Advanced Statistics: Golden Egg #1
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 | 0.103 | ||||
| SD | 0.201 | ||||
| Sharpe ratio (Glass type estimate) | 0.512 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.500 | ||||
| df | 32.000 | ||||
| t | 0.849 | ||||
| p | 0.201 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.681 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.696 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.689 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.688 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.192 | ||||
| Upside Potential Ratio | 5.561 | ||||
| Upside part of mean | 0.179 | ||||
| Downside part of mean | -0.076 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.581 | ||||
| Mean of criterion | 0.103 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.201 | ||||
| Covariance | -0.010 | ||||
| r | -0.185 | ||||
| b (slope, estimate of beta) | -0.136 | ||||
| a (intercept, estimate of alpha) | 0.182 | ||||
| Mean Square Error | 0.040 | ||||
| DF error | 31.000 | ||||
| t(b) | -1.048 | ||||
| p(b) | 0.849 | ||||
| t(a) | 1.276 | ||||
| p(a) | 0.106 | ||||
| Lowerbound of 95% confidence interval for beta | -0.401 | ||||
| Upperbound of 95% confidence interval for beta | 0.129 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.109 | ||||
| Upperbound of 95% confidence interval for alpha | 0.472 | ||||
| Treynor index (mean / b) | -0.755 | ||||
| Jensen alpha (a) | 0.182 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.085 | ||||
| SD | 0.180 | ||||
| Sharpe ratio (Glass type estimate) | 0.472 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.461 | ||||
| df | 32.000 | ||||
| t | 0.784 | ||||
| p | 0.220 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.719 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.656 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.726 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.649 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.630 | ||||
| Upside Potential Ratio | 4.992 | ||||
| Upside part of mean | 0.162 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.176 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.533 | ||||
| Mean of criterion | 0.085 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.180 | ||||
| Covariance | -0.008 | ||||
| r | -0.183 | ||||
| b (slope, estimate of beta) | -0.129 | ||||
| a (intercept, estimate of alpha) | 0.154 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 31.000 | ||||
| t(b) | -1.036 | ||||
| p(b) | 0.846 | ||||
| t(a) | 1.209 | ||||
| p(a) | 0.118 | ||||
| Lowerbound of 95% confidence interval for beta | -0.382 | ||||
| Upperbound of 95% confidence interval for beta | 0.124 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | 0.413 | ||||
| Treynor index (mean / b) | -0.662 | ||||
| Jensen alpha (a) | 0.154 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.095 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.978 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.276 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.064 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.121 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.152 | ||||
| Mean of outliers high | 1.102 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.139 | ||||
| VaR(95%) (moments method) | 0.012 | ||||
| Expected Shortfall (moments method) | 0.015 | ||||
| Extreme Value Index (regression method) | -0.455 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.043 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.064 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.064 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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) | 0.155 | ||||
| Compounded annual return (geometric extrapolation) | 0.138 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.142 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.142 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.448 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.092 | ||||
| SD | 0.120 | ||||
| Sharpe ratio (Glass type estimate) | 0.763 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.762 | ||||
| df | 722.000 | ||||
| t | 1.268 | ||||
| p | 0.103 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.418 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.943 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.418 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.943 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.521 | ||||
| Upside Potential Ratio | 5.095 | ||||
| Upside part of mean | 0.308 | ||||
| Downside part of mean | -0.216 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 123.000 | ||||
| N negative terms | 600.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 723.000 | ||||
| Mean of predictor | 0.640 | ||||
| Mean of criterion | 0.092 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.120 | ||||
| Covariance | -0.001 | ||||
| r | -0.015 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | 0.095 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 721.000 | ||||
| t(b) | -0.399 | ||||
| p(b) | 0.655 | ||||
| t(a) | 1.304 | ||||
| p(a) | 0.096 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.239 | ||||
| Treynor index (mean / b) | -17.607 | ||||
| Jensen alpha (a) | 0.095 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.085 | ||||
| SD | 0.119 | ||||
| Sharpe ratio (Glass type estimate) | 0.712 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.711 | ||||
| df | 722.000 | ||||
| t | 1.183 | ||||
| p | 0.119 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.469 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.892 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.469 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.892 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.370 | ||||
| Upside Potential Ratio | 4.891 | ||||
| Upside part of mean | 0.303 | ||||
| Downside part of mean | -0.218 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 123.000 | ||||
| N negative terms | 600.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 723.000 | ||||
| Mean of predictor | 0.580 | ||||
| Mean of criterion | 0.085 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.119 | ||||
| Covariance | -0.001 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | 0.088 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 721.000 | ||||
| t(b) | -0.380 | ||||
| p(b) | 0.648 | ||||
| t(a) | 1.215 | ||||
| p(a) | 0.112 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.054 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | -17.334 | ||||
| Jensen alpha (a) | 0.088 | ||||
| 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 | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 723.000 | ||||
| Minimum | 0.933 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.067 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 151.000 | ||||
| Percentage of outliers low | 0.209 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 135.000 | ||||
| Percentage of outliers high | 0.187 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.712 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.632 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.090 | ||||
| Maximum | 0.098 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.063 | ||||
| Mean of quarter 3 | 0.090 | ||||
| Mean of quarter 4 | 0.098 | ||||
| Inter Quartile Range | 0.067 | ||||
| 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) | 0.155 | ||||
| Compounded annual return (geometric extrapolation) | 0.137 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.398 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.398 | ||||
| Compounded annual return / Expected Shortfall lognormal | 9.327 | ||||
| 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 | 1.178 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.510 | ||||
| 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 | 1.046 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.514 | ||||
| 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) | -8730442358005852.000 | ||||
| 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) | 1275992656742059751325401585025024.000 | ||||
| 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 | ||||