Negative Correlation Explained: How It Affects Your Portfolio

Search Fintrev

Search our guides, reviews and glossary.

Negative correlation is a statistical relationship between two variables in which one tends to rise when the other falls, and the reverse. It is also called inverse correlation, a negative association or a negative relationship. On a scatter plot the points slope down from left to right. The strength of the relationship is measured by the correlation coefficient, which runs from -1.0 to +1.0. Any value below zero means the two variables are negatively correlated, and -1.0 is a perfect negative correlation.

For investors, negative correlation matters because of what it does to a portfolio. When two holdings tend to move in opposite directions, the gains in one can offset losses in the other. The combined portfolio then swings less than either holding on its own.

What negative correlation means

Two variables are negatively correlated when above-average values of one tend to appear alongside below-average values of the other. This describes a pattern across many observations, not a rule that holds every time. Two stocks with a correlation of -0.4 will still rise together on some days. Across the whole sample, opposite moves outweighed matching ones.

Familiar examples come from everyday life and basic economics:

• Price and quantity demanded. A demand curve slopes downward because buyers generally purchase more of something as its price falls.
• A car’s age and its resale value. Older cars of the same model usually sell for less.
• Altitude and air temperature. Within the lower atmosphere, temperature generally drops as altitude rises.

A perfect negative correlation (a coefficient of exactly -1.0) means every data point sits on one straight downward-sloping line, with each move in one variable matched by a proportional opposite move in the other. Real financial data almost never behaves this way: the trend points down, but individual points scatter around it.

How the correlation coefficient measures it

The correlation coefficient, usually written as r for a sample or the Greek letter ρ (rho) for a population, condenses the relationship between two variables into one number:

• +1.0: perfect positive correlation. The variables move in lockstep in the same direction.
• Between 0 and +1.0: positive correlation. They tend to move together, more consistently as the value approaches 1.
• 0: no linear relationship. Knowing the direction of one tells you nothing about the direction of the other, at least in a straight-line sense.
• Between 0 and -1.0: negative correlation. They tend to move in opposite directions, more consistently as the value approaches -1.
• -1.0: perfect negative correlation.

The sign tells you the direction. The distance from zero tells you how tightly the points cluster around a straight line. A coefficient of -0.9 describes a tight, reliable inverse pattern, while -0.1 is barely distinguishable from no relationship. Labels such as “weak” or “strong” use cutoffs that vary between fields, so the number itself is more informative.

The formula

The most widely used measure is the Pearson correlation coefficient. It is the covariance of the two variables divided by the product of their standard deviations:

r = Cov(X, Y) / (σX × σY)

Covariance measures whether the variables move together (positive covariance) or apart (negative covariance), but its size depends on the units of the data. Dividing by both standard deviations strips out those units and forces the result into the -1 to +1 range. That is why a correlation between a stock in dollars and a bond yield in percent can be compared with a correlation between two currencies.

In computational form, for paired observations:

r = Σ[(xᵢ − x̄)(yᵢ − ȳ)] / √[Σ(xᵢ − x̄)² × Σ(yᵢ − ȳ)²]

Here x̄ and ȳ are the averages of each series. The numerator multiplies each pair of deviations from the average. When one variable is above its average while the other is below, the product is negative. If those negative products dominate, r comes out negative.

Worked example

Hypothetical data. Suppose two assets, A and B, produced these monthly returns over five months:

Step 1: Find the averages. A averages 0.0%. B’s returns sum to 2.5, so B averages 0.5%.

Step 2: Find each deviation from the average. For A: -2, -1, 0, 1, 2. For B: 2.0, 1.0, 0.5, -1.0, -2.5.

Step 3: Multiply the paired deviations and add them. (-2 × 2.0) + (-1 × 1.0) + (0 × 0.5) + (1 × -1.0) + (2 × -2.5) = -4 - 1 + 0 - 1 - 5 = -11.

Step 4: Square each deviation and add. For A: 4 + 1 + 0 + 1 + 4 = 10. For B: 4 + 1 + 0.25 + 1 + 6.25 = 12.5.

Step 5: Divide. r = -11 / √(10 × 12.5) = -11 / √125 = -11 / 11.18 ≈ -0.98.

The two assets are strongly negatively correlated over this sample: in every month, one was above its average while the other was below. Spreadsheet functions such as CORREL or PEARSON perform the same calculation in one step.

