Advanced Statistics: MaxProfits
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 | 0.582 | ||||
| SD | 0.648 | ||||
| Sharpe ratio (Glass type estimate) | 0.899 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.880 | ||||
| df | 36.000 | ||||
| t | 1.578 | ||||
| p | 0.062 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.242 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.028 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.255 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.014 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.804 | ||||
| Upside Potential Ratio | 4.605 | ||||
| Upside part of mean | 0.705 | ||||
| Downside part of mean | -0.123 | ||||
| Upside SD | 0.643 | ||||
| Downside SD | 0.153 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | 0.582 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.648 | ||||
| Covariance | -0.040 | ||||
| r | -0.238 | ||||
| b (slope, estimate of beta) | -0.597 | ||||
| a (intercept, estimate of alpha) | 0.892 | ||||
| Mean Square Error | 0.407 | ||||
| DF error | 35.000 | ||||
| t(b) | -1.450 | ||||
| p(b) | 0.922 | ||||
| t(a) | 2.116 | ||||
| p(a) | 0.021 | ||||
| Lowerbound of 95% confidence interval for beta | -1.433 | ||||
| Upperbound of 95% confidence interval for beta | 0.239 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 1.747 | ||||
| Treynor index (mean / b) | -0.975 | ||||
| Jensen alpha (a) | 0.892 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.422 | ||||
| SD | 0.516 | ||||
| Sharpe ratio (Glass type estimate) | 0.818 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.801 | ||||
| df | 36.000 | ||||
| t | 1.437 | ||||
| p | 0.080 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.319 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.945 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.331 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.932 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.379 | ||||
| Upside Potential Ratio | 3.149 | ||||
| Upside part of mean | 0.558 | ||||
| Downside part of mean | -0.136 | ||||
| Upside SD | 0.492 | ||||
| Downside SD | 0.177 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.476 | ||||
| Mean of criterion | 0.422 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.516 | ||||
| Covariance | -0.029 | ||||
| r | -0.229 | ||||
| b (slope, estimate of beta) | -0.484 | ||||
| a (intercept, estimate of alpha) | 0.652 | ||||
| Mean Square Error | 0.259 | ||||
| DF error | 35.000 | ||||
| t(b) | -1.392 | ||||
| p(b) | 0.914 | ||||
| t(a) | 1.954 | ||||
| p(a) | 0.029 | ||||
| Lowerbound of 95% confidence interval for beta | -1.190 | ||||
| Upperbound of 95% confidence interval for beta | 0.222 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.025 | ||||
| Upperbound of 95% confidence interval for alpha | 1.330 | ||||
| Treynor index (mean / b) | -0.871 | ||||
| Jensen alpha (a) | 0.652 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.189 | ||||
| Expected Shortfall on VaR | 0.237 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.736 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.764 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.244 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.868 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.162 | ||||
| Mean of outliers high | 1.366 | ||||
| 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) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.264 | ||||
| Quartile 1 | 0.264 | ||||
| Median | 0.264 | ||||
| Quartile 3 | 0.264 | ||||
| Maximum | 0.264 | ||||
| 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) | 1.039 | ||||
| Compounded annual return (geometric extrapolation) | 0.593 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.244 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.504 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.556 | ||||
| SD | 0.531 | ||||
| Sharpe ratio (Glass type estimate) | 1.047 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.046 | ||||
| df | 811.000 | ||||
| t | 1.844 | ||||
| p | 0.033 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.068 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.161 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.068 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.161 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.808 | ||||
| Upside Potential Ratio | 5.122 | ||||
| Upside part of mean | 1.576 | ||||
| Downside part of mean | -1.020 | ||||
| Upside SD | 0.434 | ||||
| Downside SD | 0.308 | ||||
| N nonnegative terms | 82.000 | ||||
| N negative terms | 730.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 812.000 | ||||
| Mean of predictor | 0.513 | ||||
| Mean of criterion | 0.556 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.531 | ||||
| Covariance | -0.005 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.056 | ||||
| a (intercept, estimate of alpha) | 0.585 | ||||
| Mean Square Error | 0.282 | ||||
| DF error | 810.000 | ||||
| t(b) | -0.923 | ||||
| p(b) | 0.822 | ||||
| t(a) | 1.929 | ||||
| p(a) | 0.027 | ||||
| Lowerbound of 95% confidence interval for beta | -0.175 | ||||
| Upperbound of 95% confidence interval for beta | 0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.010 | ||||
| Upperbound of 95% confidence interval for alpha | 1.181 | ||||
| Treynor index (mean / b) | -9.913 | ||||
| Jensen alpha (a) | 0.585 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.419 | ||||
| SD | 0.520 | ||||
| Sharpe ratio (Glass type estimate) | 0.806 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.806 | ||||
| df | 811.000 | ||||
| t | 1.420 | ||||
| p | 0.078 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.308 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.920 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.308 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.920 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.266 | ||||
| Upside Potential Ratio | 4.503 | ||||
| Upside part of mean | 1.491 | ||||
| Downside part of mean | -1.072 | ||||
| Upside SD | 0.401 | ||||
| Downside SD | 0.331 | ||||
| N nonnegative terms | 82.000 | ||||
| N negative terms | 730.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 812.000 | ||||
| Mean of predictor | 0.465 | ||||
| Mean of criterion | 0.419 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.520 | ||||
| Covariance | -0.005 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.053 | ||||
| a (intercept, estimate of alpha) | 0.444 | ||||
| Mean Square Error | 0.271 | ||||
| DF error | 810.000 | ||||
| t(b) | -0.905 | ||||
| p(b) | 0.817 | ||||
| t(a) | 1.497 | ||||
| p(a) | 0.067 | ||||
| Lowerbound of 95% confidence interval for beta | -0.169 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.138 | ||||
| Upperbound of 95% confidence interval for alpha | 1.027 | ||||
| Treynor index (mean / b) | -7.847 | ||||
| Jensen alpha (a) | 0.444 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 812.000 | ||||
| Minimum | 0.765 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.314 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 60.000 | ||||
| Percentage of outliers low | 0.074 | ||||
| Mean of outliers low | 0.949 | ||||
| Number of outliers high | 82.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.726 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.121 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.132 | ||||
| Maximum | 0.548 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.036 | ||||
| Mean of quarter 3 | 0.097 | ||||
| Mean of quarter 4 | 0.323 | ||||
| Inter Quartile Range | 0.116 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.548 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.988 | ||||
| VaR(95%) (moments method) | 0.314 | ||||
| Expected Shortfall (moments method) | 0.315 | ||||
| Extreme Value Index (regression method) | -0.216 | ||||
| VaR(95%) (regression method) | 0.606 | ||||
| Expected Shortfall (regression method) | 0.796 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.034 | ||||
| Compounded annual return (geometric extrapolation) | 0.589 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.075 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.827 | ||||
| Compounded annual return / Expected Shortfall lognormal | 9.422 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.849 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.736 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.478 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8759956511183715.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 384262929034766979099843987767296.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| 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 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) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| 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 | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||