Advanced Statistics: Value Trades
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 | 1.134 | ||||
| SD | 1.035 | ||||
| Sharpe ratio (Glass type estimate) | 1.095 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.067 | ||||
| df | 29.000 | ||||
| t | 1.732 | ||||
| p | 0.047 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.185 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.357 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.203 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.336 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.760 | ||||
| Upside Potential Ratio | 4.553 | ||||
| Upside part of mean | 1.870 | ||||
| Downside part of mean | -0.736 | ||||
| Upside SD | 0.987 | ||||
| Downside SD | 0.411 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.665 | ||||
| Mean of criterion | 1.134 | ||||
| SD of predictor | 0.360 | ||||
| SD of criterion | 1.035 | ||||
| Covariance | 0.091 | ||||
| r | 0.245 | ||||
| b (slope, estimate of beta) | 0.705 | ||||
| a (intercept, estimate of alpha) | 0.665 | ||||
| Mean Square Error | 1.043 | ||||
| DF error | 28.000 | ||||
| t(b) | 1.336 | ||||
| p(b) | 0.096 | ||||
| t(a) | 0.904 | ||||
| p(a) | 0.187 | ||||
| Lowerbound of 95% confidence interval for beta | -0.376 | ||||
| Upperbound of 95% confidence interval for beta | 1.785 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.841 | ||||
| Upperbound of 95% confidence interval for alpha | 2.170 | ||||
| Treynor index (mean / b) | 1.609 | ||||
| Jensen alpha (a) | 0.665 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.686 | ||||
| SD | 0.891 | ||||
| Sharpe ratio (Glass type estimate) | 0.770 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.749 | ||||
| df | 29.000 | ||||
| t | 1.217 | ||||
| p | 0.117 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.492 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.018 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.505 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.004 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.405 | ||||
| Upside Potential Ratio | 3.125 | ||||
| Upside part of mean | 1.525 | ||||
| Downside part of mean | -0.839 | ||||
| Upside SD | 0.754 | ||||
| Downside SD | 0.488 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.592 | ||||
| Mean of criterion | 0.686 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.891 | ||||
| Covariance | 0.082 | ||||
| r | 0.283 | ||||
| b (slope, estimate of beta) | 0.771 | ||||
| a (intercept, estimate of alpha) | 0.229 | ||||
| Mean Square Error | 0.757 | ||||
| DF error | 28.000 | ||||
| t(b) | 1.560 | ||||
| p(b) | 0.065 | ||||
| t(a) | 0.368 | ||||
| p(a) | 0.358 | ||||
| Lowerbound of 95% confidence interval for beta | -0.241 | ||||
| Upperbound of 95% confidence interval for beta | 1.783 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.047 | ||||
| Upperbound of 95% confidence interval for alpha | 1.506 | ||||
| Treynor index (mean / b) | 0.890 | ||||
| Jensen alpha (a) | 0.229 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.306 | ||||
| Expected Shortfall on VaR | 0.374 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.130 | ||||
| Expected Shortfall on VaR | 0.252 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 30.000 | ||||
| Minimum | 0.641 | ||||
| Quartile 1 | 0.924 | ||||
| Median | 1.030 | ||||
| Quartile 3 | 1.238 | ||||
| Maximum | 2.007 | ||||
| Mean of quarter 1 | 0.808 | ||||
| Mean of quarter 2 | 0.967 | ||||
| Mean of quarter 3 | 1.143 | ||||
| Mean of quarter 4 | 1.463 | ||||
| Inter Quartile Range | 0.314 | ||||
| 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 | 0.067 | ||||
| Mean of outliers high | 1.860 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.115 | ||||
| VaR(95%) (moments method) | 0.188 | ||||
| Expected Shortfall (moments method) | 0.276 | ||||
| Extreme Value Index (regression method) | -0.813 | ||||
| VaR(95%) (regression method) | 0.158 | ||||
| Expected Shortfall (regression method) | 0.171 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.137 | ||||
| Maximum | 0.705 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | 0.077 | ||||
| Mean of quarter 3 | 0.137 | ||||
| Mean of quarter 4 | 0.705 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.705 | ||||
| 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) | 2.080 | ||||
| Compounded annual return (geometric extrapolation) | 1.075 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.525 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.525 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.870 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.395 | ||||
| SD | 1.171 | ||||
| Sharpe ratio (Glass type estimate) | 1.192 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.190 | ||||
| df | 663.000 | ||||
| t | 1.897 | ||||
