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.