Advanced Statistics: Turning Points
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 | 0.158 | ||||
| SD | 0.593 | ||||
| Sharpe ratio (Glass type estimate) | 0.267 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.265 | ||||
| df | 96.000 | ||||
| t | 0.759 | ||||
| p | 0.225 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.424 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.957 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.426 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.955 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.695 | ||||
| Upside Potential Ratio | 1.781 | ||||
| Upside part of mean | 0.406 | ||||
| Downside part of mean | -0.248 | ||||
| Upside SD | 0.546 | ||||
| Downside SD | 0.228 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 97.000 | ||||
| Mean of predictor | 0.189 | ||||
| Mean of criterion | 0.158 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.593 | ||||
| Covariance | -0.045 | ||||
| r | -0.272 | ||||
| b (slope, estimate of beta) | -0.573 | ||||
| a (intercept, estimate of alpha) | 0.267 | ||||
| Mean Square Error | 0.330 | ||||
| DF error | 95.000 | ||||
| t(b) | -2.752 | ||||
| p(b) | 0.996 | ||||
| t(a) | 1.296 | ||||
| p(a) | 0.099 | ||||
| Lowerbound of 95% confidence interval for beta | -0.986 | ||||
| Upperbound of 95% confidence interval for beta | -0.160 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.142 | ||||
| Upperbound of 95% confidence interval for alpha | 0.675 | ||||
| Treynor index (mean / b) | -0.277 | ||||
| Jensen alpha (a) | 0.267 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.473 | ||||
| Sharpe ratio (Glass type estimate) | 0.071 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.070 | ||||
| df | 96.000 | ||||
| t | 0.202 | ||||
| p | 0.420 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.619 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.760 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.619 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.760 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.117 | ||||
| Upside Potential Ratio | 1.097 | ||||
| Upside part of mean | 0.316 | ||||
| Downside part of mean | -0.282 | ||||
| Upside SD | 0.373 | ||||
| Downside SD | 0.288 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 97.000 | ||||
| Mean of predictor | 0.150 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.473 | ||||
| Covariance | -0.038 | ||||
| r | -0.296 | ||||
| b (slope, estimate of beta) | -0.509 | ||||
| a (intercept, estimate of alpha) | 0.110 | ||||
| Mean Square Error | 0.207 | ||||
| DF error | 95.000 | ||||
| t(b) | -3.016 | ||||
| p(b) | 0.998 | ||||
| t(a) | 0.678 | ||||
| p(a) | 0.250 | ||||
| Lowerbound of 95% confidence interval for beta | -0.844 | ||||
| Upperbound of 95% confidence interval for beta | -0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.212 | ||||
| Upperbound of 95% confidence interval for alpha | 0.431 | ||||
| Treynor index (mean / b) | -0.066 | ||||
| Jensen alpha (a) | 0.110 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.199 | ||||
| Expected Shortfall on VaR | 0.243 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.127 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 97.000 | ||||
| Minimum | 0.517 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 2.312 | ||||
| Mean of quarter 1 | 0.930 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.140 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.196 | ||||
| Mean of outliers low | 0.911 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.165 | ||||
| Mean of outliers high | 1.201 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.898 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 1.118 | ||||
| VaR(95%) (regression method) | 0.051 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.195 | ||||
| Quartile 1 | 0.252 | ||||
| Median | 0.276 | ||||
| Quartile 3 | 0.331 | ||||
| Maximum | 0.483 | ||||
| Mean of quarter 1 | 0.195 | ||||
| Mean of quarter 2 | 0.271 | ||||
| Mean of quarter 3 | 0.281 | ||||
| Mean of quarter 4 | 0.483 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.483 | ||||
| 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) | 0.108 | ||||
| Compounded annual return (geometric extrapolation) | 0.081 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.167 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.167 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.333 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.254 | ||||
| SD | 0.695 | ||||
| Sharpe ratio (Glass type estimate) | 0.365 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.365 | ||||
| df | 2132.000 | ||||
| t | 1.041 | ||||
