Correlation and cointegration are two regression based concepts that are commonly misused by the trading community. Complex in their formulation, both are inter related and are used to calculate the relationships between two or more products (ie commodities, forex, stock prices) over a specific time period.
Correlation
A value of +1 (positive correlation) or -1 (negative correlation) is assigned based on the how efficiently the two prices react to each other. Correlation identifies pairs that move in either tandem or opposing directions.
A good example of a long term correlation pairing is that of the EURUSD and the USDCHF crosses, which trade in a similar direction. On the other side of the coin, the EURGBP and the AUDNZD trade in opposing directions. They show a negative correlation of -0.81.
Although this figure indicates that the crosses moved against each other, there is a slight degree of uncertainty over the long term sustainability of this negative result. Professional traders commonly set the entry benchmark for pairs above or below 0.9 or -0.9.
Correlation does have a significant drawback, which can greatly affect profitability. Although two pairs may be correlated, they are still not in complete unison, which can cause a slight drift in the prices. In the case of the EURGBP and the AUDNZD, it is a drift -0.19.
Read the post on forex correlation for more details on the topic.
Image credit: Vassia Atanassova
The left box shows a strong correlation. The middle shows a weak correlation. The far right shows an image with no correlation.
Cointegration
Cointegration analyses the movements in prices and identifies the degree to which two values are sensitive to the same mean or average price over a given time period. It doesn’t say anything about the direction that the pairs will move. Cointegration only measures whether or not the distance between them remains stable over time.
If we look at gold and silver, for example, we may find that they track a common average value. They may trade in opposite directions from day to day. At some unknown point in the future, they should revert back towards that average and hence they are cointegrated. Hedge funds commonly use this formula to program statistical arbitrage models to identify pairs to trade.
Another important factor to keep in mind is the look back period of the mean and standard deviation. In essence, if you make the look back value 700, then the regression channel will calculate what the average price is over 700 periods. This can be too inefficient and will limit the sensitivity to changes in the market dynamic.
On the other hand, if you set a short look back period, then it will cause a whipsaw effect and will be far too sensitive. It is important to get a balanced look back within the range of 200-350.
Gold / Silver Example
• Top Section: Standard Deviation and Linear Regression
• Middle Section: Relative Performance Gold (dark blue) and Silver (light/ turquoise blue)
• Bottom Section: Gold Daily Chart and Time Line
The above chart highlights the overall correlation of Gold and Silver and the degree to which breakouts could trigger trade opportunities. I have circled a number of different cointegration scenarios and referenced these on the second section with P1, P2, P3 and P4 labels.
Silver Spike – March
A significant spike in the price of Silver in March sent the linear regression value below the lower standard deviation channel of -2.0. To capitalize on the significant discrepancy in prices, the trader would have looked at shorting silver and going long gold. Performance wise, this would have resulted in an overall profit as silver weakened heavily, crossing below gold in May.
Silver Oversold – July
The silver price continues to weaken on a relative level to gold. In June and July, the regression value passes above the top standard deviation channel, indicating that silver is oversold and the price will have to revert back to its mean. The trader decides to open a long position in silver and short gold. As forecast, it returns to its mean and the gap between both spot prices closes quickly.
Silver Overshoots – December
Once again the silver price overshoots gold. This sets up a long gold, short silver opportunity. On a performance level, the trader would capitalize on
the spread and profit from the position.
Silver Selloff – April
Puncturing the second standard deviation channel, the gold price stabilises whilst silver weakens heavily. This has now supplied the trader with a long
silver, short gold opportunity.
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