Advanced Statistics: extreme-os
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 | 0.151 | ||||
| SD | 0.290 | ||||
| Sharpe ratio (Glass type estimate) | 0.522 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.521 | ||||
| df | 250.000 | ||||
| t | 2.389 | ||||
| p | 0.009 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.091 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.953 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.090 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.952 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.669 | ||||
| Upside Potential Ratio | 1.676 | ||||
| Upside part of mean | 0.379 | ||||
| Downside part of mean | -0.228 | ||||
| Upside SD | 0.185 | ||||
| Downside SD | 0.226 | ||||
| N nonnegative terms | 159.000 | ||||
| N negative terms | 92.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 251.000 | ||||
| Mean of predictor | 0.056 | ||||
| Mean of criterion | 0.151 | ||||
| SD of predictor | 0.196 | ||||
| SD of criterion | 0.290 | ||||
| Covariance | 0.028 | ||||
| r | 0.492 | ||||
| b (slope, estimate of beta) | 0.729 | ||||
| a (intercept, estimate of alpha) | 0.111 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 249.000 | ||||
| t(b) | 8.929 | ||||
| p(b) | -0.000 | ||||
| t(a) | 1.999 | ||||
| p(a) | 0.023 | ||||
| Lowerbound of 95% confidence interval for beta | 0.568 | ||||
| Upperbound of 95% confidence interval for beta | 0.890 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.002 | ||||
| Upperbound of 95% confidence interval for alpha | 0.220 | ||||
| Treynor index (mean / b) | 0.207 | ||||
| Jensen alpha (a) | 0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.086 | ||||
| SD | 0.417 | ||||
| Sharpe ratio (Glass type estimate) | 0.206 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.206 | ||||
| df | 250.000 | ||||
| t | 0.943 | ||||
| p | 0.173 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.223 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.635 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.223 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.634 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.227 | ||||
| Upside Potential Ratio | 0.956 | ||||
| Upside part of mean | 0.362 | ||||
| Downside part of mean | -0.276 | ||||
| Upside SD | 0.173 | ||||
| Downside SD | 0.379 | ||||
| N nonnegative terms | 159.000 | ||||
| N negative terms | 92.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 251.000 | ||||
| Mean of predictor | 0.035 | ||||
| Mean of criterion | 0.086 | ||||
| SD of predictor | 0.202 | ||||
| SD of criterion | 0.417 | ||||
| Covariance | 0.036 | ||||
| r | 0.427 | ||||
| b (slope, estimate of beta) | 0.879 | ||||
| a (intercept, estimate of alpha) | 0.055 | ||||
| Mean Square Error | 0.143 | ||||
| DF error | 249.000 | ||||
| t(b) | 7.450 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.662 | ||||
| p(a) | 0.254 | ||||
| Lowerbound of 95% confidence interval for beta | 0.647 | ||||
| Upperbound of 95% confidence interval for beta | 1.112 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.108 | ||||
| Upperbound of 95% confidence interval for alpha | 0.217 | ||||
| Treynor index (mean / b) | 0.098 | ||||
| Jensen alpha (a) | 0.055 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.174 | ||||
| Expected Shortfall on VaR | 0.213 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 251.000 | ||||
| Minimum | 0.209 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.019 | ||||
| Quartile 3 | 1.052 | ||||
| Maximum | 1.333 | ||||
| Mean of quarter 1 | 0.931 | ||||
| Mean of quarter 2 | 1.005 | ||||
| Mean of quarter 3 | 1.034 | ||||
| Mean of quarter 4 | 1.095 | ||||
| Inter Quartile Range | 0.062 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.734 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.012 | ||||
| Mean of outliers high | 1.215 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.580 | ||||
| VaR(95%) (moments method) | 0.047 | ||||
| Expected Shortfall (moments method) | 0.134 | ||||
| Extreme Value Index (regression method) | 0.553 | ||||
| VaR(95%) (regression method) | 0.056 | ||||
| Expected Shortfall (regression method) | 0.155 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.100 | ||||
| Maximum | 0.791 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | 0.082 | ||||
| Mean of quarter 4 | 0.285 | ||||
| Inter Quartile Range | 0.082 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.522 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.548 | ||||
| VaR(95%) (moments method) | 0.302 | ||||
| Expected Shortfall (moments method) | 0.727 | ||||
| Extreme Value Index (regression method) | 0.870 | ||||
| VaR(95%) (regression method) | 0.341 | ||||
| Expected Shortfall (regression method) | 2.444 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.676 | ||||
| Compounded annual return (geometric extrapolation) | 0.139 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.175 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.487 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.650 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.704 | ||||
| SD | 1.470 | ||||
| Sharpe ratio (Glass type estimate) | 0.479 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.479 | ||||
| df | 5482.000 | ||||
| t | 2.190 | ||||
| p | 0.014 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.050 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.907 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.050 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.907 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.368 | ||||
| Upside Potential Ratio | 4.470 | ||||
| Upside part of mean | 2.299 | ||||
| Downside part of mean | -1.596 | ||||
| Upside SD | 1.377 | ||||
| Downside SD | 0.514 | ||||
| N nonnegative terms | 2913.000 | ||||
| N negative terms | 2570.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 5483.000 | ||||
| Mean of predictor | 0.096 | ||||
| Mean of criterion | 0.704 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 1.470 | ||||
| Covariance | 0.138 | ||||
| r | 0.269 | ||||
| b (slope, estimate of beta) | 1.134 | ||||
| a (intercept, estimate of alpha) | 0.594 | ||||
| Mean Square Error | 2.004 | ||||
| DF error | 5481.000 | ||||
| t(b) | 20.698 | ||||
| p(b) | -0.000 | ||||
| t(a) | 1.921 | ||||
| p(a) | 0.027 | ||||
| Lowerbound of 95% confidence interval for beta | 1.027 | ||||
| Upperbound of 95% confidence interval for beta | 1.241 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.012 | ||||
| Upperbound of 95% confidence interval for alpha | 1.201 | ||||
| Treynor index (mean / b) | 0.620 | ||||
