1. TD Strategies QF206: Quantitative Trading Strategies
Gui Feng | Darren Lew | Boon Hao | Charlton Tan | Shao Jie | T Kumereash

2. Introduction
TD Strategies
Equity Curves
Order Flow

3. INTRODUCTION SGX Nikkei 225 Index Futures Key Information
1. Derivatives product offered by the Singapore Stock Exchange
2. Derived from Japan’s premiere stock index, the Nikkei 225 index
3.Nikkei 225 was established in 1950, and consists of 225 blue-chip companies listed on the Tokyo Stock Exchange
Key Information
Trading Hours:
Monday to Friday, 0730 – 1430 (SGT)
Trading Period:
We define each trading bar as one minute, and each dataset as one day.
Commission:
Each market order (long/short) incurs a commission of ¥225. A total of ¥450 is incurred for each round trip.
Contract specification:
One contract size = ¥500 x Nikkei 225 Index Futures Price
Minimum price fluctuation: Outright: 5 index points (¥2500)
Trading conditions
All positions must be closed at the end of each day
Only one contract can be traded for each transaction
Introduction
TD Strategies
Equity Curve
Order Flow

4. Define theta as the holding period before position is squared off.
Procedure 1 2 3 4
Back test each strategy on the historical data. Identify the trading signals (long/short) based on each individual strategy’s conditions.
Define theta as the holding period before position is squared off.
70% of the signals identified are used to find the optimal value of theta, which results in the highest level of profits.
Using the previously identified optimal value of theta, measure the out-of-sample performance of the trading strategy in the other 30% of the signals.
Introduction
TD Strategies
Equity Curve
Order Flow

5. 70% of signals to find theta
TD Strategies
Interpretations of the 5 TD alternative strategies
Number of buy/sell signals generated from data set:
Strategy
# of Buy Signals
# of Sell Signals
Total # of Signals
70% of signals to find theta
TD Clop
TD Camouflage 2 4 6
TD Clopwin
443
436
879
615
TD Open
494
473
967
677
TD Trap
1471
1527
2998
2099
Optimal holding period without commission factor
We want to backtest without commission factor to identify any potential strategy that can perform without commission factor. Also, this helps us to identify any strategy that produce consistent negative PnL and t-distribution (without commission factor), so that we can flip the strategy around to create a viable strategy.
Introduction
TD Strategies
Equity Curve
Order Flow

6. Overall performance was poor, did not conduct further test on 30% data
Results
TD Camouflage
TD Clopwin
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1 4
¥2,500.00
-¥1,250.00
0.50
0.522 2
-¥7,500.00
¥5,000.00
-¥4,166.67
0.25
-0.792 3
¥0.00
-¥2,500.00
0.000
¥10,000.00
1.732 5
1.414 6
¥12,500.00
¥4,166.67
0.75
1.987 7 8
-¥3,750.00
0.225 9
¥6,250.00
-¥5,000.00
0.182 10
-¥12,500.00
-0.951 11
-¥10,000.00
-0.739 12 13
-¥22,500.00
-¥5,625.00
0.00
-1.711 14
-¥25,000.00
-¥6,250.00
-1.353 15 16
-¥20,000.00
-¥8,333.33
-1.414 17
-¥9,166.67
-1.362 18
-0.816 19
-0.174 20
¥7,500.00
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
615
-¥500.00
¥74.33
-¥28.70
0.423
-0.162 2
614
-¥1,750.00
¥74.62
-¥38.36
0.428
-0.480 3
605
-¥1,175.00
¥86.40
-¥55.21
0.507
-0.233 4
592
¥1,150.00
¥102.91
-¥62.23
0.508
0.253 5
585
¥1,300.00
¥104.07
-¥71.52
0.525
0.276 6
568
¥3,300.00
¥114.14
-¥69.71
0.523
0.699 7
551
¥3,550.00
¥116.08
-¥78.71
0.544
0.728 8
535
¥5,475.00
¥127.72
-¥82.82
0.566
1.076 9
526
¥2,800.00
¥129.11
-¥89.16
0.532
0.554 10
516
¥1,450.00
¥129.02
-¥104.49
0.543
0.279 11
512
¥1,525.00
¥139.91
-¥97.96
0.518
0.289 12
502
¥2,225.00
¥146.47
-¥106.41
0.536
0.412 13
495
¥1,100.00
¥140.67
-¥123.26
0.590
0.197 14
488
¥1,250.00
¥167.57
-¥115.97
0.551
0.199 15
477
¥725.00
¥172.36
-¥125.43
0.537
0.121 16
469
-¥100.00
¥169.11
-¥128.86
0.561
-0.017 17
462
¥25.00
¥180.88
-¥128.28
0.552
0.004 18
457
-¥50.00
¥177.65
-¥136.92
0.578
-0.008 19
450
-¥250.00
¥177.15
-¥138.17
0.569
-0.041 20
444
¥425.00
¥177.37
-¥148.19
0.595
0.069
Overall performance was poor, did not conduct further test on 30% data
Introduction
TD Strategies
Equity Curve
Order Flow