| p | 0.149 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.322 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.052 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.322 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.052 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.634 | ||||
| Upside Potential Ratio | 3.879 | ||||
| Upside part of mean | 1.551 | ||||
| Downside part of mean | -1.298 | ||||
| Upside SD | 0.568 | ||||
| Downside SD | 0.400 | ||||
| N nonnegative terms | 451.000 | ||||
| N negative terms | 1682.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2133.000 | ||||
| Mean of predictor | 0.296 | ||||
| Mean of criterion | 0.254 | ||||
| SD of predictor | 0.516 | ||||
| SD of criterion | 0.695 | ||||
| Covariance | -0.068 | ||||
| r | -0.189 | ||||
| b (slope, estimate of beta) | -0.255 | ||||
| a (intercept, estimate of alpha) | 0.329 | ||||
| Mean Square Error | 0.466 | ||||
| DF error | 2131.000 | ||||
| t(b) | -8.887 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.374 | ||||
| p(a) | 0.085 | ||||
| Lowerbound of 95% confidence interval for beta | -0.311 | ||||
| Upperbound of 95% confidence interval for beta | -0.199 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.140 | ||||
| Upperbound of 95% confidence interval for alpha | 0.798 | ||||
| Treynor index (mean / b) | -0.995 | ||||
| Jensen alpha (a) | 0.329 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.033 | ||||
| SD | 0.661 | ||||
| Sharpe ratio (Glass type estimate) | 0.050 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.050 | ||||
| df | 2132.000 | ||||
| t | 0.142 | ||||
| p | 0.443 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.637 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.737 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.637 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.737 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.069 | ||||
| Upside Potential Ratio | 3.008 | ||||
| Upside part of mean | 1.431 | ||||
| Downside part of mean | -1.398 | ||||
| Upside SD | 0.459 | ||||
| Downside SD | 0.476 | ||||
| N nonnegative terms | 451.000 | ||||
| N negative terms | 1682.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2133.000 | ||||
| Mean of predictor | 0.165 | ||||
| Mean of criterion | 0.033 | ||||
| SD of predictor | 0.512 | ||||
| SD of criterion | 0.661 | ||||
| Covariance | -0.065 | ||||
| r | -0.191 | ||||
| b (slope, estimate of beta) | -0.247 | ||||
| a (intercept, estimate of alpha) | 0.074 | ||||
| Mean Square Error | 0.421 | ||||
| DF error | 2131.000 | ||||
| t(b) | -9.001 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.324 | ||||
| p(a) | 0.373 | ||||
| Lowerbound of 95% confidence interval for beta | -0.301 | ||||
| Upperbound of 95% confidence interval for beta | -0.193 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.372 | ||||
| Upperbound of 95% confidence interval for alpha | 0.520 | ||||
| Treynor index (mean / b) | -0.134 | ||||
| Jensen alpha (a) | 0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2133.000 | ||||
| Minimum | 0.477 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.076 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 434.000 | ||||
| Percentage of outliers low | 0.203 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 461.000 | ||||
| Percentage of outliers high | 0.216 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.969 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.284 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.039 | ||||
| Quartile 1 | 0.051 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.288 | ||||
| Maximum | 0.523 | ||||
| Mean of quarter 1 | 0.044 | ||||
| Mean of quarter 2 | 0.065 | ||||
| Mean of quarter 3 | 0.149 | ||||
| Mean of quarter 4 | 0.449 | ||||
| Inter Quartile Range | 0.237 | ||||
| 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) | -1387.914 | ||||
| VaR(95%) (moments method) | 0.470 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -5.331 | ||||
| VaR(95%) (regression method) | 0.971 | ||||
| Expected Shortfall (regression method) | 0.971 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.107 | ||||
| Compounded annual return (geometric extrapolation) | 0.080 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.153 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.178 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.994 | ||||
| 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 | 1.118 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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 | 0.990 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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) | -8735171404548070.000 | ||||
| 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) | -115176221133348169563099319238656.000 | ||||
| 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 | ||||