pairs trading

Investigating Pairs Trading
Written by Bolade Ewarawon. 29th
April, 2016
ABSTRACT
Our aim is to investigate cointegration and profit from arbitrage opportunities that tend to occur
through pair trading. We did this by measuring the long run relationship among securities, then
investigated convergence and divergence attributes. Interesting, this short term attribute
resulted in arbitrage opportunities and then we took position to profit from the anomaly. The
two way Engel Granger approach was used to determine the stationarity of our residual series
and our trading position was taken about a standard deviation of 1.0 and 1.5 respectively. We
then measure the performance of the pairs based on type of market.

INTRODUCTION
The Law of One Price (LOP) is a fundamental concept in finance, an idea which serve as a
building block for modern finance. It states that two assets with the same payoﬀ in every state
or nature must have the same current value (Ingersoll, 1987). Therefore, the spread between
close substitutes should have a long term stable equilibrium over time. Hendry & Juselius
(2001), was able to show that short term deviations in price of close substitute can result in
arbitrage opportunity depending on the duration. This leads to the idea of pairs trading, where
reversion to constant spread or in other words a constant value, is expected over time.
According to Douglas, 2006, pg.2 “Pairs trading is a nondirectional relative-value investment
strategy that seeks to identify two companies with similar characteristics whose equity
securities are currently trading at a price relationship that is outside their historical trading
range. This investment strategy entails buying the undervalued security while short-selling the
overvalued security, thereby maintaining market neutrality”.
Arbitrage opportunity is therefore a major component of pairs trading and it occurs when
mispricing is discovered during asset valuation. Based on the above definition we seek relative
valuation rather than absolute valuation and this can be achieved using statistical methods to
determine the historical relationship that exist between given pairs. Therefore, statistical
arbitrage basically points to the use statistical tools to take advantage of arbitrage opportunities.
This concept however is done using multiple assets, hence, we have pair trading which involves
the use of regression to determine the stochastic order of a series and at the same time making
sure the spread or residual term in series of combined pair is mean reverting, in other words,
testing for stationarity.
The underlying concept of pair trading is simple. We simply perform some statistical time
series analysis on assets and later linearly combine them to achieve cointegration. Two assets
are said to be cointegrated if there is a co-movement in asset prices (Alexander et al., 2001).
This concept suggest strongly that trends may diverge on the short run but surely will converge
on the long run for equilibrium spread to be maintained. This however leads to the risk
neutrality element of this strategy that comes from the idea of arbitrating, once cointegration is
established, we use the Long-Short trading rules (Jacobs et al., 1993), which can be achieved
through leveraging or self-funding.

PAIR SELECTION
Now, if we establish cointegration in the past prices of the assets under management, it is
therefore worth knowing that they must share common fundamentals. Again, Gatev et al., 2006
suggested that pairs should be determined by merely looking out for combinations that
minimizes the sum of squared deviations between two normalized price series. Armed with
these facts in mind, we therefore give an introduction to some pair selected based on
fundamental and statistical reasoning.
Table 1: Pair Selection Overview
Table 1 is an overview of the pairs obtained for the period shown above for US and Nigerian
stocks from sectors ranging from automobile to consumer goods. We pegged our average
residual crossing value to at least twice the average period of crossing. Essentially the higher
the ratio of former to the latter, the better our profitability. Also note that we seek high (long
run) correlation to find a short run convergence and divergence quality.
METHODOLOGY
At this point, we will analyze how we fundamentally built the cointegration process. First, we
check if the pairs are correlated and at the same time cointegrated and this is done through the
Engle-Granger two step method.
Individual element of pairs should be at least I(1) order of integration, meaning not stationary,
using the Dicker-Fuller test and should be I(0) order, meaning stationary, once pair
Companies Round 0 Ave. Period R2 period frequency Sector
Ford 50 17 0.88 04/2012 -04/2016 Daily
GM
Berkshire Hathaway A 55 17 0.94 04/2012 -04/2016 Daily
BlackRock
Berkshire Hathaway B 55 17 0.94 04/2012 -04/2016 Daily
BlackRock
JPMorgan 37 26 0.87 04/2012 -04/2016 Daily
WellsFargo
49.25 19.25 0.91
Zenith Bank Nigeria 108 11 0.86 04/2010 -04/2016 Daily
Guaranty Trust Nigeria
Nestle Nigeria 67 21 0.76 04/2010 -04/2016 Daily
Unilever Nigeria
87.5 16 0.81
Consumer Goods
Automobile
Financial Services
Financial Services
Financial Services
Financial Services
Residual Crossing
Portfolio Average(US)
Portfolio Average (Nigeria)
Pair D
Pair C
Pair B
Pair A
Pair E
Pair F

