Minimum return (MinReturn)
factor.formula
MinReturn = -min(R_t, R_{t-1}, ..., R_{t-K+1})
This formula calculates the minimum value of the daily return sequence of the past K months and takes a negative number. The purpose of taking a negative number is to make the larger the value of the minimum return, the smaller the extreme negative risk it represents, making the meaning of the factor more intuitive.
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Minimum rate of return factor
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The asset return rate on day t
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The lookback window period represents the past K months, usually in natural months, such as 3 months, 6 months, 12 months, etc.
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Minimum function
factor.explanation
The minimum return factor is designed to capture the worst performance of an asset in the past K months. It is different from traditional volatility indicators and focuses on the risk of extreme negative returns. Studies have shown that assets with higher minimum returns may mean that they have lower tail risks, that is, they are less likely to suffer extreme losses under adverse market conditions. This factor can be regarded as a proxy indicator of investors' extreme risk preferences. Investors tend to require higher expected returns for assets that bear extreme negative return risks, while assets with higher minimum returns may have lower expected returns. Therefore, the minimum return can be used to construct a risk-adjusted investment portfolio to better suit investors' risk preferences. In addition, this factor also has application value in risk management, and assets that may face extreme risks can be identified in a timely manner by monitoring the minimum return.