Portfolio Analysis

1. UNIVERSITY AT BUFFALO
MGF 402 Project #1
Portfolio Analysis
Reilly, Matthew
11/6/2012

2. 1. Stock Choices
Name Ticker Market Cap Price
(11/03/12)
Nike NKE $42.6B $94.54
Ford Motor Co. F $42.59B $11.17
Darden DRI $19.22B $52.63
Time Warner Cable Inc. TWC $30.08B $98.17
Kellogg Co. K $6.77B $53.69
2. Continuously Compounded Returns:
This was calculated by calculating the logarithm of the current price (current open price) minus
the logarithm of the previous price (previous open price) for each time interval for each
stock.=LN(current open price)-LN(previous open price). Please see Appendix A for calculations.
3. Calculations & Graphs
a. Average Annualized Returns &Volatilities
–Average Annualized Returns- this was calculated by taking the average of all of the
returns for each stock and multiplying by 12
-Volatility – this is calculated by taking the standard deviation of the returns and
multiplying by the square root of 12
b. Rolling Correlations (two year window) – This was calculated by using the correlation
(=CORREL) function in excel. Each correlation takes into account all of the returns from
each stock (the two that are being compared) for all of the previous time periods. Please
see Appendix B for calculations.
c. Arithmetic Average Correlations between each of the 5 stocks (10 correlations) – This is
calculated by taking the average of all of the previous rolling correlations up to each
individual time period. Please see Appendix B for calculations.
d. Plot–Please see Appendix C for the S&P 500 returns.
Following graphs reflect Rolling correlations vs. Historical S+P 500 returns
NKE T TWC K DRI
Average Annualized Returns 0.10224327 0.01838907 0.20304818 -0.0193815 0.0430243
Volitility 0.27270514 0.70819968 0.3275498 0.19012823 0.38749785
0%
33%
66%
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
NKE - F
S&P 500

3. -correlations are historically high when the market is performing poorly as seen in the
above graph. Additionally, because both Ford and Nike carry more expensive product
lines then there competitors, it would make sense that the two company’s average
correlations show very little movement in a downed economy.
The above graph clearly indicates the companies correlation growing almost exactly
invercely to the market conditions. Which, makes for the case that the two companies correlation is
historically consistent and high.
Nike-K correlation reflects the fact that the market is more likely to go to substitute
food-stuffs then discount clothing when in a down economy. That being said the correlation
between the two companies is quite low
0.00%
33.00%
66.00%
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
NKE- TWC
S&P 500
0
0.33
0.66
10/1/2…
1/1/20…
4/1/20…
7/1/20…
10/1/2…
1/1/20…
4/1/20…
7/1/20…
10/1/2…
1/1/20…
4/1/20…
7/1/20…
NKE-K
S&P 500

4. The above correlation reflects that neither new clothing/footwear are neccesities, due
that reasoning it would make sense that the correlation rise when market conditions are worst.
The companies correlation is low
Ford-TWC correlation reflects consumers preference for more inexpensive
entertainment and increased likely-hood to fix older cars rather then buy new ones in a down
economy that being said the correlation didn’t have a large reaction to changing market
conditions, the correlations are historically high
0
0.25
0.5
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
NKE-DRI
S&P 500
0
0.33
0.66
0.99
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
F-TWC
S&P 500

5. Ford-K’s correlation moves inversely with market conditions signifying a more consistent
correlation for the companies. Historically the correlation is somewhat average not too high not
too low
The above correlation reflects that buying new cars and going out to eat are activites
more widely practiced in a strong economy. That being said historically the companies have a
low correlation
0.00%
25.00%
50.00%
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
F - K
S&P 500
0
0.25
0.5
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
F- DRI
S&P 500
0
0.25
0.5
TWC-K
S&P 500

6. Correlations between these two companies don’t change very much, but they seem to
move with the market conditions implying inverse relation, most likely due to consumers lack of
subsititute for cable, with the opposite being true with Kellog
Again Correlations in the above graph show that for a short time while the market was
performing poorly the two moved with one another, however as time goes on the coorelation
again lowers that being the case it seems its hard to trust this correlation.
This correlation is perhaps the easiest to recognize due to the fact that the two companies are
in similar industries. Furthermore, it would make sense that in order for consumers to save
money in a down economy they would be buying more kellog products as opposed to going out
to eat.
4. Fama-French
a. Please see Appendix D for Regressions of excess returns for each stock.
0
0.25
0.5
0.75
TWC-DRI
S&P 500
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
10/1/2009
1/1/2010
4/1/2010
7/1/2010
10/1/2010
1/1/2011
4/1/2011
7/1/2011
10/1/2011
1/1/2012
4/1/2012
7/1/2012
K-DRI
S&P 500