combination is observed. This can simply be done by regressing the dependent variable using
an OLS regression method to also capture the independent variable. However, it is essential to
note the R-squared value which signifies goodness of fit is also helpful to determine whether
to proceed or not. A high R-squared can be gotten from securities that share the same
fundamentals and can take up the short-sell strategy. In this project, we place minimum R-
squared to be 0.70.
PA = βPB + µ + ɛt 1
Equation 1 represent the regressed equation, where A and B are the dependent and independent
variables or securities. µ is the equilibrium value, β is the hedge ratio which keeps the quantities
of securities traded equal and ɛt is the error or residual we seek to manipulate. Now, the next
step is to test for cointegration by ensuring that the residual is white noise, mean reverting and
zero order of integration. We do this using the Engle-Granger test statistics found using the
augmented Dickey Fuller test for stationarity of residual and compare t-statistics with Engle-
Granger. Fortunately, this can be done in Stata at the ADF section. If equation 2 satisfies the
conditions stated, then we have pairs that are cointegrated. It is worth noting that all pairs used
in this analyses are high quality candidates.
µ + ɛt = PA - βPB 2
The residual equation above is fundamental in developing our trading strategy. This defines
the character of our series random walk and allows us to take appropriate trading positions for
meeting our objectives.
Next, we develop our strategy based on the deviation of the residual plot from the mean.
Remember that arbitrage opportunity will only occur if the left hand of equation 2 is not equal
to zero. See equation 3 and 4. We already confirmed it to be zero carrying out the task above.
PA - βPB = 0 , No arbitrage 3
PA - βPB ≠ 0, Arbitrage Exist 4
Now that we have an understanding of our plot, we seek to take advantage of equation 4 by
positioning ourselves at points above or below zero. See figure 1.

Figure 1: Residual Plot
For example our entry points in figure 1, shows that we took positions at a standard deviation
of 1 above and below the mean of zero. We also repeated the same process for a standard
deviation value of 1.5. When the value of the residual is extreme positive and above a set
deviation limit, we simply short the dependent variable, meaning it is over-bought and take the
reverse positon for extreme negative. Our aim is to take position and close out effectively at
zero, which is the point where the two price series cross each other to satisfy non-arbitrage of
equation 3.

RESULTS AND FINDINGS
Our methods were processed using Bloomberg analytics spreadsheets and also Stata to check
for stationarity based on the Augmented Dickey Fuller unit root test. However, the Bloomberg
tool provides a testing method which can also be easily incorporated. Now, we approach this
results and findings using standard deviation values of 1.0 and 1.5 with 100,000 shares of A
and slope matching the quantities of B using β as seen in equations 1 through 4. First, we
analyze the US pairs of A through D and secondly we compare with the Nigerian pairs and
seek to conclude on our finding.
Table 2: profitability Analysis
Table 2 is simply a summary of the appendix 1 through 4, which indicates trend analysis,
regression plot, trade performance, residual and profitability plot.
We had a good outing from the US pairs, with the highest percentage return coming from the
SDM 1 strategy. This is due to the fact that the strategy took advantage of the amount of zero
crossing per period rate as seen also in appendix 4B. However, Pair D had the lowest run of
return as seen from the crossing ratio.
At same standard deviation, the Nigerian pairs of E and F had the highest return of 809% which
can be attributed to extremely high zero residual crossing (table 1, appendix 3 and 4) and high
correlation among competing brands. The US market is extremely liquid, which narrows
spread. However, same cannot be said of the Nigerian market as volatility is relatively high
under series of economic uncertainty, therefore, spread widens for such profit seen above.
At SDM of 1.5, we our profit reduced as we cannot take advantage of the total zero crossings.
SD 1 SD 1.5 Negative Positve Negative Positive
Ford/GM 1.28 0.78 -0.20 0.13 -0.15 0.15 2.94
Return 106% 65%
Berkshire Hathaway A/BlackRock 9,923.13 10,239.89 -1,469.62 1,230.30 -1,163.71 1,689.05 3.24
Return 83% 85%
Berkshire Hathaway B/BlackRock 7.81 6.72 -0.98 0.85 -0.78 1.11 3.24
Return 98% 84%
JPMorgan/WellsFargo 2.02 2.58 -0.47 0.56 -0.30 0.64 2.18
Return 45% 58%
9934.24 10249.97 -1471.29 1231.88 -1164.95 1690.96
Zenith Bank/GTBank 13,062.79 8,157.05 -1,639.26 1,525.32 -1,188.39 2,635.8 6.35
Return 171% 109%
Nestle Nigeria/Unilever 1,013'708.74 75,4642.2 -225,757.25 103,366.13 -132,130.19 169,896.65 3.94
Return 809% 602%
1,026,771.53 762,799.25 -227,396.51 104,891.45 -133,318.58 172,532.45
Zero
crossing/period
NIGERIAN TOTAL
Cummulative Profit $ ('M) Excursion SD 1.0 Excursion SD 1.5
Cummulative Profit($) Excursion SD 1.0 Excursion SD 1.5
US Companies
Nigerian Companies
US TOTAL
Pair E
Pair F
Pair B
Pair C
Pair D
Pair A

Pair B was the only exception with an impressive ratio of zero crossing per period and an
outstanding level of R-squared. We attribute this to the ability of the SDM 1.5 strategy to
minimize excursion effects as seen in Table 2 and appendix 4.2B. We observed that although
this strategy is conservative, it maximizes profit at extreme random walk.

