Advanced Statistics: xUpgraded and replaced w MMO2.0
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 | 0.231 | ||||
| SD | 0.590 | ||||
| Sharpe ratio (Glass type estimate) | 0.392 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.387 | ||||
| df | 69.000 | ||||
| t | 0.946 | ||||
| p | 0.174 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.424 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.204 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.427 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.202 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.225 | ||||
| Upside Potential Ratio | 1.882 | ||||
| Upside part of mean | 0.356 | ||||
| Downside part of mean | -0.124 | ||||
| Upside SD | 0.559 | ||||
| Downside SD | 0.189 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 66.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.284 | ||||
| Mean of criterion | 0.231 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.590 | ||||
| Covariance | -0.023 | ||||
| r | -0.121 | ||||
| b (slope, estimate of beta) | -0.226 | ||||
| a (intercept, estimate of alpha) | 0.296 | ||||
| Mean Square Error | 0.349 | ||||
| DF error | 68.000 | ||||
| t(b) | -1.005 | ||||
| p(b) | 0.841 | ||||
| t(a) | 1.170 | ||||
| p(a) | 0.123 | ||||
| Lowerbound of 95% confidence interval for beta | -0.675 | ||||
| Upperbound of 95% confidence interval for beta | 0.223 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.209 | ||||
| Upperbound of 95% confidence interval for alpha | 0.800 | ||||
| Treynor index (mean / b) | -1.023 | ||||
| Jensen alpha (a) | 0.296 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.110 | ||||
| SD | 0.461 | ||||
| Sharpe ratio (Glass type estimate) | 0.239 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.237 | ||||
| df | 69.000 | ||||
| t | 0.578 | ||||
| p | 0.283 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.574 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.051 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.576 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.049 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.441 | ||||
| Upside Potential Ratio | 1.039 | ||||
| Upside part of mean | 0.260 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.385 | ||||
| Downside SD | 0.250 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 66.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.232 | ||||
| Mean of criterion | 0.110 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.461 | ||||
| Covariance | -0.014 | ||||
| r | -0.098 | ||||
| b (slope, estimate of beta) | -0.143 | ||||
| a (intercept, estimate of alpha) | 0.143 | ||||
| Mean Square Error | 0.214 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.809 | ||||
| p(b) | 0.789 | ||||
| t(a) | 0.732 | ||||
| p(a) | 0.233 | ||||
| Lowerbound of 95% confidence interval for beta | -0.494 | ||||
| Upperbound of 95% confidence interval for beta | 0.209 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.247 | ||||
| Upperbound of 95% confidence interval for alpha | 0.534 | ||||
| Treynor index (mean / b) | -0.773 | ||||
| Jensen alpha (a) | 0.143 | ||||
| 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 | 0.232 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.549 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.216 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.116 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.100 | ||||
| Mean of outliers low | 0.931 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 1.348 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.463 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 2.921 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.117 | ||||
| Median | 0.228 | ||||
| Quartile 3 | 0.339 | ||||
| Maximum | 0.451 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.451 | ||||
| Inter Quartile Range | 0.222 | ||||
| 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) | 0.250 | ||||
| Compounded annual return (geometric extrapolation) | 0.167 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.370 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.370 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.719 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.057 | ||||
| SD | 1.554 | ||||
| Sharpe ratio (Glass type estimate) | 0.680 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.680 | ||||
| df | 1540.000 | ||||
| t | 1.650 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.128 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.489 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.128 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.489 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.551 | ||||
| Upside Potential Ratio | 3.820 | ||||
| Upside part of mean | 2.603 | ||||
| Downside part of mean | -1.546 | ||||
| Upside SD | 1.397 | ||||
| Downside SD | 0.682 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 1476.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1541.000 | ||||
| Mean of predictor | 0.398 | ||||
| Mean of criterion | 1.057 | ||||
| SD of predictor | 0.555 | ||||
| SD of criterion | 1.554 | ||||
| Covariance | -0.122 | ||||
| r | -0.141 | ||||
| b (slope, estimate of beta) | -0.396 | ||||
| a (intercept, estimate of alpha) | 1.215 | ||||
| Mean Square Error | 2.368 | ||||
| DF error | 1539.000 | ||||
| t(b) | -5.598 | ||||
| p(b) | 0.590 | ||||
| t(a) | 1.913 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | -0.534 | ||||
| Upperbound of 95% confidence interval for beta | -0.257 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.031 | ||||
| Upperbound of 95% confidence interval for alpha | 2.461 | ||||
| Treynor index (mean / b) | -2.673 | ||||
| Jensen alpha (a) | 1.215 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.109 | ||||
| SD | 1.341 | ||||
| Sharpe ratio (Glass type estimate) | 0.081 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.081 | ||||
| df | 1540.000 | ||||
| t | 0.197 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.727 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.889 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.727 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.889 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.119 | ||||
| Upside Potential Ratio | 2.187 | ||||
| Upside part of mean | 1.995 | ||||
| Downside part of mean | -1.886 | ||||
| Upside SD | 0.983 | ||||
| Downside SD | 0.912 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 1476.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1541.000 | ||||
| Mean of predictor | 0.246 | ||||
| Mean of criterion | 0.109 | ||||
| SD of predictor | 0.551 | ||||
| SD of criterion | 1.341 | ||||
| Covariance | -0.116 | ||||
| r | -0.158 | ||||
| b (slope, estimate of beta) | -0.384 | ||||
| a (intercept, estimate of alpha) | 0.204 | ||||
| Mean Square Error | 1.756 | ||||
| DF error | 1539.000 | ||||
| t(b) | -6.264 | ||||
| p(b) | 0.600 | ||||
| t(a) | 0.373 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.505 | ||||
| Upperbound of 95% confidence interval for beta | -0.264 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.869 | ||||
| Upperbound of 95% confidence interval for alpha | 1.276 | ||||
| Treynor index (mean / b) | -0.284 | ||||
| Jensen alpha (a) | 0.204 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.127 | ||||
| Expected Shortfall on VaR | 0.156 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1541.000 | ||||
| Minimum | 0.410 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.480 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.040 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 96.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.908 | ||||
| Number of outliers high | 94.000 | ||||
| Percentage of outliers high | 0.061 | ||||
| Mean of outliers high | 1.163 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.925 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| 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 | 11.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.125 | ||||
| Quartile 3 | 0.268 | ||||
| Maximum | 0.700 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.046 | ||||
| Mean of quarter 3 | 0.205 | ||||
| Mean of quarter 4 | 0.530 | ||||
| Inter Quartile Range | 0.261 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.700 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -73.623 | ||||
| VaR(95%) (moments method) | 0.520 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.863 | ||||
| VaR(95%) (regression method) | 1.009 | ||||
| Expected Shortfall (regression method) | 1.014 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.248 | ||||
| Compounded annual return (geometric extrapolation) | 0.165 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.236 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.312 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.057 | ||||
| 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 | 1.146 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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 | 1.015 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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) | -8733950738914677.000 | ||||
| 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) | -126563258962967490108519899725824.000 | ||||
| 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 | ||||