𝜎22 + [𝐸(𝑅2) − 𝑅𝑓]𝜎12 − [𝐸(𝑅1) − 𝑅𝑓 + 𝐸(𝑅2) − 𝑅𝑓]𝜎12)
𝑊1
=
(−0.0620% − 0.28%)0.06052 − (2.3495% − 0.28%)𝑥0.0007395
[−0.0620 − 0.28%]0.0605 + [2.3495% − 2.8%]0.05108 − [−0.0620% − 0.28% + 2.3495% − 0.28%]0.0007395)
𝑊1 = −97%
4
𝑊2 = 1 − −97% = 197%
Return: 4.68%
Variance: 1.3774%
SD: 11.7363%
Risk free rate (2013-2017): 0.28%
𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 =
2.5%
4.68% − 0.28%
= 0.37
11.7363
Capital Allication Line (CAL)
Expected return
2.0%
1.5%
ORP
1.0%
Market Index
0.5%
Rf
0.0%
4.0%
4.5%
-0.5%
5.0%
5.5%
6.0%
6.5%
Standard deviation
Investment opportunity set when Correlation is +1
2.5%
MSFT
Expected return
2.0%
1.5%
Investment
Opportunity Set
1.0%
Correration= 1
0.5%
0.0%
4.0%
-0.5%
4.5%
5.0%
IBM
5.5%
Standard deviation
6.0%
6.5%
5
Investment opportunity set When correlation is -1
2.5%
Expected return
2.0%
MSFT
Correration= -1
1.5%
1.0%
0.5%
0.0%
4.0%
-0.5%
4.5%
IBM
5.0%
5.5%
Standard deviation
6.0%
6.5%
MSFT
Date
1/1/2013
2/1/2013
3/1/2013
4/1/2013
5/1/2013
6/1/2013
7/1/2013
8/1/2013
9/1/2013
10/1/2013
11/1/2013
12/1/2013
1/1/2014
2/1/2014
3/1/2014
4/1/2014
5/1/2014
6/1/2014
7/1/2014
8/1/2014
9/1/2014
10/1/2014
11/1/2014
12/1/2014
1/1/2015
2/1/2015
3/1/2015
4/1/2015
5/1/2015
6/1/2015
7/1/2015
8/1/2015
9/1/2015
10/1/2015
11/1/2015
12/1/2015
1/1/2016
2/1/2016
3/1/2016
4/1/2016
5/1/2016
6/1/2016
7/1/2016
8/1/2016
9/1/2016
10/1/2016
11/1/2016
12/1/2016
1/1/2017
2/1/2017
3/1/2017
4/1/2017
5/1/2017
IBM
MSFT
S&P500
Adj Close Adj Close Adj Close
166.326 23.72848
1498.11
164.4913 24.03102
1514.68
175.4404 24.93597
1569.19
166.5902 28.84938
1597.57
171.0975 30.41822
1630.74
157.9257 30.31555
1606.28
161.1733 27.94578
1685.73
150.6207 29.31498
1632.97
153.7904 29.41548
1681.55
148.8324 31.29815
1756.54
149.2227 33.70231
1805.81
156.6118 33.31668
1848.36
147.5192 33.69962
1782.59
154.6079 34.11821
1859.45
161.6008 36.77871
1872.34
164.9422 36.24931
1883.95
154.7755 36.73384
1923.57
153.0674 37.67971
1960.23
161.8493 38.99896
1930.67
162.3813
41.0501
2003.37
161.2436 42.15208
1972.29
139.6431 42.68853
2018.05
137.7489 43.47047
2067.56
137.2121 42.50029
2058.9
131.1144 36.96473
1994.99
138.495 40.12137
2104.5
138.2263 37.46738
2067.89
147.519 44.82079
2085.51
146.1065 43.18055
2107.39
142.2341 40.94774
2063.11
141.6482 43.31279
2103.84
129.3188 40.36343
1972.18
127.8178 41.32045
1920.03
123.5064
49.1439
2079.36
122.9245 50.74033
2080.41
122.4756
52.1444
2043.94
111.0575 51.77785
1940.24
116.6108 47.82096
1932.23
136.1604 52.28214
2059.74
131.2067 47.20822
2065.3
138.2193 50.17115
2096.95
139.0961 48.77763
2098.86
147.1974 54.03002
2173.6
145.6028 54.77355
2170.95