CONCLUSION
We took advantage of arbitrage opportunity that exist in cointegration concept of securities that
are said to have long run relationship. We measured our performance based on the standard
deviation values of 1.0 and 1.5. The higher the residual crossing about the mean the likely we
make more profit about an SDM of 1.0. However, the more conservative strategy seems to
minimize the effect of excursion, where our random walk tend to take longer time deviating
from the normal.
Basically, both strategy was able to show that pairs trading still works in both the advanced
and developing market. We also experience increased convergence as oppose to Do and Faff
(2009), which found increasing failure of stock to converge.
However, we did not consider transaction cost and negative excursion effects in our profit. So
we proposed that future research should engage in cost inclusion models and excursion effects
should be duly measured.

REFERENCES
Carol Alexander, Ian Giblin and Wayne WeddingtonIII (2001) Cointegration and Asset
Allocation: A New Active Hedge Funds Strategy, ISMA Centre: The University of Reading.
Do, B., & Faff, R. (2009). Does Simple Pairs Trading Still Work? Financial Analysts Journal,
1-18.
Douglas, S. E. (2006) The Handbook of Pairs Trading: Strategies Using Equities, Options, and
Futures,: John Wiley & Sons.
Gatev, Evan and Goetz Mann, William N. and Rouwenhorst, K. Geert. 2006. Pairs Trading:
Performance of a Relative Value Arbitrage Rule. Yale ICF Working Paper No. 08-03.
Hendry, D., & Juselius, K. 2001. Explaining cointegration analysis: part II. Energy Journal, 22,
75–120
Ingersoll, J., Jr., 1987, Theory of Financial Decision-Making, Rowman and Littlefiled, New
Jersey.
Jacobs, B., Levy, K., & Starer, D.1993. Long-Short Equity Investing. Journal of Portfolio
Management, 1, 52–64.

Appendix One: Trend Analysis
Graph 1.1
Graph 1.2
Graph 1.3: BRK B/ BLK

Appendix Two: Regression Plot
Graph 2.1
Graph 2.2
Graph 2.3

Appendix Three: Residual plots
Graph 3.1: FORD/GM
Graph 3.2: BRK A/BLK
Graph 3.3: BRK B/BLK

Graph 3.4:JPM/WFC
Graph 3.5: ZENITH/GTB
Graph 3.6: NESTLE/UNILEVER

Appendix Four: Results
Part One : American Pairs
(A)SDM = 1
FORD/GM
Graph 4.1.1(A): Profit/Loss
Graph 4.1.2(A):
Total Profit (Loss) if open positions are closed on last day: $ 1,295,080.89
Profit(Loss) on closed positions: $ 1,281,390.13
Is position open on last day: Yes
Maximum negative excursion of any trade: $ (203,433.28)
Maximum positive excursion of any trade: $ 132,588.76
No. of crossings around 0: 50
Avg. crossing period: 17

Graph 4.1.4(A):
BRK A/BLK
No. of Price (A) Price (B) Qty (A) Qty (B) Entry/Exit Cumulative Individual Cumulative
Date Entry/Exit Trading Days F US Equity GM US Equity F US Equity GM US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 12.07 24.3 -100000 51667 (48,508.10) (48,508.10)
17/08/2012 Exit 90 9.63 22.01 100000 -51667 174,190.67 125,682.57 125,682.57 125,682.57
02/10/2012 Entry 9.79 23.68 100000 -43004 39,334.72 165,017.29
26/10/2012 Exit 19 10.36 23.28 -100000 43004 34,866.88 199,884.17 74,201.60 199,884.17
16/01/2013 Entry 14.22 29.31 -100000 50466 (57,158.46) 142,725.71
15/04/2013 Exit 61 12.95 28.91 100000 -50466 163,972.06 306,697.77 106,813.60 306,697.77
03/07/2013 Entry 16.43 34.14 -100000 50059 (66,014.26) 240,683.51
01/11/2013 Exit 86 16.89 37.39 100000 -50059 182,706.01 423,389.52 116,691.75 423,389.52
06/12/2013 Entry 16.7 40.17 100000 -43244 67,111.48 490,501.00
31/03/2014 Exit 78 15.6 34.42 -100000 43244 71,541.52 562,042.52 138,653.00 562,042.52
11/04/2014 Entry 15.63 31.93 -100000 50918 (62,811.74) 499,230.78
06/05/2014 Exit 17 15.56 34.75 100000 -50918 213,400.50 712,631.28 150,588.76 712,631.28
24/07/2014 Entry 17.84 35.74 -100000 51922 (71,692.28) 640,939.00
01/10/2014 Exit 49 14.59 32.49 100000 -51922 227,945.78 868,884.78 156,253.50 868,884.78
17/11/2014 Entry 15.54 32.31 -100000 50030 (62,469.30) 806,415.48
29/12/2014 Exit 29 15.52 34.6 100000 -50030 179,038.00 985,453.48 116,568.70 985,453.48
06/01/2015 Entry 14.62 34.85 100000 -43637 58,749.45 1,044,202.93
30/01/2015 Exit 18 14.71 32.62 -100000 43637 47,561.06 1,091,763.99 106,310.51 1,091,763.99
09/03/2015 Entry 16.03 37.66 100000 -44276 64,434.16 1,156,198.15
29/06/2015 Exit 79 15.02 33.23 -100000 44276 30,708.52 1,186,906.67 95,142.68 1,186,906.67
17/07/2015 Entry 14.69 30.65 -100000 49854 (59,025.10) 1,127,881.57
14/09/2015 Exit 41 13.78 30.72 100000 -49854 153,514.88 1,281,396.45 94,489.78 1,281,396.45
29/10/2015 Entry 14.73 34.75 100000 -44092 59,197.00 1,340,593.45
Trades List
Total Profit (Loss) if open positions are closed on last day: $ 10,921,106,995.08
Profit(Loss) on closed positions: $ 9,923,013,213.63
Maximum negative excursion of any trade: $ (1,469,623,945.38)
Maximum positive excursion of any trade: $ 1,230,334,951.05

