Advanced Statistics: Trader's Prophets
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 | 816.984 | ||||
| SD | 1630.939 | ||||
| Sharpe ratio (Glass type estimate) | 0.501 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.493 | ||||
| df | 47.000 | ||||
| t | 1.002 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.487 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.483 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.492 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.478 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1492.104 | ||||
| Upside Potential Ratio | 1492.995 | ||||
| Upside part of mean | 817.471 | ||||
| Downside part of mean | -0.488 | ||||
| Upside SD | 1631.002 | ||||
| Downside SD | 0.548 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.451 | ||||
| Mean of criterion | 816.984 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 1630.939 | ||||
| Covariance | -60.410 | ||||
| r | -0.147 | ||||
| b (slope, estimate of beta) | -946.167 | ||||
| a (intercept, estimate of alpha) | 1243.899 | ||||
| Mean Square Error | 2659386.929 | ||||
| DF error | 46.000 | ||||
| t(b) | -1.005 | ||||
| p(b) | 0.840 | ||||
| t(a) | 1.353 | ||||
| p(a) | 0.091 | ||||
| Lowerbound of 95% confidence interval for beta | -2841.093 | ||||
| Upperbound of 95% confidence interval for beta | 948.759 | ||||
| Lowerbound of 95% confidence interval for alpha | -606.727 | ||||
| Upperbound of 95% confidence interval for alpha | 3094.525 | ||||
| Treynor index (mean / b) | -0.863 | ||||
| Jensen alpha (a) | 1243.899 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.196 | ||||
| SD | 6.202 | ||||
| Sharpe ratio (Glass type estimate) | 0.032 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.031 | ||||
| df | 47.000 | ||||
| t | 0.063 | ||||
| p | 0.475 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.948 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.012 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.949 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.011 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.044 | ||||
| Upside Potential Ratio | 0.602 | ||||
| Upside part of mean | 2.704 | ||||
| Downside part of mean | -2.508 | ||||
| Upside SD | 4.181 | ||||
| Downside SD | 4.493 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.413 | ||||
| Mean of criterion | 0.196 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 6.202 | ||||
| Covariance | -0.089 | ||||
| r | -0.059 | ||||
| b (slope, estimate of beta) | -1.512 | ||||
| a (intercept, estimate of alpha) | 0.820 | ||||
| Mean Square Error | 39.165 | ||||
| DF error | 46.000 | ||||
| t(b) | -0.402 | ||||
| p(b) | 0.655 | ||||
| t(a) | 0.235 | ||||
| p(a) | 0.408 | ||||
| Lowerbound of 95% confidence interval for beta | -9.083 | ||||
| Upperbound of 95% confidence interval for beta | 6.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.210 | ||||
| Upperbound of 95% confidence interval for alpha | 7.850 | ||||
| Treynor index (mean / b) | -0.130 | ||||
| Jensen alpha (a) | 0.820 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.947 | ||||
| Expected Shortfall on VaR | 0.970 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.124 | ||||
| Expected Shortfall on VaR | 0.273 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3263.000 | ||||
| Mean of quarter 1 | 0.849 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 273.493 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.229 | ||||
| Mean of outliers low | 0.836 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 364.324 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.216 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| 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) | 0.404 | ||||
| Compounded annual return (geometric extrapolation) | 0.272 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.272 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.280 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2649.546 | ||||
| SD | 4018.985 | ||||
| Sharpe ratio (Glass type estimate) | 0.659 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.659 | ||||
| df | 1050.000 | ||||
| t | 1.320 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.320 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.638 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.320 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.638 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3547.598 | ||||
| Upside Potential Ratio | 3549.556 | ||||
| Upside part of mean | 2651.008 | ||||
| Downside part of mean | -1.462 | ||||
| Upside SD | 4020.406 | ||||
| Downside SD | 0.747 | ||||
| N nonnegative terms | 239.000 | ||||
| N negative terms | 812.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1051.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | 2649.546 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 4018.985 | ||||
| Covariance | -52.610 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -500.197 | ||||
| a (intercept, estimate of alpha) | 2892.472 | ||||
| Mean Square Error | 16141294.301 | ||||
| DF error | 1049.000 | ||||
| t(b) | -1.308 | ||||
| p(b) | 0.526 | ||||
| t(a) | 1.436 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -1250.365 | ||||
| Upperbound of 95% confidence interval for beta | 249.972 | ||||
| Lowerbound of 95% confidence interval for alpha | -1060.470 | ||||
| Upperbound of 95% confidence interval for alpha | 6845.414 | ||||
| Treynor index (mean / b) | -5.297 | ||||
| Jensen alpha (a) | 2892.472 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.197 | ||||
| SD | 8.764 | ||||
| Sharpe ratio (Glass type estimate) | 0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.022 | ||||
| df | 1050.000 | ||||
| t | 0.045 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.956 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.001 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.956 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.001 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.031 | ||||
| Upside Potential Ratio | 0.895 | ||||
| Upside part of mean | 5.630 | ||||
| Downside part of mean | -5.433 | ||||
| Upside SD | 6.097 | ||||
| Downside SD | 6.290 | ||||
| N nonnegative terms | 239.000 | ||||
| N negative terms | 812.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1051.000 | ||||
| Mean of predictor | 0.432 | ||||
