Advanced Statistics: The Momentum of Now
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 | 0.179 | ||||
| SD | 0.221 | ||||
| Sharpe ratio (Glass type estimate) | 0.810 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.806 | ||||
| df | 160.000 | ||||
| t | 2.966 | ||||
| p | 0.386 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.266 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.351 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.264 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.348 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.859 | ||||
| Upside Potential Ratio | 3.587 | ||||
| Upside part of mean | 0.346 | ||||
| Downside part of mean | -0.167 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 161.000 | ||||
| Mean of predictor | 0.089 | ||||
| Mean of criterion | 0.179 | ||||
| SD of predictor | 0.152 | ||||
| SD of criterion | 0.221 | ||||
| Covariance | -0.001 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.042 | ||||
| a (intercept, estimate of alpha) | 0.183 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 159.000 | ||||
| t(b) | -0.365 | ||||
| p(b) | 0.518 | ||||
| t(a) | 2.977 | ||||
| p(a) | 0.355 | ||||
| Lowerbound of 95% confidence interval for beta | -0.270 | ||||
| Upperbound of 95% confidence interval for beta | 0.186 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.062 | ||||
| Upperbound of 95% confidence interval for alpha | 0.304 | ||||
| Treynor index (mean / b) | -4.258 | ||||
| Jensen alpha (a) | 0.183 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.155 | ||||
| SD | 0.208 | ||||
| Sharpe ratio (Glass type estimate) | 0.748 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.745 | ||||
| df | 160.000 | ||||
| t | 2.740 | ||||
| p | 0.394 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.206 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.288 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.203 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.286 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.555 | ||||
| Upside Potential Ratio | 3.268 | ||||
| Upside part of mean | 0.326 | ||||
| Downside part of mean | -0.171 | ||||
| Upside SD | 0.187 | ||||
| Downside SD | 0.100 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 161.000 | ||||
| Mean of predictor | 0.077 | ||||
| Mean of criterion | 0.155 | ||||
| SD of predictor | 0.154 | ||||
| SD of criterion | 0.208 | ||||
| Covariance | -0.001 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | 0.157 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 159.000 | ||||
| t(b) | -0.272 | ||||
| p(b) | 0.514 | ||||
| t(a) | 2.743 | ||||
| p(a) | 0.366 | ||||
| Lowerbound of 95% confidence interval for beta | -0.240 | ||||
| Upperbound of 95% confidence interval for beta | 0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.044 | ||||
| Upperbound of 95% confidence interval for alpha | 0.271 | ||||
| Treynor index (mean / b) | -5.345 | ||||
| Jensen alpha (a) | 0.157 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.082 | ||||
| Expected Shortfall on VaR | 0.105 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 161.000 | ||||
| Minimum | 0.891 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.009 | ||||
| Quartile 3 | 1.041 | ||||
| Maximum | 1.366 | ||||
| Mean of quarter 1 | 0.956 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.026 | ||||
| Mean of quarter 4 | 1.096 | ||||
| Inter Quartile Range | 0.061 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.050 | ||||
| Mean of outliers high | 1.213 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.300 | ||||
| VaR(95%) (moments method) | 0.048 | ||||
| Expected Shortfall (moments method) | 0.079 | ||||
| Extreme Value Index (regression method) | 0.111 | ||||
| VaR(95%) (regression method) | 0.043 | ||||
| Expected Shortfall (regression method) | 0.060 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 22.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.039 | ||||
| Quartile 3 | 0.090 | ||||
| Maximum | 0.169 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.030 | ||||
| Mean of quarter 3 | 0.064 | ||||
| Mean of quarter 4 | 0.131 | ||||
| Inter Quartile Range | 0.071 | ||||
| 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) | -4.496 | ||||
| VaR(95%) (moments method) | 0.137 | ||||
| Expected Shortfall (moments method) | 0.137 | ||||
| Extreme Value Index (regression method) | -0.871 | ||||
| VaR(95%) (regression method) | 0.148 | ||||
| Expected Shortfall (regression method) | 0.157 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.221 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.305 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.689 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.110 | ||||
| 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 | 0.202 | ||||
| Sharpe ratio (Glass type estimate) | 0.868 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.867 | ||||
| df | 3519.000 | ||||
| t | 3.180 | ||||
| p | 0.001 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.332 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.403 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.332 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.403 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.406 | ||||
| Upside Potential Ratio | 7.619 | ||||
| Upside part of mean | 0.952 | ||||
| Downside part of mean | -0.776 | ||||
| Upside SD | 0.160 | ||||
| Downside SD | 0.125 | ||||
| N nonnegative terms | 1966.000 | ||||
| N negative terms | 1554.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 3520.000 | ||||
| Mean of predictor | 0.095 | ||||
| Mean of criterion | 0.176 | ||||
| SD of predictor | 0.171 | ||||
| SD of criterion | 0.202 | ||||
| Covariance | -0.000 | ||||
| r | -0.010 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | 0.177 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 3518.000 | ||||
| t(b) | -0.585 | ||||
| p(b) | 0.721 | ||||
| t(a) | 3.198 | ||||
| p(a) | 0.001 | ||||
| Lowerbound of 95% confidence interval for beta | -0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.068 | ||||
| Upperbound of 95% confidence interval for alpha | 0.285 | ||||
| Treynor index (mean / b) | -15.017 | ||||