Graph 4.1.6(A):
Graph 4.1.7(A):

Graph 4.1.8(A):
BRK B/BLK
Date Entry/Exit Trading Days BRK/A US Equity BLK US Equity BRK/A US Equity BLK US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 120173 201.71 100000 -49192226 (2,094,736,093.54) (2,094,736,093.54)
08/05/2012 Exit 19 123744 182.34 -100000 49192226 3,404,689,511.16 1,309,953,417.62 1,309,953,417.62 1,309,953,417.62
22/05/2012 Entry 120550 163.37 -100000 60927296 2,101,307,652.48 3,411,261,070.10
10/12/2012 Exit 139 130788 195.72 100000 -60927296 (1,154,109,626.88) 2,257,151,443.22 947,198,025.60 2,257,151,443.22
17/01/2013 Entry 143484 232 100000 -51066076 (2,501,070,368.00) (243,918,924.78)
13/06/2013 Exit 102 172604 272.43 -100000 51066076 3,348,468,915.32 3,104,549,990.54 847,398,547.32 3,104,549,990.54
21/06/2013 Entry 168200 248.67 -100000 55849540 2,931,894,888.20 6,036,444,878.74
22/07/2013 Exit 21 178223 286 100000 -55849540 (1,849,331,560.00) 4,187,113,318.74 1,082,563,328.20 4,187,113,318.74
17/10/2013 Entry 175286 298.51 100000 -48484771 (3,055,411,008.79) 1,131,702,309.95
21/03/2014 Exit 107 187850 301.86 -100000 48484771 4,149,387,025.94 5,281,089,335.89 1,093,976,017.15 5,281,089,335.89
08/10/2014 Entry 209950 324.89 -100000 53357630 3,659,639,589.30 8,940,728,925.19
13/02/2015 Exit 89 222555 376.04 100000 -53357630 (2,190,896,814.80) 6,749,832,110.39 1,468,742,774.50 6,749,832,110.39
28/07/2015 Entry 215091 336.84 -100000 52724878 3,749,252,094.48 10,499,084,204.87
14/10/2015 Exit 56 196898.98 322.47 100000 -52724878 (2,687,706,591.34) 7,811,377,613.53 1,061,545,503.14 7,811,377,613.53
05/11/2015 Entry 204694 357.3 100000 -47303045 (3,568,022,021.50) 4,243,355,592.03
14/12/2015 Exit 27 198040 319.6 -100000 47303045 4,685,946,818.00 8,929,302,410.03 1,117,924,796.50 8,929,302,410.03
09/02/2016 Entry 192635 294.53 -100000 54003594 3,357,821,459.18 12,287,123,869.21
16/02/2016 Exit 5 193465 314.47 100000 -54003594 (2,363,989,794.82) 9,923,134,074.39 993,831,664.36 9,923,134,074.39
29/02/2016 Entry 202555 311.96 -100000 53611882 3,530,737,291.28 13,453,871,365.67
Trades List

Graph 4.1.10(A):
Graph 4.1.11(A):
Graph 4.1.12(A):

