Advanced Statistics: Multimentum
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 | 0.164 | ||||
| SD | 0.282 | ||||
| Sharpe ratio (Glass type estimate) | 0.583 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.578 | ||||
| df | 87.000 | ||||
| t | 1.580 | ||||
| p | 0.059 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.147 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.311 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.151 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.307 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.976 | ||||
| Upside Potential Ratio | 2.443 | ||||
| Upside part of mean | 0.411 | ||||
| Downside part of mean | -0.247 | ||||
| Upside SD | 0.229 | ||||
| Downside SD | 0.168 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.226 | ||||
| Mean of criterion | 0.164 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.282 | ||||
| Covariance | 0.022 | ||||
| r | 0.322 | ||||
| b (slope, estimate of beta) | 0.368 | ||||
| a (intercept, estimate of alpha) | 0.081 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 86.000 | ||||
| t(b) | 3.157 | ||||
| p(b) | 0.001 | ||||
| t(a) | 0.792 | ||||
| p(a) | 0.215 | ||||
| Lowerbound of 95% confidence interval for beta | 0.136 | ||||
| Upperbound of 95% confidence interval for beta | 0.600 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.123 | ||||
| Upperbound of 95% confidence interval for alpha | 0.285 | ||||
| Treynor index (mean / b) | 0.446 | ||||
| Jensen alpha (a) | 0.081 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.124 | ||||
| SD | 0.280 | ||||
| Sharpe ratio (Glass type estimate) | 0.444 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.440 | ||||
| df | 87.000 | ||||
| t | 1.202 | ||||
| p | 0.116 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.284 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.169 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.287 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.167 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.667 | ||||
| Upside Potential Ratio | 2.074 | ||||
| Upside part of mean | 0.386 | ||||
| Downside part of mean | -0.262 | ||||
| Upside SD | 0.210 | ||||
| Downside SD | 0.186 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.197 | ||||
| Mean of criterion | 0.124 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 0.280 | ||||
| Covariance | 0.023 | ||||
| r | 0.364 | ||||
| b (slope, estimate of beta) | 0.459 | ||||
| a (intercept, estimate of alpha) | 0.034 | ||||
| Mean Square Error | 0.069 | ||||
| DF error | 86.000 | ||||
| t(b) | 3.625 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.336 | ||||
| p(a) | 0.369 | ||||
| Lowerbound of 95% confidence interval for beta | 0.207 | ||||
| Upperbound of 95% confidence interval for beta | 0.711 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.165 | ||||
| Upperbound of 95% confidence interval for alpha | 0.232 | ||||
| Treynor index (mean / b) | 0.271 | ||||
| Jensen alpha (a) | 0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.115 | ||||
| Expected Shortfall on VaR | 0.144 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 88.000 | ||||
| Minimum | 0.711 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 1.014 | ||||
| Quartile 3 | 1.044 | ||||
| Maximum | 1.273 | ||||
| Mean of quarter 1 | 0.928 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.029 | ||||
| Mean of quarter 4 | 1.113 | ||||
| Inter Quartile Range | 0.061 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.805 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.201 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.151 | ||||
| VaR(95%) (moments method) | 0.056 | ||||
| Expected Shortfall (moments method) | 0.088 | ||||
| Extreme Value Index (regression method) | 0.433 | ||||
| VaR(95%) (regression method) | 0.056 | ||||
| Expected Shortfall (regression method) | 0.113 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.033 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.110 | ||||
| Quartile 3 | 0.218 | ||||
| Maximum | 0.311 | ||||
| Mean of quarter 1 | 0.056 | ||||
| Mean of quarter 2 | 0.110 | ||||
| Mean of quarter 3 | 0.168 | ||||
| Mean of quarter 4 | 0.282 | ||||
| Inter Quartile Range | 0.143 | ||||
| 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) | -2.348 | ||||
| VaR(95%) (moments method) | 0.294 | ||||
| Expected Shortfall (moments method) | 0.296 | ||||
| Extreme Value Index (regression method) | -0.318 | ||||
| VaR(95%) (regression method) | 0.329 | ||||
| Expected Shortfall (regression method) | 0.364 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.332 | ||||
