Advanced Statistics: MP Trades
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.376 | ||||
| SD | 0.813 | ||||
| Sharpe ratio (Glass type estimate) | 1.693 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.666 | ||||
| df | 48.000 | ||||
| t | 3.421 | ||||
| p | 0.001 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.658 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.712 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.641 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.692 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.748 | ||||
| Upside Potential Ratio | 5.819 | ||||
| Upside part of mean | 1.686 | ||||
| Downside part of mean | -0.310 | ||||
| Upside SD | 0.849 | ||||
| Downside SD | 0.290 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 12.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | 1.376 | ||||
| SD of predictor | 0.209 | ||||
| SD of criterion | 0.813 | ||||
| Covariance | 0.140 | ||||
| r | 0.825 | ||||
| b (slope, estimate of beta) | 3.210 | ||||
| a (intercept, estimate of alpha) | 0.126 | ||||
| Mean Square Error | 0.215 | ||||
| DF error | 47.000 | ||||
| t(b) | 10.022 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.483 | ||||
| p(a) | 0.316 | ||||
| Lowerbound of 95% confidence interval for beta | 2.566 | ||||
| Upperbound of 95% confidence interval for beta | 3.854 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.399 | ||||
| Upperbound of 95% confidence interval for alpha | 0.652 | ||||
| Treynor index (mean / b) | 0.429 | ||||
| Jensen alpha (a) | 0.126 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.050 | ||||
| SD | 0.717 | ||||
| Sharpe ratio (Glass type estimate) | 1.465 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.442 | ||||
| df | 48.000 | ||||
| t | 2.959 | ||||
| p | 0.002 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.445 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.471 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.430 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.453 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.727 | ||||
| Upside Potential Ratio | 3.688 | ||||
| Upside part of mean | 1.420 | ||||
| Downside part of mean | -0.370 | ||||
| Upside SD | 0.668 | ||||
| Downside SD | 0.385 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 12.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.363 | ||||
| Mean of criterion | 1.050 | ||||
| SD of predictor | 0.196 | ||||
| SD of criterion | 0.717 | ||||
| Covariance | 0.114 | ||||
| r | 0.812 | ||||
| b (slope, estimate of beta) | 2.965 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.179 | ||||
| DF error | 47.000 | ||||
| t(b) | 9.536 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.107 | ||||
| p(a) | 0.542 | ||||
| Lowerbound of 95% confidence interval for beta | 2.339 | ||||
| Upperbound of 95% confidence interval for beta | 3.590 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.503 | ||||
| Upperbound of 95% confidence interval for alpha | 0.453 | ||||
| Treynor index (mean / b) | 0.354 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.223 | ||||
| Expected Shortfall on VaR | 0.286 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.086 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 49.000 | ||||
| Minimum | 0.489 | ||||
| Quartile 1 | 1.006 | ||||
| Median | 1.068 | ||||
| Quartile 3 | 1.176 | ||||
| Maximum | 1.916 | ||||
| Mean of quarter 1 | 0.906 | ||||
| Mean of quarter 2 | 1.045 | ||||
| Mean of quarter 3 | 1.109 | ||||
| Mean of quarter 4 | 1.432 | ||||
| Inter Quartile Range | 0.170 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.020 | ||||
| Mean of outliers low | 0.489 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.102 | ||||
| Mean of outliers high | 1.652 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.305 | ||||
| VaR(95%) (regression method) | 0.133 | ||||
| Expected Shortfall (regression method) | 0.286 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.019 | ||||
| Quartile 1 | 0.088 | ||||
| Median | 0.111 | ||||
| Quartile 3 | 0.168 | ||||
| Maximum | 0.539 | ||||
| Mean of quarter 1 | 0.052 | ||||
| Mean of quarter 2 | 0.101 | ||||
| Mean of quarter 3 | 0.122 | ||||
| Mean of quarter 4 | 0.377 | ||||
| Inter Quartile Range | 0.080 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.539 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 21.049 | ||||
| Compounded annual return (geometric extrapolation) | 1.985 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.681 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.271 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.948 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.552 | ||||
