What it means
Correlation is a measure of consistency of direction rather than size of effect. Two series can be almost perfectly correlated while one moves a fraction of a per cent and the other moves 20%, so correlation tells you about pattern, not magnitude.
It matters most in portfolio work, because the whole logic of diversification rests on combining assets that are not strongly positively correlated. If everything you own moves together, you have far less protection than the number of holdings suggests, which is what surprises investors in a severe market fall when correlations across assets tend to rise.
Outside investing it is a workhorse of business analysis. Marketing teams look for positive correlation between advertising spend and enquiries, operations teams between staffing hours and order throughput, and finance teams between commodity prices and input costs.
Interpretation needs care in two respects. A high correlation does not prove causation, because both series may be driven by a third factor such as the season or the state of the economy, and a correlation calculated over a short or unusual period may not hold in normal conditions.
Rough conventions help when reading a number. A coefficient above about 0.7 is generally described as a strong positive relationship, 0.3 to 0.7 as moderate, and below 0.3 as weak, though the sensible thresholds vary a great deal by field and by how noisy the data is.
In practice
Real-world examples.
Example
An analyst at an equity fund notices that two of her largest holdings, a bank and an insurer, have a correlation of 0.86 over five years. Holding both feels like diversification but behaves like a single larger bet on financial services, so she trims one position.
Example
A logistics company plots weekly overtime hours against parcels delivered and finds a strong positive correlation. Rather than treating this as a discovery, the operations director uses it to build a staffing model that forecasts overtime from the parcel volume in the order book.
Example
A bakery chain finds that its ingredient costs correlate positively with a published wheat price index. The finance team uses that relationship to forecast next year's cost of sales under three wheat price scenarios instead of assuming a flat percentage increase.
Formula
Calculation
The correlation coefficient r is calculated as:
r = sum of (dx x dy) / square root of (sum of dx squared x sum of dy squared)
where dx is each x value minus the average x, and dy is each y value minus the average y.
A retailer wants to know whether monthly advertising spend moves with sales. Working in thousands of dollars, spend over five months was 10, 20, 30, 40 and 50, and sales were 100, 130, 150, 190 and 230.
The average spend is 150 / 5 = 30 and the average sales figure is 800 / 5 = 160.
Spend deviations (dx): -20, -10, 0, +10, +20
Sales deviations (dy): -60, -30, -10, +30, +70
Sum of dx x dy = 1,200 + 300 + 0 + 300 + 1,400 = 3,200
Sum of dx squared = 400 + 100 + 0 + 100 + 400 = 1,000
Sum of dy squared = 3,600 + 900 + 100 + 900 + 4,900 = 10,400
r = 3,200 / square root of (1,000 x 10,400) = 3,200 / 3,225 = 0.99
That is a very strong positive correlation. It still does not prove that advertising caused the sales, since the retailer may simply have spent more in months it already expected to be busy.Case study
Seen in the real world.
Merrifield Wealth Advisers is a fictional advisory firm used purely as an illustrative example. It offered clients a portfolio marketed as broadly diversified, holding 22 funds across what the brochure described as several distinct strategies.
A new analyst ran the correlations between the 22 funds over the previous seven years. Fourteen of them showed correlations above 0.85 with each other, because despite different names they all held large developed-market company shares. The genuinely different exposures, short-dated government bonds and an infrastructure fund, made up under 12% of the average client portfolio.
The firm rebuilt its model portfolio around six funds chosen for low correlation with each other rather than for variety of labels, and started reporting a correlation matrix in client reviews. In this illustrative account the change reduced both the number of holdings and the portfolio's swings in the following market downturn, which made the annual review conversations considerably easier.
Watch out
Common mistakes.
- Reading positive correlation as proof of cause and effect, when a third factor such as seasonality or general economic growth may be driving both series.
- Assuming a large number of holdings means a diversified portfolio, without checking whether those holdings are highly positively correlated with one another.
- Calculating correlation over a short or unusual window, such as a single volatile quarter, and treating the result as a stable long-term relationship.
Questions
People also ask.
What counts as a strong positive correlation?
As a rough guide, above about 0.7 is strong, 0.3 to 0.7 is moderate and below 0.3 is weak, though the appropriate threshold depends heavily on the field and the noisiness of the data.
Is positive correlation good or bad?
Neither in itself; it is helpful when you are trying to forecast one variable from another, and unhelpful when you were relying on two assets to behave differently in a downturn.
Can correlation change over time?
Yes, and this is one of its most important properties, because correlations between assets frequently rise sharply during market stress, exactly when the diversification benefit is most needed.
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