7. Results TD Open – on 70% data TD Open (Reversed) – on 70% data
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
677
-¥112,500.00
¥4,297.24
-¥2,271.74
0.321
-0.671 2
674
-¥50,000.00
¥5,746.12
-¥3,683.89
0.383
-0.214 3
661
-¥150,000.00
¥6,564.75
-¥5,156.66
0.421
-0.535 4
648
-¥312,500.00
¥7,527.88
-¥6,167.55
0.415
-1.015 5
627
-¥342,500.00
¥9,077.95
-¥7,500.00
0.419
-0.818 6
609
-¥400,000.00
¥9,767.21
-¥7,769.34
0.406
-0.902 7
593
-¥442,500.00
¥9,783.46
-¥8,635.69
0.428
-0.879 8
577
-¥320,000.00
¥10,396.83
-¥9,046.15
0.437
-0.643 9
564
-¥407,500.00
¥10,873.49
-¥9,888.89
0.441
-0.804 10
556
-¥555,000.00
¥11,097.56
-¥10,596.77
0.442
-1.068 11
547
-¥637,500.00
¥11,336.03
-¥11,458.33
0.452
-1.190 12
543
-¥415,000.00
¥12,076.77
-¥12,050.17
0.468
-0.763 13
538
-¥520,000.00
¥13,119.83
-¥12,483.11
0.450
-0.927 14
529
-¥597,500.00
¥14,008.44
-¥13,416.10
0.448
-0.975 15
518
-¥307,500.00
¥15,240.17
-¥13,140.14
-0.498 16
506
-¥490,000.00
¥15,010.87
-¥14,284.42
0.455
-0.784 17
498
-¥425,000.00
¥15,443.72
-¥14,953.18
0.464
-0.678 18
486
-¥667,500.00
¥15,136.36
-¥15,028.20
0.453
-1.116 19
480
-¥837,500.00
¥15,271.23
-¥15,205.22
-1.371 20
472
-¥215,000.00
¥16,040.72
-¥14,980.08
-0.358
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
677
¥112,500
¥4,624
-¥2,068
0.334
0.671 2
674
¥35,000
¥5,984
-¥3,536
0.377
0.150 3
664
¥202,500
¥7,586
-¥4,440
0.395
0.729 4
646
¥297,500
¥8,666
-¥5,357
0.415
0.967 5
627
¥295,000
¥10,000
-¥6,690
0.429
0.708 6
604
¥352,500
¥10,277
-¥7,305
0.449
0.795 7
596
¥445,000
¥11,327
-¥7,440
0.436
0.884 8
576
¥290,000
¥11,163
-¥8,267
0.451
0.584 9
562
¥405,000
¥12,500
-¥8,583
0.441
0.800 10
554
¥575,000
¥13,236
-¥8,848
0.448
1.107 11
550
¥585,000
¥14,053
-¥9,218
0.442
1.093 12
542
¥490,000
¥15,281
-¥9,775
0.426
0.901 13
536
¥535,000
¥15,657
-¥10,533
0.440
0.954 14
525
¥517,500
¥15,861
-¥11,637
0.459
0.850 15
518
¥272,500
¥15,985
-¥12,411
0.456 16
505
¥485,000
¥17,270
-¥12,464
0.776 17
498
¥425,000
¥17,124
-¥13,453
0.468
0.678 18
488
¥772,500
¥17,608
-¥12,939
0.475
1.266 19
482
¥707,500
¥17,731
-¥13,010
0.471
1.157 20
476
¥180,000
¥16,883
-¥14,170
0.299
As for TD Open, the P&L and t-distribution is consistently negative, hence we flip over the buy and sell conditions for another round of backtesting.
For the reversed TD Open, the results were fair, with consistent positive P&L and t-distribution. The optimal holding period is around 10, so we’ve carried out the reversed TD Open on the remaining 30% of the data to test whether it is true that optimal theta is at 10
Since the TD open strategy consistently generates negative P&L and t-distribution, the buy and sell strategy are flipped for another round of backtesting
Introduction
TD Strategies
Equity Curve
Order Flow