| SD | 0.847 | ||||
| Sharpe ratio (Glass type estimate) | 1.832 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.831 | ||||
| df | 1088.000 | ||||
| t | 3.735 | ||||
| p | 0.444 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.867 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.796 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.867 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.795 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.771 | ||||
| Upside Potential Ratio | 8.986 | ||||
| Upside part of mean | 5.035 | ||||
| Downside part of mean | -3.483 | ||||
| Upside SD | 0.642 | ||||
| Downside SD | 0.560 | ||||
| N nonnegative terms | 577.000 | ||||
| N negative terms | 512.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1089.000 | ||||
| Mean of predictor | 0.426 | ||||
| Mean of criterion | 1.552 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.847 | ||||
| Covariance | 0.149 | ||||
| r | 0.755 | ||||
| b (slope, estimate of beta) | 2.736 | ||||
| a (intercept, estimate of alpha) | 0.386 | ||||
| Mean Square Error | 0.309 | ||||
| DF error | 1087.000 | ||||
| t(b) | 37.928 | ||||
| p(b) | 0.070 | ||||
| t(a) | 1.407 | ||||
| p(a) | 0.473 | ||||
| Lowerbound of 95% confidence interval for beta | 2.594 | ||||
| Upperbound of 95% confidence interval for beta | 2.877 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.152 | ||||
| Upperbound of 95% confidence interval for alpha | 0.925 | ||||
| Treynor index (mean / b) | 0.567 | ||||
| Jensen alpha (a) | 0.386 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.186 | ||||
| SD | 0.856 | ||||
| Sharpe ratio (Glass type estimate) | 1.385 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.384 | ||||
| df | 1088.000 | ||||
| t | 2.824 | ||||
| p | 0.457 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.422 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.348 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.421 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.347 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.949 | ||||
| Upside Potential Ratio | 7.960 | ||||
| Upside part of mean | 4.843 | ||||
| Downside part of mean | -3.657 | ||||
| Upside SD | 0.607 | ||||
| Downside SD | 0.608 | ||||
| N nonnegative terms | 577.000 | ||||
| N negative terms | 512.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1089.000 | ||||
| Mean of predictor | 0.398 | ||||
| Mean of criterion | 1.186 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.856 | ||||
| Covariance | 0.151 | ||||
| r | 0.754 | ||||
| b (slope, estimate of beta) | 2.758 | ||||
| a (intercept, estimate of alpha) | 0.087 | ||||
| Mean Square Error | 0.317 | ||||
| DF error | 1087.000 | ||||
| t(b) | 37.836 | ||||
| p(b) | 0.070 | ||||
| t(a) | 0.313 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | 2.615 | ||||
| Upperbound of 95% confidence interval for beta | 2.901 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.458 | ||||
| Upperbound of 95% confidence interval for alpha | 0.632 | ||||
| Treynor index (mean / b) | 0.430 | ||||
| Jensen alpha (a) | 0.087 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1089.000 | ||||
| Minimum | 0.701 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.023 | ||||
| Maximum | 1.302 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.066 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 70.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.886 | ||||
| Number of outliers high | 87.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.117 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.350 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.074 | ||||
| Extreme Value Index (regression method) | 0.224 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | 0.081 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.098 | ||||
| Maximum | 0.797 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.029 | ||||
| Mean of quarter 3 | 0.066 | ||||
| Mean of quarter 4 | 0.231 | ||||
| Inter Quartile Range | 0.081 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.107 | ||||
| Mean of outliers high | 0.363 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.374 | ||||
| VaR(95%) (moments method) | 0.250 | ||||
| Expected Shortfall (moments method) | 0.450 | ||||
| Extreme Value Index (regression method) | 0.305 | ||||
| VaR(95%) (regression method) | 0.236 | ||||
| Expected Shortfall (regression method) | 0.388 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 39.732 | ||||
| Compounded annual return (geometric extrapolation) | 2.422 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.037 | ||||