146.8326 55.24923
2168.27
142.0629 57.47454
2126.15
149.9476 57.80066
2198.81
154.8244 60.00659
2238.83
162.7806 62.43042
2278.87
167.7241 61.78342
2363.64
163.7104 63.98444
2362.72
150.6899
66.5104
2384.2
143.4887
67.8511
2411.8
IBM
-0.01103
0.06656
-0.05045
0.02706
-0.07698
0.02056
-0.06547
0.02104
-0.03224
0.00262
0.04952
-0.05806
0.04805
0.04523
0.02068
-0.06164
-0.01104
0.05737
0.00329
-0.00701
-0.13396
-0.01356
-0.00390
-0.04444
0.05629
-0.00194
0.06723
-0.00957
-0.02650
-0.00412
-0.08704
-0.01161
-0.03373
-0.00471
-0.00365
-0.09323
0.05000
0.16765
-0.03638
0.05345
0.00634
0.05824
-0.01083
0.00845
-0.03248
0.05550
0.03252
0.05139
0.03037
-0.02393
-0.07953
-0.04779
MSFT
Returns
0.01275
0.03766
0.15694
0.05438
-0.00338
-0.07817
0.04900
0.00343
0.06400
0.07681
-0.01144
0.01149
0.01242
0.07798
-0.01439
0.01337
0.02575
0.03501
0.05259
0.02684
0.01273
0.01832
-0.02232
-0.13025
0.08540
-0.06615
0.19626
-0.03660
-0.05171
0.05776
-0.06809
0.02371
0.18934
0.03248
0.02767
-0.00703
-0.07642
0.09329
-0.09705
0.06276
-0.02778
0.10768
0.01376
0.00868
0.04028
0.00567
0.03816
0.04039
-0.01036
0.03562
0.03948
0.02016
S&P500
0.01106
0.03599
0.01809
0.02076
-0.01500
0.04946
-0.03130
0.02975
0.04460
0.02805
0.02356
-0.03558
0.04312
0.00693
0.00620
0.02103
0.01906
-0.01508
0.03766
-0.01551
0.02320
0.02453
-0.00419
-0.03104
0.05489
-0.01740
0.00852
0.01049
-0.02101
0.01974
-0.06258
-0.02644
0.08298
0.00050
-0.01753
-0.05074
-0.00413
0.06599
0.00270
0.01532
0.00091
0.03561
-0.00122
-0.00123
-0.01943
0.03417
0.01820
0.01788
0.03720
-0.00039
0.00909
0.01158
IBM&MSFT
Portfolio Return
3.57%
0.98%
35.71%
8.08%
6.77%
-17.35%
15.95%
-1.36%
15.69%
14.84%
-7.03%
7.86%
-2.20%
10.96%
-4.82%
8.58%
6.13%
1.34%
10.02%
5.95%
15.43%
4.91%
-4.01%
-21.31%
11.35%
-12.81%
32.08%
-6.27%
-7.60%
11.75%
-4.98%
5.78%
40.46%
6.84%
5.79%
7.62%
-19.84%
2.15%
-15.56%
7.18%
-6.07%
15.54%
3.75%
0.89%
11.05%
-4.24%
4.36%
2.98%
-4.97%
9.31%
15.43%
8.57%
6/1/2017
7/1/2017
8/1/2017
9/1/2017
10/1/2017
11/1/2017
12/1/2017
146.0296
137.334
135.7772
139.1784
147.7931
143.054
148.6502
67.35087
71.0345
73.05708
73.17127
81.70744
82.67991
84.44764
2423.41
2470.3
2471.65
2519.36
2575.26
2584.84
2673.61
0.01771
-0.05955
-0.01134
0.02505
0.06190
-0.03207
0.03912
-0.00737
0.05469
0.02847
0.00156
0.11666
0.01190
0.02138
0.00481
0.01935
0.00055
0.01930
0.02219
0.00372
0.03434
-3.16%
16.50%
6.69%
-2.11%
16.95%
5.43%
0.43%
Risk free rate
Excess return
Exercise 1
3.29%
0.70%
35.43%
7.80%
6.49%
-17.63%
15.67%
-1.64%
15.41%
14.56%
-7.31%
7.58%
-2.48%
10.68%
-5.10%
8.30%
5.85%
1.06%
9.74%
5.67%
15.15%
4.63%
-4.29%
-21.59%
11.07%
-13.09%
31.80%
-6.55%
-7.88%