8. Overall performance was poor
Results
TD Open (Reversed) – on 30% data
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
290
¥210,000.00
¥5,024.75
-$1,574.07
0.348
1.762 2
288
¥200,000.00
¥5,491.45
-$2,587.72
0.406
1.547 3
283
¥162,500.00
¥6,080.00
-$3,781.65
0.442
0.928 4
278
-¥35,000.00
¥6,320.00
-$5,392.16
0.450
-0.143 5
276
¥27,500.00
¥7,747.93
-$5,870.97
0.438
0.103 6
268
-¥137,500.00
¥8,557.69
-$6,265.24
0.388
-0.506 7
260
¥0.00
¥9,086.96
-$7,206.90
0.000 8
256
-¥72,500.00
¥9,791.67
-$7,635.14
0.422
-0.249 9
252
¥5,000.00
¥10,044.25
-$8,129.50
0.448
0.017 10
249
-¥107,500.00
¥10,514.02
-$8,679.58
0.430
-0.352 11
246
-¥97,500.00
¥10,306.60
-$8,500.00
0.431
-0.331 12
241
-¥105,000.00
¥11,480.58
-$9,329.71
0.427
-0.317 13
238
-¥60,000.00
¥11,533.02
-$9,715.91
0.445
-0.182 14
234
-¥92,500.00
¥12,075.00
-$9,701.49
-0.276 15
228
-¥50,000.00
¥13,421.05
-$9,962.41
0.417
-0.146 16
222
-¥52,500.00
¥12,500.00
-$10,120.00
0.437
-0.159 17
221
-¥142,500.00
¥13,152.17
-$10,484.50
0.416
-0.435 18
219
-¥312,500.00
¥12,419.35
-$11,646.83
0.425
-0.941 19
217
-¥307,500.00
¥11,975.00
-$12,863.25
0.461
-0.900 20
213
-¥147,500.00
¥13,385.42
-$12,243.59
0.451
-0.432
However, on the 30% of the data, when holding period is at 10, it produces huge amount of losses and the t-distribution is negative at
Hence due to the inconsistency of the optimal holding period we’ve conlcuded from different sets of data, the reversed TD Open will not be a viable strategy
Overall performance was poor
Introduction
TD Strategies
Equity Curve
Order Flow

