Negative Correlation: How it Works, Examples And FAQ

It's important for investors to understand the concept of negative correlation since balanced portfolios often include assets that have this relationship with one another. That way, should one part drop in value, others might not. Negative correlation is also called inverse correlation, which is a relationship between two variables in which one increases as the other decreases, and vice versa. A perfectly negative correlation means the relationship that exists between two variables is exactly opposite. In a line graph, you would see a downward slope.

In economics, price and quantity are generally negatively correlated on a demand curve. These are almost always downward-sloping, reflecting the willingness of consumers to buy more of something as its price goes lower.

In statistics, a perfectly negative correlation is represented by the value -1.0, while 0 indicates no correlation, and +1.0 indicates a perfectly positive correlation. The supply curve is almost always upward-sloping and represented with a positive correlation, reflecting how producers are willing to bring more of a product to the market as prices go higher.

Below, we examine negative correlation in more depth while providing real-world examples to show how this information can be used while building a balanced portfolio.

Understanding Negative Correlation

Negative or inverse correlation indicates that two individual variables have prices that generally move in opposite directions. If, for instance, variables X and Y have a negative correlation, as X increases in value, Y will decrease; similarly, if X decreases in value, Y will increase.

In statistical terms, a perfect negative correlation is represented by a correlation coefficient of -1.0. This means that for every unit increase in one variable, there is a unit decrease in the other. However, in most real-world scenarios, negative correlations are imperfect, meaning that while the general trend is downward, individual data points might not fit the trend exactly (as in the chart above).

Negative correlations are commonly observed in various fields, such as finance or economics, where there's typically a negative correlation between the supply of a product and its price. As supply increases, prices tend to fall, and vice versa.

Negative Correlation and the Correlation Coefficient

The correlation coefficient is how you'll typically get information about the correlations (negative or otherwise) between different things. It's given as a number ranging from -1.0 to +1.0. A coefficient of +1.0 is a perfect positive correlation, indicating that two assets move in perfect unison. Meanwhile, a coefficient of -1.0 signifies a perfectly negative correlation, where the assets move in exactly opposite directions. When the coefficient is 0, there is no discernible relationship between the movements of the two assets.

For investors, these numbers can be quite meaningful since they can be used to manage and create portfolios and handle risk. A diversified portfolio often aims to include assets with low or negative correlations to each other. This strategy can help mitigate overall portfolio risk, as losses in one asset might be offset by gains in another.

However, like any tool in finance, the correlation coefficient has its limits. It only measures linear relationships and can be sensitive to outliers in the data. In addition, correlation doesn't imply causation and historical correlations don't guarantee future results.

Watching for Outliers

An outlier in financial data is an extreme value that significantly deviates from other observations in a dataset. These can occur because of exceptional market events, data errors, or genuinely unusual occurrences.

Suppose we're analyzing the correlation between the S&P 500 index and a tech stock over the past year, using daily returns. Most days, the stock moves similarly to the broader market, with returns ranging between -2% and +2%. However, one day the following occurs:

• S&P 500 return: +0.5%
• Tech stock return: +30%

This 30% jump in the tech stock could have come from unexpected news, like a major product breakthrough. This single day's outsized return will pull up the average return for the tech stock, potentially misrepresenting its typical relationship with the market.

Thus, if we calculate the correlation coefficient including this outlier, it would suggest a weaker correlation between the stock and the S&P 500 than actually exists on most trading days. More broadly, this means watching out for times when the data might not be representative of most trading situations.

Negative Correlation and Investing

For investors, negative correlation refers to the relationship between two assets whose prices tend to move in opposite directions. When one asset's value increases, the other tends to decrease, and vice versa. Taking advantage of inverse relationships can be a great way to manage risk and optimize portfolios.

Here are two major uses of finance and investing:

• Managing risk and diversification: By including negatively correlated assets in a portfolio, investors can reduce overall volatility. When one asset declines in value, the other may increase, helping to offset losses.
• Hedging: Investors often use negatively correlated assets as a hedge against potential losses in their core holdings.