JPM VS WFC
Graph 4.1.14(A):
Graph 4.1.15(A):
Date Entry/Exit Trading Days BRK/B US Equity BLK US Equity BRK/B US EquityBLK US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 80.06 201.71 100000 -32759 (1,398,182.11) (1,398,182.11)
10/05/2012 Exit 21 81.78 179.68 -100000 32759 2,291,862.88 893,680.77 893,680.77 893,680.77
22/05/2012 Entry 79.65 163.37 -100000 40240 1,390,991.20 2,284,671.97
10/12/2012 Exit 139 87.1 195.72 100000 -40240 (834,227.20) 1,450,444.77 556,764.00 1,450,444.77
17/01/2013 Entry 95.3 232 100000 -33904 (1,664,272.00) (213,827.23)
01/03/2013 Exit 30 102.05 236.83 -100000 33904 2,175,515.68 1,961,688.45 511,243.68 1,961,688.45
15/03/2013 Entry 102.79 256.74 100000 -33045 (1,795,026.70) 166,661.75
13/06/2013 Exit 63 114.99 272.43 -100000 33045 2,496,550.65 2,663,212.40 701,523.95 2,663,212.40
21/06/2013 Entry 112.38 248.67 -100000 37300 1,962,609.00 4,625,821.40
22/07/2013 Exit 21 118.94 286 100000 -37300 (1,226,200.00) 3,399,621.40 736,409.00 3,399,621.40
17/10/2013 Entry 116.92 298.51 100000 -32328 (2,041,768.72) 1,357,852.68
20/03/2014 Exit 106 124.44 300.99 -100000 32328 2,713,595.28 4,071,447.96 671,826.56 4,071,447.96
14/08/2014 Entry 135.3 314.72 -100000 35483 2,362,790.24 6,434,238.20
26/08/2014 Exit 9 136.25 336.47 100000 -35483 (1,686,034.99) 4,748,203.21 676,755.25 4,748,203.21
07/10/2014 Entry 136.72 318.85 -100000 35391 2,387,579.65 7,135,782.86
13/02/2015 Exit 90 148.34 376.04 100000 -35391 (1,525,568.36) 5,610,214.50 862,011.29 5,610,214.50
15/04/2015 Entry 142.71 376.66 100000 -31272 (2,492,088.48) 3,118,126.02
08/05/2015 Exit 18 148.31 370.04 -100000 31272 3,259,109.12 6,377,235.14 767,020.64 6,377,235.14
28/07/2015 Entry 143.22 336.84 -100000 35094 2,500,937.04 8,878,172.18
14/10/2015 Exit 56 131.18 322.47 100000 -35094 (1,801,237.82) 7,076,934.36 699,699.22 7,076,934.36
05/11/2015 Entry 136.57 357.3 100000 -31548 (2,384,899.60) 4,692,034.76
14/12/2015 Exit 27 132.02 319.6 -100000 31548 3,119,259.20 7,811,293.96 734,359.60 7,811,293.96
08/03/2016 Entry 137.8 320.4 -100000 35498 2,406,440.80 10,217,734.76
Trades List
Total Profit (Loss) if open positions are closed on last day: 2,029,554.07$
Profit(Loss) on closed positions: 2,029,554.07$
Maximum negative excursion of any trade: (477,821.57)$
Maximum positive excursion of any trade: 563,418.90$

Graph 4.1.16(A):
Part One : Nigerian Pairs
(A)SDM = 1
ZENITH/GTB
Graph 4.1.1.1(A): Profit/Loss
Date Entry/Exit Trading Days JPM US Equity WFC US Equity JPM US Equity WFC US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 44.84 34.02 -100000 135585 (128,601.70) (128,601.70)
11/05/2012 Exit 22 36.96 33.31 100000 -135585 820,336.35 691,734.65 691,734.65 691,734.65
14/05/2012 Entry 35.79 32.41 100000 -113596 102,646.36 794,381.01
11/10/2012 Exit 106 42.1 35.18 -100000 113596 213,692.72 1,008,073.73 316,339.08 1,008,073.73
16/10/2012 Entry 42.83 33.73 -100000 130621 (122,846.33) 885,227.40
17/03/2014 Exit 354 57.58 48.13 100000 -130621 528,788.73 1,414,016.13 405,942.40 1,414,016.13
05/05/2014 Entry 54.22 49.56 100000 -112541 155,531.96 1,569,548.09
23/06/2015 Exit 287 69.75 57.89 -100000 112541 460,001.51 2,029,549.60 615,533.47 2,029,549.60
Trades List

Graph 4.1.1.2(A):
Graph 4.1.1.3(A):

