How to determine the number of future contracts

There are two questions in this index pairs trading strategy:

1. The ratio of long/short contracts
2. The number of future contracts

At the beginning of 2015, 1 contract of E-mini NASDAQ 100 Index (NQ) is worth  $85, 459. The value of 1 contract of mini size of Dow Jones Avg Index future (YM) is $89,692. At the market close of April 30, these numbers are $88, 285 for NQ and $89, 202 for YM. Therefore, maintaining 1 for the ratio of long/short contracts is appropriate.

Backtesting results indicate that the maximum potential loss from our pairs trading strategy is less than $2000 per contract. However, in order to control the risk and the leverage, we would open 1 long/short contract for each $10,000 cash in the trading account. This will be sufficient to buff any market shocks.

Current signal: April 30

The current signal of the pairs trading is to long NASDAQ 100 and short Dow Jones Avg Industry. The signal appeared at 9:45 am April 30, 2015 EST. The current P&L is -$331.82 per future contract.

The theory of pairs trading

The pairs trading strategy has a long trading history. Many investors are still trading this strategy with different versions of model. The basic idea is still the mean reversion, which people believe that the relationship between two securities tends to return to its long-term mean.

However, as indicated in the paper, "Pairs trading with a fundamental flavor", Jussa, Chen, et al, Deutsche Bank global quantitative strategy, March 20, 2012, the profitability of pairs trading strategies has been declining in recent years, possible due to:

"

• The proliferation of quant and hedge funds that mobilize automated, instantaneous trading strategies
• Large inflows of capital chasing similar investment strategies could potentially have impacted arbitrage strategies like pairs trading.
• The dramatic increase in the availability of pricing and fundamental data enables savvy investors to easily develop standard pairs trading models.
• Limits to arbitrage may be a result of constraining transaction costs.

"

Therefore, in order to explore the market with the pairs idea, a unique model is required.

We have adopted a different approach in pairs trading with NASDAQ 100 Index future (NQ) and Dow Jones Industry Average Index future (YM). Generally speaking, stocks in NASDAQ 100 Index tend to be growth oriented stocks, while Dow Jones Industry Avg Index consists of value oriented stocks. Since both indices are broad market indices, they are highly correlated. In a bull market, growth stocks tend to outpace value stocks, and in a bear market, value stocks perform better.

We implement the model on intraday base. During the trading hours (9:30 am - 4:00 PM, EST), the model calculates whether NASDAQ 100 Index is overbought or oversold relative to Dow Jones Industry Average Index. If NASDAQ 100 Index is overbought, we will short its future NQ and long Dow Jones Industry Average Index future (YM) with 1-on-1 contract ratio. If NASDAQ 100 Index is oversold, we will long its future NQ and short Dow Jones Industry Average Index future (YM) with 1-on-1 contract ratio. 

Historical results and live performance illustrate that our model works well. Following picture shows results in 2015: