Advanced Statistics: Pearl ][
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 | -0.012 | ||||
| SD | 0.248 | ||||
| Sharpe ratio (Glass type estimate) | -0.050 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.050 | ||||
| df | 71.000 | ||||
| t | -0.123 | ||||
| p | 0.549 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.850 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.750 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.850 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.750 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.059 | ||||
| Upside Potential Ratio | 1.001 | ||||
| Upside part of mean | 0.210 | ||||
| Downside part of mean | -0.223 | ||||
| Upside SD | 0.129 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.314 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.248 | ||||
| Covariance | 0.034 | ||||
| r | 0.466 | ||||
| b (slope, estimate of beta) | 0.393 | ||||
| a (intercept, estimate of alpha) | -0.136 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 70.000 | ||||
| t(b) | 4.410 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.439 | ||||
| p(a) | 0.923 | ||||
| Lowerbound of 95% confidence interval for beta | 0.215 | ||||
| Upperbound of 95% confidence interval for beta | 0.570 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.324 | ||||
| Upperbound of 95% confidence interval for alpha | 0.052 | ||||
| Treynor index (mean / b) | -0.032 | ||||
| Jensen alpha (a) | -0.136 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.295 | ||||
| Sharpe ratio (Glass type estimate) | -0.170 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.169 | ||||
| df | 71.000 | ||||
| t | -0.417 | ||||
| p | 0.661 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.970 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.631 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.969 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.632 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.189 | ||||
| Upside Potential Ratio | 0.756 | ||||
| Upside part of mean | 0.202 | ||||
| Downside part of mean | -0.252 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.267 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.268 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.295 | ||||
| Covariance | 0.048 | ||||
| r | 0.553 | ||||
| b (slope, estimate of beta) | 0.558 | ||||
| a (intercept, estimate of alpha) | -0.200 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 70.000 | ||||
| t(b) | 5.554 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.909 | ||||
| p(a) | 0.970 | ||||
| Lowerbound of 95% confidence interval for beta | 0.358 | ||||
| Upperbound of 95% confidence interval for beta | 0.758 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.408 | ||||
| Upperbound of 95% confidence interval for alpha | 0.009 | ||||
| Treynor index (mean / b) | -0.090 | ||||
| Jensen alpha (a) | -0.200 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.134 | ||||
| Expected Shortfall on VaR | 0.164 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.108 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.549 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.027 | ||||
| Maximum | 1.174 | ||||
| Mean of quarter 1 | 0.935 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.069 | ||||
| Inter Quartile Range | 0.027 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.876 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 1.100 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.326 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.511 | ||||
| VaR(95%) (regression method) | 0.069 | ||||
| Expected Shortfall (regression method) | 0.197 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.037 | ||||
| Quartile 1 | 0.074 | ||||
| Median | 0.136 | ||||
| Quartile 3 | 0.255 | ||||
| Maximum | 0.462 | ||||
| Mean of quarter 1 | 0.037 | ||||
| Mean of quarter 2 | 0.086 | ||||
| Mean of quarter 3 | 0.186 | ||||
| Mean of quarter 4 | 0.462 | ||||
| Inter Quartile Range | 0.182 | ||||
| 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) | -0.006 | ||||
| Compounded annual return (geometric extrapolation) | -0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.014 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.014 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.038 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.336 | ||||
| Sharpe ratio (Glass type estimate) | 0.028 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.028 | ||||
| df | 1573.000 | ||||
| t | 0.068 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.772 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.827 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.772 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.827 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.036 | ||||
| Upside Potential Ratio | 3.706 | ||||
| Upside part of mean | 0.951 | ||||
| Downside part of mean | -0.942 | ||||
| Upside SD | 0.217 | ||||
| Downside SD | 0.257 | ||||
| N nonnegative terms | 428.000 | ||||
| N negative terms | 1146.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1574.000 | ||||
| Mean of predictor | 0.336 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.368 | ||||
| SD of criterion | 0.336 | ||||
| Covariance | 0.050 | ||||
| r | 0.403 | ||||
| b (slope, estimate of beta) | 0.368 | ||||
| a (intercept, estimate of alpha) | -0.114 | ||||
| Mean Square Error | 0.095 | ||||
| DF error | 1572.000 | ||||
| t(b) | 17.448 | ||||
| p(b) | 0.299 | ||||
| t(a) | -0.908 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.326 | ||||
| Upperbound of 95% confidence interval for beta | 0.409 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.361 | ||||
| Upperbound of 95% confidence interval for alpha | 0.133 | ||||
| Treynor index (mean / b) | 0.025 | ||||
| Jensen alpha (a) | -0.114 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.351 | ||||
| Sharpe ratio (Glass type estimate) | -0.143 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.143 | ||||
| df | 1573.000 | ||||
| t | -0.351 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.943 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.656 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.943 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.657 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.177 | ||||
| Upside Potential Ratio | 3.273 | ||||
| Upside part of mean | 0.929 | ||||
| Downside part of mean | -0.979 | ||||
| Upside SD | 0.207 | ||||
| Downside SD | 0.284 | ||||
| N nonnegative terms | 428.000 | ||||
| N negative terms | 1146.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1574.000 | ||||
| Mean of predictor | 0.267 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.371 | ||||
| SD of criterion | 0.351 | ||||
| Covariance | 0.053 | ||||
| r | 0.404 | ||||
| b (slope, estimate of beta) | 0.382 | ||||
| a (intercept, estimate of alpha) | -0.152 | ||||
| Mean Square Error | 0.103 | ||||
| DF error | 1572.000 | ||||
| t(b) | 17.490 | ||||
| p(b) | 0.298 | ||||
| t(a) | -1.161 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.339 | ||||
| Upperbound of 95% confidence interval for beta | 0.425 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.410 | ||||
| Upperbound of 95% confidence interval for alpha | 0.105 | ||||
| Treynor index (mean / b) | -0.132 | ||||
| Jensen alpha (a) | -0.152 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1574.000 | ||||
| Minimum | 0.662 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.190 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 264.000 | ||||
| Percentage of outliers low | 0.168 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 338.000 | ||||
| Percentage of outliers high | 0.215 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.004 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.561 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 21.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.027 | ||||
| Quartile 3 | 0.089 | ||||
| Maximum | 0.505 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.020 | ||||
| Mean of quarter 3 | 0.065 | ||||
| Mean of quarter 4 | 0.213 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 0.364 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.554 | ||||
| VaR(95%) (moments method) | 0.237 | ||||
| Expected Shortfall (moments method) | 0.554 | ||||
| Extreme Value Index (regression method) | 1.379 | ||||
| VaR(95%) (regression method) | 0.260 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.006 | ||||
| Compounded annual return (geometric extrapolation) | -0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.012 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.029 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.143 | ||||
| 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 | 1.080 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.503 | ||||
| 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 | 0.951 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8741214361833693.000 | ||||
| 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) | 75079662739691577307336917647360.000 | ||||
| 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 | ||||