Graph 4.1.1.4(A):
NESTLE/UNILEVER
Graph 4.1.1.5(A)
Graph 4.1.1.6(A)
Graph 4.1.1.7(A):
TRADE LIST
Date Entry/Exit Trading Days ZENITHBA NL Equity GUARANTY NL Equity ZENITHBA NL Equity GUARANTY NL Equity Cashflow Cashflow P&L P&L
12/04/2010 Entry 15.1 14.66 -100000 88244 216,342.96 216,342.96
19/07/2010 Exit 68 12.5 13.95 100000 -88244 (18,996.20) 197,346.76 197,346.76 197,346.76
27/07/2010 Entry 13.95 13.6 -100000 87877 199,872.80 397,219.56
25/10/2011 Exit 309 12.27 13.6 100000 -87877 (31,872.80) 365,346.76 168,000.00 365,346.76
25/11/2011 Entry 11.51 14.38 100000 -68574 (164,905.88) 200,440.88
24/01/2012 Exit 40 11.96 13.02 -100000 68574 303,166.52 503,607.40 138,260.64 503,607.40
25/06/2013 Entry 17.88 24 100000 -63826 (256,176.00) 247,431.40
16/07/2013 Exit 16 21.47 25.9 -100000 63826 493,906.60 741,338.00 237,730.60 741,338.00
30/12/2013 Entry 24.87 27 -100000 78914 356,322.00 1,097,660.00
08/01/2014 Exit 7 22.7 28.15 100000 -78914 (48,570.90) 1,049,089.10 307,751.10 1,049,089.10
17/03/2014 Entry 21.38 22.67 -100000 80797 306,332.01 1,355,421.11
24/03/2014 Exit 6 20.15 25.7 100000 -80797 61,482.90 1,416,904.01 367,814.91 1,416,904.01
14/10/2014 Entry 21.38 29.14 100000 -62858 (306,317.88) 1,110,586.13
22/10/2014 Exit 7 22.6 27.41 -100000 62858 537,062.22 1,647,648.35 230,744.34 1,647,648.35
12/12/2014 Entry 17.25 22.49 100000 -65711 (247,159.61) 1,400,488.74
15/01/2015 Exit 21 15.7 17.52 -100000 65711 418,743.28 1,819,232.02 171,583.67 1,819,232.02
06/02/2015 Entry 16.1 21 100000 -65682 (230,678.00) 1,588,554.02
12/02/2015 Exit 5 15.69 17.86 -100000 65682 395,919.48 1,984,473.50 165,241.48 1,984,473.50
27/02/2015 Entry 17.6 23.5 100000 -64163 (252,169.50) 1,732,304.00
05/03/2015 Exit 5 19 22.03 -100000 64163 486,489.11 2,218,793.11 234,319.61 2,218,793.11
20/03/2015 Entry 16.49 22.9 100000 -61691 (236,276.10) 1,982,517.01
07/04/2015 Exit 11 23.8 28.79 -100000 61691 603,916.11 2,586,433.12 367,640.01 2,586,433.12
29/04/2015 Entry 20.9 28.3 100000 -63270 (299,459.00) 2,286,974.12
Maximum negative excursion of any trade: (44,699,937.92)$
Maximum positive excursion of any trade: 30,803,107.27$

Graph 4.1.1.8(A)
Part Two: American Pairs
(B) SDM = 1.5
FORD/GM
Graph 4.2.1(B): Profit/Loss
Graph 4.2.2(B):
TRADE LIST
Date Entry/Exit Trading Days NESTLE NL Equity UNILEVER NL Equity NESTLE NL Equity UNILEVER NL Equity Cashflow Cashflow P&L P&L
12/04/2010 Entry 248.15 27.25 100000 -1590849 18,535,635.25 18,535,635.25
25/05/2010 Exit 30 298.38 23.7 -100000 1590849 (7,865,121.30) 10,670,513.95 10,670,513.95 10,670,513.95
12/10/2010 Entry 299.25 28.81 100000 -1814563 22,352,560.03 33,023,073.98
13/12/2010 Exit 43 315.83 24.2 -100000 1814563 (12,329,424.60) 20,693,649.38 10,023,135.43 20,693,649.38
21/01/2011 Entry 337.5 30.61 100000 -1926157 25,209,665.77 45,903,315.15
24/02/2011 Exit 24 391.67 27.6 -100000 1926157 (13,994,933.20) 31,908,381.95 11,214,732.57 31,908,381.95
11/04/2011 Entry 366.67 22.56 -100000 2839340 (27,388,510.40) 4,519,871.55
14/06/2011 Exit 42 400.49 29 100000 -2839340 42,291,860.00 46,811,731.55 14,903,349.60 46,811,731.55
28/09/2012 Entry 580 42.11 100000 -2406157 43,323,271.27 90,135,002.82
19/12/2013 Exit 304 1190 53 -100000 2406157 (8,526,321.00) 81,608,681.82 34,796,950.27 81,608,681.82
26/02/2014 Entry 1071.31 43.32 -100000 4320240 (80,021,796.80) 1,586,885.02
10/06/2014 Exit 71 1080.01 50.65 100000 -4320240 110,819,156.00 112,406,041.02 30,797,359.20 112,406,041.02
22/10/2014 Entry 983 40.16 -100000 4276032 (73,425,445.12) 38,980,595.90
20/05/2015 Exit 144 880 45.1 100000 -4276032 104,849,043.20 143,829,639.10 31,423,598.08 143,829,639.10
21/07/2015 Entry 856.93 38.1 -100000 3929176 (64,008,605.60) 79,821,033.50
04/09/2015 Exit 34 820 44.1 100000 -3929176 91,276,661.60 171,097,695.10 27,268,056.00 171,097,695.10
02/11/2015 Entry 821 36.75 -100000 3902716 (61,324,813.00) 109,772,882.10
02/12/2015 Exit 23 807 43.98 100000 -3902716 90,941,449.68 200,714,331.78 29,616,636.68 200,714,331.78
01/02/2016 Entry 739.99 33.48 -100000 3861193 (55,273,741.64) 145,440,590.14
Total Profit (Loss) if open positions are closed on last day: $ 833,774.75
Profit(Loss) on closed positions: $ 779,928.67

