Tail asymmetric probability difference
factor.formula
Tail asymmetric probability difference:
in:
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is the idiosyncratic return $ε_{i,d}$, obtained by performing a multi-factor regression model on the asset return $R_{i,d}$, that is, $R_{i,d} = α_i + \sum_{j=1}^{n} β_{i,j}F_{j,d} + ε_{i,d}$. Among them, $F_{j,d}$ represents the factor exposure of the j-th factor at time d.
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is the number of factors in the multifactor regression model
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The tail threshold is used to define the boundary between a sharp rise and a sharp fall, and is generally between 1.5 and 2.5 standard deviations. This parameter affects the sensitivity of the factor to tail risk.
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It represents the probability that the characteristic return rate x exceeds the positive threshold k, that is, the probability of a sharp rise in the asset
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Indicates the probability that the characteristic return rate x is lower than the negative threshold -k, that is, the probability of a sharp drop in the asset
factor.explanation
The tail asymmetric probability difference is a supplement to the traditional skewness, focusing more on measuring the asymmetry of the tail of the return distribution. Specifically, this factor calculates the difference between the probabilities of the idiosyncratic return exceeding the positive threshold and falling below the negative threshold. A positive value indicates that the probability of a sharp rise in the asset's history is higher than the probability of a sharp fall, which may reflect the market's optimism and pursuit of the asset, but also implies that the asset may face the risk of a price correction in the future. A negative value, on the contrary, may indicate that the asset has a higher probability of a sharp fall in history, and investors may have a risk-averse sentiment, but it may also mean a potential rebound opportunity in the future. This factor takes into account the tail characteristics of the return distribution and can better capture the possibility of extreme events, thereby better assisting investment decisions.