Advanced Statistics: PTQQS 2.0.B The Aftermath
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 | 0.042 | ||||
| SD | 0.158 | ||||
| Sharpe ratio (Glass type estimate) | 0.268 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.263 | ||||
| df | 39.000 | ||||
| t | 0.489 | ||||
| p | 0.314 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.809 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.341 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.812 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.338 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.358 | ||||
| Upside Potential Ratio | 6.778 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.156 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.515 | ||||
| Mean of criterion | 0.042 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.158 | ||||
| Covariance | 0.001 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.019 | ||||
| a (intercept, estimate of alpha) | 0.033 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.205 | ||||
| p(b) | 0.419 | ||||
| t(a) | 0.327 | ||||
| p(a) | 0.373 | ||||
| Lowerbound of 95% confidence interval for beta | -0.167 | ||||
| Upperbound of 95% confidence interval for beta | 0.205 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.169 | ||||
| Upperbound of 95% confidence interval for alpha | 0.234 | ||||
| Treynor index (mean / b) | 2.243 | ||||
| Jensen alpha (a) | 0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.032 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | 0.230 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.225 | ||||
| df | 39.000 | ||||
| t | 0.420 | ||||
| p | 0.338 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.303 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.849 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.300 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.537 | ||||
| Upside Potential Ratio | 5.958 | ||||
| Upside part of mean | 0.075 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.136 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.470 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | 0.001 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | 0.022 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.247 | ||||
| p(b) | 0.403 | ||||
| t(a) | 0.250 | ||||
| p(a) | 0.402 | ||||
| Lowerbound of 95% confidence interval for beta | -0.155 | ||||
| Upperbound of 95% confidence interval for beta | 0.198 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.154 | ||||
| Upperbound of 95% confidence interval for alpha | 0.198 | ||||
| Treynor index (mean / b) | 1.481 | ||||
| Jensen alpha (a) | 0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.288 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.029 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.025 | ||||
| Mean of outliers high | 1.288 | ||||
| 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) | 0.086 | ||||
| Compounded annual return (geometric extrapolation) | 0.079 | ||||
| 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 | 1.029 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.036 | ||||
| SD | 0.104 | ||||
| Sharpe ratio (Glass type estimate) | 0.346 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.345 | ||||
| df | 883.000 | ||||
| t | 0.635 | ||||
| p | 0.263 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.721 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.413 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.722 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.413 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 13.202 | ||||
| Upside Potential Ratio | 29.370 | ||||
| Upside part of mean | 0.080 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 882.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 884.000 | ||||
| Mean of predictor | 0.546 | ||||
| Mean of criterion | 0.036 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.104 | ||||
| Covariance | -0.001 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | 0.041 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 882.000 | ||||
| t(b) | -0.880 | ||||
| p(b) | 0.810 | ||||
| t(a) | 0.724 | ||||
| p(a) | 0.235 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.070 | ||||
| Upperbound of 95% confidence interval for alpha | 0.153 | ||||
| Treynor index (mean / b) | -3.735 | ||||
| Jensen alpha (a) | 0.041 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.031 | ||||
| SD | 0.097 | ||||
| Sharpe ratio (Glass type estimate) | 0.318 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.318 | ||||
| df | 883.000 | ||||
| t | 0.584 | ||||
| p | 0.280 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.749 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.385 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.750 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.385 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 11.384 | ||||
| Upside Potential Ratio | 27.552 | ||||
| Upside part of mean | 0.075 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 882.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 884.000 | ||||
| Mean of predictor | 0.494 | ||||
| Mean of criterion | 0.031 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.097 | ||||
| Covariance | -0.001 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 882.000 | ||||
| t(b) | -0.870 | ||||
| p(b) | 0.808 | ||||
| t(a) | 0.664 | ||||
| p(a) | 0.253 | ||||
| Lowerbound of 95% confidence interval for beta | -0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.069 | ||||
| Upperbound of 95% confidence interval for alpha | 0.140 | ||||
| Treynor index (mean / b) | -3.468 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| 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 | 884.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.137 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.002 | ||||
| Mean of outliers high | 1.135 | ||||
| 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) | 0.085 | ||||
| Compounded annual return (geometric extrapolation) | 0.078 | ||||
| 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 | 6.377 | ||||
| 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 | 1.033 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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 | 0.906 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.503 | ||||
| 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) | -8745330530335360.000 | ||||
| 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) | -1834636232162360235978615544610816.000 | ||||
| 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 | ||||