Advanced Statistics: new
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 | -0.252 | ||||
| SD | 0.312 | ||||
| Sharpe ratio (Glass type estimate) | -0.809 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.801 | ||||
| df | 74.000 | ||||
| t | -2.023 | ||||
| p | 0.977 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.601 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.012 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.595 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.006 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.813 | ||||
| Upside Potential Ratio | 0.189 | ||||
| Upside part of mean | 0.059 | ||||
| Downside part of mean | -0.311 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.310 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.200 | ||||
| Mean of criterion | -0.252 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.312 | ||||
| Covariance | 0.013 | ||||
| r | 0.139 | ||||
| b (slope, estimate of beta) | 0.145 | ||||
| a (intercept, estimate of alpha) | -0.281 | ||||
| Mean Square Error | 0.097 | ||||
| DF error | 73.000 | ||||
| t(b) | 1.199 | ||||
| p(b) | 0.117 | ||||
| t(a) | -2.220 | ||||
| p(a) | 0.985 | ||||
| Lowerbound of 95% confidence interval for beta | -0.096 | ||||
| Upperbound of 95% confidence interval for beta | 0.386 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.534 | ||||
| Upperbound of 95% confidence interval for alpha | -0.029 | ||||
| Treynor index (mean / b) | -1.741 | ||||
| Jensen alpha (a) | -0.281 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.331 | ||||
| SD | 0.445 | ||||
| Sharpe ratio (Glass type estimate) | -0.744 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.737 | ||||
| df | 74.000 | ||||
| t | -1.861 | ||||
| p | 0.967 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.535 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.051 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.530 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.056 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.740 | ||||
| Upside Potential Ratio | 0.125 | ||||
| Upside part of mean | 0.056 | ||||
| Downside part of mean | -0.387 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.447 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.155 | ||||
| Mean of criterion | -0.331 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.445 | ||||
| Covariance | 0.016 | ||||
| r | 0.120 | ||||
| b (slope, estimate of beta) | 0.180 | ||||
| a (intercept, estimate of alpha) | -0.359 | ||||
| Mean Square Error | 0.198 | ||||
| DF error | 73.000 | ||||
| t(b) | 1.031 | ||||
| p(b) | 0.153 | ||||
| t(a) | -1.996 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.168 | ||||
| Upperbound of 95% confidence interval for beta | 0.527 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.717 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | -1.841 | ||||
| Jensen alpha (a) | -0.359 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.212 | ||||
| Expected Shortfall on VaR | 0.253 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.177 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 75.000 | ||||
| Minimum | 0.370 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.151 | ||||
| Mean of quarter 1 | 0.910 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.021 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.147 | ||||
| Mean of outliers low | 0.845 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 1.037 | ||||
| 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) | 0.390 | ||||
| VaR(95%) (regression method) | 0.124 | ||||
| Expected Shortfall (regression method) | 0.343 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.834 | ||||
| Quartile 1 | 0.834 | ||||
| Median | 0.834 | ||||
| Quartile 3 | 0.834 | ||||
| Maximum | 0.834 | ||||
| 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) | -0.133 | ||||
| Compounded annual return (geometric extrapolation) | -0.250 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.299 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.987 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.169 | ||||
| SD | 1.169 | ||||
| Sharpe ratio (Glass type estimate) | 0.145 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.145 | ||||
| df | 1643.000 | ||||
| t | 0.362 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.638 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.927 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.638 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.927 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.323 | ||||
| Upside Potential Ratio | 2.839 | ||||
| Upside part of mean | 1.484 | ||||
| Downside part of mean | -1.315 | ||||
| Upside SD | 1.045 | ||||
| Downside SD | 0.523 | ||||
| N nonnegative terms | 213.000 | ||||
| N negative terms | 1431.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1644.000 | ||||
| Mean of predictor | 0.348 | ||||
| Mean of criterion | 0.169 | ||||
| SD of predictor | 0.531 | ||||
| SD of criterion | 1.169 | ||||
| Covariance | 0.052 | ||||
| r | 0.083 | ||||
| b (slope, estimate of beta) | 0.183 | ||||
| a (intercept, estimate of alpha) | 0.105 | ||||
| Mean Square Error | 1.357 | ||||
| DF error | 1642.000 | ||||
| t(b) | 3.390 | ||||
| p(b) | 0.458 | ||||
| t(a) | 0.226 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.290 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.808 | ||||
| Upperbound of 95% confidence interval for alpha | 1.018 | ||||
| Treynor index (mean / b) | 0.921 | ||||
| Jensen alpha (a) | 0.105 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.330 | ||||
| SD | 0.977 | ||||
| Sharpe ratio (Glass type estimate) | -0.338 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.338 | ||||
| df | 1643.000 | ||||
| t | -0.846 | ||||
| p | 0.513 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.120 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.445 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.120 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.445 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.455 | ||||
| Upside Potential Ratio | 1.647 | ||||
| Upside part of mean | 1.193 | ||||
| Downside part of mean | -1.523 | ||||
| Upside SD | 0.655 | ||||
| Downside SD | 0.724 | ||||
| N nonnegative terms | 213.000 | ||||
| N negative terms | 1431.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1644.000 | ||||
| Mean of predictor | 0.209 | ||||
| Mean of criterion | -0.330 | ||||
| SD of predictor | 0.526 | ||||
| SD of criterion | 0.977 | ||||
| Covariance | 0.051 | ||||
| r | 0.100 | ||||
| b (slope, estimate of beta) | 0.186 | ||||
| a (intercept, estimate of alpha) | -0.369 | ||||
| Mean Square Error | 0.945 | ||||
| DF error | 1642.000 | ||||
| t(b) | 4.079 | ||||
| p(b) | 0.450 | ||||
| t(a) | -0.950 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | 0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.275 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.393 | ||||
| Treynor index (mean / b) | -1.775 | ||||
| Jensen alpha (a) | -0.369 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.096 | ||||
| Expected Shortfall on VaR | 0.118 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1644.000 | ||||
| Minimum | 0.370 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.701 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 216.000 | ||||
| Percentage of outliers low | 0.131 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 214.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.953 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.140 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.526 | ||||
| Quartile 1 | 0.603 | ||||
| Median | 0.681 | ||||
| Quartile 3 | 0.758 | ||||
| Maximum | 0.835 | ||||
| Mean of quarter 1 | 0.526 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.835 | ||||
| Inter Quartile Range | 0.154 | ||||
| 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) | -0.133 | ||||
| Compounded annual return (geometric extrapolation) | -0.249 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.298 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.298 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.109 | ||||
| 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 | 2.098 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.599 | ||||
| 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 | 1.911 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.602 | ||||
| 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) | -8634085258767860.000 | ||||
| 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) | -2631386495751297193237325346242560.000 | ||||
| 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 | ||||