What negative correlation is not

Several ideas get mixed up with negative correlation. Each one can lead to a different portfolio decision.

Negative correlation is not negative return. Two assets can both earn positive returns over a year and still be negatively correlated. Correlation compares each asset’s moves to its own average, not to zero. In the example above, B averaged a gain of 0.5% a month even though it moved opposite to A.

Negative correlation is not the same as zero correlation. A correlation of zero means there is no consistent linear tendency either way. Uncorrelated assets do not offset each other on average. They simply move independently. Combining them still reduces portfolio volatility, but less than combining negatively correlated assets of the same volatility.

Correlation is not slope. The slope shows how much Y changes per unit of X. The correlation shows how closely the points hug the line. A gentle slope with tightly clustered points can have a correlation near -1, while a steep slope with widely scattered points can have one near zero. In finance, beta is the slope-type measure: how much an asset tends to move for each 1% move in a benchmark. Correlation describes only how consistently it moves with it.

Correlation is not causation. Two variables can be negatively correlated because one affects the other, because a third factor drives both, or by coincidence in a limited sample. A falling dollar and rising gold prices may both reflect a common influence such as interest rate expectations, rather than one causing the other.

Correlation does not measure size. A correlation of -0.9 means the moves are consistently opposite, not that they are equally large. A small position in a low-volatility asset that is negatively correlated with stocks will offset only a small part of a stock decline.

Methods and types of correlation

Correlation can be positive, negative or zero, and there are several ways to calculate a coefficient, each suited to different data:

• Pearson correlation measures the linear relationship between two continuous variables, such as daily returns. It is the default in most financial software.
• Spearman rank correlation converts the data to ranks before calculating. It captures whether one variable consistently rises or falls as the other rises, even when the relationship is curved rather than straight.
• Kendall rank correlation (tau) also works on ranks. It counts how often pairs of observations move in the same order versus the opposite order, and it is often preferred for small samples.
• Point-biserial correlation applies when one variable is continuous and the other is binary, such as returns on days with and without a central bank announcement.

Rank-based measures are less sensitive to a few extreme values, which leads to one of the main practical problems with correlation in market data.

How outliers distort correlation

An outlier is an observation far from the rest of the data. In markets, outliers come from earnings surprises, mergers, crashes, policy shocks or data errors. Pearson correlation squares deviations, so a single extreme point can carry enormous weight.

Hypothetical extension of the worked example. Add a sixth month in which both assets jump sharply: A returns +6.0% and B returns +5.0%. Repeating the calculation:

• New averages: A is 1.0%, B is 1.25%.
• Sum of paired deviation products: +11.5.
• Sum of squared deviations: 40 for A, 29.375 for B.
• r = 11.5 / √(40 × 29.375) = 11.5 / 34.28 ≈ +0.34.

One unusual month turned a strong negative correlation of -0.98 into a moderate positive one. The other five months still show the assets moving in opposite directions. The coefficient no longer describes them.

The reverse also happens. A single day when one stock jumps on company-specific news, while the broader market barely moves, can make that stock look less correlated with the market than it is on ordinary trading days. Ways to handle the problem include:

• Plotting the data before trusting the number, since a scatter plot shows outliers immediately.
• Comparing Pearson with Spearman or Kendall. A large gap between them signals that a few points are driving the result.
• Checking whether an extreme value is a data error or a real event. Real events should usually stay in the sample, because they are exactly the kind of move a hedge is supposed to handle.
• Calculating correlation over several periods to see whether a result depends on one episode.

Negative correlation in investing

Investors use negative correlation for two related purposes: diversification and hedging.

Diversification: why opposite moves reduce risk

The value of negative correlation becomes concrete in the formula for the variance of a two-asset portfolio, a standard result of modern portfolio theory:

σp² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂

where w is each asset’s weight, σ is each asset’s standard deviation (volatility), and ρ is their correlation. The first two terms depend only on the individual assets. The third term is where correlation enters. When ρ is positive, it adds to portfolio risk. When ρ is negative, it subtracts.

Hypothetical example 1: two assets with equal volatility. Assume each asset has 10% annual volatility and the portfolio holds 50% in each.