| Jensen alpha (a) | 0.177 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.156 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | 0.784 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.784 | ||||
| df | 3519.000 | ||||
| t | 2.875 | ||||
| p | 0.002 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.249 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.319 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.249 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.319 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.215 | ||||
| Upside Potential Ratio | 7.337 | ||||
| Upside part of mean | 0.940 | ||||
| Downside part of mean | -0.784 | ||||
| Upside SD | 0.152 | ||||
| Downside SD | 0.128 | ||||
| N nonnegative terms | 1966.000 | ||||
| N negative terms | 1554.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 3520.000 | ||||
| Mean of predictor | 0.080 | ||||
| Mean of criterion | 0.156 | ||||
| SD of predictor | 0.171 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | 0.156 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 3518.000 | ||||
| t(b) | -0.409 | ||||
| p(b) | 0.659 | ||||
| t(a) | 2.886 | ||||
| p(a) | 0.002 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.050 | ||||
| Upperbound of 95% confidence interval for alpha | 0.263 | ||||
| Treynor index (mean / b) | -19.475 | ||||
| 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%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 3520.000 | ||||
| Minimum | 0.849 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.266 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 212.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 220.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.435 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| Extreme Value Index (regression method) | 0.264 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.017 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 110.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.044 | ||||
| Maximum | 0.373 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.111 | ||||
| Inter Quartile Range | 0.040 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.100 | ||||
| Mean of outliers high | 0.173 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.071 | ||||
| VaR(95%) (moments method) | 0.103 | ||||
| Expected Shortfall (moments method) | 0.135 | ||||
| Extreme Value Index (regression method) | 0.033 | ||||
| VaR(95%) (regression method) | 0.088 | ||||
| Expected Shortfall (regression method) | 0.117 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.014 | ||||
| Compounded annual return (geometric extrapolation) | 0.221 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.593 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.993 | ||||
| Compounded annual return / Expected Shortfall lognormal | 9.065 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.060 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | 2.087 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.075 | ||||
| df | 130.000 | ||||
| t | 1.476 | ||||
| p | 0.436 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.700 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.867 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.708 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.858 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.495 | ||||
| Upside Potential Ratio | 8.813 | ||||
| Upside part of mean | 0.151 | ||||
| Downside part of mean | -0.091 | ||||
| Upside SD | 0.023 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 98.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.198 | ||||
| Mean of criterion | 0.060 | ||||
| SD of predictor | 0.161 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | 0.000 | ||||
| r | 0.099 | ||||
| b (slope, estimate of beta) | 0.018 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.131 | ||||
| p(b) | 0.437 | ||||
| t(a) | 1.387 | ||||
| p(a) | 0.423 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.024 | ||||
| Upperbound of 95% confidence interval for alpha | 0.137 | ||||
| Treynor index (mean / b) | 3.388 | ||||
| Jensen alpha (a) | 0.056 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.059 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | 2.075 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.063 | ||||
| df | 130.000 | ||||
| t | 1.467 | ||||
| p | 0.436 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.713 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.854 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.721 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.846 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.464 | ||||
| Upside Potential Ratio | 8.780 | ||||
| Upside part of mean | 0.151 | ||||
| Downside part of mean | -0.091 | ||||
| Upside SD | 0.023 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 98.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | 0.059 | ||||
| SD of predictor | 0.160 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | 0.000 | ||||
| r | 0.096 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.096 | ||||
| p(b) | 0.439 | ||||
| t(a) | 1.386 | ||||
| p(a) | 0.423 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.024 | ||||
| Upperbound of 95% confidence interval for alpha | 0.136 | ||||
| Treynor index (mean / b) | 3.462 | ||||
| Jensen alpha (a) | 0.056 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.994 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.008 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.107 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19.196 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.433 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.002 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.006 | ||||
| Maximum | 0.006 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.005 | ||||
| Mean of quarter 4 | 0.006 | ||||
| Inter Quartile Range | 0.003 | ||||
| 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) | -0.881 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.591 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.106 | ||||
| Compounded annual return (geometric extrapolation) | 0.109 | ||||
| Calmar ratio (compounded annual return / max draw down) | 17.870 | ||||
| Compounded annual return / average of 25% largest draw downs | 18.339 | ||||
| Compounded annual return / Expected Shortfall lognormal | 31.899 | ||||