Advanced Statistics: Isonomy Turbo
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 | -0.062 | ||||
| SD | 0.176 | ||||
| Sharpe ratio (Glass type estimate) | -0.353 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.350 | ||||
| df | 97.000 | ||||
| t | -1.007 | ||||
| p | 0.842 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.039 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.336 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.037 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.338 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.473 | ||||
| Upside Potential Ratio | 1.040 | ||||
| Upside part of mean | 0.137 | ||||
| Downside part of mean | -0.199 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.132 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.205 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.187 | ||||
| SD of criterion | 0.176 | ||||
| Covariance | -0.004 | ||||
| r | -0.123 | ||||
| b (slope, estimate of beta) | -0.117 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 96.000 | ||||
| t(b) | -1.219 | ||||
| p(b) | 0.887 | ||||
| t(a) | -0.592 | ||||
| p(a) | 0.722 | ||||
| Lowerbound of 95% confidence interval for beta | -0.307 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.166 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | 0.533 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -0.436 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.433 | ||||
| df | 97.000 | ||||
| t | -1.246 | ||||
| p | 0.892 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.123 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.254 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.121 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.256 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.549 | ||||
| Upside Potential Ratio | 0.919 | ||||
| Upside part of mean | 0.130 | ||||
| Downside part of mean | -0.208 | ||||
| Upside SD | 0.109 | ||||
| Downside SD | 0.141 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.186 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.186 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.004 | ||||
| r | -0.118 | ||||
| b (slope, estimate of beta) | -0.113 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 96.000 | ||||
| t(b) | -1.161 | ||||
| p(b) | 0.876 | ||||
| t(a) | -0.875 | ||||
| p(a) | 0.808 | ||||
| Lowerbound of 95% confidence interval for beta | -0.306 | ||||
| Upperbound of 95% confidence interval for beta | 0.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | 0.072 | ||||
| Treynor index (mean / b) | 0.689 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.106 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 98.000 | ||||
| Minimum | 0.776 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.219 | ||||
| Mean of quarter 1 | 0.946 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.048 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 24.000 | ||||
| Percentage of outliers low | 0.245 | ||||
| Mean of outliers low | 0.944 | ||||
| Number of outliers high | 21.000 | ||||
| Percentage of outliers high | 0.214 | ||||
| Mean of outliers high | 1.057 | ||||
| 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) | 0.113 | ||||
| VaR(95%) (regression method) | 0.050 | ||||
| Expected Shortfall (regression method) | 0.088 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.026 | ||||
| Median | 0.048 | ||||
| Quartile 3 | 0.191 | ||||
| Maximum | 0.568 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.029 | ||||
| Mean of quarter 3 | 0.066 | ||||
| Mean of quarter 4 | 0.568 | ||||
| Inter Quartile Range | 0.166 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.568 | ||||
| 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) | -0.029 | ||||
| Compounded annual return (geometric extrapolation) | -0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.058 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.058 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.311 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.184 | ||||
| Sharpe ratio (Glass type estimate) | -0.329 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.329 | ||||
| df | 2142.000 | ||||
| t | -0.941 | ||||
| p | 0.827 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.014 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.356 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.014 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.356 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.441 | ||||
| Upside Potential Ratio | 4.447 | ||||
| Upside part of mean | 0.610 | ||||
| Downside part of mean | -0.671 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.137 | ||||
| N nonnegative terms | 480.000 | ||||
| N negative terms | 1663.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2143.000 | ||||
| Mean of predictor | 0.215 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.184 | ||||
| Covariance | -0.002 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 2141.000 | ||||
| t(b) | -2.090 | ||||
| p(b) | 0.982 | ||||
| t(a) | -0.827 | ||||
| p(a) | 0.796 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | -0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.179 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | 1.781 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | -0.417 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.417 | ||||
| df | 2142.000 | ||||
| t | -1.194 | ||||
| p | 0.884 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.103 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.268 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.103 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.268 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.545 | ||||
| Upside Potential Ratio | 4.233 | ||||
| Upside part of mean | 0.603 | ||||
| Downside part of mean | -0.680 | ||||
| Upside SD | 0.120 | ||||
| Downside SD | 0.142 | ||||
| N nonnegative terms | 480.000 | ||||
| N negative terms | 1663.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2143.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | -0.002 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 2141.000 | ||||
| t(b) | -2.058 | ||||
| p(b) | 0.980 | ||||
| t(a) | -1.098 | ||||
| p(a) | 0.864 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | -0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.199 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 2.318 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2143.000 | ||||
| Minimum | 0.824 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.106 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 478.000 | ||||
| Percentage of outliers low | 0.223 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 486.000 | ||||
| Percentage of outliers high | 0.227 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.072 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.129 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.016 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 49.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.033 | ||||
| Maximum | 0.587 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.103 | ||||
| Inter Quartile Range | 0.026 | ||||
| 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 | 0.061 | ||||
| Mean of outliers high | 0.269 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.793 | ||||
| VaR(95%) (moments method) | 0.105 | ||||
| Expected Shortfall (moments method) | 0.486 | ||||
| Extreme Value Index (regression method) | 1.388 | ||||
| VaR(95%) (regression method) | 0.089 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.029 | ||||
| Compounded annual return (geometric extrapolation) | -0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.056 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.322 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.394 | ||||
| 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 | 1.052 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.400 | ||||
| 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 | 0.969 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.403 | ||||
| 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) | -8703724208431632.000 | ||||
| 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) | 196933276143517515803047221002240.000 | ||||
| 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 | ||||