Advanced Statistics: INVERTERATE - 1 Day Only
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.021 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | 0.275 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.272 | ||||
| df | 56.000 | ||||
| t | 0.600 | ||||
| p | 0.275 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.627 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.175 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.629 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.172 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.409 | ||||
| Upside Potential Ratio | 2.153 | ||||
| Upside part of mean | 0.110 | ||||
| Downside part of mean | -0.089 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.324 | ||||
| Mean of criterion | 0.021 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | 0.006 | ||||
| r | 0.340 | ||||
| b (slope, estimate of beta) | 0.113 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 55.000 | ||||
| t(b) | 2.678 | ||||
| p(b) | 0.005 | ||||
| t(a) | -0.444 | ||||
| p(a) | 0.670 | ||||
| Lowerbound of 95% confidence interval for beta | 0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.198 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 0.184 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | 0.238 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.235 | ||||
| df | 56.000 | ||||
| t | 0.519 | ||||
| p | 0.303 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.663 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.137 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.665 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.135 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.347 | ||||
| Upside Potential Ratio | 2.083 | ||||
| Upside part of mean | 0.108 | ||||
| Downside part of mean | -0.090 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.220 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | 0.006 | ||||
| r | 0.352 | ||||
| b (slope, estimate of beta) | 0.121 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 55.000 | ||||
| t(b) | 2.785 | ||||
| p(b) | 0.004 | ||||
| t(a) | -0.500 | ||||
| p(a) | 0.690 | ||||
| Lowerbound of 95% confidence interval for beta | 0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.207 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.053 | ||||
| Treynor index (mean / b) | 0.149 | ||||
| Jensen alpha (a) | -0.018 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 57.000 | ||||
| Minimum | 0.947 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 1.063 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.035 | ||||
| Mean of outliers low | 0.952 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.018 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.283 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | 0.022 | ||||
| Extreme Value Index (regression method) | -0.201 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.038 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.039 | ||||
| Quartile 3 | 0.078 | ||||
| Maximum | 0.102 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.070 | ||||
| Mean of quarter 4 | 0.102 | ||||
| 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) | 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) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.626 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.626 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.503 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.095 | ||||
| Sharpe ratio (Glass type estimate) | 0.300 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.299 | ||||
| df | 1259.000 | ||||
| t | 0.657 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.594 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.193 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.594 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.193 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.412 | ||||
| Upside Potential Ratio | 5.795 | ||||
| Upside part of mean | 0.400 | ||||
| Downside part of mean | -0.372 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.069 | ||||
| N nonnegative terms | 590.000 | ||||
| N negative terms | 670.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1260.000 | ||||
| Mean of predictor | 0.339 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 0.095 | ||||
| Covariance | 0.005 | ||||
| r | 0.194 | ||||
| b (slope, estimate of beta) | 0.065 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 1258.000 | ||||
| t(b) | 7.003 | ||||
| p(b) | 0.403 | ||||
| t(a) | 0.153 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | 0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | 0.440 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.095 | ||||
| Sharpe ratio (Glass type estimate) | 0.251 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.251 | ||||
| df | 1259.000 | ||||
| t | 0.550 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.643 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.145 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.643 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.145 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.340 | ||||
| Upside Potential Ratio | 5.662 | ||||
| Upside part of mean | 0.398 | ||||
| Downside part of mean | -0.374 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 590.000 | ||||
| N negative terms | 670.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1260.000 | ||||
| Mean of predictor | 0.298 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.095 | ||||
| Covariance | 0.005 | ||||
| r | 0.196 | ||||
| b (slope, estimate of beta) | 0.066 | ||||
| a (intercept, estimate of alpha) | 0.004 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 1258.000 | ||||
| t(b) | 7.100 | ||||
| p(b) | 0.402 | ||||
| t(a) | 0.103 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.088 | ||||
| Treynor index (mean / b) | 0.365 | ||||
| Jensen alpha (a) | 0.004 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1260.000 | ||||
| Minimum | 0.930 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.059 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 84.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 84.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.504 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| 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 | 43.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.114 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.040 | ||||
| Inter Quartile Range | 0.014 | ||||
| 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 | 0.070 | ||||
| Mean of outliers high | 0.088 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.682 | ||||
| VaR(95%) (moments method) | 0.048 | ||||
| Expected Shortfall (moments method) | 0.147 | ||||
| Extreme Value Index (regression method) | 1.560 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.080 | ||||
| Compounded annual return (geometric extrapolation) | 0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.617 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.759 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.866 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.127 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | 1.388 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.380 | ||||
| df | 130.000 | ||||
| t | 0.982 | ||||
| p | 0.457 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.391 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.162 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.397 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.157 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.939 | ||||
| Upside Potential Ratio | 8.946 | ||||
| Upside part of mean | 0.585 | ||||
| Downside part of mean | -0.458 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.065 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.947 | ||||
| Mean of criterion | 0.127 | ||||
| SD of predictor | 0.487 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | 0.022 | ||||
| r | 0.504 | ||||
| b (slope, estimate of beta) | 0.095 | ||||
| a (intercept, estimate of alpha) | 0.037 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.633 | ||||
| p(b) | 0.193 | ||||
| t(a) | 0.330 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | 0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.123 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.186 | ||||
| Upperbound of 95% confidence interval for alpha | 0.260 | ||||
| Treynor index (mean / b) | 1.340 | ||||
| Jensen alpha (a) | 0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.123 | ||||
| SD | 0.092 | ||||
| Sharpe ratio (Glass type estimate) | 1.339 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.331 | ||||
| df | 130.000 | ||||
| t | 0.947 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.440 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.113 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.445 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.108 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.859 | ||||
| Upside Potential Ratio | 8.839 | ||||
| Upside part of mean | 0.583 | ||||
| Downside part of mean | -0.460 | ||||
| Upside SD | 0.063 | ||||
| Downside SD | 0.066 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.826 | ||||
| Mean of criterion | 0.123 | ||||
| SD of predictor | 0.491 | ||||
| SD of criterion | 0.092 | ||||
| Covariance | 0.023 | ||||
| r | 0.503 | ||||
| b (slope, estimate of beta) | 0.094 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.609 | ||||
| p(b) | 0.194 | ||||
| t(a) | 0.399 | ||||
| p(a) | 0.478 | ||||
| Lowerbound of 95% confidence interval for beta | 0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.122 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.178 | ||||
| Upperbound of 95% confidence interval for alpha | 0.268 | ||||
| Treynor index (mean / b) | 1.306 | ||||
| Jensen alpha (a) | 0.045 | ||||
| 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 | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.971 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.014 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.208 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | 0.194 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.025 | ||||
| Maximum | 0.035 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.013 | ||||
| Mean of quarter 4 | 0.030 | ||||
| Inter Quartile Range | 0.020 | ||||
| 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) | -1.749 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | 0.034 | ||||
| Extreme Value Index (regression method) | -0.066 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.174 | ||||
| Compounded annual return (geometric extrapolation) | 0.181 | ||||
| Calmar ratio (compounded annual return / max draw down) | 5.149 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.997 | ||||
| Compounded annual return / Expected Shortfall lognormal | 16.283 | ||||