Downside Beta
factor.formula
Downside Risk Beta:
in:
- :
The monthly return sequence of stock i over the past K months. The monthly return is calculated by compounding the daily returns of the month.
- :
The monthly return series of a market index (e.g. CSI 300 or S&P 500) over the past K months. The monthly return is calculated by compounding the daily returns of the month.
- :
The arithmetic mean of the daily returns of a market index over the past K months, used to distinguish the boundaries between market ups and downs.
- :
The time window for back-calculating downside risk beta is usually set to 12 months. To ensure the robustness of the calculation, the number of trading days in the time window should be no less than 50.
- :
The covariance of stock i's monthly return with the market's monthly return, assuming the market's monthly return is less than its daily return mean $\mu_m$ over the past K months. This represents the co-movement of stock and market returns when the market falls.
- :
The variance of the market's monthly return when it is less than its daily mean $\mu_m$ over the past K months. This represents the degree of volatility when the market falls.
factor.explanation
Downside risk beta focuses on measuring the sensitivity of individual stock returns to market returns when the market falls. It can better capture the downside risks that investors are concerned about than traditional beta. Specifically, it calculates the covariance between the monthly returns of individual stocks and the monthly returns of the market under the condition that the monthly returns of the market are less than its historical daily average returns, and divides it by the variance of the monthly returns of the market. By excluding the months when the market rises, the downside risk beta can more accurately reflect the systematic risk exposure of stocks when the market falls. Therefore, this factor is often used to construct risk management and hedging strategies, and has been confirmed by empirical studies to have a significant downside risk premium.