| Compounded annual return (geometric extrapolation) | 0.183 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.589 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.649 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.270 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.176 | ||||
| SD | 0.296 | ||||
| Sharpe ratio (Glass type estimate) | 0.595 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.595 | ||||
| df | 1926.000 | ||||
| t | 1.615 | ||||
| p | 0.482 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.128 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.318 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.128 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.318 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.830 | ||||
| Upside Potential Ratio | 7.104 | ||||
| Upside part of mean | 1.506 | ||||
| Downside part of mean | -1.330 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.212 | ||||
| N nonnegative terms | 1023.000 | ||||
| N negative terms | 904.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1927.000 | ||||
| Mean of predictor | 0.240 | ||||
| Mean of criterion | 0.176 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.296 | ||||
| Covariance | 0.030 | ||||
| r | 0.376 | ||||
| b (slope, estimate of beta) | 0.406 | ||||
| a (intercept, estimate of alpha) | 0.078 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 1925.000 | ||||
| t(b) | 17.824 | ||||
| p(b) | 0.266 | ||||
| t(a) | 0.775 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | 0.361 | ||||
| Upperbound of 95% confidence interval for beta | 0.451 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | 0.277 | ||||
| Treynor index (mean / b) | 0.434 | ||||
| Jensen alpha (a) | 0.078 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.132 | ||||
| SD | 0.298 | ||||
| Sharpe ratio (Glass type estimate) | 0.443 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.443 | ||||
| df | 1926.000 | ||||
| t | 1.201 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.280 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.166 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.280 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.165 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.600 | ||||
| Upside Potential Ratio | 6.762 | ||||
| Upside part of mean | 1.485 | ||||
| Downside part of mean | -1.353 | ||||
| Upside SD | 0.201 | ||||
| Downside SD | 0.220 | ||||
| N nonnegative terms | 1023.000 | ||||
| N negative terms | 904.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1927.000 | ||||
| Mean of predictor | 0.204 | ||||
| Mean of criterion | 0.132 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.298 | ||||
| Covariance | 0.031 | ||||
| r | 0.392 | ||||
| b (slope, estimate of beta) | 0.434 | ||||
| a (intercept, estimate of alpha) | 0.043 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 1925.000 | ||||
| t(b) | 18.685 | ||||
| p(b) | 0.257 | ||||
| t(a) | 0.430 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | 0.388 | ||||
| Upperbound of 95% confidence interval for beta | 0.479 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 0.242 | ||||
| Treynor index (mean / b) | 0.304 | ||||
| Jensen alpha (a) | 0.043 | ||||
| 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 | 0.037 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1927.000 | ||||
| Minimum | 0.856 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.140 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 116.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 108.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.506 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | 0.040 | ||||
| Extreme Value Index (regression method) | 0.278 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.029 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 28.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.031 | ||||
| Quartile 3 | 0.138 | ||||
| Maximum | 0.489 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.076 | ||||
| Mean of quarter 4 | 0.253 | ||||
| Inter Quartile Range | 0.133 | ||||
| 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 | 0.036 | ||||
| Mean of outliers high | 0.489 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.202 | ||||
| VaR(95%) (moments method) | 0.281 | ||||
| Expected Shortfall (moments method) | 0.399 | ||||
| Extreme Value Index (regression method) | 0.681 | ||||
| VaR(95%) (regression method) | 0.233 | ||||
| Expected Shortfall (regression method) | 0.466 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.360 | ||||
| Compounded annual return (geometric extrapolation) | 0.192 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.393 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.762 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.235 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.931 | ||||