11.47%
-5.26%
5.50%
40.19%
6.56%
5.51%
7.34%
-20.12%
1.87%
-15.84%
6.90%
-6.35%
15.26%
3.47%
0.61%
10.77%
-4.52%
4.08%
2.70%
-5.25%
9.03%
15.16%
8.30%
IBM
Average
Standard deviation of returns
Variance of returns
Covariance (IBM & MSFT)
Correlation (IBM & MSFT)
-0.0620%
0.051084677
0.002609644
0.000739566
0.239185835
Exercise 2
Portfolio composition
IBM
MSFT
MSFT
2.3495%
0.060527
0.003664
-97%
197%
Average
Variance of portfolio returns
Standard deviation of Portfolio returns
4.68%
1.3774%
11.7363%
Standard deviation of excess return
11.7363%
Market return
1.023%
2.5%
2.0%
Expected return
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
1.5%
1.0%
0.5%
0.0%
4.0%
-0.5%
4.5%
Minimum variance Portfolio
W1
W2
Risk free rate
Sharpe ratio
5.0%
5.5%
Standard deviation
32.8%
67.2%
0.28%
0.37
6.0%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
0.28%
-3.44%
16.22%
6.41%
-2.39%
16.67%
5.16%
0.15%
S&P500
0.01023
0.027149
0.000737
% in IBM Portfolio SD Portfolio Er
-97%
12%
5%
0%
6.1%
2.3%
10%
5.6%
2.1%
20%
5.2%
1.9%
30%
4.8%
1.6%
40%
4.6%
1.4%
50%
4.4%
1.1%
60%
4.3%
0.9%
70%
4.4%
0.7%
80%
4.5%
0.4%
90%
4.8%
0.2%
100%
5.1%
-0.1%
Num
Den
W1
W2
6.0%
6.5%
-2.77835E-05
2.87855E-05
-97%
197%
4 WEEKS
8 WEEKS
COUPON
BANK
BANK
DATE
EQUIVALE
DISCOUNT
DISCOUNT
NT
1/2/2013
0.07
0.07 N/A
13 WEEKS
COUPON
BANK
EQUIVALE
DISCOUNT
NT
N/A
0.08
26 WEEKS
COUPON
BANK
EQUIVALE
DISCOUNT
NT
0.08
0.12
52 WEEKS
COUPON
EQUIVALE
NT
0.12
1/3/2013
0.06
0.06 N/A
N/A
0.08
0.08
0.12
0.12
1/4/2013
0.06
0.06 N/A
N/A
0.07
0.07
0.11
0.11
1/7/2013
0.05
0.05 N/A
N/A
0.07
0.07
0.11
0.11
1/8/2013
0.06
0.06 N/A
N/A
0.07
0.07
0.11
0.11
1/9/2013
0.04
0.04 N/A
N/A
0.06
0.06
0.09
0.09
1/10/2013
0.05
0.05 N/A
N/A
0.06
0.06
0.1
0.1
1/11/2013
0.04
0.04 N/A
N/A
0.07
0.07
0.1
0.1
1/14/2013
0.05
0.05 N/A
N/A
0.08
0.08
0.11
0.11
1/15/2013
0.09
0.09 N/A
N/A
0.09
0.09
0.11
0.11
1/16/2013
0.07
0.07 N/A
N/A
0.08
0.08
0.11
0.11
1/17/2013
0.05
0.05 N/A
N/A
0.07
0.07
0.11
0.11
1/18/2013
0.04
0.04 N/A
N/A
0.08
0.08
0.1
0.1
1/22/2013
0.03
0.03 N/A
N/A
0.08
0.08
0.1
0.1
1/23/2013
0.06
0.06 N/A
N/A
0.08
0.08
0.1
0.1
1/24/2013
0.06
0.06 N/A
N/A
0.08
0.08
0.1
0.1
1/25/2013
0.06
0.06 N/A
N/A
0.08
0.08
0.11
0.11
1/28/2013
0.03
0.03 N/A
N/A
0.07
0.07
0.11
0.11
1/29/2013
0.03
0.03 N/A
N/A
0.07
0.07
0.11
0.11
1/30/2013
0.04
0.04 N/A
N/A
0.07
0.07
0.11
0.11
1/31/2013
0.04
0.04 N/A
N/A
0.07
0.07
0.12
0.12
2/1/2013
0.02
0.02 N/A
N/A
0.06
0.06
0.11
0.11
2/4/2013
0.03
0.03 N/A
N/A
0.07
0.07
0.11
0.11
2/5/2013
0.06
0.06 N/A
N/A
0.07
0.07
0.11
0.11
2/6/2013
0.06
0.06 N/A
N/A
0.07
0.07
0.12
0.12
2/7/2013
0.03
0.03 N/A
N/A
0.07
0.07
0.11
0.11
2/8/2013
0.03
