The Importance of Asset Correlation in a Balanced Portfolio

Correlation measures how closely two assets' returns move together in a straight-line (linear) way, on a scale from -1 to +1. Together with the weights and each asset's own volatility, it sets how much of the two assets' swings offset each other in a portfolio. The catch is that the number is an estimate from a particular window of history, and for US stocks and Treasuries it has changed sign more than once.

Key takeaways

• Correlation of +1 means returns move in perfect linear step and diversification removes no volatility; for a mix of long holdings, any value below +1 brings portfolio volatility below the weighted average of the parts.
• In annual data for 1928-2025, US stocks and 10-year Treasuries had a correlation of about 0.02 over the whole period, but 10-year windows ranged from -0.86 (ending 2009) to +0.74 (ending 1994).
• For an illustrative 60/40 mix (stocks 16% volatility, bonds 6%), portfolio volatility is about 9.2% at a correlation of -0.3 and about 11.2% at +0.6, against 12.0% at +1.
• The estimate depends on the window length, the data frequency and the sign convention, so one figure from one source is a snapshot, not a constant.

What correlation measures

The Pearson correlation coefficient, usually written r, is a unitless number between -1 and 1. According to Penn State's applied regression course notes, it describes the strength of a linear relationship: -1 is a perfect negative line, +1 a perfect positive line, and 0 means no linear relationship. A zero does not rule out a nonlinear link, such as two assets that move together only in sharp sell-offs.

Two points are easy to miss. First, correlation describes co-movement, not cause; the same course lists this among its cautions on r. Two assets can move together because both respond to interest rates, growth or sentiment, without either driving the other. Second, it ignores size. The same Penn State notes show that r equals the regression slope multiplied by the ratio of the two standard deviations. A stock that moves 0.5% for each 1% in the market and one that moves 2% can both show a correlation near +1 with the market, while their betas (the slopes) differ fourfold. Beta and covariance carry the size information; correlation strips it out.

Portfolio volatility needs both. The two-asset formula, as written in an MIT investments lecture, is:

variance = w1^2 x s1^2 + w2^2 x s2^2 + 2 x w1 x w2 x s1 x s2 x r
volatility = square root of variance

Here w1 and w2 are portfolio weights, s1 and s2 are the standard deviations (volatilities) of the two assets, and r is their correlation. The first two terms are fixed by the weights and volatilities. Only the last term, the cross term, depends on correlation.

How the number gets measured

Correlation is always computed over a sample: a set of dates, a return frequency and a pair of return series. Change any of the three and the result can change. A Federal Reserve Board working paper on "good" and "bad" inflation uses rolling three-month correlations of daily returns on the overall US stock market and on 5-year Treasury bonds. From July 2004 onward, that three-month figure ranged from about -78 percent to +54 percent and averaged about -30 percent, according to the paper.

The same pair, measured over longer windows in annual data, gives tighter ranges. The table below uses the S&P 500 total return (dividends included) and the 10-year Treasury bond return from Aswath Damodaran's historical returns file, 1928-2025, downloaded for this guide. Windows of 5, 10 and 20 years roll forward one year at a time.

Shorter windows swing more because a handful of observations can dominate; Penn State's cautions note that r can be greatly affected by one or a few data points. The whole-period figure near zero hides regimes that were far from zero in both directions.

Sign conventions also differ between sources. An October 2026 FEDS Note measures the correlation between stock returns and changes in bond yields, so a positive value there means bond prices rose when stocks fell. A correlation between stock returns and bond returns has the opposite sign for the same behavior. Check which one a chart uses before comparing numbers.

One caveat on the data: Damodaran's 10-year bond return is constructed from constant-maturity yields, by repricing a 10-year bond issued at par at the prior year's yield, rather than taken from a traded fund. The S&P 500 itself dates from 1957, and the file fills in earlier years with other large-company indices. Annual figures also give only 98 observations, which is thin for a correlation estimate.

