Idiosyncratic Volatility
factor.formula
The formula for the idiosyncratic volatility of individual stocks is:
Capital Asset Pricing Model (CAPM) Regression:
Fama-French Three-Factor Model (FF3) Regression:
In the formula:
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is the idiosyncratic volatility of stock i at time t, which is equal to the standard deviation of the residual term \epsilon_{i,t} and is usually calculated based on the historical data of the last K months.
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is the return of stock i at time t.
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is the risk-free rate of return at time t.
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is the market return at time t, usually expressed as the return of the market index.
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is the intercept term of stock i, representing the average return of stock i beyond the market or factor model explanation, and can also be regarded as risk compensation that cannot be explained by the model.
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is the sensitivity of individual stock i to the market risk premium, that is, the market risk exposure.
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is the residual term of stock i at time t, representing the part of stock-specific returns that cannot be explained by the factor model.
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is the market risk premium factor at time t, which is equal to the market rate of return minus the risk-free rate of return.
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is the size factor (Small Minus Big) at time t, representing the difference between the stock returns of small companies and the stock returns of large companies.
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is the value factor (High Minus Low) at time t, representing the difference between the stock returns of companies with high book-to-market ratio and the stock returns of companies with low book-to-market ratio.
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are the sensitivities of individual stock i to the market risk premium factor, scale factor and value factor, that is, the exposure of the individual stock to these three risk factors.
factor.explanation
The idiosyncratic volatility of individual stocks reflects the stock-specific risk in stock returns that is unrelated to the market or multi-factor model. It is a relatively independent risk measurement indicator. Empirical studies have shown that there is a negative correlation between the idiosyncratic volatility of individual stocks and stock returns. That is, stocks with lower idiosyncratic volatility usually have higher returns, which is considered to be a manifestation of low-risk anomalies. The existence of this anomaly suggests that the market may not be completely efficient, and investors can obtain excess returns by selecting stocks with low idiosyncratic volatility. However, this strategy may also have some risks, such as strategy crowding and model failure.