What it means
Imagine plotting monthly advertising spend on one axis and monthly sales on the other. If the dots form a tight upward-sloping line, the Pearson coefficient will be close to +1.
If they scatter randomly, it will be close to 0. The coefficient is calculated by comparing how each pair of values differs from its own average.
When both are above or below average together the result pushes towards +1, and when one is above while the other is below it pushes towards -1. The result is then scaled by the spread of each series so the answer always stays between -1 and +1.
In investing, the coefficient is the standard way to measure correlation between assets. Combining two investments with a low or negative correlation reduces portfolio risk, because they do not fall at the same time.
This is the logic behind diversification. Rules of thumb help with interpretation.
Values above 0.7 are usually seen as strong, 0.3 to 0.7 as moderate and below 0.3 as weak, in either direction. These are conventions rather than laws, and what counts as strong depends on the field and the amount of data.
The measure has important limits. It only detects straight-line relationships, so a perfect curved relationship can produce a coefficient near 0, and a single extreme data point can distort it.
Most of all, correlation is not causation: two things can move together because of a third factor, or by coincidence. Correlations also change over time.
Assets that appear uncorrelated in calm periods often become highly correlated during a crisis, when investors sell everything at once. Analysts therefore check how stable the figure is across different periods before relying on it.
In practice
Real-world examples.
Example
A retailer finds a Pearson coefficient of 0.85 between monthly footfall and sales. It uses this to justify spending on promotions that bring more visitors, while still checking whether the extra visitors actually buy.
Example
A portfolio manager calculates a coefficient of -0.4 between a gold fund and an equity fund over five years. She includes both in a client portfolio because the negative link means losses in one are often partly offset by the other.
Example
A utility company tests whether daily temperature and electricity demand are related and finds r = 0.9 in summer. The planners use the relationship to forecast demand and decide how much power to buy in advance.
Formula
Calculation
R = Sum of [(x - mean of x) x (y - mean of y)] / square root of [Sum of (x - mean of x)^2 x Sum of (y - mean of y)^2]
Suppose a business tracks advertising spend x (in $000) and sales y (in $000) over five months. Spend is 1, 2, 3, 4, 5 with a mean of 3. Sales are 6, 10, 8, 14, 12 with a mean of 10. The deviations of x are -2, -1, 0, 1, 2 and of y are -4, 0, -2, 4, 2. Products: 8, 0, 0, 4, 4, which sum to 16. Sum of squared x deviations = 4 + 1 + 0 + 1 + 4 = 10. Sum of squared y deviations = 16 + 0 + 4 + 16 + 4 = 40. So r = 16 / square root of (10 x 40) = 16 / 20 = 0.8, a strong positive relationship.Case study
Seen in the real world.
Halcyon Wealth is an illustrative, fictional advisory firm that built a portfolio from two sector funds believed to be unrelated. Using three years of monthly returns, its analyst found a Pearson coefficient of 0.15 and described the pair as well diversified.
During a market panic, both funds fell about 18% in the same month. When the analyst repeated the calculation using only stressed months, the coefficient was 0.82, showing that the two funds had moved together exactly when protection was needed.
The firm added assets from different asset classes and began checking correlations in several market conditions. The illustrative lesson is that a single coefficient from calm times can overstate how much diversification a portfolio really has.
Watch out
Common mistakes.
- Treating correlation as proof of cause, when two series may move together because of a hidden third factor.
- Assuming a coefficient near 0 means no relationship, when the link may be curved rather than straight.
- Relying on a short run of data, which can produce a coefficient that looks strong by chance.
Questions
People also ask.
What does a Pearson coefficient of 0.8 mean?
It means the two series have a strong positive straight-line relationship, and about 64% of the variation in one is explained by the other (0.8 squared).
What is the difference between Pearson and Spearman?
Pearson measures straight-line links using actual values, while Spearman uses rankings and handles curved but consistent links better.
Can the coefficient be larger than 1?
No. It always lies between -1 and +1, and a result outside that range signals a calculation error.
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