Comprehensive Guide
Learn more in our Investing Guide.
How it works
Portfolio volatility is the standard deviation of the whole mix's returns — the number that turns 'my funds wiggle' into 'my account typically swings X%'. It cannot be averaged from holdings: variance comes from every PAIR of assets interacting, which is why the formula squares weights, multiplies volatilities pairwise, and weights each pair by its correlation. Two assets at 18% and 6% volatility split 60/40 do NOT carry a 12% blend; with +0.2 correlation the combination runs closer to 11%, and the gap versus the naive average is diversification made arithmetic. Push correlations toward +1 and the benefit evaporates; push toward −1 and pairs can nearly cancel. This calculator handles two or three assets, normalizes weights automatically, and decomposes results the way professionals do — each asset's CONTRIBUTION to total risk (often wildly unequal to its capital share) plus an effective-count metric showing how many genuinely independent bets the mix contains. Standard deviation describes typical dispersion, never a worst case; pair it with drawdown analysis before deciding whether the ride fits your temperament. Inputs are illustrative estimates, not measured statistics.Formula
σp² = w1²σ1² + w2²σ2² + 2·w1·w2·σ1·σ2·Ï12 (+ third-asset terms) | σp = √σp²
Tips
- Use long-run vols and correlations; single-year snapshots mislead badly.
- Watch the correlation input hardest — it moves answers more than weights do.
- Compare risk contribution to capital share; mismatches reveal hidden concentration.
- Effective bets well below the holding count means overlapping exposures.
- Pair volatility with drawdown scenarios — typical swings and worst cases differ.
Frequently asked questions
How do you calculate two-asset portfolio volatility?
Square each weight times its volatility squared, add double the product of both weights, vols and their correlation, then take the square root: σp = √(w1²σ1² + w2²σ2² + 2w1w2σ1σ2Ï12). For 60/40 at 18%/6% with Ï=0.2, that lands near 11%.
What correlation gives maximum diversification benefit?
The lower the better. Below zero, assets partially cancel each other and combinations can beat BOTH individual volatilities; near +1, blending achieves nothing beyond averaging. Most stock/bond pairs have hovered mildly positive over long stretches — helpful, though far from magic.
Why does my 50/50 portfolio feel riskier than half-stock volatility?
Because correlations rise in crises. Long-term averages near +0.2 can spike toward +0.6 during panics as everything sells together, so realized swings exceed calm-market predictions. A mix computed at 11% can plausibly deliver 15% turbulence — stress inputs at elevated correlations before trusting comfort.
What does effective number of bets mean?
It converts concentration into an intuitive count: equal thirds score 3.0, while a 70/20/10 split scores effectively about 1.9 because dominant positions drive outcomes. Counts well below your holding count flag portfolios that look diversified but behave like concentrated bets on one engine.
Is lower portfolio volatility always better?
No — volatility is a cost measure, not a goal. An 8%-volatility mix returning about 4% loses badly to a 14%-volatility mix returning 8% over decades of compounding. The right level is the LEAST turbulence that still funds your goals; then confirm survivability through drawdown scenarios.