9. Relatively consistent and solid PnL returns
Results
TD Trap without commission – on 70% data
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
2099
¥840,000.00
¥7,658.47
-¥3,831.07
0.368
1.659 2
1709
¥825,000.00
¥9,531.95
-¥5,395.75
0.394
1.304 3
1494
¥315,000.00
¥10,927.62
-¥7,001.68
0.402
0.477 4
1339
¥1,132,500.00
¥12,678.25
-¥7,686.38
0.419
1.641 5
1218
¥982,500.00
¥13,372.09
-¥8,429.49
0.424
1.389 6
1125
¥420,000.00
¥13,713.24
-¥9,410.63
0.423
0.604 7
1060
¥430,000.00
¥14,682.02
-¥10,372.52
0.430
0.544 8
989
-¥177,500.00
¥14,133.72
-¥11,189.62
0.435
-0.238 9
932
¥60,000.00
¥14,782.08
-¥11,647.40
0.443
0.081 10
878
¥67,500.00
¥15,693.72
-¥11,950.60
0.089 11
838
¥490,000.00
¥16,554.23
-¥12,538.04
0.451
0.634 12
810
¥15,000.00
¥16,764.71
-¥14,346.33
0.462
0.019 13
769
¥1,482,500.00
¥18,180.59
-¥13,222.36
0.482
1.908 14
742
-¥52,500.00
¥17,478.45
-¥15,571.07
0.469
-0.064 15
716
¥610,000.00
¥19,489.49
-¥15,352.48
0.465
0.754 16
689
¥390,000.00
¥19,283.54
-¥16,440.44
0.476 17
663
¥272,500.00
¥20,538.08
-¥16,426.59
0.456
0.317 18
649
¥890,000.00
¥21,599.33
-¥15,696.02
0.458
1.074 19
628
¥537,500.00
¥20,790.82
-¥16,691.62
0.468
0.664 20
607
¥337,500.00
¥20,955.36
-¥16,911.31
0.461
0.415
Relatively consistent and solid PnL returns
Introduction
TD Strategies
Equity Curve
Order Flow

10. Results TD Trap without commission – on 30% data
Holding Period
Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
899
¥1,005,000.00
¥8,856.30
-$3,611.11
0.379
1.818 2
748
¥875,000.00
¥10,289.97
-$5,611.89
0.426
1.438 3
656
¥1,152,500.00
¥12,282.99
-$6,480.98
0.439
1.759 4
591
¥882,500.00
¥13,541.67
-$7,463.13
1.319 5
553
¥657,500.00
¥13,000.00
-$8,206.17
0.443
0.983
From 70% data, we observe that optimal theta is between the range of 1 to 5
Results from 30% for theta between the range of 1 to 5 further proves this:
Relatively consistent and high positive PnL
Highest PnL of ¥1,152, at theta = 3
High t-distribution with an average of 1.46
Highest t-distribution of at theta = 1
Introduction
TD Strategies
Equity Curve
Order Flow

11. Results TD Trap - Optimal holding period with commission factor
By applying the optimal value of theta = 1 to 5 to the 70% of dataset (with commission), we obtain the following results:
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
2099
-¥94,055.00
¥7,213.47
-$4,276.07
0.368
-0.186 2
1709
¥64,495.00
¥9,086.95
-$5,840.75
0.394
0.102 3
1494
-¥349,830.00
¥10,482.62
-$7,446.68
0.402
-0.529 4
1339
¥536,645.00
¥12,233.25
-$8,131.38
0.419
0.778 5
1218
¥440,490.00
¥12,927.09
-$8,874.49
0.424
0.623 6
1125
-¥80,625.00
¥13,268.24
-$9,855.63
0.423
-0.116 7
1060
-¥41,700.00
¥14,237.02
-$10,817.52
0.430
-0.053 8
989
-¥617,605.00
¥13,688.72
-$11,634.62
0.435
-0.827 9
932
-¥354,740.00
¥14,337.08
-$12,092.40
0.443
-0.478 10
878
-¥323,210.00
¥15,248.72
-$12,395.60
-0.428 11
838
¥117,090.00
¥16,109.23
-$12,983.04
0.451
0.152 12
810
-¥345,450.00
¥16,319.71
-$14,791.33
0.462
-0.429 13
769
¥1,140,295.00
¥17,735.59
-$13,667.36
0.482
1.468 14
742
-¥382,690.00
¥17,033.45
-$16,016.07
0.469
-0.468 15
716
¥291,380.00
¥19,044.49
-$15,797.48
0.465
0.360 16
689
¥83,395.00
¥18,838.54
-$16,885.44
0.476 17
663
-¥22,535.00
¥20,093.08
-$16,871.59
0.456
-0.026 18
649
¥601,195.00
¥21,154.33
-$16,141.02
0.458
0.725 19
628
¥258,040.00
¥20,345.82
-$17,136.62
0.468
0.319 20
607
¥67,385.00
¥20,510.36
-$17,356.31
0.461
0.083
With the addition of the commission factor, the P&L for the TD Trap strategy reflects its infeasibility for the 70% data
Introduction
TD Strategies
Equity Curve
Order Flow

