Why Combining Volatile Assets Smooths Returns

Volatility causes anxiety, but a volatile asset is not the same thing as a risky portfolio. Combining two volatile assets whose prices do not move in lockstep can produce smoother overall returns, because their movements partly offset each other.

This paper explains the mathematics in plain English, shows why diversification depends on correlation rather than volatility alone, warns that correlations can rise in a crisis, and covers the behavioural biases that make diversified portfolios feel riskier than they are.

Key findings

• Portfolio variance is set by weights, volatilities and correlation: σp² = w1²σ1² + w2²σ2² + 2w1w2σ1σ2ρ.
• Any correlation below 1 reduces combined variance, and a correlation of −1 can in theory eliminate volatility altogether.
• Diversification works only when correlations stay low or negative. Equities and bonds were negatively correlated in the 2000s but turned positive in 2022 amid inflation.
• Salience bias, recency bias and overconfidence make diversification feel risky, because some parts of a diversified portfolio will always be underperforming.
• Diversification rearranges risk rather than eliminating it; the aim is consistent growth, not the absence of fluctuation.

What the paper covers

1. Diversification: reducing portfolio volatility
2. Portfolio risk: variance, correlation and the frontier
3. Offsetting movements smooth portfolio risk
4. Statistical reality: correlation, not coincidence
5. Behavioural biases that sabotage diversification
6. Optimising risk versus return
7. Intelligent diversification: three asset pairings
8. Designing useful volatility