Portfolio volatility: why 60/40 does not mean 60/40 risk
A 60/40 capital split can leave most portfolio volatility attributable to stocks. Correlation changes that balance, but capital weights alone do not reveal it. The calculation is especially useful when comparing portfolios through a Sharpe ratio, whose denominator is portfolio volatility relative to its benchmark.
The main Sharpe guide distinguishes this statistic from geometric wealth growth. Covariance is a diagnostic input, not an objective: reducing it does not by itself demonstrate higher net compounded wealth. This article separates the contributions of weights, unequal asset volatility and covariance, rather than assuming both assets carry the same risk.
Key takeaways
A 60/40 capital allocation need not divide portfolio volatility in the same proportions.
Weights, asset volatilities and correlation all enter the variance calculation.
Lower volatility alone does not establish higher geometric wealth growth or identify a growth-optimal allocation.
Start with one disclosed hypothetical model
Assume 60% in stocks and 40% in government bonds, with annual return volatilities of 18% and 6% respectively. Assume arithmetic annual expected total returns of 8% and 3%, and constant 2% cash. All returns are hypothetical nominal US-dollar returns before fees and taxes. No empirical correlation estimate or forecast is implied.
The model specifies means, variances and correlation, but not a complete return distribution. It therefore cannot calculate exact expected log growth or identify a growth-optimal allocation.
The weighted arithmetic expected return is 0.6 × 8% + 0.4 × 3% = 6%. It stays fixed while we vary only correlation. The assumed expected excess return is therefore 4%.
For weights w, volatilities σ, and correlation ρ:
Portfolio variance = wA²σA² + wB²σB² + 2wAwBσAσBρ
Volatility is the square root of variance. In decimal-return units, our three terms are 0.011664 + 0.000576 + 0.005184ρ. Adding 18% and 6%, or averaging them without covariance, would miss the diversification effect.
Change correlation, holding everything else fixed
Assumed correlation
Portfolio volatility
Sharpe ratio
−0.5
9.82%
0.407
0.0
11.06%
0.362
+0.5
12.18%
0.328
+0.8
12.80%
0.312
+1.0
13.20%
0.303
These are original hypothetical calculations. The covariance and risk-contribution CSV includes all terms and the −1 endpoint. The ratio uses the constant 2% cash assumption, so excess-return volatility equals portfolio volatility.
At perfect positive correlation, diversification provides no volatility reduction beyond the weighted asset risks: 0.6 × 18% + 0.4 × 6% = 13.2%. Perfect negative correlation still leaves 8.4% volatility because the weighted exposures, 10.8% and 2.4%, do not cancel. Negative correlation is not enough to make this mix riskless.
Allocate the variance rather than the money
At zero correlation, the stock variance term is 0.011664, out of total variance 0.012240. Its share is 95.29%; bonds contribute 4.71%. The money split remains 60/40.
For non-zero correlation, a standard covariance allocation gives each asset its own variance term plus half the covariance term. The stock share is:
[wA²σA² + wAwBσAσBρ] ÷ portfolio variance
At correlation −0.5, that share becomes 107.46%, while the bond share becomes −7.46%. A negative contribution means bonds offset some portfolio fluctuations in this model. It does not mean bonds have negative standalone volatility, nor that stocks literally account for more than all money at risk.
These are shares of variance, also matching the normalised Euler contributions to volatility. They are not shares of a maximum possible loss or probabilities of a crash. A contribution calculated from one covariance estimate is also conditional on that estimate: changing the observation window, frequency or asset definitions can change the result even when the capital weights stay fixed.
A crisis scenario asks a different question
Hold the initial 60/40 weights for one hypothetical period. If stocks lose 35% and bonds gain 8%, the portfolio loses 17.8%. If stocks lose 35% and bonds lose 15%, it loses 27.0%. The scenario CSV records these assumed total returns.
Neither outcome is inferred from the correlation table. A correlation across many observations does not specify one crisis return. The historical diversification study documents changing relationships; purchased puts introduce a different, contractual payoff with its own cost and expiry limits.
Sources and interpretation
The portfolio principle follows Markowitz's Nobel lecture and the ratio follows Sharpe's 1994 paper. All model inputs here are assumptions, not fitted historical statistics. Lower model volatility alone establishes neither maximum geometric growth nor an appropriate portfolio; the CAGR comparison shows why.
Calculations checked on 28 October 2026. This is a sensitivity analysis, not an allocation recommendation.
FAQ
How do I calculate two-asset portfolio volatility?
Portfolio variance is wA²σA² + wB²σB² + 2wAwBσAσBρ, where weights sum to one and ρ is return correlation. Volatility is its square root. The assets' return frequencies and volatility units must match.
Why can stocks contribute more than 60% of risk in a 60/40 portfolio?
Capital weight is not a variance contribution. In our hypothetical 60/40 mix, stocks have 18% annual volatility and bonds 6%. At zero correlation, stocks contribute 95.29% of portfolio variance, despite receiving 60% of capital.
Can a risk contribution exceed 100%?
Under a covariance-based allocation, yes. With sufficiently negative correlation, one asset's contribution can be negative because it offsets another's fluctuations. In our -0.5 correlation scenario, stocks contribute 107.46% and bonds -7.46%; the shares still sum to 100%.
Does negative correlation guarantee protection during a crash?
No. Correlation describes co-movement across observations. A historical average does not impose a contractual crisis payoff or establish the returns in a particular shock. Scenario losses must be examined separately.
