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# What is correlation?

So you are looking for a correlation definition? The best place to start is in the centre of the word, with the middle eight letters borrowed from “relate”. Correlation describes the extent to which two or more securities show related behaviour, rising and falling together. You will hear also of “negative correlations”, in which securities move in opposite directions. Identifying correlations is a key task for investment managers and analysts.

## Key takeaways:

• Correlation in finance is a measure of the relationship between the returns of two or more assets or investments.

• Correlation is expressed on a scale of -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation.

• Positive correlation implies that the two assets move in the same direction, while negative correlation means that they move in opposite directions.

• Investors and traders use correlation analysis to identify relationships between different assets and to diversify their portfolios.

## Where have you heard about correlation?

As an investor, you are likely to have read about correlation in reports and other literature supplied by your financial adviser, who will use a correlation formula to gauge the degree of correlation in the securities concerned. In most, but not all, cases, such material is likely to stress the low levels of correlation in a portfolio. This is because of the high priority given by many investors and their advisers to using correlation analysis to help diversify their investments, in order to limit risk. You may have read about it also in the financial media and in guides to investment.

## What you need to know about correlation

Correlation can be described mathematically and can appear as positive and negative correlation. When two securities move in a perfectly synchronised way, they are said to have a positive correlation of 1. On the other hand, when they move in the exactly opposite direction to each other, they have a negative correlation of minus 1. There is a third type of relationship other than positive and negative correlation - a reading of zero says they have no relationship, positive or negative, with each other, that there is no pattern of past trading suggesting that they influence each other in any way.

This is known as the “correlation co-efficient”, and emerges from the use of a correlation formula in the process of correlation analysis.

Why does this matter? Well, because correlations, or the absence of them, indicate the extent to which a portfolio of securities is diversified or not. One with a high degree of correlation will be a lot less diversified than one with a very low degree.

In general, portfolio managers seek high diversification through low levels of correlation, given that diversification is seen as a key to risk management, so let’s first look at how they may go about this.

## Correlations: obvious and hidden

Securities don’t come with a “correlation rating” attached helpfully supplied by a credit agency. Investors need either to work out for themselves the degree of correlation or rely on the work of financial analysts who have examined the linear relationship that underlies correlations. That said, some correlations are fairly easy to spot.

For example, an oil exchange-traded fund (ETF) and shares in a large petroleum-extraction company would show a high degree of correlation. The same factors propelling the oil price (thus the ETF) would act in the same way on the shares of the oil explorer. What is good for one tends to be good for another, and vise versa. This is a textbook positive correlation.

But this would not hold true for any energy company. Let’s suppose the investor holds stock in a company specialising in wind power, or nuclear energy. All things being equal, the same movement in the oil price that would be good – or bad – for an oil ETF would have the opposite effect on the shares concerned. A lower oil price would be generally negative for non-oil energy generators, as the business case for using them would diminish.

But a higher oil price would make the non-oil generators more attractive, as their own product became cheaper in relative terms. The oil ETF and the energy-company shares can be said to be negatively correlated.

Many correlations, however, are less obvious. For example, someone with, perhaps, an ETF in emerging-market growth or shares in an investment company specialising in emerging Asia may also have stock in one of the big mining houses. There is no obvious correlation there, but the huge importance of Chinese demand for producers of coal, iron ore and other primary commodities means there is a much tighter link between the two investments than may seem to be the case. This, in turn, makes the portfolio rather less diversified than may have been thought.

## Who’s afraid of correlation?

Correlation is not always a bad thing. Both positive and negative correlation have their part to play in investment and sometimes positive correlations are sought out, as when tracker funds are set up to mimic the movements of major share indices such as the Standard & Poor’s 500 Index or the FTSE 100. In such a case, the investor would be understandably aggrieved if the portfolio manager decided to pursue a low correlation strategy.

Less obviously, correlation can be used to advantage when an investor seeks a low-cost method of increasing exposure to what they believe to be benign market factors. Thus they already hold some stock in Company A, but these shares have become more expensive recently so the investor seeks out less expensive shares with a high degree of correlation to those of Company A.

A slightly more complex way to exploit positive correlations is to trade the correlated securities in pairs. Let’s imagine Company A and Company B tend to rise and fall together. If there is a temporary divergence, with one rising and the other falling, the trader can go short on the one that has risen and take a long position on the share that has dropped, on the assumption that the previous correlation will reassert itself, allowing the trader to profit.

The risk to this strategy is that there is an underlying reason as to the divergence and that the old correlated relationship is over.

## Correlation and beta: what’s the difference?

Beta measures the extent to which a stock or a collection of stocks is related to the volatility of the entire market. If a stock has a beta of 1, it responds, on average to volatility in the same way as the market. A beta of above 1 means it is more responsive to market volatility than is the market as a whole, while below 1 means it is less responsive.

The two big differences are, first, that there are no limits to beta – a stock can be five or ten or more times more or less responsive to market volatility than the market as a whole, whereas the correlation co-efficient must always lie between minus 1 and 1.

The second is that beta measures a stock against a benchmark, while correlation can measure two, or more, of anything against each other.

### Finally

Calculating correlations is a complex business. Here is a relatively-simple correlation formula for working out the linear relationship that underpins them.

## Find out more about correlations

Our glossary contains a number of terms closely related to correlation, including diversification and risk.

The Prudent Investors Network has an article here that is fun and easy to read, explaining correlation in terms of sales of umbrellas on the one hand and sunscreen on the other, setting out the linear relationship in a clear way. The opening is forthright: ‘Should you care about “correlation”? Absolutely!’ Bear in mind that this piece stresses the benefits of using correlation to ensure diversification, which is quite correct, but remember also that correlations can be used to maximise an unhedged position – as the legendary investor Max Gunther said: ‘Putting all your eggs in one basket, then watching that basket.’

Correlation analysis is, in this sense, neutral. It helps the investor to achieve whatever goals they have set. It does not dictate those goals.

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