Graph 4.2.3(B):
Table 4.2.1(B):
BRK A/BLK
Graph 4.2.4(B):
Date Entry/Exit Trading Days F US Equity GM US Equity F US Equity GM US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 12.07 24.3 -100000 51667 (48,508.10) (48,508.10)
17/08/2012 Exit 90 9.63 22.01 100000 -51667 174,190.67 125,682.57 125,682.57 125,682.57
22/01/2013 Entry 14.17 28.63 -100000 51483 (56,958.29) 68,724.28
15/04/2013 Exit 58 12.95 28.91 100000 -51483 193,373.53 262,097.81 136,415.24 262,097.81
23/10/2013 Entry 17.52 35.05 -100000 51995 (70,424.75) 191,673.06
01/11/2013 Exit 8 16.89 37.39 100000 -51995 255,093.05 446,766.11 184,668.30 446,766.11
09/12/2013 Entry 16.56 40.9 100000 -42116 66,544.40 513,310.51
31/03/2014 Exit 77 15.6 34.42 -100000 42116 110,367.28 623,677.79 176,911.68 623,677.79
24/07/2014 Entry 17.84 35.74 -100000 51922 (71,692.28) 551,985.51
01/10/2014 Exit 49 14.59 32.49 100000 -51922 227,945.78 779,931.29 156,253.50 779,931.29
05/11/2015 Entry 14.57 35.44 100000 -42764 58,556.16 838,487.45
Trades List

Graph 4.2.5(B):
Graph 4.2.6(B):
Total Profit (Loss) if open positions are closed on last day: $ 10,239,745,017.32
Profit(Loss) on closed positions: $ 10,239,745,017.32
Is position open on last day: No
Maximum negative excursion of any trade: $ (1,163,710,869.47)
Maximum positive excursion of any trade: $ 1,689,058,898.68

Table 4.2.2(B):
BRK B/BLK
Graph 4.2.7(B):
Graph 4.2.8(B):
Date Entry/Exit Trading Days BRK/A US Equity BLK US Equity BRK/A US Equity BLK US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 120173 201.71 100000 -49192226 (2,094,736,093.54) (2,094,736,093.54)
08/05/2012 Exit 19 123744 182.34 -100000 49192226 3,404,689,511.16 1,309,953,417.62 1,309,953,417.62 1,309,953,417.62
27/06/2012 Entry 122950 166.38 -100000 61016095 2,143,142,113.90 3,453,095,531.52
10/12/2012 Exit 114 130788 195.72 100000 -61016095 (1,136,729,886.60) 2,316,365,644.92 1,006,412,227.30 2,316,365,644.92
20/03/2013 Entry 153397 258.7 100000 -48959552 (2,673,863,897.60) (357,498,252.68)
13/06/2013 Exit 60 172604 272.43 -100000 48959552 3,922,349,248.64 3,564,850,995.96 1,248,485,351.04 3,564,850,995.96
22/10/2013 Entry 176140 306.22 100000 -47494294 (3,070,297,291.32) 494,553,704.64
21/03/2014 Exit 104 187850 301.86 -100000 47494294 4,448,372,413.16 4,942,926,117.80 1,378,075,121.84 4,942,926,117.80
10/10/2014 Entry 205150 308.87 -100000 54841938 3,575,970,609.94 8,518,896,727.74
13/02/2015 Exit 87 222555 376.04 100000 -54841938 (1,632,737,634.48) 6,886,159,093.26 1,943,232,975.46 6,886,159,093.26
31/08/2015 Entry 202531 302.47 -100000 55287404 3,530,318,912.12 10,416,478,005.38
14/10/2015 Exit 32 196898.98 322.47 100000 -55287404 (1,861,368,832.12) 8,555,109,173.26 1,668,950,080.00 8,555,109,173.26
30/11/2015 Entry 201360 363.72 100000 -45711242 (3,509,907,059.76) 5,045,202,113.50
14/12/2015 Exit 11 198040 319.6 -100000 45711242 5,194,687,056.80 10,239,889,170.30 1,684,779,997.04 10,239,889,170.30
Trades List
Maximum positive excursion of any trade: $ 1,109,269.44