Here are examples of assets traditionally said to be negatively correlated:

• Stocks and bonds: When stock prices fall, bond prices often rise as investors seek safer havens.
• Gold and the U.S. dollar: Gold prices frequently rise when the U.S. dollar weakens (as in the first half of the 2020s and late 1970s), and vice versa.
• Defensive stocks and cyclical stocks: Defensive stocks (e.g., utilities) often perform better when cyclical stocks (e.g., technology) struggle.

That said, while these are often said to be true, the significance of the correlation over time can change, so it's best to look at the data first before acting. Below, we've put together a correlation table comparing many of the major assets included in portfolios. As you can see, there are positive correlations, but few that are negative, and only moderately so, at least when the asset classes are diversified within a class and compared.

Negative Correlation and Portfolio Diversification

Negative correlation is a key when constructing a portfolio. When found between sectors or assets from different locales, negative correlations can be used to create diversified portfolios that can better withstand market volatility, smoothing out portfolio returns over the long term. The building of large and complex portfolios where the correlations are carefully balanced is called strategic asset allocation.

Consider the generally historic long-term negative correlation between stocks and bonds. Stocks generally outperform bonds during periods of strong economic performance, but as the economy slows down and the U.S. Federal Reserve and other central banks reduce interest rates to stimulate the economy, bonds often outperform stocks. In the chart above, bonds tend to have a moderately negative to neutral correlation with stocks.

Example: Constructing a Portfolio With Negative Correlations

Using the table of asset correlations above, let's see if we can construct a relatively well-balanced portfolio given the data about the relationship among the different assets. This is for informational purposes only. After all, there are many more reasons for including certain assets and excluding others than their correlations. We would need better information about recent performance, as well as our risk tolerance, needs for liquidity, time horizon, and other details that are up to the individual investor and depend on what's happening in the present market. But doing so will help to demonstrate the concept.

A well-balanced portfolio often includes a mix of positively and negatively correlated assets to manage risk and potentially optimize returns over the long term. Let's choose a mix of ETFs representing stocks, bonds, a bit of gold, and commodities from the table above:

• S&P 500 large-caps (IVV): 20%
• U.S. mid-caps (IJH): 10%
• U.S. small-caps (IJR): 10%
• International (non-U.S.) stocks (EFA): 10%
• Emerging market stocks (EEM): 10%
• U.S. investment grade bonds (AGG): 15%
• 7-to-10-year Treasurys (IEF): 10%
• Gold (GLD): 5%
• Commodities (DBC): 10%

This is a portfolio that isn't well-balanced along other lines (two-thirds of the stock allocation is in more volatile markets), but let's see how we do balancing the correlations.

How To Calculate the Weighted Average Correlation

To determine the overall correlation of the portfolio, we compute the weighted average correlation, which means first figuring out each ETF's correlation with the others in the portfolio.

Step 1: For each ETF, we identified its correlation with all other ETFs in the correlation table. For example, for the S&P 500 large-cap ETF (IVV), we have to find its correlation with the others. Here's IVV with the others:

• IJH: 0.91
• IJR: 0.85
• EFA: 0.86
• EEM: 0.76
• AGG: 0.07
• IEF: -0.20
• GLD: 0.02
• DBC: 0.35

You'll need to do the same with each of the ETFs in the portfolio: IJH, IJ, etc. This can be done quickly in a spreadsheet.

Step 2: Sum the correlations above. Quickly doing so with the sum formula in our Google Sheet, we get 3.62.

Step 3: Divide by eight to get the average, which is about 0.45.

Step 4: Now do the same for each of the other ETFs in the portfolio and their correlations. We've calculated the average correlations for them with each other ETF as below:

• IVV: 0.45
• IJH: 0.46
• IJR: 0.44
• EFA: 0.47
• EEM: 0.43
• AGG: 0.20
• IEF: 0.02
• GLD: 0.16
• DBC: 0.25

Step 5: Now, we can calculate the weighted correlations. That's because each one represents a specific portion of the portfolio, and we want to ensure we capture that. So, we multiply the averages above by the percentage share of the portfolio for each:

• IVV: 0.45×0.20=0.09
• IJH: 0.46×0.10=0.046
• IJR: 0.44×0.10=0.044
• EFA: 0.47×0.10=0.047
• EEM: 0.43×0.10=0.043
• AGG: 0.20×0.15=0.03
• IEF: 0.02×0.10=0.002
• GLD: 0.16×0.05=0.008
• DBC: 0.25×0.10=0.025

Step 6: Now we add these together to get 0.34 (rounded to two decimal places). This is the weighted average correlation for the portfolio.

