Advanced Statistics: Hybrid One
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 | 0.034 | ||||
| SD | 0.103 | ||||
| Sharpe ratio (Glass type estimate) | 0.330 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.325 | ||||
| df | 49.000 | ||||
| t | 0.674 | ||||
| p | 0.252 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.634 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.291 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.637 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.288 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.650 | ||||
| Upside Potential Ratio | 2.234 | ||||
| Upside part of mean | 0.117 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.088 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.404 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.103 | ||||
| Covariance | 0.000 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | 0.031 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 48.000 | ||||
| t(b) | 0.111 | ||||
| p(b) | 0.456 | ||||
| t(a) | 0.555 | ||||
| p(a) | 0.291 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.128 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.082 | ||||
| Upperbound of 95% confidence interval for alpha | 0.145 | ||||
| Treynor index (mean / b) | 5.103 | ||||
| Jensen alpha (a) | 0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.101 | ||||
| Sharpe ratio (Glass type estimate) | 0.286 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.282 | ||||
| df | 49.000 | ||||
| t | 0.584 | ||||
| p | 0.281 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.677 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.246 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.680 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.243 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.537 | ||||
| Upside Potential Ratio | 2.105 | ||||
| Upside part of mean | 0.113 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.085 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.368 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.101 | ||||
| Covariance | 0.001 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | 0.024 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 48.000 | ||||
| t(b) | 0.219 | ||||
| p(b) | 0.414 | ||||
| t(a) | 0.439 | ||||
| p(a) | 0.331 | ||||
| Lowerbound of 95% confidence interval for beta | -0.108 | ||||
| Upperbound of 95% confidence interval for beta | 0.135 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | 0.134 | ||||
| Treynor index (mean / b) | 2.179 | ||||
| Jensen alpha (a) | 0.024 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.934 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.100 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.120 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 1.052 | ||||
| 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) | -0.152 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.040 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.120 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.050 | ||||
| Mean of quarter 4 | 0.120 | ||||
| Inter Quartile Range | 0.051 | ||||
| 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) | 0.085 | ||||
| Compounded annual return (geometric extrapolation) | 0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.631 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.631 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.350 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.036 | ||||
| SD | 0.125 | ||||
| Sharpe ratio (Glass type estimate) | 0.293 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.292 | ||||
| df | 1092.000 | ||||
| t | 0.598 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.667 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.252 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.667 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.252 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.470 | ||||
| Upside Potential Ratio | 4.308 | ||||
| Upside part of mean | 0.334 | ||||
| Downside part of mean | -0.298 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 195.000 | ||||
| N negative terms | 898.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1093.000 | ||||
| Mean of predictor | 0.424 | ||||
| Mean of criterion | 0.036 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.125 | ||||
| Covariance | 0.001 | ||||
| r | 0.014 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | 0.034 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 1091.000 | ||||
| t(b) | 0.462 | ||||
| p(b) | 0.491 | ||||
| t(a) | 0.557 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | 0.154 | ||||
| Treynor index (mean / b) | 6.596 | ||||
| Jensen alpha (a) | 0.034 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.123 | ||||
| Sharpe ratio (Glass type estimate) | 0.233 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.233 | ||||
| df | 1092.000 | ||||
| t | 0.476 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.727 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.193 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.727 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.193 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.361 | ||||
| Upside Potential Ratio | 4.135 | ||||
| Upside part of mean | 0.330 | ||||
| Downside part of mean | -0.301 | ||||
| Upside SD | 0.094 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 195.000 | ||||
| N negative terms | 898.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1093.000 | ||||
| Mean of predictor | 0.374 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.123 | ||||
| Covariance | 0.001 | ||||
| r | 0.015 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | 0.027 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 1091.000 | ||||
| t(b) | 0.496 | ||||
| p(b) | 0.490 | ||||
| t(a) | 0.438 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.146 | ||||
| Treynor index (mean / b) | 4.880 | ||||
| Jensen alpha (a) | 0.027 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1093.000 | ||||
| Minimum | 0.903 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.117 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 176.000 | ||||
| Percentage of outliers low | 0.161 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 199.000 | ||||
| Percentage of outliers high | 0.182 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.813 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| Extreme Value Index (regression method) | 0.534 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 24.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.020 | ||||
| Maximum | 0.171 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.014 | ||||
| Mean of quarter 4 | 0.060 | ||||
| Inter Quartile Range | 0.015 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.094 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.626 | ||||
| VaR(95%) (moments method) | 0.067 | ||||
| Expected Shortfall (moments method) | 0.188 | ||||
| Extreme Value Index (regression method) | 1.652 | ||||
| VaR(95%) (regression method) | 0.073 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.085 | ||||
| Compounded annual return (geometric extrapolation) | 0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.441 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.260 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.873 | ||||
| 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 | 1.063 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.520 | ||||
| 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 | 0.925 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.525 | ||||
| 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) | -8747698015521128.000 | ||||
| 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) | -114333780954696206196502742171648.000 | ||||
| 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 | ||||