Stock-bond correlation, 1928-2025

The next table splits the same annual data into calendar decades. These are 10 observations each (12 in the first row, 6 in the last), so each figure is rough.

Small samples are noisy. With 10 annual observations, a correlation has to be beyond about ±0.63 before it is statistically distinguishable from zero at the usual 5% level; with 6 observations the bar is about ±0.81. Of the rows above, only 2000-2009 clears its bar, so read the table for its broad pattern rather than its individual values.

Two features stand out. The correlation was positive in each decade from the 1970s through the 1990s, then negative in the 2000s and 2010s. Over 2000-2021 it was -0.65; including 2022-2025 brings the 2000-2025 figure to -0.37, and the 10-year window ending 2025 gives +0.66. The FEDS working paper cited above, using daily data from 1970 onward, describes the same shift: the stock-bond return correlation "was strongly positive until the late 1990s, then shifted to a predominantly negative regime." It also links the regimes to whether inflation news is read as good or bad for growth.

The earlier decades are a reminder that the negative stretch was not the norm. The annual data reaches back before that paper's 1970 start, and in it the 1950s and 1960s were also negative, then the 1970s and 1980s turned positive. An assumption that bonds always offset stocks would have rested on one regime of a relationship that had flipped before.

Gold is a different case and a less stable one. Using the year-end gold prices in the same file (Damodaran notes that gold prices were fixed before 1971), the correlation of annual gold returns with stocks is -0.17 for 1971-2025, but -0.35 for 1971-1999 and +0.16 for 2000-2025. The sign changed, but with 29 and 26 years neither sub-period figure is far enough from zero to be statistically distinguishable from it at the 5% level, so the safer reading is that gold showed no stable relationship with stocks.

How correlation shapes 60/40 risk

Illustrative example: a portfolio holds 60% stocks with 16% annual volatility and 40% bonds with 6%. These volatilities are round assumptions chosen for the arithmetic, not forecasts. The weighted average of the two volatilities is 0.6 x 16% + 0.4 x 6% = 12.0%, which is what the portfolio would show if correlation were +1.

The fixed terms are 0.6 squared times 0.16 squared, which is 0.009216, and 0.4 squared times 0.06 squared, which is 0.000576. The cross term is 2 x 0.6 x 0.4 x 0.16 x 0.06 x r = 0.004608 x r. Adding them and taking the square root gives:

Moving from +0.6 to -0.3 cuts volatility by about 2.0 percentage points (11.21% to 9.17%), while the portfolio still holds the same 60/40 weights. Even at +0.6, volatility is 0.79 points below the +1 case, so a correlation below 1 helps even when it is not low. Stocks still dominate the result: at r = 0 the stock term (0.009216) is about 94% of the variance (0.009216 / 0.009792).

Correlation is one lever, not the only one. In the same example at r = 0, raising the stock volatility assumption from 16% to 20% lifts portfolio volatility from 9.90% to 12.24%, a bigger move than the whole -0.3 to +0.6 correlation range above.

The calculation uses only volatility. It does not say anything about returns, and it says nothing about how the portfolio behaves in a specific bad year. Correlation also touches rebalancing. Weights drift whenever the two assets' returns differ, as in the SEC's Investor.gov example where a 60% stock allocation rises to 80% after market gains, and Investor.gov notes that such drift changes the portfolio's risk level. With volatilities fixed, a lower correlation makes the gap between the two assets' returns more variable from year to year, so weights tend to wander further between rebalancing dates. To work out the trades that bring a drifted mix back to its target weights, use the rebalancing calculator.