0.03 N/A
N/A
0.07
0.07
0.11
0.11
2/11/2013
0.05
0.05 N/A
N/A
0.09
0.09
0.12
0.12
2/12/2013
0.08
0.08 N/A
N/A
0.09
0.09
0.12
0.12
2/13/2013
0.09
0.09 N/A
N/A
0.1
0.1
0.12
0.12
2/14/2013
0.1
0.1 N/A
N/A
0.11
0.11
0.13
0.13
2/15/2013
0.09
0.09 N/A
N/A
0.1
0.1
0.13
0.13
2/19/2013
0.09
0.09 N/A
N/A
0.12
0.12
0.13
0.13
2/20/2013
0.12
0.12 N/A
N/A
0.12
0.12
0.13
0.13
2/21/2013
0.12
0.12 N/A
N/A
0.13
0.13
0.13
0.13
2/22/2013
0.11
0.11 N/A
N/A
0.13
0.13
0.14
0.14
2/25/2013
0.09
0.09 N/A
N/A
0.12
0.12
0.14
0.14
2/26/2013
0.11
0.11 N/A
N/A
0.14
0.14
0.14
0.14
2/27/2013
0.11
0.11 N/A
N/A
0.11
0.11
0.13
0.13
2/28/2013
0.07
0.07 N/A
N/A
0.11
0.11
0.13
0.13
3/1/2013
0.07
0.07 N/A
N/A
0.11
0.11
0.12
0.12
3/4/2013
0.06
0.06 N/A
N/A
0.11
0.11
0.12
0.12
3/5/2013
0.09
0.09 N/A
N/A
0.08
0.08
0.12
0.12
3/6/2013
0.09
0.09 N/A
N/A
0.1
0.1
0.12
0.12
3/7/2013
0.1
0.1 N/A
N/A
0.1
0.1
0.11
0.11
3/8/2013
0.09
0.09 N/A
N/A
0.1
0.1
0.11
0.11
3/11/2013
0.09
0.09 N/A
N/A
0.1
0.1
0.12
0.12
3/12/2013
0.1
0.1 N/A
N/A
0.1
0.1
0.12
0.12
3/13/2013
0.09
0.09 N/A
N/A
0.09
0.09
0.12
0.12
3/14/2013
0.08
0.08 N/A
N/A
0.1
0.1
0.12
0.12
3/15/2013
0.07
0.07 N/A
N/A
0.09
0.09
0.11
0.11
3/18/2013
0.07
0.07 N/A
N/A
0.07
0.07
0.11
0.11
3/19/2013
0.08
0.08 N/A
N/A
0.07
0.07
0.11
0.11
3/20/2013
0.08
0.08 N/A
N/A
0.07
0.07
0.11
0.11
3/21/2013
0.08
0.08 N/A
N/A
0.07
0.07
0.11
0.11
3/22/2013
0.07
0.07 N/A
N/A
0.07
0.07
0.11
0.11
3/25/2013
0.06
0.06 N/A
N/A
0.08
0.08
0.11
0.11
3/26/2013
0.08
0.08 N/A
N/A
0.07
0.07
0.11
0.11
3/27/2013
0.06
0.06 N/A
N/A
0.09
0.09
0.12
0.12
3/28/2013
0.04
0.04 N/A
N/A
0.07
0.07
0.11
0.11
4/1/2013
0.06
0.06 N/A
N/A
0.08
0.08
0.11
0.11
4/2/2013
0.06
0.06 N/A
N/A
0.07
0.07
0.11
0.11
4/3/2013
0.06
0.06 N/A
N/A
0.06
0.06
0.1
0.1
4/4/2013
0.07
0.07 N/A
N/A
0.07
0.07
0.1
0.1
4/5/2013
0.05
0.05 N/A
N/A
0.07
0.07
0.1
0.1
4/8/2013
0.05
0.05 N/A
N/A
0.07
0.07
0.1
0.1
4/9/2013
0.06
0.06 N/A
N/A
0.06
0.06
0.1
0.1
4/10/2013
0.07
0.07 N/A
N/A
0.07
0.07
0.1
0.1
4/11/2013
0.06
0.06 N/A
N/A
0.07
0.07
0.1
0.1
4/12/2013
0.05
0.05 N/A
N/A
0.06
0.06
0.09
0.09
4/15/2013
0.04
0.04 N/A
N/A
0.06
0.06
0.09
0.09
4/16/2013
0.06
0.06 N/A
N/A
0.06
0.06
0.09
0.09
4/17/2013
0.05
0.05 N/A
N/A
0.06
0.06
0.09
0.09
4/18/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.09
0.09
4/19/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.09
0.09
4/22/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.09
0.09
4/23/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.09
0.09
4/24/2013
0.05
0.05 N/A
N/A
0.06
0.06
0.09
0.09
4/25/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
4/26/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.09
0.09