With perfect positive correlation, combining the two does nothing for risk. With zero correlation, volatility drops by about 29%. With perfect negative correlation, the movements cancel completely. That theoretical case is essentially a perfect hedge, and it also cancels the return differences between the two assets.

Hypothetical example 2: a stock and bond mix. Assume a stock fund with 16% volatility and a bond fund with 6% volatility, held 60/40.

The effect is real but smaller here, because the bond fund is less volatile and carries less weight, so it has less movement available to offset the stocks. A modestly negative correlation helps, but it does not turn a stock-heavy portfolio into a low-risk one. Correlation, volatility and position size work together, which is why measures such as the Sharpe ratio look at return relative to total portfolio volatility rather than at correlation alone.

This mechanism lets diversification reduce risk without giving up expected return. Each asset’s expected return is unchanged by what it is paired with. Only the variability of the combination changes. Smoother returns also matter for compounding: a portfolio with smaller drawdowns needs smaller recoveries, which affects long-run growth measured by CAGR.

Hedging

A hedge is a position taken mainly to offset losses elsewhere. Hedging relies on negative correlation more directly than diversification does. An investor holding a stock portfolio might buy an instrument expected to rise when stocks fall, such as put options, a short index position or an inverse fund. The closer the hedge’s correlation to the core holding is to -1, the more precisely it offsets losses, and the more it also offsets gains. A hedge reduces the range of outcomes in both directions.

The line between diversification and hedging is one of intent and cost. Diversifying assets are held because they are expected to earn their own return while also smoothing the portfolio. Hedges are often held despite an expected cost, as insurance.

Pairs often described as negatively correlated

Several relationships appear repeatedly in investment discussions. Each describes a tendency with an economic rationale, not a fixed law:

• Stocks and bonds. When growth slows and central banks such as the U.S. Federal Reserve cut interest rates, bond prices tend to rise while stocks struggle. Investors also move toward high-quality bonds during equity selloffs. In strong economies, stocks generally outperform. The relationship depends on what is driving markets. In 2022, when inflation and rising rates were the main concern, U.S. stocks and bonds fell together. Stock-bond correlation has ranged from moderately negative to positive in different eras.
• Gold and the U.S. dollar. Gold is priced in dollars, so a weaker dollar tends to make gold more expensive in dollar terms, and the reverse. Periods such as the late 1970s and the early 2020s are often cited as times when a weakening dollar coincided with rising gold.
• Defensive and cyclical stocks. Defensive sectors such as utilities and consumer staples sell products people buy in any economy. They often hold up better when cyclical sectors such as technology, industrials or discretionary retail fall on recession fears. Because both are stocks, they usually share a positive correlation with the overall market, so the “negative” relationship is often relative performance rather than opposite price moves.

Measured correlations between broad funds, such as a stock index fund and a bond index fund, are often closer to zero or only mildly negative than the textbook pairings suggest. Strong, durable negative correlations between broad asset classes are uncommon, so most of the risk reduction in a typical diversified portfolio comes from low correlations rather than strongly negative ones.

Assets with low correlation to the S&P 500

No asset holds a permanent, guaranteed low correlation with the S&P 500. Any answer depends on the period measured and market conditions, but some general points hold:

• Short-term Treasury bills and cash have returns that barely fluctuate, so their correlation with stocks tends to sit near zero almost by construction. They reduce portfolio volatility mainly by being stable, not by moving opposite to stocks.
• Longer-term Treasuries have historically shown negative correlation with stocks during growth scares and rate-cutting cycles, and positive correlation during inflation-driven selloffs.
• Gold and broad commodities have at times shown low correlation with U.S. equities, driven by their own supply, demand and currency factors.
• Hedging instruments such as put options or inverse funds are built to move opposite to the index, at a cost.

The more useful question is which asset’s relationship with stocks is likely to hold under the conditions you are worried about. An asset that is uncorrelated in calm markets but falls alongside stocks in a crash offers less protection than its long-run average suggests.

Measuring a portfolio’s overall correlation

With more than two assets, the number of pairwise correlations grows quickly. Five holdings have 10 pairs, and ten holdings have 45. To summarize them, some investors calculate a weighted average correlation.

Hypothetical portfolio. A portfolio holds 60% in a stock fund (S), 30% in a bond fund (B) and 10% in a gold fund (G). Assume these pairwise correlations:

• S and B: -0.2
• S and G: +0.1
• B and G: +0.2

Method 1: average each asset’s correlations, then weight by holding.

