Quantitative trading is a strategy which uses mathematical models and price movement theories to enter and exit a trade. The strategies are back-tested using the historical price data points and refined to create the future entry and exit points. These techniques have been in existence even before the advent of computers, but then it was very time consuming and complex. Many common investment theories like those of diversification have all evolved from quantitative studies.
The advantage of trading with quant strategies is that they suggest trades based on back-tested strategies which have offered good returns in the past. Also, there’s a proper discipline attached to the strategy due to the model defined entry and exit points. Most strategies also provide the maximum profit or loss generated for any specific time frame, which helps define the risk in the strategy.
The disadvantages of these types of strategies are that there can be many unforeseen circumstances or events that can cause the entire strategy to collapse and create a much bigger loss/ risk than the one foreseen earlier.
Pair trade strategy:
Introduction:
Pair trade strategy is one of the many strategies based on Mathematical Quant analysis. This strategy involves taking a long and a short position in two pairs respectively which have good fundamental and mathematical correlation. Pair trading strategy is also known as ‘Market Neutral’ Strategy which means overall market direction doesn’t affect the trade as the trade is made of hedge positions, i.e. one buy trade and one sell trade.
The pair trade strategy is a trade on the spread or the ratio of two products. The prerequisite for any pair trade strategy is the requirement of a couple of pairs which have very similar fundamentals, for example, German DAX Index & France CAC index. These pairs also need to have a positive correlation in terms of movement statistically. Correlation measures the strength of association between the two pairs and the direction of their relationship. Pairs which have a correlation of 0.8 and above are ideal for such kind of strategies.
Spread Vs Ratio Trade:
For understanding the strategy wealso need to understand the difference between the change in spread &ratio. Spread means the absolute difference between the rates of the two instruments.Ex.: If the current price of US S&P 500 index is 2723 &Russel 2000 index is 1623, then the spread is 2723 – 1623 = 1100. When we buythis spread and it increases to 1200, we make a profit of 200 points.
The ratio for the same index is 1.68 if the ratio is bought, which means buy S$P 500 & sell Russel 2000 index. Now if the ratio increases to 1.8, considering the assumption that the price of Russel 2000 remains the same and the price of S&P 500 would increase to 2921, it would lead to a profit of 100 points approximately.
Another example of absolute spread based trade can be seen in the above chart. One could have initiated the buy Nasdaq 100 index and sell S&P 500 index trade at 3800 levels of spread and closed the positions when the spread increased to 4000. One would need to do a proportionate number of units in this case which means 1 unit of Nasdaq 100 index for 1 unit of S&P index to execute this view.
In case of a ratio based trade, one needs to trade equal dollar amount of both indices when entering a trade and exiting the same.
Mean Reversion Strategy:
One of the popular ways of defining entry and exit points for a pair trade is the Mean reversion strategy. This strategy uses the moving average of the ratio of prices to determine when there is a substantial deviation from the mean of the price ratio, and accordingly, one enters into a Buy and Sell trade in the respective instruments based on the expected reversal.
To understand the mean reversion we need to understand the concept of bell curve or normal distribution of price movement.
The above image portrays a normal distribution curve of a sample size. The law of normal distribution states that if we were to map all the price data in a chart, they would form a curve as the above. The Greek letter σ represents the standard deviation or variation of the price from the mean. One can also see the probability of prices deviating to higher levels given in percentage terms.
Coming back to the case of the pair trades, we expect the spread/ ratio to go back to the mean whenever it deviates substantially from the mean spread/ ratio. One of the easier ways of measuring deviation for mean reversion strategy is the Z-Score. Z score represents the point on the X-axis above which the price point is plotted.
The following is the back-tested performance on the pair of Nasdaq & S&P 500 for an exposure value of 50,000 dollars on each leg of the strategy. It takes entry and exit for a target of 2000 dollars and stop-loss of 1500 dollars. The strategy uses 20-day average to calculate the entry and exit points.
Year |
2009 |
2010 |
2011 |
2012 |
2013 |
2014 |
2015 |
2016 |
2017 |
2018 |
Profit |
2977 |
0 |
2335 |
-2537 |
2010 |
2698 |
-3106 |
6220 |
4722 |
2566 |
The maximum draw down on the same has been $3106.
There are many advantages of pair trades as it’s a direction neutral strategy, but one must maintain strict discipline in terms of the exposure taken, as high exposures can cause huge risk in terms of any six-sigma event which is beyond the strategy’s purview. Diversification into multiple pairs for the pair trading strategy is also advisable.