4/29/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.08
0.08
4/30/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.09
0.09
5/1/2013
0.03
0.03 N/A
N/A
0.06
0.06
0.08
0.08
5/2/2013
0.02
0.02 N/A
N/A
0.05
0.05
0.08
0.08
5/3/2013
0.02
0.02 N/A
N/A
0.05
0.05
0.08
0.08
5/6/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.08
0.08
5/7/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.08
0.08
5/8/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.08
0.08
5/9/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.08
0.08
5/10/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.08
0.08
5/13/2013
0.02
0.02 N/A
N/A
0.05
0.05
0.08
0.08
5/14/2013
0.01
0.01 N/A
N/A
0.05
0.05
0.09
0.09
5/15/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.09
0.09
5/16/2013
0
0 N/A
N/A
0.03
0.03
0.08
0.08
5/17/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.08
0.08
5/20/2013
0.01
0.01 N/A
N/A
0.05
0.05
0.09
0.09
5/21/2013
0.04
0.04 N/A
N/A
0.04
0.04
0.09
0.09
5/22/2013
0.04
0.04 N/A
N/A
0.04
0.04
0.08
0.08
5/23/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.08
0.08
5/24/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.07
0.07
5/28/2013
0.02
0.02 N/A
N/A
0.05
0.05
0.09
0.09
5/29/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
5/30/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.07
0.07
5/31/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.07
0.07
6/3/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.08
0.08
6/4/2013
0.05
0.05 N/A
N/A
0.04
0.04
0.08
0.08
6/5/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/6/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/7/2013
0.04
0.04 N/A
N/A
0.04
0.04
0.07
0.07
6/10/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/11/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.08
0.08
6/12/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/13/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/14/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/17/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.08
0.08
6/18/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/19/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.08
0.08
6/20/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.09
0.09
6/21/2013
0.02
0.02 N/A
N/A
0.05
0.05
0.09
0.09
6/24/2013
0.01
0.01 N/A
N/A
0.06
0.06
0.11
0.11
6/25/2013
0.03
0.03 N/A
N/A
0.06
0.06
0.11
0.11
6/26/2013
0.02
0.02 N/A
N/A
0.06
0.06
0.11
0.11
6/27/2013
0.02
0.02 N/A
N/A
0.06
0.06
0.11
0.11
6/28/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.1
0.1
7/1/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.09
0.09
7/2/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.08
0.08
7/3/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.08
0.08
7/5/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.08
0.08
7/8/2013
0.02
0.02 N/A
N/A
0.05
0.05
0.07
0.07
7/9/2013
0.04
0.04 N/A
N/A
0.04
0.04
0.08
0.08
7/10/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.08
0.08
7/11/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.07
0.07
7/12/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.07
0.07
7/15/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.07
0.07
7/16/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.07
0.07
7/17/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.08
0.08
7/18/2013
0.01
0.01 N/A
N/A
0.03
0.03
0.07
0.07
7/19/2013
0.01
0.01 N/A
N/A
0.03
0.03
0.07
0.07
7/22/2013
0.01
0.01 N/A
N/A
0.04
0.04
0.07
0.07
7/23/2013
0.02
0.02 N/A
N/A
0.02
0.02
0.07
0.07
7/24/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.07
0.07
7/25/2013
0.02
0.02 N/A
N/A
0.02
0.02
0.06
0.06
7/26/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.07
0.07
7/29/2013
0.01
0.01 N/A
N/A
0.03
0.03
0.07
0.07
7/30/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.07
0.07
7/31/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.08
0.08
8/1/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.08
0.08
8/2/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.07
0.07
8/5/2013
0.03
0.03 N/A
N/A
0.05
0.05
0.08
0.08
8/6/2013
0.05
0.05 N/A
N/A
0.04
0.04
0.08
0.08
8/7/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.08
0.08
8/8/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.07
0.07
8/9/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.07
0.07
8/12/2013
0.05
0.05 N/A
N/A
0.06
0.06
0.08
0.08
8/13/2013
0.06
0.06 N/A
N/A
0.06
0.06
0.08
0.08
8/14/2013
0.06
0.06 N/A
N/A
0.05
0.05
0.07
0.07
8/15/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.08
0.08
8/16/2013
0.05
0.05 N/A
N/A
0.05
0.05
0.08
0.08
8/19/2013
0.03
0.03 N/A
N/A
0.06
0.06
0.08
0.08
8/20/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.07
0.07
8/21/2013
0.02
0.02 N/A
N/A
0.04
0.04
0.07
0.07
8/22/2013
0.01
0.01 N/A
N/A
0.03
0.03
0.06
0.06
8/23/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.06
0.06
8/26/2013
0.03
0.03 N/A
N/A
0.04
0.04
0.07
0.07
8/27/2013
0.04
0.04 N/A
N/A
0.05
0.05
0.07
0.07
8/28/2013
0.04
0.04 N/A
N/A
0.03
0.03
0.07
0.07
8/29/2013
0.03
0.03 N/A
N/A
0.02
0.02
0.06
0.06
8/30/2013
0.02
0.02 N/A
N/A
0.03
0.03
0.05
0.05
9/3/2013
0.03
0.03 N/A
N/A
0.02
0.02
0.05
0.05
9/4/2013
0.02
0.02 N/A
N/A
0.02
0.02
0.05
0.05
9/5/2013
0.03
0.03 N/A
N/A
0.02
0.02
0.06
0.06
9/6/2013
0.02
0.02 N/A
N/A
0.02
0.02
0.05
0.05
9/9/2013
0.02
0....