| SD | 0.637 | ||||
| Sharpe ratio (Glass type estimate) | 3.034 | ||||
| Sharpe ratio (Hedges UMVUE) | 3.016 | ||||
| df | 130.000 | ||||
| t | 2.145 | ||||
| p | 0.408 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.232 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.824 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.220 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.812 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.732 | ||||
| Upside Potential Ratio | 12.032 | ||||
| Upside part of mean | 4.910 | ||||
| Downside part of mean | -2.979 | ||||
| Upside SD | 0.500 | ||||
| Downside SD | 0.408 | ||||
| N nonnegative terms | 79.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.269 | ||||
| Mean of criterion | 1.931 | ||||
| SD of predictor | 0.395 | ||||
| SD of criterion | 0.637 | ||||
| Covariance | 0.218 | ||||
| r | 0.866 | ||||
| b (slope, estimate of beta) | 1.395 | ||||
| a (intercept, estimate of alpha) | 0.162 | ||||
| Mean Square Error | 0.102 | ||||
| DF error | 129.000 | ||||
| t(b) | 19.643 | ||||
| p(b) | 0.029 | ||||
| t(a) | 0.351 | ||||
| p(a) | 0.480 | ||||
| Lowerbound of 95% confidence interval for beta | 1.254 | ||||
| Upperbound of 95% confidence interval for beta | 1.535 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.751 | ||||
| Upperbound of 95% confidence interval for alpha | 1.075 | ||||
| Treynor index (mean / b) | 1.385 | ||||
| Jensen alpha (a) | 0.162 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.724 | ||||
| SD | 0.637 | ||||
| Sharpe ratio (Glass type estimate) | 2.705 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.689 | ||||
| df | 130.000 | ||||
| t | 1.913 | ||||
| p | 0.417 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.092 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.491 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.102 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.480 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.054 | ||||
| Upside Potential Ratio | 11.267 | ||||
| Upside part of mean | 4.790 | ||||
| Downside part of mean | -3.066 | ||||
| Upside SD | 0.483 | ||||
| Downside SD | 0.425 | ||||
| N nonnegative terms | 79.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.188 | ||||
| Mean of criterion | 1.724 | ||||
| SD of predictor | 0.395 | ||||
| SD of criterion | 0.637 | ||||
| Covariance | 0.218 | ||||
| r | 0.866 | ||||
| b (slope, estimate of beta) | 1.398 | ||||
| a (intercept, estimate of alpha) | 0.062 | ||||
| Mean Square Error | 0.102 | ||||
| DF error | 129.000 | ||||
| t(b) | 19.679 | ||||
| p(b) | 0.029 | ||||
| t(a) | 0.135 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | 1.258 | ||||
| Upperbound of 95% confidence interval for beta | 1.539 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.848 | ||||
| Upperbound of 95% confidence interval for alpha | 0.972 | ||||
| Treynor index (mean / b) | 1.233 | ||||
| Jensen alpha (a) | 0.062 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.057 | ||||
| Expected Shortfall on VaR | 0.072 | ||||
| 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 | 131.000 | ||||
| Minimum | 0.859 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.011 | ||||
| Quartile 3 | 1.030 | ||||
| Maximum | 1.140 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.019 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.040 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.880 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.120 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.864 | ||||
| VaR(95%) (moments method) | 0.032 | ||||
| Expected Shortfall (moments method) | 0.035 | ||||
| Extreme Value Index (regression method) | -0.118 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.059 | ||||
| Maximum | 0.241 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.050 | ||||
| Mean of quarter 4 | 0.181 | ||||
| Inter Quartile Range | 0.051 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.176 | ||||
| Mean of outliers high | 0.200 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.658 | ||||
| VaR(95%) (moments method) | 0.134 | ||||
| Expected Shortfall (moments method) | 0.134 | ||||
| Extreme Value Index (regression method) | -1.356 | ||||
| VaR(95%) (regression method) | 0.223 | ||||
| Expected Shortfall (regression method) | 0.233 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.840 | ||||
| Compounded annual return (geometric extrapolation) | 4.857 | ||||
| Calmar ratio (compounded annual return / max draw down) | 20.137 | ||||
| Compounded annual return / average of 25% largest draw downs | 26.875 | ||||
| Compounded annual return / Expected Shortfall lognormal | 67.635 | ||||