12. Results TD Trap - Optimal holding period with commission factor
By applying the optimal value of theta = 1 to 5 to the 30% of dataset (with commission), we obtain the following results:
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution 1
899
¥600,450.00
¥8,406.30
-$4,061.11
0.379
1.086 2
748
¥538,400.00
¥9,839.97
-$6,061.89
0.426
0.885 3
656
¥857,300.00
¥11,832.99
-$6,930.98
0.439
1.308 4
591
¥616,550.00
¥13,091.67
-$7,913.13
0.921 5
553
¥408,650.00
¥12,550.00
-$8,656.17
0.443
0.611 6
520
¥311,000.00
¥13,870.18
-$9,765.07
0.438
0.456 7
480
-¥1,053,500.00
¥11,512.62
-$13,222.56
0.446
-1.554 8
445
-¥600,250.00
¥11,816.36
-$13,545.24
0.481
-0.883 9
427
¥972,850.00
¥15,763.94
-$10,529.91
0.487
1.472 10
412
¥1,037,100.00
¥16,502.74
-$10,805.45
0.488
1.559 11
393
¥860,650.00
¥17,547.31
-$11,609.42
0.473
1.257 12
382
¥555,600.00
¥16,983.16
-$13,437.18
0.490
0.794 13
365
¥508,250.00
¥17,944.89
-$14,021.43
0.482
0.741 14
358
-¥183,600.00
¥15,552.82
-$16,223.48
0.494
-0.268 15
350
-¥460,000.00
¥15,762.12
-$16,544.59
0.471
-0.676 16
345
-¥462,750.00
¥16,153.77
-$16,296.77
0.461
-0.678 17
336
¥473,800.00
¥20,388.82
-$14,267.93
0.452
0.664 18
322
-¥824,900.00
¥16,101.72
-$17,851.13
0.450
-1.245 19
306
-¥675,200.00
¥17,264.29
-$18,627.71
0.458
-0.983 20
297
-¥211,150.00
¥19,242.03
-$18,028.62
0.465
-0.299
With the addition of the commission factor, the P&L for the TD Trap strategy shows promise for the 30% data
Introduction
TD Strategies
Equity Curve
Order Flow

13. Equity Curve TD Open – with vs without commission
The max drawdown duration for TD Open is 99 days (August – November
The max drawdown duration for TD Open is 113 days (July – November ).
The Max drawdown for TD Open strategy is -90,750 – (-236,100) = 145,350
The Max drawdown for TD Open strategy is 152,500 – 52,500 = 100,000
Introduction
TD Strategies
Equity Curve
Order Flow

14. Equity Curve TD Trap – with vs without commission
1,670,000
August 12, :01 AM
November 9, :41 PM
The max drawdown duration for TD Trap is 56 days (September – November ).
The max drawdown duration for TD Trap is 90 days (August – November ).
The Max drawdown for TD trap strategy is ,450 – 408,450 = 399,000
The Max drawdown for TD trap strategy is 1,720,000 – 1,312,500 = 407,500
Introduction
TD Strategies
Equity Curve
Order Flow

