Calculate two-asset portfolio volatility
Enter two positive portfolio weights, each asset's annualized volatility, and their correlation. Use volatility figures measured over comparable windows.
Private by design: values stay in your browserPortfolio volatility formula, quick answer
Portfolio volatility is the standard deviation of portfolio returns. For two assets, it depends on each asset's weight, each asset's volatility, and the correlation between the two assets.
σp = √(w12σ12 + w22σ22 + 2w1w2σ1σ2ρ1,2)For an N-asset portfolio, use σp = √(wTΣw). To annualize daily volatility, multiply daily volatility by √252. To annualize monthly volatility, multiply by √12.
What You'll Learn
- The portfolio volatility formula for two-asset and multi-asset portfolios
- The square-root-of-time rule for converting daily to annualized volatility
- Why annualization uses 252 (trading days), not 365
- The difference between historical, realized, and implied volatility
- A worked example converting a 1 percent daily volatility into an annual figure
What Is Portfolio Volatility?
Portfolio volatility is the standard deviation of a portfolio's returns. It measures how widely the portfolio's value swings around its average return. Volatility is the most widely cited risk metric in finance because it is the input to the Sharpe ratio, Value at Risk, option pricing, and most other risk frameworks.
Volatility is typically expressed as an annualized percentage, even when computed from daily or weekly data. A 15 percent annualized volatility means returns typically fall within a range of plus or minus 15 percent of the average return about two-thirds of the time (under a normal-distribution assumption).
The Portfolio Volatility Formula
Two-Asset Portfolio
Multi-Asset Portfolio (Matrix Form)
| wi | Weight of asset i in the portfolio (must sum to 1.0 across all assets) |
| σi | Standard deviation of asset i's returns |
| ρi,j | Correlation coefficient between asset i and asset j |
| Σ | Variance-covariance matrix (diagonal: variances; off-diagonal: covariances) |
| σp | Portfolio volatility (standard deviation of portfolio returns) |
Volatility vs total risk
Volatility and total portfolio risk are the same number under the standard definition. Both refer to the standard deviation of returns. "Volatility" is the trading and options-market term; "standard deviation" is the statistical term; "total risk" is the portfolio-theory term. They mean the same thing.
Three-Asset Portfolio (Expanded)
The matrix form is compact but hides the terms. Written out for three assets, portfolio variance has three variance terms and three covariance terms; volatility is the square root:
The Square-Root-of-Time Rule (Annualization)
Volatility is typically computed from daily, weekly, or monthly returns, then scaled to an annual figure. The scaling rule:
| Period | n (Periods per Year) | Multiplier | Example: 1% period vol → annual |
|---|---|---|---|
| Daily (trading days) | 252 | √252 ≈ 15.87 | 1% × 15.87 = 15.87% |
| Daily (calendar days) | 365 | √365 ≈ 19.10 | 1% × 19.10 = 19.10% |
| Weekly | 52 | √52 ≈ 7.21 | 1% × 7.21 = 7.21% |
| Monthly | 12 | √12 ≈ 3.46 | 1% × 3.46 = 3.46% |
| Quarterly | 4 | √4 = 2.00 | 1% × 2.00 = 2.00% |
The 252 vs 365 question
For equities and other instruments observed on trading days, 252 is the common convention. For assets with one return observation for every calendar day, such as continuously priced crypto data, 365 may be appropriate. Match the annualization factor to the frequency of the return series and use a consistent convention when comparing assets.
How to Calculate Annualized Portfolio Volatility: Step-by-Step
Example: Daily Returns to Annualized Volatility
For each trading day in the lookback window (say, 1 year = 252 trading days), calculate:
Or, for log returns: rt = ln(Pt / Pt-1). Log returns are preferred for volatility work because they are additive across periods.
Average return = (sum of all Rt) / n
Suppose mean daily return is 0.05% across the 252 observations.
For each day, compute the squared deviation: (Rt − mean)2.
Average these squared deviations (divide by n − 1 for sample standard deviation): Variance = Σ(Rt − mean)2 / (n − 1).
Take the square root: σdaily = √variance
Suppose daily standard deviation = 1.00%
σannual = σdaily × √252
σannual = 1.00% × 15.87
The S&P 500 has averaged about 15-16% annualized volatility over the last 50 years. A computed annual volatility of 15.87% from daily returns is in the right ballpark for a broad equity portfolio. Anything dramatically different signals either an unusual portfolio composition or an issue with the calculation.
Realized vs Implied vs EWMA Volatility
"Portfolio volatility" can be computed three common ways, each with different uses:
| Type | What It Measures | Pros | Cons |
|---|---|---|---|
| Historical (Realized) | Standard deviation of past returns over a fixed window | Simple, objective, easy to compute | Backward-looking; treats all observations equally |
| EWMA | Exponentially weighted moving average of squared returns | Reacts faster to recent regime changes | Requires a decay parameter (RiskMetrics uses 0.94 for daily data) |
| GARCH | Models volatility as a function of prior squared returns and prior volatility | Captures volatility clustering well | Parameter estimation can be unstable; harder to explain |
| Implied | Volatility inferred from current option prices (e.g. VIX) | Forward-looking; reflects market expectations | Only available for assets with liquid options; affected by supply/demand of options themselves |
EWMA in one sentence
EWMA weights yesterday's squared return by (1 − lambda) and yesterday's variance by lambda, where lambda is typically 0.94 for daily data (the RiskMetrics standard). This means the most recent observations matter most, and the influence of older observations decays exponentially.
Typical Volatility Values by Asset Class
| Asset Class | Annualized Volatility (Typical Range) |
|---|---|
| Cash / T-bills | 0% to 1% |
| US Aggregate Bonds | 4% to 7% |
| 60/40 Stock/Bond Portfolio | 9% to 12% |
| S&P 500 | 14% to 18% |
| Long Treasury (TLT) | 13% to 16% |
| Nasdaq 100 | 20% to 25% |
| Single large-cap stocks | 20% to 40% |
| Single small-cap stocks | 30% to 60% |
| Bitcoin | 50% to 90% |
| Single early-stage growth stocks | 60% to 100%+ |
From Volatility to a Broader Portfolio Risk Check
This calculator applies the exact two-asset equation to the values you provide. It does not fetch return history, estimate correlations, or model more than two assets. For a broader view, Guardfolio analyzes synchronized portfolio holdings and tracks rolling 30-day volatility against the portfolio's historical baseline.
The free portfolio risk check requires no connected account and helps examine:
- Portfolio volatility in the context of other risk dimensions
- Concentration and diversification
- ETF overlap and repeated underlying exposure
- Portfolio health signals beyond standard deviation alone