| Compounded annual return / average of 25% largest draw downs | 10.473 | ||||
| Compounded annual return / Expected Shortfall lognormal | 24.424 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.865 | ||||
| SD | 1.709 | ||||
| Sharpe ratio (Glass type estimate) | 1.676 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.667 | ||||
| df | 130.000 | ||||
| t | 1.185 | ||||
| p | 0.448 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.106 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.452 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.113 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.446 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.434 | ||||
| Upside Potential Ratio | 10.482 | ||||
| Upside part of mean | 12.339 | ||||
| Downside part of mean | -9.474 | ||||
| Upside SD | 1.243 | ||||
| Downside SD | 1.177 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.972 | ||||
| Mean of criterion | 2.865 | ||||
| SD of predictor | 0.444 | ||||
| SD of criterion | 1.709 | ||||
| Covariance | 0.624 | ||||
| r | 0.822 | ||||
| b (slope, estimate of beta) | 3.167 | ||||
| a (intercept, estimate of alpha) | -0.215 | ||||
| Mean Square Error | 0.953 | ||||
| DF error | 129.000 | ||||
| t(b) | 16.420 | ||||
| p(b) | 0.044 | ||||
| t(a) | -0.154 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 2.785 | ||||
| Upperbound of 95% confidence interval for beta | 3.549 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.971 | ||||
| Upperbound of 95% confidence interval for alpha | 2.542 | ||||
| Treynor index (mean / b) | 0.905 | ||||
| Jensen alpha (a) | -0.215 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.364 | ||||
| SD | 1.754 | ||||
| Sharpe ratio (Glass type estimate) | 0.778 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.773 | ||||
| df | 130.000 | ||||
| t | 0.550 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.997 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.550 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.546 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.038 | ||||
| Upside Potential Ratio | 8.861 | ||||
| Upside part of mean | 11.636 | ||||
| Downside part of mean | -10.273 | ||||
| Upside SD | 1.155 | ||||
| Downside SD | 1.313 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.872 | ||||
| Mean of criterion | 1.364 | ||||
| SD of predictor | 0.446 | ||||
| SD of criterion | 1.754 | ||||
| Covariance | 0.644 | ||||
| r | 0.824 | ||||
| b (slope, estimate of beta) | 3.240 | ||||
| a (intercept, estimate of alpha) | -1.463 | ||||
| Mean Square Error | 0.995 | ||||
| DF error | 129.000 | ||||
| t(b) | 16.511 | ||||
| p(b) | 0.043 | ||||
| t(a) | -1.029 | ||||
| p(a) | 0.557 | ||||
| Lowerbound of 95% confidence interval for beta | 2.852 | ||||
| Upperbound of 95% confidence interval for beta | 3.628 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.275 | ||||
| Upperbound of 95% confidence interval for alpha | 1.349 | ||||
| Treynor index (mean / b) | 0.421 | ||||
| Jensen alpha (a) | -1.463 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.159 | ||||
| Expected Shortfall on VaR | 0.195 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.155 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.701 | ||||
| Quartile 1 | 0.954 | ||||
| Median | 1.024 | ||||
| Quartile 3 | 1.078 | ||||
| Maximum | 1.302 | ||||
| Mean of quarter 1 | 0.875 | ||||
| Mean of quarter 2 | 0.984 | ||||
| Mean of quarter 3 | 1.050 | ||||
| Mean of quarter 4 | 1.136 | ||||
| Inter Quartile Range | 0.124 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.725 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.302 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.003 | ||||
| VaR(95%) (moments method) | 0.110 | ||||
| Expected Shortfall (moments method) | 0.151 | ||||
| Extreme Value Index (regression method) | -0.189 | ||||
| VaR(95%) (regression method) | 0.141 | ||||
| Expected Shortfall (regression method) | 0.183 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.046 | ||||
| Quartile 1 | 0.054 | ||||
| Median | 0.117 | ||||
| Quartile 3 | 0.277 | ||||
| Maximum | 0.795 | ||||
| Mean of quarter 1 | 0.049 | ||||
| Mean of quarter 2 | 0.087 | ||||
| Mean of quarter 3 | 0.157 | ||||
| Mean of quarter 4 | 0.596 | ||||
| Inter Quartile Range | 0.223 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.795 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.043 | ||||
| Compounded annual return (geometric extrapolation) | 3.086 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.884 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.179 | ||||
| Compounded annual return / Expected Shortfall lognormal | 15.789 | ||||