Limits of correlation estimates

Correlation tends to behave worst when it matters most. In a 2001 Journal of Finance paper, Longin and Solnik studied monthly returns of the five largest stock markets from 1959 to 1996 and found that the correlation of large negative returns was much greater than expected under multivariate normality, while the correlation of large positive returns was not inconsistent with it. That is a finding about equity markets in different countries, not about stocks and bonds, but it shows why a calm-period average can understate co-movement in a sell-off. The same abstract adds a warning: even when the underlying correlation is constant, correlation measured only in volatile periods comes out higher than in calm periods, so a crisis-period figure has to be judged against that benchmark before concluding that the relationship changed.

Three practical points follow from the data above. Treat any single correlation as a range, since the 10-year figures in this dataset span -0.86 to +0.74. The Fed working paper ties the sign to the economic regime, specifically how inflation news relates to growth, not to the asset class alone, and the October 2026 FEDS Note concludes, from US, euro-area and UK data, that bonds' value as a hedge depends on how stable inflation expectations are. And remember that diversification still works as long as the correlation is below +1, but how much it helps is uncertain and can shrink at the wrong time. None of this is a forecast for any future period.

Frequently asked questions

Does a correlation of zero mean two assets are unrelated?

No. Pearson's r measures only the linear part of the relationship, so a value of 0 means no linear relationship, according to Penn State's course notes. Two assets can still move together in a nonlinear way, for example only during large declines.

Can a mix be less volatile than its safest asset?

Yes, if the correlation is below the ratio of the lower volatility to the higher one and the weights are right. With the same illustrative volatilities (16% and 6%), that threshold is 6 / 16 = 0.375. A 20% stock and 80% bond mix then has about 5.77% volatility at r = 0 and about 4.91% at r = -0.3, both below the 6% of bonds alone. At r = +0.6 the same mix is about 7.2%, and no mix of the two without short selling gets below 6%.

Why do the stock-bond figures here differ from other sources?

Window, frequency, bond maturity, total return versus price return and sign convention all change the result. This guide uses annual returns for the S&P 500 with dividends and for a constructed 10-year Treasury return, while the Fed working paper cited above uses daily returns on the whole US stock market and 5-year Treasuries over three-month windows. Compare only figures built the same way.

Does gold reliably move against stocks?

Not in this dataset. Annual gold returns had a correlation of -0.35 with stocks from 1971 to 1999 and +0.16 from 2000 to 2025, using year-end prices, and neither figure is statistically distinguishable from zero with so few years. A diversifier whose sign changes between periods cannot be treated as a fixed hedge.

Is a shorter window better than a longer one?

Neither is correct in general. A shorter window reacts faster to a regime change but is noisier: in the annual data, 5-year correlations ranged from -0.97 to +0.99 against -0.75 to +0.49 for 20-year windows. Comparing several windows side by side shows how stable the estimate is.

A short checklist for correlation

1. Write down the window, frequency and return type behind any correlation figure, and the sign convention if bond yields are involved.
2. Compute or look up the correlation over at least two windows (for example 3 and 10 years) and note how far they differ.
3. Run the volatility formula with a range of correlations, such as -0.3 to +0.6, and see how much your portfolio's risk moves.
4. Check what each asset is exposed to, such as inflation, growth or rates, because shared exposures can raise correlation.
5. Revisit the mix when you rebalance, and treat the result as an estimate rather than a promise.

Sources

• Aswath Damodaran, Historical Returns on Stocks, Bonds and Bills, 1928-2025 (NYU Stern)
• Bonelli, Palazzo and Yamarthy, "Good" Inflation, "Bad" Inflation, FEDS 2025-002 (Federal Reserve Board)
• Li and Yoldas, Government Bonds' Safe-Haven Property and Inflationary Pressures, FEDS Note, October 16, 2026
• Longin and Solnik, Extreme Correlation of International Equity Markets, Journal of Finance 56(2), 2001
• Penn State STAT 462, (Pearson) Correlation Coefficient r
• Penn State STAT 462, R-squared Cautions
• MIT OpenCourseWare 15.433 Investments, Portfolio Theory Part 3
• SEC Investor.gov, Asset Allocation and Diversification