Standard Deviation

Standard Deviation (σ) quantifies the dispersion of a fund's periodic returns around its mean — the foundational measure of total volatility in mutual fund risk analysis. Higher σ = wider return swings = higher risk.

Formula

σ = √[ (1/(N−1)) × Σ (R_i − R̄)² ]

Where: R_i = return in period i, R̄ = mean return over N periods, N = number of observations. The (N−1) denominator applies for sample standard deviation (standard in finance).

Annualisation: Daily σ × √252 = annualised σ (252 NSE trading days). Monthly σ × √12 = annualised σ. SEBI Circular 2021/647 mandates disclosure of annualised standard deviation using trailing 3-year monthly returns.

How it is Computed for Indian MFs

AMFI and AMC factsheets disclose standard deviation as an annualised figure. The standard methodology: collect 36 monthly NAV-based returns (or 52 weekly, depending on the platform); compute sample σ; multiply by √12 (monthly) or √52 (weekly). MintByte uses monthly returns × √12 matching SEBI/AMFI convention. AdvisorKhoj uses the same. Morningstar India uses trailing 36 monthly observations.

NSE/BSE price-series data has 252 trading days per year. When computing intraday or daily-return σ for ETFs, the √252 scaling factor applies. Do not mix weekly σ × √52 with monthly σ × √12 — both annualise to the same figure only if the return autocorrelation is zero.

Worked Example (Indian Context)

HDFC Mid-Cap Opportunities Fund – Direct Plan: 36 monthly returns (Jan 2023 – Dec 2025) have a sample standard deviation of 5.1% (monthly). Annualised: 5.1% × √12 = 5.1% × 3.464 = 17.7% p.a.

Compare: Nifty Midcap 150 TRI annualised σ = 19.3% over same period. The fund's σ (17.7%) is lower than the benchmark (19.3%) — it delivered its return with less total volatility.

For context, Nifty 50 TRI annualised σ ≈ 14–15% in normal markets; a diversified large-cap fund at 13–16% σ is broadly in line with index volatility. Mid-cap and small-cap categories typically run 18–25% annualised σ.

Interpreting Standard Deviation

σ Range (equity MF, annualised)	Category signal
< 12%	Conservative: balanced hybrid, debt-oriented
12 – 17%	Moderate: large-cap equity, flexicap
17 – 23%	Elevated: mid-cap, multi-cap
> 23%	High: small-cap, thematic, sectoral

Caveats

Standard deviation assumes symmetrical (normal) return distribution — not valid for Indian equity funds that exhibit fat tails and negative skew. σ treats upside and downside volatility equally; the Sortino Ratio isolates downside. Additionally, σ computed over a calm 3-year window (e.g. 2014–2017) understates true long-run risk. Rolling σ over multiple windows is more informative than a single point estimate.

Related terms: Sharpe Ratio, Sortino Ratio, Beta, Volatility, Rolling Returns.

Primary source: SEBI Circular SEBI/HO/IMD/DF2/CIR/P/2021/647 (mandated risk ratio disclosures including annualised standard deviation); AMFI: MF Scheme Performance Details — standard deviation published in factsheets.

Past performance is not indicative of future returns. Mutual fund investments are subject to market risks. Read all scheme-related documents carefully. ARN-314872. APMI APRN-01658. Content is informational and not investment advice.