Quote from Steven.Davis:
Various product and websites recommend different position sizing when pair trading.
I would like to do an analysis of different position sizing methods when pair trading. Does anyone have a pair trading history they would like to share? (I know I could type it in from this Journal, but a CSV/XLS would be so much easier.)
Please email me a CSV/XLS file with at least date, symbol long, symbol short, and whether you wish to be anonymous.
Thank you in advance.
I analyzed a trading record of 93 pair trades from October/November of 2010.
I calculated the Profit/Loss for these trades as if they had been sized each of the following four ways:
Method 1. Equal Number of Shares
Method 2. Equal Dollars (Face Value)
Method 3. Inverse to Beta
Method 4. Equal Long-Term Risk (Volatility, 10 year/max std dev)
Code:
ALL TRADES
Method 1 Method 2 Method 3 Method 4
Avg P/L 4.93 6.15 7.16 17.08
Std P/L 286.12 295.97 277.35 293.46
Sample Size 91 91 91 91
T-statistic 0 0.03 0.05 0.28
0 0.02 0.25
0 0.23
0
P-statistic 100.00% 98.00% 96.00% 78.00%
100% = 100.00% 98.00% 80.00%
insignificant 100.00% 82.00%
100.00%
Code:
WINNING TRADES
Method 1 Method 2 Method 3 Method 4
Avg P/L 159.69 158.1 158.04 185.23
Std P/L 110.78 104.17 112.26 124.9
Sample Size 62 65 61 59
T-statistic 0 -0.08 -0.08 1.19
0 0 1.31
0 1.25
0
P-statistic 100.00% 93.00% 94.00% 24.00%
100% = 100.00% 100.00% 19.00%
insignificant 100.00% 21.00%
100.00%
Code:
LOSING TRADES
Method 1 Method 2 Method 3 Method 4
Avg P/L -325.91 -373.71 -299.63 -292.95
Std P/L 216.2 228.83 207.75 213.31
Sample Size 29 26 30 32
T-statistic 0 -0.79 0.48 0.6
0 1.26 1.38
0 0.12
0
P-statistic 100.00% 43.00% 64.00% 55.00%
100% = 100.00% 21.00% 17.00%
insignificant 100.00% 90.00%
100.00%
There is a clear pattern to the results, but the sample size is too small to claim statistical significance.
Method 4 (Risk) would have produced the highest average profits, highest average winning trade, and least average loss. The 10-year volatility was computed from after the fact using in-sample data so it is not the exact number available at the beginning of the trade. For stocks with less than 10 years, the maximal available timeframe was used. Since this underestimates volatility and since the early history is probably not representative of the equilibrium, greater care should be used in real trading.
Method 3 (Beta) and Method 2 (Dollar Neutral) did equally well on winning trades. Method 3 (Beta) did quite a bit better on losing trades, but not statistically significantly.
Method 1 (Equal #) was probably treated unfairly. The entry prices differed by as much as 11 to 1. Someone really trading by equal number of shares would presumably have forgone of these trades, but the sample size is too small to fairly compare it with these trades removed either.
I would love to have more trades to add to this study, and I would love to have a working C++/C# Johansen cointegration module to compare against these results. (Having trouble getting even the core components of GRETL to compile under Visual Studio.)