| Mean of criterion | 0.197 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 8.764 | ||||
| Covariance | -0.092 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.853 | ||||
| a (intercept, estimate of alpha) | 0.566 | ||||
| Mean Square Error | 76.808 | ||||
| DF error | 1049.000 | ||||
| t(b) | -1.033 | ||||
| p(b) | 0.520 | ||||
| t(a) | 0.129 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | -2.474 | ||||
| Upperbound of 95% confidence interval for beta | 0.767 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.049 | ||||
| Upperbound of 95% confidence interval for alpha | 9.180 | ||||
| Treynor index (mean / b) | -0.231 | ||||
| Jensen alpha (a) | 0.566 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.589 | ||||
| Expected Shortfall on VaR | 0.666 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1051.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 7363.000 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 41.435 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 238.000 | ||||
| Percentage of outliers low | 0.226 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 240.000 | ||||
| Percentage of outliers high | 0.228 | ||||
| Mean of outliers high | 45.310 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.317 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.029 | ||||
| Mean of quarter 4 | 0.559 | ||||
| Inter Quartile Range | 0.032 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.559 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.565 | ||||
| VaR(95%) (moments method) | 0.230 | ||||
| Expected Shortfall (moments method) | 0.671 | ||||
| Extreme Value Index (regression method) | 2.454 | ||||
| VaR(95%) (regression method) | 1.983 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.406 | ||||
| Compounded annual return (geometric extrapolation) | 0.273 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.273 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.488 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.409 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 13.515 | ||||
| SD | 9.503 | ||||
| Sharpe ratio (Glass type estimate) | 1.422 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.414 | ||||
| df | 130.000 | ||||
| t | 1.006 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.358 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.197 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.363 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.191 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 285.799 | ||||
| Upside Potential Ratio | 293.315 | ||||
| Upside part of mean | 13.870 | ||||
| Downside part of mean | -0.355 | ||||
| Upside SD | 9.503 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 95.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.996 | ||||
| Mean of criterion | 13.515 | ||||
| SD of predictor | 0.506 | ||||
| SD of criterion | 9.503 | ||||
| Covariance | 0.606 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 2.365 | ||||
| a (intercept, estimate of alpha) | 11.159 | ||||
| Mean Square Error | 89.556 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.442 | ||||
| p(b) | 0.420 | ||||
| t(a) | 0.828 | ||||
| p(a) | 0.454 | ||||
| Lowerbound of 95% confidence interval for beta | -0.880 | ||||
| Upperbound of 95% confidence interval for beta | 5.610 | ||||
| Lowerbound of 95% confidence interval for alpha | -15.517 | ||||
| Upperbound of 95% confidence interval for alpha | 37.834 | ||||
| Treynor index (mean / b) | 5.713 | ||||
| Jensen alpha (a) | 11.159 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 4.160 | ||||
| SD | 2.891 | ||||
| Sharpe ratio (Glass type estimate) | 1.439 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.431 | ||||
| df | 130.000 | ||||
| t | 1.018 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.341 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.214 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.346 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.208 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 87.654 | ||||
| Upside Potential Ratio | 95.165 | ||||
| Upside part of mean | 4.516 | ||||
| Downside part of mean | -0.356 | ||||
| Upside SD | 2.891 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 95.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.866 | ||||
| Mean of criterion | 4.160 | ||||
| SD of predictor | 0.511 | ||||
| SD of criterion | 2.891 | ||||
| Covariance | 0.185 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.710 | ||||
| a (intercept, estimate of alpha) | 3.545 | ||||
| Mean Square Error | 8.288 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.437 | ||||
| p(b) | 0.420 | ||||
| t(a) | 0.866 | ||||
| p(a) | 0.452 | ||||
| Lowerbound of 95% confidence interval for beta | -0.268 | ||||
| Upperbound of 95% confidence interval for beta | 1.688 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.555 | ||||
| Upperbound of 95% confidence interval for alpha | 11.645 | ||||
| Treynor index (mean / b) | 5.857 | ||||
| Jensen alpha (a) | 3.545 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.243 | ||||
| Expected Shortfall on VaR | 0.296 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.986 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 7.720 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.210 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 22.000 | ||||
| Percentage of outliers low | 0.168 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 3.252 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -70.315 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 24.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.006 | ||||
| Maximum | 0.014 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.006 | ||||
| Mean of quarter 4 | 0.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.003 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.083 | ||||
| Mean of outliers high | 0.014 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.497 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 14.365 | ||||
| Compounded annual return (geometric extrapolation) | 65.952 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4597.073 | ||||
| Compounded annual return / average of 25% largest draw downs | 7538.582 | ||||
| Compounded annual return / Expected Shortfall lognormal | 223.136 | ||||