| p | 0.029 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.042 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.424 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.043 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.423 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.961 | ||||
| Upside Potential Ratio | 9.140 | ||||
| Upside part of mean | 6.502 | ||||
| Downside part of mean | -5.107 | ||||
| Upside SD | 0.932 | ||||
| Downside SD | 0.711 | ||||
| N nonnegative terms | 333.000 | ||||
| N negative terms | 331.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 664.000 | ||||
| Mean of predictor | 0.690 | ||||
| Mean of criterion | 1.395 | ||||
| SD of predictor | 0.369 | ||||
| SD of criterion | 1.171 | ||||
| Covariance | 0.177 | ||||
| r | 0.409 | ||||
| b (slope, estimate of beta) | 1.298 | ||||
| a (intercept, estimate of alpha) | 0.500 | ||||
| Mean Square Error | 1.142 | ||||
| DF error | 662.000 | ||||
| t(b) | 11.542 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.739 | ||||
| p(a) | 0.230 | ||||
| Lowerbound of 95% confidence interval for beta | 1.077 | ||||
| Upperbound of 95% confidence interval for beta | 1.518 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.827 | ||||
| Upperbound of 95% confidence interval for alpha | 1.827 | ||||
| Treynor index (mean / b) | 1.075 | ||||
| Jensen alpha (a) | 0.500 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.726 | ||||
| SD | 1.155 | ||||
| Sharpe ratio (Glass type estimate) | 0.629 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.628 | ||||
| df | 663.000 | ||||
| t | 1.001 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.603 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.860 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.603 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.860 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.912 | ||||
| Upside Potential Ratio | 7.694 | ||||
| Upside part of mean | 6.126 | ||||
| Downside part of mean | -5.399 | ||||
| Upside SD | 0.837 | ||||
| Downside SD | 0.796 | ||||
| N nonnegative terms | 333.000 | ||||
| N negative terms | 331.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 664.000 | ||||
| Mean of predictor | 0.621 | ||||
| Mean of criterion | 0.726 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 1.155 | ||||
| Covariance | 0.175 | ||||
| r | 0.409 | ||||
| b (slope, estimate of beta) | 1.278 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 1.112 | ||||
| DF error | 662.000 | ||||
| t(b) | 11.546 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.100 | ||||
| p(a) | 0.540 | ||||
| Lowerbound of 95% confidence interval for beta | 1.060 | ||||
| Upperbound of 95% confidence interval for beta | 1.495 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.374 | ||||
| Upperbound of 95% confidence interval for alpha | 1.241 | ||||
| Treynor index (mean / b) | 0.568 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.134 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.091 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 664.000 | ||||
| Minimum | 0.563 | ||||
| Quartile 1 | 0.975 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.028 | ||||
| Maximum | 1.570 | ||||
| Mean of quarter 1 | 0.933 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.087 | ||||
| Inter Quartile Range | 0.053 | ||||
| Number outliers low | 26.000 | ||||
| Percentage of outliers low | 0.039 | ||||
| Mean of outliers low | 0.830 | ||||
| Number of outliers high | 37.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.190 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.438 | ||||
| VaR(95%) (moments method) | 0.070 | ||||
| Expected Shortfall (moments method) | 0.139 | ||||
| Extreme Value Index (regression method) | 0.396 | ||||
| VaR(95%) (regression method) | 0.060 | ||||
| Expected Shortfall (regression method) | 0.110 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 21.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.040 | ||||
| Median | 0.125 | ||||
| Quartile 3 | 0.166 | ||||
| Maximum | 0.756 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.081 | ||||
| Mean of quarter 3 | 0.150 | ||||
| Mean of quarter 4 | 0.468 | ||||
| Inter Quartile Range | 0.126 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.566 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.069 | ||||
| VaR(95%) (moments method) | 0.380 | ||||
| Expected Shortfall (moments method) | 0.381 | ||||
| Extreme Value Index (regression method) | 0.260 | ||||
| VaR(95%) (regression method) | 0.456 | ||||
| Expected Shortfall (regression method) | 0.741 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.385 | ||||
| Compounded annual return (geometric extrapolation) | 1.161 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.536 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.481 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.651 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 4.304 | ||||