Graph 4.2.9(B):
Table 4.2.3(B):
JPM/WFC
Graph 4.2.10(B):
Date Entry/Exit Trading DaysBRK/B US EquityBLK US Equity BRK/B US Equity BLK US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 80.06 201.71 100000 -32759 (1,398,182.11) (1,398,182.11)
10/05/2012 Exit 21 81.78 179.68 -100000 32759 2,291,862.88 893,680.77 893,680.77 893,680.77
27/06/2012 Entry 81.98 166.38 -100000 40668 1,431,658.16 2,325,338.93
10/12/2012 Exit 114 87.1 195.72 100000 -40668 (750,459.04) 1,574,879.89 681,199.12 1,574,879.89
21/05/2013 Entry 112.7 291.69 100000 -31890 (1,968,005.90) (393,126.01)
13/06/2013 Exit 17 114.99 272.43 -100000 31890 2,811,207.30 2,418,081.29 843,201.40 2,418,081.29
22/10/2013 Entry 117.49 306.22 100000 -31668 (2,051,625.04) 366,456.25
20/03/2014 Exit 103 124.44 300.99 -100000 31668 2,912,248.68 3,278,704.93 860,623.64 3,278,704.93
10/10/2014 Entry 136.76 308.87 -100000 36545 2,388,345.85 5,667,050.78
13/02/2015 Exit 87 148.34 376.04 100000 -36545 (1,091,618.20) 4,575,432.58 1,296,727.65 4,575,432.58
31/08/2015 Entry 134.04 302.47 -100000 36576 2,340,857.28 6,916,289.86
14/10/2015 Exit 32 131.18 322.47 100000 -36576 (1,323,337.28) 5,592,952.58 1,017,520.00 5,592,952.58
30/11/2015 Entry 134.09 363.72 100000 -30428 (2,341,727.84) 3,251,224.74
14/12/2015 Exit 11 132.02 319.6 -100000 30428 3,477,211.20 6,728,435.94 1,135,483.36 6,728,435.94
Trades List

Graph 4.2.11(B):
Graph 4.2.12(B):
Table 4.2.4
Part Two: Nigerian Pairs
(B) SDM = 1.5
Date Entry/Exit Trading Days JPM US Equity WFC US Equity JPM US Equity WFC US Equity Cashflow Cashflow P&L P&L
12/04/2012 Entry 44.84 34.02 -100000 135585 (128,601.70) (128,601.70)
11/05/2012 Exit 22 36.96 33.31 100000 -135585 820,336.35 691,734.65 691,734.65 691,734.65
21/05/2012 Entry 32.51 31.4 100000 -106505 93,257.00 784,991.65
11/10/2012 Exit 101 42.1 35.18 -100000 106505 463,154.10 1,248,145.75 556,411.10 1,248,145.75
14/01/2013 Entry 45.88 34.77 -100000 135738 (131,610.26) 1,116,535.49
17/03/2014 Exit 295 57.58 48.13 100000 -135738 775,069.94 1,891,605.43 643,459.68 1,891,605.43
02/07/2014 Entry 56.97 52.66 100000 -111288 163,426.08 2,055,031.51
23/06/2015 Exit 246 69.75 57.89 -100000 111288 532,537.68 2,587,569.19 695,963.76 2,587,569.19
Trades List

ZENITH/GTB
Graph 4.2.1.1(B): Profit/Loss
Graph 4.2.1.2(B):
Graph 4.2.1.3(B):

Table 4.2.1.1(B):
NESTLE/UNILEVER
Graph 4.2.1.4(B):
Graph 4.2.1.5(B):
TRADE LIST
Date Entry/Exit Trading Days ZENITHBA NL Equity GUARANTY NL Equity ZENITHBA NL Equity GUARANTY NL Equity Cashflow Cashflow P&L P&L
13/04/2010 Entry 14.84 14.11 -100000 90105 212,618.45 212,618.45
19/07/2010 Exit 67 12.5 13.95 100000 -90105 6,964.75 219,583.20 219,583.20 219,583.20
30/07/2010 Entry 14.21 13.44 -100000 90581 203,591.36 423,174.56
25/10/2011 Exit 306 12.27 13.6 100000 -90581 4,901.60 428,076.16 208,492.96 428,076.16
31/12/2013 Entry 27.4 27.02 -100000 86877 392,583.46 820,659.62
08/01/2014 Exit 6 22.7 28.15 100000 -86877 175,587.55 996,247.17 568,171.01 996,247.17
18/12/2014 Entry 15.37 21 100000 -62704 (220,216.00) 776,031.17
15/01/2015 Exit 17 15.7 17.52 -100000 62704 471,425.92 1,247,457.09 251,209.92 1,247,457.09
20/03/2015 Entry 16.49 22.9 100000 -61691 (236,276.10) 1,011,180.99
07/04/2015 Exit 11 23.8 28.79 -100000 61691 603,916.11 1,615,097.10 367,640.01 1,615,097.10
06/07/2015 Entry 19 26.8 100000 -60738 (272,221.60) 1,342,875.50
Maximum negative excursion of any trade: (39,374,797.60)$
Maximum positive excursion of any trade: 50,629,204.20$

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