The in-sample test ran from 2010-02-01 to 2020-12-30. The portfolio achieved a daily return of 0.027% (t-statistic of 0.938) with a standard deviation of 1.497%. The annualized Sharpe ratio is 0.29. The largest daily loss was -17%. The fraction of daily returns more negative than three times the daily standard deviation was % and 46% all of trading days resulted in a negative realized return. The p-value for the null hypothesis that portfolio returns were normally distributed was 0 (JB test). The skewness and kurtosis of portfolio returns were -1.43 and 22.56. The return distribution fit a Skew Student-t distribution.
The 5% and 1% daily Value-at-Risk (VaR) evaluated over the full in-sample period were -2.04% and -4.4%. The number of actual portfolio returns lower than the 1% VaR based on simulated data was [XX].
The corresponding expected shortfall (ES) were -3.72% and -7.29%. The ES estimates reflect the average percentage loss if invested capital in the worst trading day out of 20 and 100. The average predicted ES based on simulated data was [XX].
The median MDD within a month [6]% while the 90th and worst outcomes were [15]% and [44]%. The corresponding
| mean | tval | sd | skew | kurt | JBpvalue | Month |
|---|---|---|---|---|---|---|
| 0.181 | 1.289 | 2.060 | 0.182 | 5.382 | 0 | Jan |
| -0.107 | -0.717 | 2.220 | -2.110 | 21.208 | 0 | Feb |
| 0.047 | 0.733 | 0.977 | 0.647 | 6.751 | 0 | Mar |
| 0.080 | 0.986 | 1.173 | 0.670 | 8.060 | 0 | Apr |
| 0.174 | 2.190 | 1.161 | 2.162 | 15.869 | 0 | May |
| -0.003 | -0.037 | 1.068 | -0.102 | 4.840 | 0 | Jun |
| 0.044 | 0.608 | 1.140 | 0.302 | 5.697 | 0 | Jul |
| -0.139 | -1.377 | 1.576 | -2.089 | 18.201 | 0 | Aug |
| 0.135 | 2.021 | 1.022 | 0.445 | 6.706 | 0 | Sep |
| 0.037 | 0.515 | 1.112 | 0.235 | 4.174 | 0 | Oct |
| -0.019 | -0.157 | 1.837 | -3.047 | 33.108 | 0 | Nov |
| -0.092 | -0.681 | 1.947 | -1.879 | 11.837 | 0 | Dec |