| Jensen alpha (a) | 0.594 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.087 | ||||
| SD | 1.092 | ||||
| Sharpe ratio (Glass type estimate) | 0.080 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.080 | ||||
| df | 5482.000 | ||||
| t | 0.364 | ||||
| p | 0.358 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.349 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.508 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.508 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.105 | ||||
| Upside Potential Ratio | 2.321 | ||||
| Upside part of mean | 1.923 | ||||
| Downside part of mean | -1.836 | ||||
| Upside SD | 0.711 | ||||
| Downside SD | 0.828 | ||||
| N nonnegative terms | 2913.000 | ||||
| N negative terms | 2570.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 5483.000 | ||||
| Mean of predictor | 0.036 | ||||
| Mean of criterion | 0.087 | ||||
| SD of predictor | 0.348 | ||||
| SD of criterion | 1.092 | ||||
| Covariance | 0.116 | ||||
| r | 0.305 | ||||
| b (slope, estimate of beta) | 0.958 | ||||
| a (intercept, estimate of alpha) | 0.053 | ||||
| Mean Square Error | 1.082 | ||||
| DF error | 5481.000 | ||||
| t(b) | 23.750 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.232 | ||||
| p(a) | 0.408 | ||||
| Lowerbound of 95% confidence interval for beta | 0.879 | ||||
| Upperbound of 95% confidence interval for beta | 1.037 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.393 | ||||
| Upperbound of 95% confidence interval for alpha | 0.498 | ||||
| Treynor index (mean / b) | 0.091 | ||||
| Jensen alpha (a) | 0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.105 | ||||
| Expected Shortfall on VaR | 0.129 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 5483.000 | ||||
| Minimum | 0.142 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 5.716 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 351.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.934 | ||||
| Number of outliers high | 345.000 | ||||
| Percentage of outliers high | 0.063 | ||||
| Mean of outliers high | 1.101 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.910 | ||||
| VaR(95%) (moments method) | 0.018 | ||||
| Expected Shortfall (moments method) | 0.214 | ||||
| Extreme Value Index (regression method) | 0.744 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 166.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.861 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.161 | ||||
| Inter Quartile Range | 0.027 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 25.000 | ||||
| Percentage of outliers high | 0.151 | ||||
| Mean of outliers high | 0.239 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.625 | ||||
| VaR(95%) (moments method) | 0.136 | ||||
| Expected Shortfall (moments method) | 0.418 | ||||
| Extreme Value Index (regression method) | 0.427 | ||||
| VaR(95%) (regression method) | 0.160 | ||||
| Expected Shortfall (regression method) | 0.355 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.692 | ||||
| Compounded annual return (geometric extrapolation) | 0.140 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.162 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.869 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.081 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.093 | ||||
| Sharpe ratio (Glass type estimate) | 0.266 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.264 | ||||
| df | 130.000 | ||||
| t | 0.188 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.507 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.037 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.508 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.036 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.381 | ||||
| Upside Potential Ratio | 8.987 | ||||
| Upside part of mean | 0.584 | ||||
| Downside part of mean | -0.559 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.065 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.131 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.137 | ||||
| SD of criterion | 0.093 | ||||
| Covariance | 0.005 | ||||
| r | 0.424 | ||||
| b (slope, estimate of beta) | 0.287 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.310 | ||||
| p(b) | 0.239 | ||||
| t(a) | -0.107 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.180 | ||||
| Upperbound of 95% confidence interval for beta | 0.394 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.250 | ||||
| Upperbound of 95% confidence interval for alpha | 0.224 | ||||
| Treynor index (mean / b) | 0.086 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.020 | ||||
| SD | 0.093 | ||||
| Sharpe ratio (Glass type estimate) | 0.219 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.218 | ||||
| df | 130.000 | ||||
| t | 0.155 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.553 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.991 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.554 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.990 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.313 | ||||
| Upside Potential Ratio | 8.909 | ||||
| Upside part of mean | 0.582 | ||||
| Downside part of mean | -0.561 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.065 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.122 | ||||
| Mean of criterion | 0.020 | ||||
| SD of predictor | 0.137 | ||||
| SD of criterion | 0.093 | ||||
| Covariance | 0.005 | ||||
| r | 0.423 | ||||
| b (slope, estimate of beta) | 0.286 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.299 | ||||
| p(b) | 0.239 | ||||
| t(a) | -0.120 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.179 | ||||
| Upperbound of 95% confidence interval for beta | 0.393 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.252 | ||||
| Upperbound of 95% confidence interval for alpha | 0.223 | ||||
| Treynor index (mean / b) | 0.071 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.983 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.017 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.118 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | -0.010 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.056 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.029 | ||||
| Mean of quarter 4 | 0.042 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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) | 0.065 | ||||
| Compounded annual return (geometric extrapolation) | 0.067 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.196 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.573 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.682 | ||||