After establishing the strategy, the effectiveness of the model is verified by calculating the probability of the returns, excess returns, and the performance of high-return portfolios compared to the benchmark, as well as the underperformance of low-return portfolios compared to the benchmark under different market conditions. The complete process can be referred to as follows:
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For combinations of sequences 1, 2, 3, ..., n, the annual returns and the size of factors need to have a certain correlation, that is, they should satisfy the correlation requirement. If the annualized return of combination i is Xi, then the absolute value of the correlation between Xi and i should satisfy: Abs(Corr(Xi, i)) > MinCorr. Here, MinCorr is the given minimum correlation threshold, and in general, an ideal MinCorr = 0.3.
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The excess returns of the extreme combinations represented by sequences 1 and n are AR1 and ARn, respectively. The minimum excess return thresholds are represented by MinARtop and MinARbottom. In general, an ideal MinARbottom = -0.05 and MinARtop = 0.05. If AR1 > ARn, that is, the smaller the factor, the greater the return, then it should satisfy:
AR1 > MinARtop > 0 AND ARn < MinARbottom < 0
If AR1 < ARn, that is, the smaller the factor, the smaller the return, then it should satisfy:
ARn > MinARtop > 0 AND AR1 < MinARbottom < 0
These conditions ensure that the two combinations with the maximum and minimum factors, one clearly outperforms the market and the other clearly underperforms the market.
- In any market situation, the extreme combinations 1 and n both have a higher probability of outperforming or underperforming the market.