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Formula sheet/NISM Series V-A: Mutual Fund Distributors/Risk, Return & Performance of Funds
[ RISK, RETURN & PERFORMANCE OF FUNDS ]

Volatility (Standard Deviation) & Annualization

Sample Variance(s2)=[∑(Rt−Ravg)2]/(n−1)  ⇒  Standard Deviation(s)=s2\text{Sample Variance} (s^{2}) = [ \sum (R_{t} - R_{\text{avg}})^{2} ] / (n - 1) \;\Rightarrow\; \text{Standard Deviation} (s) = \sqrt{s^{2}}
Annualized Standard Deviation(σannual)=σperiodic×Periods per Year\text{Annualized Standard Deviation} (\sigma_{\text{annual}}) = \sigma_{\text{periodic}} \times \sqrt{\text{Periods per Year}}
•Daily data:σdaily×252∣Weekly data:σweekly×52∣Monthly data:σmonthly×12• \text{Daily data}: \sigma_{\text{daily}} \times \sqrt{252}\quad\Big|\quad \text{Weekly data}: \sigma_{\text{weekly}} \times \sqrt{52}\quad\Big|\quad \text{Monthly data}: \sigma_{\text{monthly}} \times \sqrt{12}
Variables

Standard deviation measures total risk (dispersion around mean return); higher standard deviation implies greater return volatility. RtR_{t}: Period return; RavgR_{\text{avg}}: Mean period return.

Worked example
Annualized Standard Deviation from Weekly Returns

A fund's weekly returns over 4 consecutive weeks are: +0.50%, +0.80%, +1.30%, and +0.48%. The mean weekly return is 0.77%, and sample weekly standard deviation is calculated as 0.38%. Calculate the annualized volatility (standard deviation) of the scheme.