| SD | 1.888 | ||||
| Sharpe ratio (Glass type estimate) | 2.279 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.266 | ||||
| df | 130.000 | ||||
| t | 1.612 | ||||
| p | 0.430 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.510 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.061 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.519 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.052 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.312 | ||||
| Upside Potential Ratio | 12.365 | ||||
| Upside part of mean | 12.342 | ||||
| Downside part of mean | -8.038 | ||||
| Upside SD | 1.616 | ||||
| Downside SD | 0.998 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.453 | ||||
| Mean of criterion | 4.304 | ||||
| SD of predictor | 0.545 | ||||
| SD of criterion | 1.888 | ||||
| Covariance | 0.283 | ||||
| r | 0.275 | ||||
| b (slope, estimate of beta) | 0.953 | ||||
| a (intercept, estimate of alpha) | 2.919 | ||||
| Mean Square Error | 3.321 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.250 | ||||
| p(b) | 0.327 | ||||
| t(a) | 1.118 | ||||
| p(a) | 0.438 | ||||
| Lowerbound of 95% confidence interval for beta | 0.373 | ||||
| Upperbound of 95% confidence interval for beta | 1.534 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.249 | ||||
| Upperbound of 95% confidence interval for alpha | 8.087 | ||||
| Treynor index (mean / b) | 4.514 | ||||
| Jensen alpha (a) | 2.919 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.659 | ||||
| SD | 1.782 | ||||
| Sharpe ratio (Glass type estimate) | 1.492 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.484 | ||||
| df | 130.000 | ||||
| t | 1.055 | ||||
| p | 0.454 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.288 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.267 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.294 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.261 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.414 | ||||
| Upside Potential Ratio | 10.225 | ||||
| Upside part of mean | 11.263 | ||||
| Downside part of mean | -8.604 | ||||
| Upside SD | 1.401 | ||||
| Downside SD | 1.102 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.301 | ||||
| Mean of criterion | 2.659 | ||||
| SD of predictor | 0.546 | ||||
| SD of criterion | 1.782 | ||||
| Covariance | 0.269 | ||||
| r | 0.277 | ||||
| b (slope, estimate of beta) | 0.902 | ||||
| a (intercept, estimate of alpha) | 1.485 | ||||
| Mean Square Error | 2.954 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.269 | ||||
| p(b) | 0.326 | ||||
| t(a) | 0.604 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | 0.356 | ||||
| Upperbound of 95% confidence interval for beta | 1.448 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.377 | ||||
| Upperbound of 95% confidence interval for alpha | 6.346 | ||||
| Treynor index (mean / b) | 2.947 | ||||
| Jensen alpha (a) | 1.485 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.157 | ||||
| Expected Shortfall on VaR | 0.194 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.711 | ||||
| Quartile 1 | 0.960 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.064 | ||||
| Maximum | 1.570 | ||||
| Mean of quarter 1 | 0.896 | ||||
| Mean of quarter 2 | 0.983 | ||||
| Mean of quarter 3 | 1.030 | ||||
| Mean of quarter 4 | 1.159 | ||||
| Inter Quartile Range | 0.104 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.746 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.426 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.040 | ||||
| VaR(95%) (moments method) | 0.095 | ||||
| Expected Shortfall (moments method) | 0.132 | ||||
| Extreme Value Index (regression method) | -0.043 | ||||
| VaR(95%) (regression method) | 0.124 | ||||
| Expected Shortfall (regression method) | 0.172 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.025 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.115 | ||||
| Quartile 3 | 0.343 | ||||
| Maximum | 0.527 | ||||
| Mean of quarter 1 | 0.039 | ||||
| Mean of quarter 2 | 0.087 | ||||
| Mean of quarter 3 | 0.195 | ||||
| Mean of quarter 4 | 0.466 | ||||
| Inter Quartile Range | 0.285 | ||||
| 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) | -1.746 | ||||
| VaR(95%) (moments method) | 0.509 | ||||
| Expected Shortfall (moments method) | 0.517 | ||||
| Extreme Value Index (regression method) | -0.086 | ||||
| VaR(95%) (regression method) | 0.530 | ||||
| Expected Shortfall (regression method) | 0.594 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 5.725 | ||||
| Compounded annual return (geometric extrapolation) | 13.919 | ||||
| Calmar ratio (compounded annual return / max draw down) | 26.434 | ||||
| Compounded annual return / average of 25% largest draw downs | 29.894 | ||||
| Compounded annual return / Expected Shortfall lognormal | 71.625 | ||||