Advanced Statistics: PTQQS 2.0.B
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.321 | ||||
| Sharpe ratio (Glass type estimate) | -0.141 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.139 | ||||
| df | 47.000 | ||||
| t | -0.282 | ||||
| p | 0.610 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.120 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.840 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.119 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.842 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.168 | ||||
| Upside Potential Ratio | 0.544 | ||||
| Upside part of mean | 0.146 | ||||
| Downside part of mean | -0.191 | ||||
| Upside SD | 0.170 | ||||
| Downside SD | 0.268 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 44.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.407 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.321 | ||||
| Covariance | -0.002 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.031 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 46.000 | ||||
| t(b) | -0.182 | ||||
| p(b) | 0.572 | ||||
| t(a) | -0.185 | ||||
| p(a) | 0.573 | ||||
| Lowerbound of 95% confidence interval for beta | -0.371 | ||||
| Upperbound of 95% confidence interval for beta | 0.310 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.387 | ||||
| Upperbound of 95% confidence interval for alpha | 0.322 | ||||
| Treynor index (mean / b) | 1.469 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.114 | ||||
| SD | 0.411 | ||||
| Sharpe ratio (Glass type estimate) | -0.278 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.273 | ||||
| df | 47.000 | ||||
| t | -0.556 | ||||
| p | 0.710 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.258 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.255 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.708 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.302 | ||||
| Upside Potential Ratio | 0.351 | ||||
| Upside part of mean | 0.132 | ||||
| Downside part of mean | -0.247 | ||||
| Upside SD | 0.154 | ||||
| Downside SD | 0.377 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 44.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | -0.114 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.411 | ||||
| Covariance | 0.001 | ||||
| r | 0.007 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.118 | ||||
| Mean Square Error | 0.172 | ||||
| DF error | 46.000 | ||||
| t(b) | 0.049 | ||||
| p(b) | 0.481 | ||||
| t(a) | -0.527 | ||||
| p(a) | 0.700 | ||||
| Lowerbound of 95% confidence interval for beta | -0.456 | ||||
| Upperbound of 95% confidence interval for beta | 0.479 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.569 | ||||
| Upperbound of 95% confidence interval for alpha | 0.333 | ||||
| Treynor index (mean / b) | -10.121 | ||||
| Jensen alpha (a) | -0.118 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.185 | ||||
| Expected Shortfall on VaR | 0.224 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.052 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.474 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.241 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.050 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.698 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.104 | ||||
| Mean of outliers high | 1.120 | ||||
| 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) | 1.499 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.563 | ||||
| Quartile 1 | 0.563 | ||||
| Median | 0.563 | ||||
| Quartile 3 | 0.563 | ||||
| Maximum | 0.563 | ||||
| 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) | -0.061 | ||||
| Compounded annual return (geometric extrapolation) | -0.068 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.120 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.303 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.015 | ||||
| SD | 0.441 | ||||
| Sharpe ratio (Glass type estimate) | -0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.035 | ||||
| df | 1061.000 | ||||
| t | -0.070 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.008 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.939 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.008 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.939 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.050 | ||||
| Upside Potential Ratio | 2.318 | ||||
| Upside part of mean | 0.714 | ||||
| Downside part of mean | -0.729 | ||||
| Upside SD | 0.315 | ||||
| Downside SD | 0.308 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 1022.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1062.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.441 | ||||
| Covariance | -0.006 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.064 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.194 | ||||
| DF error | 1060.000 | ||||
| t(b) | -1.459 | ||||
| p(b) | 0.522 | ||||
| t(a) | 0.057 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.150 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.418 | ||||
| Upperbound of 95% confidence interval for alpha | 0.443 | ||||
| Treynor index (mean / b) | 0.238 | ||||
| Jensen alpha (a) | 0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.113 | ||||
| SD | 0.445 | ||||
| Sharpe ratio (Glass type estimate) | -0.254 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.254 | ||||
| df | 1061.000 | ||||
| t | -0.512 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.228 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.719 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.228 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.719 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.335 | ||||
| Upside Potential Ratio | 1.983 | ||||
| Upside part of mean | 0.669 | ||||
| Downside part of mean | -0.782 | ||||
| Upside SD | 0.290 | ||||
| Downside SD | 0.337 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 1022.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1062.000 | ||||
| Mean of predictor | 0.385 | ||||
| Mean of criterion | -0.113 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.445 | ||||
| Covariance | -0.006 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | -0.088 | ||||
| Mean Square Error | 0.198 | ||||
| DF error | 1060.000 | ||||
| t(b) | -1.479 | ||||
| p(b) | 0.523 | ||||
| t(a) | -0.397 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.523 | ||||
| Upperbound of 95% confidence interval for alpha | 0.347 | ||||
| Treynor index (mean / b) | 1.723 | ||||
| Jensen alpha (a) | -0.088 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1062.000 | ||||
| Minimum | 0.781 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.262 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 34.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.918 | ||||
| Number of outliers high | 40.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.072 | ||||
| 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) | -0.507 | ||||
| VaR(95%) (regression method) | -0.030 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.114 | ||||
| Maximum | 0.617 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.071 | ||||
| Mean of quarter 4 | 0.392 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.617 | ||||
| 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) | -0.060 | ||||
| Compounded annual return (geometric extrapolation) | -0.067 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.108 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.171 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.204 | ||||
| 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 | 1.198 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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 | 1.083 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.479 | ||||
| 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) | -8714430335723867.000 | ||||
| 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) | 415551699783473430286385541021696.000 | ||||
| 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 | ||||