Why the Weighted Average Correlation Matters

The example above gives a weighted average correlation of 0.34, which indicates that, on average, the assets in our portfolio have a moderate tendency to move in the same direction. While our portfolio is somewhat diversified, it's not entirely insulated from market trends. The correlation is not so high that all assets will move together in lockstep, but there is enough positive correlation that the portfolio is likely to experience the effects of market changes together.

A weighted average correlation in this range reflects a portfolio that combines assets with varying degrees of correlation:

• High-correlation assets (such as IVV, IJH, and EFA) are more likely to move together, offering the potential for higher returns when markets are strong but also the risk of dropping together.
• Low-correlation or modestly negative-correlation assets (such as AGG and IEF) provide stability since they've tended to behave differently from the equities in our portfolio, reducing overall volatility.
• Neutral assets (such as GLD and DBC) add further diversification, not being heavily influenced in the past decade by movements in stocks.

The portfolio’s relatively moderate average correlation hopefully will allow us to capture growth while managing risk. During a market upswing, the positively correlated assets may drive portfolio gains. Meanwhile, should there be a downturn, the assets with low or negative correlations should help mitigate losses, providing a cushion against volatility.

Fine-Tuning the Portfolio

If our goal is to further reduce the portfolio's correlation and enhance diversification, we could increase the allocation of assets with lower or negative correlations, such as bonds (AGG, IEF) or commodities (GLD, DBC). Meanwhile, if we're looking to capture more in potential gains should the market go up, we might increase our exposure to high-correlation assets like large-cap stocks (IVV) or international equities (EFA).

Limits of Using Correlations to Build a Portfolio

While correlation is essential in constructing a balanced portfolio, a well-rounded strategy also considers asset allocation, risk tolerance, time horizon, and financial goals. For example, while low or negative correlations can help cut portfolio volatility, they may also limit potential returns should the assets with correlations closer to zero underperform.

In addition, liquidity, market conditions, and economic outlook often play a bigger role in determining which assets to include in a portfolio. Here are some other drawbacks to using asset correlations in isolation from others:

1. Markets change: Correlations aren't static, given shifts in market conditions, economic cycles, or geopolitical events. An asset pair that has shown a low or negative correlation in the past may become more correlated during market stress periods, reducing diversification's effectiveness. Hence, it's essential to look at recent data on asset correlations and not just accept old truisms about stocks and bonds when building a portfolio.
2. Assumes a linear relationship: Correlation measures only the linear relationship between two assets. However, many assets may have complex, nonlinear relationships that correlation fails to capture, potentially missing important aspects of their interaction.
3. Doesn't Capture Volatility: Correlation doesn't give you any information about the magnitude of asset price movements. Two assets might have a low correlation, but if one is highly volatile, it could still contribute significantly to portfolio risk. Therefore, correlation and volatility measures, such as standard deviation, should be used as well.
4. History isn't the future: Correlation is usually calculated based on historical data, which may not accurately predict future relationships.
5. Asset class diversification: Correlation focuses on the relationship between and among sets of assets, but it doesn't account for diversification across different asset classes, sectors, or geographic regions. A portfolio could have low correlations within a single asset class but still be under-diversified if it lacks exposure to other asset types.
   

The Bottom Line

Negative correlation can be used for a strategic approach to risk management and portfolio diversification. By pairing assets that tend to move in opposite directions, investors could mitigate overall portfolio volatility and create more lasting strategies. This approach challenges the typical move of seeking only positively correlated assets, opening up new ways to navigate the financial markets.

However, correlation coefficients can shift over time, especially during extreme market events. Successfully using negative correlation strategies requires ongoing analysis, an up-to-date and subtle understanding of the market, and a willingness to adapt to changing conditions.