Advanced Statistics: No fuss
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 | 0.072 | ||||
| SD | 0.296 | ||||
| Sharpe ratio (Glass type estimate) | 0.243 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.241 | ||||
| df | 72.000 | ||||
| t | 0.600 | ||||
| p | 0.275 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.553 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.038 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.555 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.036 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.752 | ||||
| Upside Potential Ratio | 2.025 | ||||
| Upside part of mean | 0.194 | ||||
| Downside part of mean | -0.122 | ||||
| Upside SD | 0.279 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.146 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 0.296 | ||||
| Covariance | 0.009 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 0.142 | ||||
| a (intercept, estimate of alpha) | 0.051 | ||||
| Mean Square Error | 0.087 | ||||
| DF error | 71.000 | ||||
| t(b) | 1.046 | ||||
| p(b) | 0.149 | ||||
| t(a) | 0.421 | ||||
| p(a) | 0.338 | ||||
| Lowerbound of 95% confidence interval for beta | -0.129 | ||||
| Upperbound of 95% confidence interval for beta | 0.413 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.191 | ||||
| Upperbound of 95% confidence interval for alpha | 0.294 | ||||
| Treynor index (mean / b) | 0.506 | ||||
| Jensen alpha (a) | 0.051 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.037 | ||||
| SD | 0.252 | ||||
| Sharpe ratio (Glass type estimate) | 0.147 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.146 | ||||
| df | 72.000 | ||||
| t | 0.363 | ||||
| p | 0.359 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.648 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.942 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.649 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.941 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.362 | ||||
| Upside Potential Ratio | 1.600 | ||||
| Upside part of mean | 0.163 | ||||
| Downside part of mean | -0.126 | ||||
| Upside SD | 0.228 | ||||
| Downside SD | 0.102 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.113 | ||||
| Mean of criterion | 0.037 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 0.252 | ||||
| Covariance | 0.010 | ||||
| r | 0.162 | ||||
| b (slope, estimate of beta) | 0.159 | ||||
| a (intercept, estimate of alpha) | 0.019 | ||||
| Mean Square Error | 0.063 | ||||
| DF error | 71.000 | ||||
| t(b) | 1.380 | ||||
| p(b) | 0.086 | ||||
| t(a) | 0.186 | ||||
| p(a) | 0.426 | ||||
| Lowerbound of 95% confidence interval for beta | -0.071 | ||||
| Upperbound of 95% confidence interval for beta | 0.389 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | 0.223 | ||||
| Treynor index (mean / b) | 0.233 | ||||
| Jensen alpha (a) | 0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.110 | ||||
| Expected Shortfall on VaR | 0.136 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.831 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.485 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.067 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.137 | ||||
| Mean of outliers low | 0.950 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 1.121 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.444 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.047 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.098 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.076 | ||||
| Median | 0.149 | ||||
| Quartile 3 | 0.222 | ||||
| Maximum | 0.295 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.295 | ||||
| Inter Quartile Range | 0.146 | ||||
| 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) | 0.105 | ||||
| Compounded annual return (geometric extrapolation) | 0.084 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.286 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.286 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.620 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.253 | ||||
| SD | 0.742 | ||||
| Sharpe ratio (Glass type estimate) | 0.342 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.341 | ||||
| df | 1613.000 | ||||
| t | 0.848 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.448 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.131 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.448 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.131 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.722 | ||||
| Upside Potential Ratio | 3.533 | ||||
| Upside part of mean | 1.240 | ||||
| Downside part of mean | -0.986 | ||||
| Upside SD | 0.654 | ||||
| Downside SD | 0.351 | ||||
| N nonnegative terms | 146.000 | ||||
| N negative terms | 1468.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1614.000 | ||||
| Mean of predictor | 0.350 | ||||
| Mean of criterion | 0.253 | ||||
| SD of predictor | 0.595 | ||||
| SD of criterion | 0.742 | ||||
| Covariance | 0.076 | ||||
| r | 0.171 | ||||
| b (slope, estimate of beta) | 0.214 | ||||
| a (intercept, estimate of alpha) | 0.179 | ||||
| Mean Square Error | 0.535 | ||||
| DF error | 1612.000 | ||||
| t(b) | 6.983 | ||||
| p(b) | 0.414 | ||||
| t(a) | 0.606 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | 0.154 | ||||
| Upperbound of 95% confidence interval for beta | 0.274 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.400 | ||||
| Upperbound of 95% confidence interval for alpha | 0.757 | ||||
| Treynor index (mean / b) | 1.185 | ||||
| Jensen alpha (a) | 0.179 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.036 | ||||
| SD | 0.646 | ||||
| Sharpe ratio (Glass type estimate) | 0.056 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.056 | ||||
| df | 1613.000 | ||||
| t | 0.138 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.734 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.845 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.734 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.845 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.080 | ||||
| Upside Potential Ratio | 2.459 | ||||
| Upside part of mean | 1.107 | ||||
| Downside part of mean | -1.071 | ||||
| Upside SD | 0.463 | ||||
| Downside SD | 0.450 | ||||
| N nonnegative terms | 146.000 | ||||
| N negative terms | 1468.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1614.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | 0.036 | ||||
| SD of predictor | 0.585 | ||||
| SD of criterion | 0.646 | ||||
| Covariance | 0.074 | ||||
| r | 0.196 | ||||
| b (slope, estimate of beta) | 0.216 | ||||
| a (intercept, estimate of alpha) | -0.002 | ||||
| Mean Square Error | 0.401 | ||||
| DF error | 1612.000 | ||||
| t(b) | 8.005 | ||||
| p(b) | 0.402 | ||||
| t(a) | -0.010 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.163 | ||||
| Upperbound of 95% confidence interval for beta | 0.269 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.503 | ||||
| Upperbound of 95% confidence interval for alpha | 0.498 | ||||
| Treynor index (mean / b) | 0.167 | ||||
| Jensen alpha (a) | -0.002 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1614.000 | ||||
| Minimum | 0.413 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.422 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 171.000 | ||||
| Percentage of outliers low | 0.106 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 180.000 | ||||
| Percentage of outliers high | 0.112 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.159 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.203 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.037 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.341 | ||||
| Quartile 1 | 0.408 | ||||
| Median | 0.474 | ||||
| Quartile 3 | 0.541 | ||||
| Maximum | 0.608 | ||||
| Mean of quarter 1 | 0.341 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.608 | ||||
| Inter Quartile Range | 0.134 | ||||
| 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) | 0.103 | ||||
| Compounded annual return (geometric extrapolation) | 0.083 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.137 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.137 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.058 | ||||
| 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 | 1.724 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.672 | ||||
| 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 | 1.500 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.662 | ||||
| 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) | -8714181173889449.000 | ||||
| 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) | 397499964589843326216676852105216.000 | ||||
| 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 | ||||