Advanced Statistics: (45779563)
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 | 11.142 | ||||
| SD | 19.503 | ||||
| Sharpe ratio (Glass type estimate) | 0.571 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.559 | ||||
| df | 36.000 | ||||
| t | 1.003 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.556 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.691 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.564 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.683 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 9.262 | ||||
| Upside Potential Ratio | 10.759 | ||||
| Upside part of mean | 12.942 | ||||
| Downside part of mean | -1.800 | ||||
| Upside SD | 19.467 | ||||
| Downside SD | 1.203 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.249 | ||||
| Mean of criterion | 11.142 | ||||
| SD of predictor | 0.204 | ||||
| SD of criterion | 19.503 | ||||
| Covariance | -0.174 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -4.190 | ||||
| a (intercept, estimate of alpha) | 12.186 | ||||
| Mean Square Error | 390.481 | ||||
| DF error | 35.000 | ||||
| t(b) | -0.259 | ||||
| p(b) | 0.601 | ||||
| t(a) | 1.019 | ||||
| p(a) | 0.158 | ||||
| Lowerbound of 95% confidence interval for beta | -37.033 | ||||
| Upperbound of 95% confidence interval for beta | 28.653 | ||||
| Lowerbound of 95% confidence interval for alpha | -12.082 | ||||
| Upperbound of 95% confidence interval for alpha | 36.454 | ||||
| Treynor index (mean / b) | -2.659 | ||||
| Jensen alpha (a) | 12.186 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.772 | ||||
| SD | 5.180 | ||||
| Sharpe ratio (Glass type estimate) | -0.728 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.713 | ||||
| df | 36.000 | ||||
| t | -1.279 | ||||
| p | 0.895 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.852 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.405 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.841 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.415 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.802 | ||||
| Upside Potential Ratio | 0.435 | ||||
| Upside part of mean | 2.045 | ||||
| Downside part of mean | -5.816 | ||||
| Upside SD | 2.277 | ||||
| Downside SD | 4.702 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -3.772 | ||||
| SD of predictor | 0.198 | ||||
| SD of criterion | 5.180 | ||||
| Covariance | 0.012 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.306 | ||||
| a (intercept, estimate of alpha) | -3.841 | ||||
| Mean Square Error | 27.597 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.069 | ||||
| p(b) | 0.473 | ||||
| t(a) | -1.217 | ||||
| p(a) | 0.884 | ||||
| Lowerbound of 95% confidence interval for beta | -8.681 | ||||
| Upperbound of 95% confidence interval for beta | 9.292 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.247 | ||||
| Upperbound of 95% confidence interval for alpha | 2.565 | ||||
| Treynor index (mean / b) | -12.340 | ||||
| Jensen alpha (a) | -3.841 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.938 | ||||
| Expected Shortfall on VaR | 0.962 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.461 | ||||
| Expected Shortfall on VaR | 0.900 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.936 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 34.814 | ||||
| Mean of quarter 1 | 0.458 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 5.437 | ||||
| Inter Quartile Range | 0.064 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.189 | ||||
| Mean of outliers low | 0.264 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.189 | ||||
| Mean of outliers high | 6.704 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.115 | ||||
| VaR(95%) (moments method) | 0.278 | ||||
| Expected Shortfall (moments method) | 0.444 | ||||
| Extreme Value Index (regression method) | -1.355 | ||||
| VaR(95%) (regression method) | 0.441 | ||||
| Expected Shortfall (regression method) | 0.467 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.315 | ||||
| Quartile 1 | 0.640 | ||||
| Median | 0.965 | ||||
| Quartile 3 | 0.983 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.315 | ||||
| Mean of quarter 2 | 0.965 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.342 | ||||
| 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) | -0.324 | ||||
| Compounded annual return (geometric extrapolation) | -0.976 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.976 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.976 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.014 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 61.984 | ||||
| SD | 50.470 | ||||
| Sharpe ratio (Glass type estimate) | 1.228 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.227 | ||||
| df | 818.000 | ||||
| t | 2.171 | ||||
| p | 0.015 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.118 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.338 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.117 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.337 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 30.104 | ||||
| Upside Potential Ratio | 33.644 | ||||
| Upside part of mean | 69.273 | ||||
| Downside part of mean | -7.289 | ||||
| Upside SD | 50.543 | ||||
| Downside SD | 2.059 | ||||
| N nonnegative terms | 126.000 | ||||
| N negative terms | 693.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 819.000 | ||||
| Mean of predictor | 0.265 | ||||
| Mean of criterion | 61.984 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 50.470 | ||||
| Covariance | -0.788 | ||||
| r | -0.064 | ||||
| b (slope, estimate of beta) | -13.214 | ||||
| a (intercept, estimate of alpha) | 65.490 | ||||
| Mean Square Error | 2539.944 | ||||
| DF error | 817.000 | ||||
| t(b) | -1.832 | ||||
| p(b) | 0.966 | ||||
| t(a) | 2.292 | ||||
| p(a) | 0.011 | ||||
| Lowerbound of 95% confidence interval for beta | -27.374 | ||||
| Upperbound of 95% confidence interval for beta | 0.945 | ||||
| Lowerbound of 95% confidence interval for alpha | 9.412 | ||||
| Upperbound of 95% confidence interval for alpha | 121.568 | ||||
| Treynor index (mean / b) | -4.691 | ||||
| Jensen alpha (a) | 65.490 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.721 | ||||
| SD | 8.149 | ||||
| Sharpe ratio (Glass type estimate) | -0.457 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.456 | ||||
