Advanced Statistics: Exceptional Bear
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 | -0.089 | ||||
| SD | 0.342 | ||||
| Sharpe ratio (Glass type estimate) | -0.261 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.258 | ||||
| df | 62.000 | ||||
| t | -0.599 | ||||
| p | 0.724 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.117 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.596 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.115 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.598 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.452 | ||||
| Upside Potential Ratio | 1.596 | ||||
| Upside part of mean | 0.316 | ||||
| Downside part of mean | -0.405 | ||||
| Upside SD | 0.277 | ||||
| Downside SD | 0.198 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -0.089 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.342 | ||||
| Covariance | -0.023 | ||||
| r | -0.280 | ||||
| b (slope, estimate of beta) | -0.390 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.109 | ||||
| DF error | 61.000 | ||||
| t(b) | -2.277 | ||||
| p(b) | 0.987 | ||||
| t(a) | 0.354 | ||||
| p(a) | 0.362 | ||||
| Lowerbound of 95% confidence interval for beta | -0.733 | ||||
| Upperbound of 95% confidence interval for beta | -0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.260 | ||||
| Upperbound of 95% confidence interval for alpha | 0.371 | ||||
| Treynor index (mean / b) | 0.229 | ||||
| Jensen alpha (a) | 0.056 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.141 | ||||
| SD | 0.316 | ||||
| Sharpe ratio (Glass type estimate) | -0.446 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.441 | ||||
| df | 62.000 | ||||
| t | -1.023 | ||||
| p | 0.845 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.304 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.414 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.300 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.418 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.675 | ||||
| Upside Potential Ratio | 1.355 | ||||
| Upside part of mean | 0.283 | ||||
| Downside part of mean | -0.424 | ||||
| Upside SD | 0.237 | ||||
| Downside SD | 0.209 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.337 | ||||
| Mean of criterion | -0.141 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.316 | ||||
| Covariance | -0.021 | ||||
| r | -0.280 | ||||
| b (slope, estimate of beta) | -0.368 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.094 | ||||
| DF error | 61.000 | ||||
| t(b) | -2.274 | ||||
| p(b) | 0.987 | ||||
| t(a) | -0.118 | ||||
| p(a) | 0.547 | ||||
| Lowerbound of 95% confidence interval for beta | -0.692 | ||||
| Upperbound of 95% confidence interval for beta | -0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.305 | ||||
| Upperbound of 95% confidence interval for alpha | 0.271 | ||||
| Treynor index (mean / b) | 0.383 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.149 | ||||
| Expected Shortfall on VaR | 0.181 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.096 | ||||
| Expected Shortfall on VaR | 0.159 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.840 | ||||
| Quartile 1 | 0.930 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.009 | ||||
| Maximum | 1.470 | ||||
| Mean of quarter 1 | 0.900 | ||||
| Mean of quarter 2 | 0.977 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.107 | ||||
| Inter Quartile Range | 0.079 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.063 | ||||
| Mean of outliers high | 1.280 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.149 | ||||
| VaR(95%) (moments method) | 0.111 | ||||
| Expected Shortfall (moments method) | 0.143 | ||||
| Extreme Value Index (regression method) | 0.344 | ||||
| VaR(95%) (regression method) | 0.103 | ||||
| Expected Shortfall (regression method) | 0.140 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.148 | ||||
| Quartile 1 | 0.242 | ||||
| Median | 0.335 | ||||
| Quartile 3 | 0.429 | ||||
| Maximum | 0.522 | ||||
| Mean of quarter 1 | 0.148 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.522 | ||||
| Inter Quartile Range | 0.187 | ||||
| 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) | -0.076 | ||||
| Compounded annual return (geometric extrapolation) | -0.092 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.177 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.177 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.512 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.002 | ||||
| SD | 0.534 | ||||
| Sharpe ratio (Glass type estimate) | 0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.003 | ||||
| df | 1395.000 | ||||
| t | 0.008 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.853 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.846 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.853 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.005 | ||||
| Upside Potential Ratio | 6.021 | ||||
| Upside part of mean | 2.158 | ||||
| Downside part of mean | -2.156 | ||||
| Upside SD | 0.396 | ||||
| Downside SD | 0.358 | ||||
| N nonnegative terms | 467.000 | ||||
| N negative terms | 929.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1396.000 | ||||
| Mean of predictor | 0.412 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.534 | ||||
| Covariance | -0.041 | ||||
| r | -0.245 | ||||
| b (slope, estimate of beta) | -0.419 | ||||
| a (intercept, estimate of alpha) | 0.174 | ||||
| Mean Square Error | 0.268 | ||||
| DF error | 1394.000 | ||||
| t(b) | -9.415 | ||||
| p(b) | 0.622 | ||||
| t(a) | 0.774 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | -0.506 | ||||
| Upperbound of 95% confidence interval for beta | -0.332 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.267 | ||||
| Upperbound of 95% confidence interval for alpha | 0.616 | ||||
| Treynor index (mean / b) | -0.004 | ||||
| Jensen alpha (a) | 0.174 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.140 | ||||
| SD | 0.532 | ||||
| Sharpe ratio (Glass type estimate) | -0.263 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.262 | ||||
| df | 1395.000 | ||||
| t | -0.606 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.112 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.587 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.112 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.587 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.371 | ||||
| Upside Potential Ratio | 5.540 | ||||
| Upside part of mean | 2.085 | ||||
| Downside part of mean | -2.224 | ||||
| Upside SD | 0.375 | ||||
| Downside SD | 0.376 | ||||
| N nonnegative terms | 467.000 | ||||
| N negative terms | 929.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1396.000 | ||||
| Mean of predictor | 0.362 | ||||
| Mean of criterion | -0.140 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.532 | ||||
| Covariance | -0.041 | ||||
| r | -0.243 | ||||
| b (slope, estimate of beta) | -0.410 | ||||
| a (intercept, estimate of alpha) | 0.009 | ||||
| Mean Square Error | 0.266 | ||||
| DF error | 1394.000 | ||||
| t(b) | -9.354 | ||||
| p(b) | 0.622 | ||||
| t(a) | 0.040 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.496 | ||||
| Upperbound of 95% confidence interval for beta | -0.324 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.430 | ||||
| Upperbound of 95% confidence interval for alpha | 0.449 | ||||
| Treynor index (mean / b) | 0.340 | ||||
| Jensen alpha (a) | 0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1396.000 | ||||
| Minimum | 0.828 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.210 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 213.000 | ||||
| Percentage of outliers low | 0.153 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 216.000 | ||||
| Percentage of outliers high | 0.155 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.497 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | 0.050 | ||||
| Extreme Value Index (regression method) | 0.097 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.048 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.050 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.188 | ||||
| Quartile 3 | 0.347 | ||||
| Maximum | 0.564 | ||||
| Mean of quarter 1 | 0.058 | ||||
| Mean of quarter 2 | 0.080 | ||||
| Mean of quarter 3 | 0.295 | ||||
| Mean of quarter 4 | 0.464 | ||||
| Inter Quartile Range | 0.277 | ||||
| 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) | -0.075 | ||||
| Compounded annual return (geometric extrapolation) | -0.091 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.162 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.196 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.383 | ||||
| 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 | 0.948 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.446 | ||||
| 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 | 0.848 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.447 | ||||
| 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) | -8739602970677566.000 | ||||
| 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) | -1451404902589637460394772109721600.000 | ||||
| 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 | ||||