7. b. Comment on the results relative to expected returns. Are the historical numbers
accurate?
3 companies, which are Nike, Ford and Kellogg, have pretty close historical
returns and expected returns that were calculated with Fama-French factor. Darden
and Time Warner Cable show completely different results. Darden expected to have
high returns, but economic situation would lead consumers to choose lower
restaurants. Moreover, Time Warner Cable would expect huge returns on their
business based on the Fama-French factor; however, their historical return was 1/20
of what Fama-French factor shows. The results of historical returns for 5 companies
would be affected by outside variables, such as technological changes or new
regulations that affect their stock prices.
i.
ii.
iii.
iv.
v.
c. Risk Premium of each factor: MKT-Rf=1.81%, SMB=3.96%, HML=(-1.48%)
5. Portfolio – Please see Appendix E for results.
a. Calculate volatilities (annualized) – This was calculated by taking the standard deviation
of all of the portfolio returns and multiplying by the square root of 12.
b. Calculate expected returns (annualized) – This was calculated by taking the average of
the portfolio returns and multiplying by 12
c. Downside risk from mean –First we used the following calculation=MAX ((expected
returns)/12-(portfolio returns,0)^2. Next we calculated the square root of the average of
our results from our first calculation.
d. Downside risks from pre-specified returns are included in Excel spread sheet.
NIKE
Er 10.22%
Hr 6.17%
Ford
Er 1.84%
Hr 1.32%
Darden
Er 61.33%
Hr 3.79%
Time Warner Cable
Er 246.00%
Hr 19.79%
Kellogg
Er -21.21%
Hr -21.73%

8. 6. Solver
Use solver to construct a constrained standard deviation optimal frontier for each expected
return from 5% to 12% in increments of .5%, constraints = minimum standard deviation (weights
must add up to 1). Please see below for the volatilities for each expected return.
This graph shows the amount of risk that is associated with each expected interval. As the
expected returns increase the risk also increases. As the solver found volatility for higher
expected returns Ford and Kellogg stocks were eliminated from the portfolio showing that these
stocks were not expected to add enough value to the portfolio in order to generate higher
returns.
7. Repeat step 6 – constraint that no weight can be smaller than 5%. Please see below for the
volatilities of each expected return. (See next page.)
Expected
Returns Volatilities
5.0% 18.17%
5.5% 18.34%
6.0% 18.53%
6.5% 18.73%
7.0% 18.96%
7.5% 19.21%
8.0% 19.48%
8.5% 19.76%
9.0% 20.07%
9.5% 20.39%
10.0% 20.73%
10.5% 21.09%
11.0% 21.46%
11.5% 21.85%
12.0% 22.25%

9. Adding this constraint has caused there to be higher volatilities for each given expected return.
It has also shifted the line down. It was more challenging to generate higher returns when all of
the stocks are required to be a part of the portfolio.
8. Plot the two efficient frontiers from part 6 & 7 (x axis = Standard Deviation, y axis = expected
returns)
Expected
Returns Volatilities
5.0% 19.56%
5.5% 19.78%
6.0% 20.03%
6.5% 20.29%
7.0% 20.58%
7.5% 20.88%
8.0% 21.20%
8.5% 21.53%
9.0% 21.88%
9.5% 22.25%
10.0% 22.62%
10.5% 23.02%
11.0% 23.42%
11.5% 23.84%
12.0% 24.27%
Expected
Returns
Volatility
6
Volatility
7
5.0% 18.17% 19.56%
5.5% 18.34% 19.78%
6.0% 18.53% 20.03%
6.5% 18.73% 20.29%
7.0% 18.96% 20.58%
7.5% 19.21% 20.88%
8.0% 19.48% 21.20%
8.5% 19.76% 21.53%
9.0% 20.07% 21.88%
9.5% 20.39% 22.25%
10.0% 20.73% 22.62%
10.5% 21.09% 23.02%
11.0% 21.46% 23.42%
11.5% 21.85% 23.84%
12.0% 22.25% 24.27%

