What’s Wrong with Multiplying by the Square Root of Twelve

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A commonly used measure of return volatility is the standard deviation of monthly returns multiplied by the square root of twelve to express it in the same unit as annual return. However, some researchers have noted that multiplying by the square root of twelve is not
mathematically correct and present the correct method. This article reviews the motivation for multiplying by the square root of twelve and explains why it does not apply to returns.

Author: Paul Kaplan, Morningstar Canada

A commonly used measure of return volatility is the standard deviation of monthly returns multiplied by the square root of 12 to express it in the same unit as annual return.  However, some researchers have noted that multiplying by the square root of 12 is not mathematically correct and present the correct method.

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