Advanced Statistics: QTIPS
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 | 0.058 | ||||
| SD | 0.395 | ||||
| Sharpe ratio (Glass type estimate) | 0.146 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.145 | ||||
| df | 81.000 | ||||
| t | 0.382 | ||||
| p | 0.352 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.604 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.896 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.605 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.895 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.208 | ||||
| Upside Potential Ratio | 0.941 | ||||
| Upside part of mean | 0.261 | ||||
| Downside part of mean | -0.203 | ||||
| Upside SD | 0.279 | ||||
| Downside SD | 0.277 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 82.000 | ||||
| Mean of predictor | 0.135 | ||||
| Mean of criterion | 0.058 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.395 | ||||
| Covariance | 0.008 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.132 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.157 | ||||
| DF error | 80.000 | ||||
| t(b) | 0.738 | ||||
| p(b) | 0.231 | ||||
| t(a) | 0.260 | ||||
| p(a) | 0.398 | ||||
| Lowerbound of 95% confidence interval for beta | -0.225 | ||||
| Upperbound of 95% confidence interval for beta | 0.489 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.266 | ||||
| Upperbound of 95% confidence interval for alpha | 0.345 | ||||
| Treynor index (mean / b) | 0.436 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.462 | ||||
| Sharpe ratio (Glass type estimate) | -0.075 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.074 | ||||
| df | 81.000 | ||||
| t | -0.196 | ||||
| p | 0.578 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.825 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.675 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.824 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.675 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.089 | ||||
| Upside Potential Ratio | 0.582 | ||||
| Upside part of mean | 0.228 | ||||
| Downside part of mean | -0.263 | ||||
| Upside SD | 0.240 | ||||
| Downside SD | 0.392 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 82.000 | ||||
| Mean of predictor | 0.104 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.462 | ||||
| Covariance | 0.014 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.236 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.213 | ||||
| DF error | 80.000 | ||||
| t(b) | 1.136 | ||||
| p(b) | 0.130 | ||||
| t(a) | -0.334 | ||||
| p(a) | 0.630 | ||||
| Lowerbound of 95% confidence interval for beta | -0.177 | ||||
| Upperbound of 95% confidence interval for beta | 0.649 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.413 | ||||
| Upperbound of 95% confidence interval for alpha | 0.295 | ||||
| Treynor index (mean / b) | -0.147 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.199 | ||||
| Expected Shortfall on VaR | 0.242 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 82.000 | ||||
| Minimum | 0.418 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.454 | ||||
| Mean of quarter 1 | 0.947 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.086 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.776 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.134 | ||||
| Mean of outliers high | 1.165 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -114.030 | ||||
| VaR(95%) (moments method) | -727946319704.699 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.826 | ||||
| VaR(95%) (regression method) | -0.025 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.198 | ||||
| Quartile 3 | 0.443 | ||||
| Maximum | 0.582 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.396 | ||||
| Mean of quarter 4 | 0.582 | ||||
| Inter Quartile Range | 0.443 | ||||
| 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) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.016 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.016 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.038 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.097 | ||||
| SD | 0.459 | ||||
| Sharpe ratio (Glass type estimate) | 0.211 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.211 | ||||
| df | 1808.000 | ||||
| t | 0.554 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.535 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.957 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.535 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.957 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.294 | ||||
| Upside Potential Ratio | 2.231 | ||||
| Upside part of mean | 0.735 | ||||
| Downside part of mean | -0.638 | ||||
| Upside SD | 0.319 | ||||
| Downside SD | 0.330 | ||||
| N nonnegative terms | 116.000 | ||||
| N negative terms | 1693.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1809.000 | ||||
| Mean of predictor | 0.246 | ||||
| Mean of criterion | 0.097 | ||||
| SD of predictor | 0.539 | ||||
| SD of criterion | 0.459 | ||||
| Covariance | 0.026 | ||||
| r | 0.106 | ||||
| b (slope, estimate of beta) | 0.090 | ||||
| a (intercept, estimate of alpha) | 0.075 | ||||
| Mean Square Error | 0.208 | ||||
| DF error | 1807.000 | ||||
| t(b) | 4.530 | ||||
| p(b) | 0.433 | ||||
| t(a) | 0.429 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | 0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.129 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.266 | ||||
| Upperbound of 95% confidence interval for alpha | 0.415 | ||||
| Treynor index (mean / b) | 1.073 | ||||
| Jensen alpha (a) | 0.075 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.556 | ||||
| Sharpe ratio (Glass type estimate) | -0.063 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.063 | ||||
| df | 1808.000 | ||||
| t | -0.165 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.809 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.683 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.809 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.683 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.073 | ||||
| Upside Potential Ratio | 1.456 | ||||
| Upside part of mean | 0.690 | ||||
| Downside part of mean | -0.725 | ||||
| Upside SD | 0.291 | ||||
| Downside SD | 0.474 | ||||
| N nonnegative terms | 116.000 | ||||
| N negative terms | 1693.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1809.000 | ||||
| Mean of predictor | 0.102 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.537 | ||||
| SD of criterion | 0.556 | ||||
| Covariance | 0.038 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.131 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.305 | ||||
| DF error | 1807.000 | ||||
| t(b) | 5.403 | ||||
| p(b) | 0.420 | ||||
| t(a) | -0.229 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.178 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.460 | ||||
| Upperbound of 95% confidence interval for alpha | 0.364 | ||||
| Treynor index (mean / b) | -0.267 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1809.000 | ||||
| Minimum | 0.336 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.311 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 146.000 | ||||
| Percentage of outliers low | 0.081 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 145.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.035 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.806 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| Extreme Value Index (regression method) | 0.663 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 30.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.693 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.164 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers high | 0.133 | ||||
| Mean of outliers high | 0.327 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.443 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.796 | ||||
| VaR(95%) (regression method) | 0.239 | ||||
| Expected Shortfall (regression method) | 1.775 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.009 | ||||
| Compounded annual return (geometric extrapolation) | 0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.013 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.056 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.135 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| 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 | 0.776 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.542 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| 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 | 0.622 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.561 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8779067139957584.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 304937997687594719096650522951680.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 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 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 | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| 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 | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||