10. There is a lower expected return and higher standard deviation for the portfolios that have a
minimum of 5% for each stock, shown as #7. For the portfolios in #6 there is a higher expected
return and lower standard deviation when there is no minimum placed on the percentage of each
stock.
9. Calculate the 95% VaR for each of the portfolios graphed in 8.
Portfolio: Constraint total weight = 1
Portfolio2: Constraint total weight = 1 each
security>= 5%
Expected
Return
PorttV
olit
95%
VaR
% -
5%(z) prob
Expected
Return
port
vol
95%
VaR
%-
5%(z) prob
5.0%
18.17
%
-
0.248
87
-
0.550
36
29.1
0% 0.05
0.195
6
-
0.271
73
-
0.255
62
0.3991
21
5.5%
18.34
%
-
0.246
67
-
0.572
52
28.3
5% 0.055
0.197
8
-
0.270
35
-
0.278
06
0.3904
84
6.0%
18.53
%
-
0.244
79
-
0.593
63
27.6
4% 0.06
0.200
3
-
0.269
46
-
0.299
55
0.3822
6
6.5%
18.73
%
-
0.243
08
-
0.613
99
26.9
6% 0.065
0.202
9
-
0.268
74
-
0.320
35
0.3743
5
7.0%
18.96
%
-
0.241
86
-
0.632
91
26.3
4% 0.07
0.205
8
-
0.268
51
-
0.340
14
0.3668
77
7.5%
19.21
%
-
0.240
98
-
0.650
7
25.7
6% 0.075
0.208
8
-
0.268
44
-
0.359
2
0.3597
24
8.0%
19.48
%
-
0.240
42
-
0.667
35
25.2
3% 8% 21% -27% -38% 35%
8.5%
19.76
%
-
0.240
02
-
0.683
2
24.7
2% 0.085
0.215
3
-
0.269
14
-
0.394
8
0.3464
96
9.0%
20.07
%
-
0.240
12
-
0.697
56
24.2
7% 0.09
0.218
8
-
0.269
89
-
0.411
33
0.3404
14
9.5%
20.39
%
-
0.240
38
-
0.711
13
23.8
5% 0.095
0.222
5
-
0.270
98
-
0.426
97
0.3347
02
10.0%
20.73
%
-
0.240
98
-
0.723
59
23.4
7% 0.1
0.226
2
-
0.272
07
-
0.442
09
0.3292
13
10.5%
21.09
%
-
0.241
-
0.734
23.1
2% 0.105
0.230
2
-
0.273
-
0.456
0.3241
5

11. 9 95 64 13
11.0%
21.46
%
-
0.242
98
-
0.745
57
22.8
0% 0.11
0.234
2
-
0.275
22
-
0.469
68
0.3192
9
11.5%
21.85
%
-
0.244
4
-
0.755
15
22.5
1% 0.115
0.238
4
-
0.277
13
-
0.482
38
0.3147
67
12.0%
22.25
%
-
0.245
98
-
0.764
04
22.2
4% 0.12
0.242
7
-
0.279
21
-
0.494
44
0.3104
99
For the portfolio with the constraint security weights adds up to 1. Neither Ford nor Darden
Restaurant is part of the portfolio due to their historically low returns and higher volatilities.
Nike, TWC and Kellogg are weighted fairly similar because their correlations are close in value.
However, K holds the largest weight due to the fact that its correlation with Nike and TWC are
lower than correlation between Nike and TWC. Furthermore, K’s volatility is lower than other
companies. Further explaining, these facts explain K’s greater weight in the optimal portfolio.
For the portfolio with the constraint security weights adds up to 1 with minimum security
weights equals to 5%, Ford and Darden have 5% weights, which is minimum security weights
that was given. Kellogg’s weight was nearly unchanged from the first portfolio, because of its
lower volatility and correlation with other companies. Overall results in weight of each
companies’ were pretty similar.
10. Choose two portfolios from #9 and calculate the probability that that the returns were lower
than -5% for any given month
expected return 8.5%
port vol 19.76%
95 % VaR -0.24
portfolio
weights nke f twc dri k total
31% 0% 30% 0% 39% 1
monthly
expected r
monthly
vol -5% 16%
0.007 0.05704 (1.00)
expected return 7.5%
port vol 20.88%
95% VaR -0.2684
portfolio
weights nke f twc dri k total
0.24022 0.05 0.27 0.05 0.389 1
monthly
expected r
monthly
vol -5% 18%

