Downside/Upside Volatility Ratio
factor.formula
Downside/Upside Volatility Ratio (DUVR):
in:
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The return of stock i at time t is usually calculated using the logarithmic return, that is, $r_{it} = \ln(P_{it}/P_{it-1})$, where $P_{it}$ is the price of stock i at time t.
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The average return of stock i during the observation period is calculated as $\bar{r_i} = \frac{1}{T} \sum_{t=1}^{T} r_{it}$, where T is the total number of time periods in the observation period.
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The number of days during the observation period when the return of stock i is greater than or equal to the average return $\bar{r_i}$, that is, the number of days with upward returns.
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The number of days during the observation period when the return of stock i is less than the average return $\bar{r_i}$, that is, the number of days with downside returns.
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The sum of the squares of the differences between the returns of all downside returns (returns less than the average return) of stock i during the observation period and the average return measures the volatility of downside returns, also known as downside variance.
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The sum of the squares of the differences between the returns of all upward returns (returns greater than or equal to the average return) of stock i during the examination period and the average return measures the volatility of upward returns, also known as the upward variance.
factor.explanation
The downside/upside volatility ratio (DUVR) measures the asymmetry of the stock return distribution by comparing the downside volatility and the upside volatility. The essence of this ratio is to measure the negative skewness risk of the return distribution, that is, whether the negative return volatility is larger than the positive return volatility. The higher the DUVR value, the higher the downside volatility relative to the upside volatility, and the more likely the stock price will fall sharply. This asymmetric risk is usually considered a systematic risk, and investors will require a higher risk premium to bear this risk.
It should be noted that the calculation of this factor usually takes the logarithm, the purpose is to narrow the numerical range and avoid the instability of the model caused by excessive values. At the same time, the logarithmic transformation also has a data smoothing effect to a certain extent.
In practical applications, different time windows can be used to calculate this factor, such as daily, weekly, monthly, etc. Different time windows may lead to differences in factor values and predictive power. In addition, this factor is often used in combination with other factors to improve the prediction effect.