FRM Exam Part II · Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

Correlation Behavior in Bonds, Commodities and Other Assets

Updated 11 October 2026 · Fact-checked

Correlation behavior in other asset classes means how correlations in bonds, commodities and credit differ from equities. Bond and default correlations are driven by rates and credit conditions, tend to rise in stress, and mean revert. To answer, identify the asset class, the driver, the direction and the risk implication.

Understand Correlation Behavior in Other Asset Classes

Correlation measures how two assets move together, from -1 to +1. Empirical work asks how it behaves in real data, not in a textbook model. Equity correlation is the benchmark: it is unstable, tends to rise in market falls, and tends to revert to a long-run level.

Bonds. Bond returns share common drivers, mainly the level of interest rates. Government bonds of similar maturity are usually highly correlated, because one rate factor explains most of their moves. Correlation falls as maturities are further apart, which is why level, slope and curvature matter. Corporate bonds add a credit spread factor, so their correlation with government bonds depends on whether rates or credit dominate.

Bond versus equity. Equity and bond correlation is not fixed. It has changed sign over time. When inflation and rate shocks dominate, stocks and bonds fall together, so correlation is positive. When growth fears dominate, bonds rally as stocks fall, so correlation is negative. Do not assume bonds always diversify equities.

Commodities. Correlations among commodities are usually low and unstable, as each has its own supply and demand drivers. Within a group, such as energy or metals, correlation is higher. Commodity correlation with equities tends to rise in global demand shocks and financial stress, when investors move together.

Credit and default. Default correlation is the tendency of firms to default together. It is low in normal times and rises in recessions, as firms share common economic factors. Credit spread correlations also rise in stress. Like equity correlations, these measures show mean reversion toward a long-run average, but the level shifts with economic and credit conditions.

Key formulas to remember

Correlation: ρ(X,Y) = Cov(X,Y) ÷ (σX × σY); Always between -1 and +1. It captures linear co-movement only.
Two-asset portfolio variance: σp² = w1²σ1² + w2²σ2² + 2·w1·w2·ρ·σ1·σ2; Higher ρ raises portfolio risk. Use it to show the cost of correlation rising in stress.
Mean reversion of correlation (stylised): Next correlation ≈ long-run level + persistence × (current − long-run level), with persistence between 0 and 1; Illustrative form. Shows pull toward the long-run mean; it is not a GARP-specified model.

How to solve Correlation Behavior in Other Asset Classes questions

Use the same sequence for any question on empirical correlation outside equities.

1Identify the asset class: government bond, corporate bond, commodity, credit or default, or a cross-asset pair.
2Name the main driver: interest rate level, credit spread, sector supply and demand, or the economic cycle.
3Decide the direction in the stated condition: usually correlation rises in stress or recession, but stock-bond sign depends on whether inflation or growth fears dominate.
4Check maturity or sector: nearer maturities and same-sector commodities are more correlated.
5Apply mean reversion if the question asks about the future: expect a drift toward the long-run level.
6State the risk implication: diversification benefit falls, VaR or loss estimates built on calm-period correlations are too low.
7Eliminate options with words like always, never or constant.

Quickest way: Driver, direction, implication

When to use it: Use for conceptual multiple-choice questions where you have under a minute.

Find the driver in the stem: rates, credit, commodity-specific, or the cycle.
Pick the direction: stress and recession push correlations up; diversification weakens.
Reject absolute words such as always or constant.
Choose the option that mentions the implication, such as underestimated risk.

Common mistakes in Correlation Behavior in Other Asset Classes

Assuming stock-bond correlation is always negative.
Many portfolios were built in periods when bonds hedged equities.
Fix: Remember the sign changes with the regime. Inflation and rate shocks can make it positive.
Treating all commodities as highly correlated.
Commodity indices move together in some global shocks.
Fix: Individual commodities have idiosyncratic drivers. Correlation is higher within a sector and in stress.
Thinking default correlation is stable over the cycle.
Models often use one fixed input.
Fix: Default correlation rises in downturns as firms share economic factors. A fixed input understates tail losses.
Forgetting mean reversion applies to correlation.
Students link mean reversion only to interest rates or volatility.
Fix: Correlations drift back toward a long-run level, but the level itself can shift by regime.
Confusing correlation of levels with correlation of returns.
Trending prices look highly correlated.
Fix: Use changes or returns when judging co-movement.

Worked examples

Example 1

A portfolio holds two assets, each with weight 50% and volatility 10%. In calm markets ρ = 0.2. In stress ρ = 0.8. What is the portfolio volatility in each case, and what does the change show?

Show the solution

Variance = 0.25×0.01 + 0.25×0.01 + 2×0.5×0.5×ρ×0.1×0.1 = 0.005 + 0.005ρ.
Calm: ρ = 0.2 gives 0.005 + 0.001 = 0.006... recompute: 2×0.25×ρ×0.01 = 0.005ρ, so variance = 0.005 + 0.005ρ.
Calm: 0.005 + 0.005×0.2 = 0.006. Volatility = √0.006 = 7.75%.
Stress: 0.005 + 0.005×0.8 = 0.009. Volatility = √0.009 = 9.49%.
The rise reflects lost diversification as correlation increases.

Answer: About 7.75% in calm markets and 9.49% in stress. Rising correlation in stress erodes diversification, so VaR from calm-period correlations is understated.

Example 2

A risk manager sees that the equity-government bond correlation turned positive during a period of sharp inflation and rate rises. Which explanation is most consistent with empirical behavior: (A) bonds are always a hedge, (B) rate shocks hit both asset classes, (C) correlation is constant, or (D) commodities drive bond returns?

Show the solution

Identify the driver: rising rates reduce bond prices directly.
Higher discount rates and weaker growth expectations also reduce equity values.
Both fall together, so correlation is positive.
A and C use absolute claims that conflict with the evidence. D is not a general driver.

Answer: B. Rate shocks hit both asset classes, so the stock-bond correlation can turn positive; it is regime dependent.

Exam tips

Watch for absolute words such as always, never and constant. They are usually wrong.
Link every correlation change to a driver: rates, credit conditions or the cycle.
For calculations, plug ρ into the portfolio variance formula and compare calm versus stress.
Expect the implication to be tested: diversification fails in stress and VaR is understated.

Practice questions from Empirical Properties of Correlation: How Do Correlations Behave in the Real World?

Correlation Behavior in Other Asset Classes: frequently asked questions

How does bond correlation behave empirically?

Bonds of similar maturity are highly correlated because a common rate factor drives them. Correlation falls as maturities diverge. Corporate bonds also carry a credit spread factor, which raises correlation in stress.

What is the difference between equity and bond correlation behavior?

Equity correlations rise in market falls and mean revert. Bond correlations depend mainly on the rate factor and maturity gap. The stock-bond correlation itself changes sign with the inflation and growth regime.

How does default correlation behave?

Default correlation is low in normal times and rises in recessions as firms share common economic drivers. Using a fixed value therefore understates joint-default risk in downturns.

Are commodity correlations stable?

No. Individual commodities have their own supply and demand drivers, so correlations are low and unstable. They tend to rise within sectors and during financial stress.