12. For expected return of 8.5% with constraint that portfolio weight adds up to 1 (Nike 31%, Ford
0%, Time Warner Cable 31%, Darden Restaurant 0%, Kellogg 39%) There’s a 16% chance for
any given month that portfolio realize -5% or less rate of return.
For expected return of 7.5% with constraint that portfolio weight adds up to 1 with minimum
security weight equals 5%, (Nike 24%. Ford 5%, TWC 27%, DRI 5%, K 39%) There’s a 18%
chance for any given month that portfolio realize -5% or less rate of return.
11. Repeat 6-8 using the downside risk from the mean as the criterion to be minimized.
11A – Allows any portfolio weights
11B – Allows 5% minimum portfolio weight
By assigning downside risk as the criterion to be minimized the relationship between the two
sets of portfolios remained the same. The portfolios that did not have a minimum stock weight
had an overall higher expected return for any given standard deviation. However the standard
deviation for each portfolio increased slightly when the downside risk was set as the criterion to
be minimized. Due to the fact that standard deviation is no longer being minimized the portfolio
can expect higher returns therefore, the further you’re expected returns stray from the negative
returns the less likely you are to have negative returns in theory.
12. Optimizer Results
port Opt 1 95% var E® nke f twc dri k
portfolio
95%var -0.095 X(1) X(2) X(3) X(4) X(5)
Expected
Returns
Volatility
11A
Volatility
11B
5.0% 18.22% 19.60%
5.5% 18.37% 19.82%
6.0% 18.55% 20.06%
6.5% 18.76% 20.33%
7.0% 18.98% 20.61%
7.5% 19.23% 20.90%
8.0% 19.49% 21.22%
8.5% 19.78% 21.56%
9.0% 20.08% 21.91%
9.5% 20.41% 22.27%
10.0% 20.75% 22.65%
10.5% 21.10% 23.04%
11.0% 21.48% 23.45%
11.5% 21.86% 23.87%
12.0% 22.26% 24.29%
0.006 0.06028 (0.93)

13. 1.000 -0.139 2.460 0.000 0.000 1.000 0.000 0.000
2.000 -0.125 2.264 0.000 0.000 0.894 0.106 0.000
3.000 -0.115 2.065 0.065 0.000 0.804 0.131 0.000
4.000 -0.096 0.650 0.234 0.000 0.247 0.155 0.363
5.000 -0.093 0.475 0.249 0.016 0.178 0.156 0.401
Opt 2 X(1) X(2) X(3) X(4) X(5)
1.000 -0.118 1.994 0.050 0.050 0.800 0.050 0.050
2.000 -0.114 1.871 0.050 0.050 0.733 0.117 0.050
3.000 -0.111 1.784 0.079 0.050 0.694 0.127 0.050
4.000 -0.095 0.439 0.239 0.050 0.165 0.151 0.395
The theoretical optimal 95% Var calculations were far less than the historical 95% Var
calculations, this in large part is due to the fact that according to the Fama-French factors the
Expected return of TWC was nearly 200% higher than the historical returns and Dardens
expected return were nearly 60% higher than Historical returns Due, to these vast inaccuracies
the theoretical optimal portfolios are much more aggressive then the historical optimal
portfolios in that they expect much higher returns per portfolio volatility.
13. Despite the fact that the theoretical optimal portfolio is far more aggressive then the historical
optimal portfolio the two do have glaring similarities. For example, in the theoretical as well as
in the historical optimal portfolios both give very little weight if any(depending on constraints)
to Ford’s security, this in large part can be explained by the accuracy of the Fama-French model,
which shows ford’s annualized returns to be less than 2%, which matches almost identically to
the historical returns. Differently however, The theoretical optimizer which expected approx..
60% return from DRI security, uses a much larger portion of DRI to optimize the portfolio, when
in reality they’ve experienced a little less than 4% historically. For three of our securities, the
Fama French factors estimated extremely accurately to historic returns, however for the two
other it for over-estimated there respective returns, which skewed our results for estimated
return and volatility. Therefore, it seems depending on the type of stock and or industry the
Fama-French factors maybe less accurate, then for others, however for 60% of our portfolio it
was quite accurate and theoretical optimal weighting was quite comparable to historical optimal
weighting.