Last Updated on March 6, 2021 by Oddmund Groette
Correlation, which measures the relationship between two datasets, is an essential variable for a trader. How your positions move in relation to other positions is crucial to understand and manage risk. Unfortunately, correlation is hard to predict because it’s not a static number but is constantly changing. Moreover, during panics and volatility, most asset classes start moving in tandem. This article briefly discusses what correlation is, how you can deal with it, and how to use it to your advantage.
What is correlation?
Correlation is a mathematical term that measures the relationship between two variables or datasets. For example, the height of children tends to correlate to the height of the parents. Likewise, your income mostly correlates to the amount of work you put in. It’s a statistical measure that shows how two variables are related but without considering causation.
The degree of the correlation is expressed by the correlation coefficient, which ranges from -1 to +1. In most statistical software, the coefficient is expressed as r. The significance of the correlation is expressed as p. The more observations you make, the more powerful your correlation is.
Something that is perfectly correlated has a correlation of 1. When the two variables correlate inversely, ie. they move opposite one another, the correlation coefficient is -1. A zero correlation coefficient means that the asset prices are uncorrelated.
In trading, the correlation is mostly used in time series data. Most stocks are highly correlated in the stock market, meaning they move up and down in tandem. Opposite, a rise in the interest rates leads typically to lower share prices, and thus the interest rates and stocks are somewhat inversely correlated.
Unfortunately, correlations are not static – they change all the time. Two stocks could be highly correlated over long intervals, but they might have a low correlation over short periods.
Examples of “obvious” correlations:
Perhaps some examples better illustrate what is meant by correlation:
- The price of oil and the Norwegian krona (a low oil price is bad)
- The price of oil and the Canadian dollar (a low oil price is bad)
- The price of commodities and the price of the Australian dollar (Australia is a commodity producer)
- Airline stocks and the price of oil
- The price of gold and the increase of the US dollar (USD) money supply
- Better than expected earnings result in increased share prices
- Low PE readings and later higher share price (inverse relationship)
- Rising interest rates and share prices (inverse relationship)
- Inventory increases and future sales (inverse relationship)
- When the price of goods drop, demand increases
- Warm temperatures increase the demand for ice cream
We hope you get the idea.
Why is correlation important?
Correlation is essential to understand for a trader. There is no point in having, for example, ten different strategies if they correlate 80% of the time. If you lose money in strategy 1, you most likely also lose in the other nine strategies (at the same time).
To give a practical example of correlation, we’d like to use a Swedish hedgefund group, Brummer & Partner, as an example. They offer a fund of funds called Multi-Strategy, a fund that invests in many asset classes using different time frames and portfolio managers. They seek a return that is uncorrelated to the overall stock market. The total returns are summarized in this graph:
The red line grows almost linearly toward the upper right corner, while the grey MSCI World Index is a lot more erratic. Brummer has thus managed the same return as the MSCI World Index but with a lot less variability in the returns.
The excerpt below shows the correlation between Brummer’s Multi-Strategy and the Swedish Total Return Index (SIX) and MSCI World:
The lower-left box shows the correlation at 0.14 and 0.19, which is pretty low (the graphs are in Swedish). Because one fund in the Multi-Strategy might have losses in one month, the other eight funds might have different performance. Hence the overall performance of the Multi-Strategy has minor drawdowns like shown in the monthly returns above.
However, when you start testing, you’ll find many seemingly interesting correlations that can potentially make you successful. But beware:
Because most of the backtesting involves predicting future prices based on history, you will likely find many spurious correlations. Many relationships are not direct but indirect. Moreover, you have to be careful to conclude whatever you do because any test might result from chance and not be proof of causation. Seemingly statistically significant correlations are often due to chance or hidden factors.
Most of the actions in the markets are a result of noise and randomness. You can find many relationships that are the result of chance.
The error of omission
In Victor Niederhoffer’s book Practical Speculation, he and Laurel Kenner mention the third variable’s omission as one of the pitfalls when researching. For example, the greater the number of storks, the greater the number of births. However, districts with large stork populations have many births and have many buildings where the storks can nest. Thus, it’s the population that explains both the frequency of births and sightings of storks.
Nierderhoffer goes on to mention sentiment indicators. A typical sentiment indicator becomes bearish when the sentiment reaches a certain optimistic level and vice versa. But there is a strong negative/inverse relationship between the recent move and the subsequent performance in the stock market. But at the same time, any sentiment indicator is positively correlated with the recent market move. Thus, when the market is up big over the previous weeks, sentiment tends to be optimistic, which is bearish. Opposite, when the market is down, the sentiment changes to pessimistic, which is bullish. Sentiment has an indirect relation to the future movements, but only because of its connection with the recent market move.
A typical error of omission in the tock market is survivorship bias. Assume you want to test some consumer staples and their performance, you grab the first ten stocks in the XLP index. But you are looking at the companies that have survived until now – you are omitting the ones which might not have made it. Likewise, many value investors make the same mistake. Value stocks often appear tempting because they presumably might suffer only temporary difficulties, but this also increases the risk for permanent financial difficulties and subsequent bankruptcy. Many end up on the graveyard, and hence they never show up in any performance statistics. Survivorship bias distorts results a lot!
Correlations break down – nothing lasts forever:
Correlations vary over time. Something that is highly correlated over long intervals might be erratic on a shorter time frame:
The lower pane on the chart shows the 10-day correlation (red line), while the black line shows the 100-day correlation. The correlation is very high over long time frames but tens to “break down” over a few days.
Opposite, the correlation between the S&P 500 and long-term interest rates is much lower:
The chart above shows the 10- and the 100-day correlation between the ETFs SPY and TLT. The black line, the 100-day average, is most of the time negative, as expected due to the inverse relationship between stock market valuation and rates.
Should you understand why correlation change?
There are many reasons why correlations break down and change. Sentiment and global factors change all the time, and luckily the world is not static. We would like to understand why things change, but we believe this is a pretty futile exercise that will keep you occupied 24/7. We think it makes more sense to accept that correlation come and go.
Non-correlation and diversification – the holy grail?
The goal in trading system development is to have strategies that cancel each other out to lower the returns’ variability. To do this, you need to include various asset classes, trade both long and short, and use different time frames. Even long-only trades done during a bear market can add diversification and profitability when the time frame is short.
Correlations can be used as a tool in strategy development. As a trader, you can use correlations to estimate the price tomorrow, next week, or next month. ETFs and futures can be used as variables to predict the price of another asset. If you subscribe to our Trading Edges, you’ll get some ideas on how to use this to your advantage in forthcoming Trading Edges:
Correlation, or more correctly, the lack of correlation, is the closest you get to a “holy grail” in trading. Moreover, inversely correlated assets are just as valuable. Why? Because adding instruments that are lowly correlated smooth the equity curve. A perfect example of that is the example above in Brummer & Partners. Because of their high risk-adjusted performance, indicated by the Sharpe-ratio, they can use leverage to boost returns. Brummer’s Multi-Strategy fund is offered both without leverage and 2x leverage.
Conclusion – how to add diversification to your portfolio of strategies:
To succeed, we recommend having a basket of many strategies. You add diversification by thinking like this:
- Learn to code so you can use trading software and develop quantified strategies.
- Quantitative trading makes you systematic and disciplined.
- There are practically no limitations on how many strategies you can run automatically (as long as you are well funded).
- Trade different asset classes.
- Trade both long and short.
- Trade different time frames.
Disclosure: We are not financial advisors. Please do your own due diligence and investment research or consult a financial professional. All articles are our opinions – they are not suggestions to buy or sell any securities.