Advanced Statistics: Endurance 1
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 | -0.132 | ||||
| SD | 0.346 | ||||
| Sharpe ratio (Glass type estimate) | -0.382 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.375 | ||||
| df | 40.000 | ||||
| t | -0.706 | ||||
| p | 0.758 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.443 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.684 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.438 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.689 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.389 | ||||
| Upside Potential Ratio | 0.246 | ||||
| Upside part of mean | 0.084 | ||||
| Downside part of mean | -0.216 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.340 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.500 | ||||
| Mean of criterion | -0.132 | ||||
| SD of predictor | 0.233 | ||||
| SD of criterion | 0.346 | ||||
| Covariance | -0.007 | ||||
| r | -0.084 | ||||
| b (slope, estimate of beta) | -0.125 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 0.122 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.529 | ||||
| p(b) | 0.700 | ||||
| t(a) | -0.312 | ||||
| p(a) | 0.621 | ||||
| Lowerbound of 95% confidence interval for beta | -0.604 | ||||
| Upperbound of 95% confidence interval for beta | 0.354 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.520 | ||||
| Upperbound of 95% confidence interval for alpha | 0.381 | ||||
| Treynor index (mean / b) | 1.054 | ||||
| Jensen alpha (a) | -0.069 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.237 | ||||
| SD | 0.536 | ||||
| Sharpe ratio (Glass type estimate) | -0.443 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.434 | ||||
| df | 40.000 | ||||
| t | -0.819 | ||||
| p | 0.791 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.505 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.625 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.499 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.630 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.447 | ||||
| Upside Potential Ratio | 0.154 | ||||
| Upside part of mean | 0.082 | ||||
| Downside part of mean | -0.319 | ||||
| Upside SD | 0.052 | ||||
| Downside SD | 0.531 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.464 | ||||
| Mean of criterion | -0.237 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.536 | ||||
| Covariance | -0.009 | ||||
| r | -0.073 | ||||
| b (slope, estimate of beta) | -0.175 | ||||
| a (intercept, estimate of alpha) | -0.156 | ||||
| Mean Square Error | 0.293 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.455 | ||||
| p(b) | 0.674 | ||||
| t(a) | -0.456 | ||||
| p(a) | 0.674 | ||||
| Lowerbound of 95% confidence interval for beta | -0.951 | ||||
| Upperbound of 95% confidence interval for beta | 0.602 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.849 | ||||
| Upperbound of 95% confidence interval for alpha | 0.537 | ||||
| Treynor index (mean / b) | 1.358 | ||||
| Jensen alpha (a) | -0.156 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.240 | ||||
| Expected Shortfall on VaR | 0.286 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.052 | ||||
| Expected Shortfall on VaR | 0.119 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.376 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.056 | ||||
| Mean of quarter 1 | 0.943 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.024 | ||||
| Mean of outliers low | 0.376 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.244 | ||||
| Mean of outliers high | 1.032 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.624 | ||||
| Quartile 1 | 0.624 | ||||
| Median | 0.624 | ||||
| Quartile 3 | 0.624 | ||||
| Maximum | 0.624 | ||||
| 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) | -0.141 | ||||
| Compounded annual return (geometric extrapolation) | -0.176 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.282 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.614 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.198 | ||||
| SD | 0.256 | ||||
| Sharpe ratio (Glass type estimate) | -0.771 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.771 | ||||
| df | 904.000 | ||||
| t | -1.433 | ||||
| p | 0.924 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.826 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.284 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.826 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.285 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.822 | ||||
| Upside Potential Ratio | 0.950 | ||||
| Upside part of mean | 0.228 | ||||
| Downside part of mean | -0.426 | ||||
| Upside SD | 0.089 | ||||
| Downside SD | 0.241 | ||||
| N nonnegative terms | 175.000 | ||||
| N negative terms | 730.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 905.000 | ||||
| Mean of predictor | 0.549 | ||||
| Mean of criterion | -0.198 | ||||
| SD of predictor | 0.346 | ||||
| SD of criterion | 0.256 | ||||
| Covariance | 0.001 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.201 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 903.000 | ||||
| t(b) | 0.238 | ||||
| p(b) | 0.406 | ||||
| t(a) | -1.449 | ||||
| p(a) | 0.926 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.054 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.473 | ||||
| Upperbound of 95% confidence interval for alpha | 0.071 | ||||
| Treynor index (mean / b) | -33.618 | ||||
| Jensen alpha (a) | -0.201 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.235 | ||||
| SD | 0.283 | ||||
| Sharpe ratio (Glass type estimate) | -0.831 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.830 | ||||
| df | 904.000 | ||||
| t | -1.544 | ||||
| p | 0.939 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.886 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.225 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.885 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.225 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.870 | ||||
| Upside Potential Ratio | 0.832 | ||||
| Upside part of mean | 0.225 | ||||
| Downside part of mean | -0.460 | ||||
| Upside SD | 0.085 | ||||
| Downside SD | 0.270 | ||||
| N nonnegative terms | 175.000 | ||||
| N negative terms | 730.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 905.000 | ||||
| Mean of predictor | 0.489 | ||||
| Mean of criterion | -0.235 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.283 | ||||
| Covariance | 0.001 | ||||
| r | 0.006 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.238 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 903.000 | ||||
| t(b) | 0.194 | ||||
| p(b) | 0.423 | ||||
| t(a) | -1.554 | ||||
| p(a) | 0.940 | ||||
| Lowerbound of 95% confidence interval for beta | -0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.538 | ||||
| Upperbound of 95% confidence interval for alpha | 0.062 | ||||
| Treynor index (mean / b) | -44.122 | ||||
| Jensen alpha (a) | -0.238 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 905.000 | ||||
| Minimum | 0.746 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 61.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 180.000 | ||||
| Percentage of outliers high | 0.199 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.732 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.164 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 28.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.015 | ||||
| Maximum | 0.626 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.124 | ||||
| Inter Quartile Range | 0.014 | ||||
| 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 | 0.071 | ||||
| Mean of outliers high | 0.366 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.153 | ||||
| VaR(95%) (moments method) | 0.094 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.995 | ||||
| VaR(95%) (regression method) | 0.088 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.140 | ||||
| Compounded annual return (geometric extrapolation) | -0.174 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.278 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.408 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.796 | ||||
| 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 | 1.011 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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 | 0.879 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.514 | ||||
| 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) | -8750718987247848.000 | ||||
| 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) | -212910507649759570846224083845120.000 | ||||
| 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 | ||||