1. Average each asset’s correlation with the others. S: (-0.2 + 0.1) / 2 = -0.05. B: (-0.2 + 0.2) / 2 = 0.00. G: (0.1 + 0.2) / 2 = 0.15.
2. Multiply each average by the asset’s portfolio weight. S: -0.05 × 0.60 = -0.030. B: 0.00 × 0.30 = 0. G: 0.15 × 0.10 = 0.015.
3. Add them: -0.015.

Method 2: weight each pair by the product of its two weights.

1. Pair weights: S-B 0.60 × 0.30 = 0.18; S-G 0.06; B-G 0.03. Total 0.27.
2. Weighted sum: (0.18 × -0.2) + (0.06 × 0.1) + (0.03 × 0.2) = -0.036 + 0.006 + 0.006 = -0.024.
3. Divide by total pair weight: -0.024 / 0.27 ≈ -0.09.

Both methods say the holdings are, on balance, close to uncorrelated with a slight negative tilt. They do not give the same number, because they weight the pairs differently. Method 2 gives more influence to the stock-bond pair, which dominates this portfolio by size. Neither figure is a standard published statistic with a single agreed formula, so state which method you used when comparing portfolios.

A weighted average correlation is a summary of the pattern, not a measure of risk. Two portfolios with the same average correlation can have very different volatility if one holds more volatile assets. To measure actual portfolio risk, use the full portfolio variance formula with every weight, volatility and correlation, which is what portfolio software does in matrix form.

The summary still helps with adjustments:

• To lower the average and increase diversification, shift weight toward holdings with low or negative correlations to the rest of the portfolio. Here that means more bonds or gold.
• To increase exposure to rising markets, shift weight toward the highly correlated growth assets, accepting that they will also tend to fall together.

Building a portfolio around a deliberate balance of correlations across asset classes is part of strategic asset allocation. There, correlation is one input alongside risk tolerance, time horizon, liquidity needs and return goals.

Limitations of correlation

1. Correlations change. The relationship between two assets can drift from negative to positive as economic regimes, monetary policy or market structure change. A pair that was negatively correlated for a decade may not be in the next one.
2. Correlations often rise in a crisis. During severe market stress, many assets that normally move independently fall together as investors sell what they can, raise cash or cut leverage. This is the downside correlation problem: diversification can weaken when it is most wanted. Broad market shocks reflect systematic risk, which diversification across risky assets cannot remove.
3. It assumes a linear relationship. Pearson correlation captures straight-line relationships only. Assets can be strongly related in a nonlinear way, for instance moving together only in large declines, and still show a modest coefficient.
4. It depends on the measurement choices. Daily, weekly and monthly returns can give different correlations for the same assets, as can a one-year versus a ten-year window. A coefficient means little without its frequency and period.
5. History is not the future. Every correlation describes what happened, not what will happen.
6. Low correlation within one asset class is not full diversification. A portfolio of stocks with low correlations to each other is still concentrated in equities and exposed to a broad equity decline.

Is negative correlation better than positive correlation?

Neither is better in the abstract. Low or negative correlation between holdings helps control risk by reducing volatility and drawdowns, but the right mix depends on what each holding is for.

Positive correlation is not bad in itself. A growth-focused investor may deliberately hold assets that are positively correlated with the stock market to capture its long-run return. The concern is concentration. A portfolio of highly correlated holdings behaves like one large position, with the full upside and full downside of that exposure. Positive correlation is also desirable when one asset should track another, as an index fund does with its benchmark.

Negative correlation has its own trade-off. A holding that reliably moves opposite to your main assets will tend to lose value when they do well, and assets with low or negative correlation to stocks often have lower expected returns than stocks. Too much of them can leave a portfolio stable but with little growth, and a pure hedge reduces gains as much as losses. Most investors want enough low-correlation exposure to keep losses within their tolerance, and enough positive market exposure to meet their return goals.

The Bottom Line

Negative correlation matters most to investors building diversified portfolios or hedging stock exposure. Pairing holdings with low or negative correlation can lower volatility without changing each asset's expected return, but correlations shift over time and often rise in a crisis. Check how a relationship behaves under the conditions you worry about, and balance low-correlation assets against enough market exposure to meet return goals.