15. Intermediate Summary of TD Strategies
Strategy
Remarks
TD Clop
No Signal
TD Camouflage
Poor Performance
TD Clopwin
TD Open
Original Strategy gave consistent negative PnL  Flipped signals to give Reversed Open Strategy
Results were however, poor when tested on 30% Data
TD Trap
Most promising Strategy in term of Consistency as well as Significant of positive PnL results for Theta = 1-5 min
However, commission factors continues to weight down on strategy feasibility  Reduce the number of trades by making the conditions more stringent?
Drawbacks of TD alternative strategy
Through the analysis of the back testing results, it is observed that the profit to commission ratio is not ideal.
This results in lacklustre net profit numbers even for the strategy (TD Trap) with the optimal theta and the most consistent t-statistic.
Introduction
TD Strategies
Equity Curve
Order Flow

16. Order Flow Strategy TD Trap with order flow strategy
In order to decrease the impact of the commission factor, Order flow is utilised as an additional condition, to decrease the number of signals
Interpretation of order flow strategy
The order flow strategy has the following conditions:
Entry
If the order flow sign over the last x trades is positive, buy one lot at the ask immediately
If the order flow sign over the last x trades is negative, sell one lot at the bid immediately
Exit
Due to the use of the TD trap in tandem with the order flow strategy, exit signal is contingent on the holding period theta.
Procedure
Run the TD Trap with order flow strategy for theta between 1-12 and for X between 5 to 20 and determine which value for X generates the best results
Introduction
TD Strategies
Equity Curve
Order Flow

17. Order Flow Strategy Results
Holding Period
Number of Trades
PnL
Average gain
Average loss
Probability of win
t-distribution
x bar order flow 1
142
-¥26,400.00
¥5,582.61
-$2,950.00
0.324
-0.398 9 2
120
¥241,000.00
¥10,670.69
-$6,095.16
0.483
1.380 3
132
¥68,100.00
¥11,587.04
-$7,148.72
0.409
0.414 4
130
-¥11,000.00
¥12,790.74
-$9,232.89
0.415
-0.055 5
125
¥371,250.00
¥21,088.46
-$9,936.30
0.416
1.351 6
113
¥21,650.00
¥15,519.39
-$11,543.75
0.434
0.086 7
117
¥204,850.00
¥19,341.67
-$10,486.23
0.410
0.791 8
124
¥64,200.00
¥18,860.34
-$15,601.52
0.468
0.210
104
¥315,700.00
¥24,161.11
-$13,077.12
0.433
0.981 10
127
¥322,850.00
¥18,550.00
-$14,240.32
0.512
1.116 11
¥521,000.00
¥19,586.76
-$15,594.23
0.567
1.515 12
122
¥347,600.00
¥27,915.38
-$15,771.43
0.426
0.829
100% of data used due to decreased number of signals cased by additional condition
Introduction
TD Strategies
Equity Curve
Order Flow

18. Order Flow Assignment Order flow strategy Results
This is with commission. ( to )
Results
Aggregate 16 1-min bars ~ t-stat of 1.1
Passes sensitivity analysis
Stop loss strategy?
X value might change over time
Introduction
TD Strategies
Equity Curve
Order Flow

19. Conclusion and Recommendation
Problems
The 5 alternative TD strategies have soft conditions that resulted in large numbers of trading signals.
Due to the constraint of trading only 1 contract per trade, the commission factor played a big part in negating the PnL effect from the back testing results.
Solutions
The order flow strategy was used in the tandem with the TD trap strategy to increase the number of conditions and lower the number of trading signals, thus lowering the commission factor effect
Results & Recommendations
Through further back testing, results for holding period = 11 for X = 9 showed most promise; PnL was high, t-statistic was significant, and number of trades were significantly lower.
Therefore, our group recommends the TD trap strategy in tandem with the order flow strategy.
Introduction
TD Strategies
Equity Curve
Order Flow