| df | 818.000 | ||||
| t | -0.807 | ||||
| p | 0.790 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.565 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.652 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.565 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.653 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.584 | ||||
| Upside Potential Ratio | 1.896 | ||||
| Upside part of mean | 12.090 | ||||
| Downside part of mean | -15.811 | ||||
| Upside SD | 5.072 | ||||
| Downside SD | 6.376 | ||||
| N nonnegative terms | 126.000 | ||||
| N negative terms | 693.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 819.000 | ||||
| Mean of predictor | 0.235 | ||||
| Mean of criterion | -3.721 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 8.149 | ||||
| Covariance | -0.287 | ||||
| r | -0.144 | ||||
| b (slope, estimate of beta) | -4.819 | ||||
| a (intercept, estimate of alpha) | -2.586 | ||||
| Mean Square Error | 65.096 | ||||
| DF error | 817.000 | ||||
| t(b) | -4.167 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.566 | ||||
| p(a) | 0.714 | ||||
| Lowerbound of 95% confidence interval for beta | -7.089 | ||||
| Upperbound of 95% confidence interval for beta | -2.549 | ||||
| Lowerbound of 95% confidence interval for alpha | -11.560 | ||||
| Upperbound of 95% confidence interval for alpha | 6.387 | ||||
| Treynor index (mean / b) | 0.772 | ||||
| Jensen alpha (a) | -2.586 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.569 | ||||
| Expected Shortfall on VaR | 0.645 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.194 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 819.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 52.207 | ||||
| Mean of quarter 1 | 0.889 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2.056 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 141.000 | ||||
| Percentage of outliers low | 0.172 | ||||
| Mean of outliers low | 0.839 | ||||
| Number of outliers high | 134.000 | ||||
| Percentage of outliers high | 0.164 | ||||
| Mean of outliers high | 2.616 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.139 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| 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 | 4.000 | ||||
| Minimum | 0.210 | ||||
| Quartile 1 | 0.373 | ||||
| Median | 0.479 | ||||
| Quartile 3 | 0.649 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.210 | ||||
| Mean of quarter 2 | 0.427 | ||||
| Mean of quarter 3 | 0.532 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.276 | ||||
| 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) | -0.320 | ||||
| Compounded annual return (geometric extrapolation) | -0.975 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.975 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.975 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.510 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.038 | ||||
| SD | 1.410 | ||||
| Sharpe ratio (Glass type estimate) | -1.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.437 | ||||
| df | 130.000 | ||||
| t | -1.022 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.220 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.335 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.340 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.445 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -2.038 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 1.410 | ||||
| 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 | 0.625 | ||||
| Mean of criterion | -2.038 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 1.410 | ||||
| Covariance | 0.006 | ||||
| r | 0.019 | ||||
| b (slope, estimate of beta) | 0.120 | ||||
| a (intercept, estimate of alpha) | -2.112 | ||||
| Mean Square Error | 2.002 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.219 | ||||
| p(b) | 0.488 | ||||
| t(a) | -1.041 | ||||
| p(a) | 0.558 | ||||
| Lowerbound of 95% confidence interval for beta | -0.962 | ||||
| Upperbound of 95% confidence interval for beta | 1.201 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.128 | ||||
| Upperbound of 95% confidence interval for alpha | 1.904 | ||||
| Treynor index (mean / b) | -17.016 | ||||
| Jensen alpha (a) | -2.112 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -11.498 | ||||
| SD | 8.099 | ||||
| Sharpe ratio (Glass type estimate) | -1.420 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.411 | ||||
| df | 130.000 | ||||
| t | -1.004 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.194 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.360 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.189 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.366 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.420 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -11.498 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 8.099 | ||||
| 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 | 0.599 | ||||
| Mean of criterion | -11.498 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 8.099 | ||||
| Covariance | 0.034 | ||||
| r | 0.019 | ||||
| b (slope, estimate of beta) | 0.668 | ||||
| a (intercept, estimate of alpha) | -11.898 | ||||
| Mean Square Error | 66.079 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.212 | ||||
| p(b) | 0.488 | ||||
| t(a) | -1.021 | ||||
| p(a) | 0.557 | ||||
| Lowerbound of 95% confidence interval for beta | -5.559 | ||||
| Upperbound of 95% confidence interval for beta | 6.895 | ||||
| Lowerbound of 95% confidence interval for alpha | -34.946 | ||||
| Upperbound of 95% confidence interval for alpha | 11.151 | ||||
| Treynor index (mean / b) | -17.209 | ||||
| Jensen alpha (a) | -11.898 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.580 | ||||
| Expected Shortfall on VaR | 0.654 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.970 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.003 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.997 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 0.997 | ||||
| Quartile 3 | 0.997 | ||||
| Maximum | 0.997 | ||||
| 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 | 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) | -1.993 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.003 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.530 | ||||