Advanced Statistics: Apeiron Global
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 | 0.016 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | 0.231 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.230 | ||||
| df | 92.000 | ||||
| t | 0.644 | ||||
| p | 0.261 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.474 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.936 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.475 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.934 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.489 | ||||
| Upside Potential Ratio | 2.281 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.058 | ||||
| Upside SD | 0.060 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.212 | ||||
| Mean of criterion | 0.016 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.000 | ||||
| r | 0.004 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | 0.016 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 91.000 | ||||
| t(b) | 0.037 | ||||
| p(b) | 0.485 | ||||
| t(a) | 0.604 | ||||
| p(a) | 0.274 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | 12.457 | ||||
| Jensen alpha (a) | 0.016 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.066 | ||||
| Sharpe ratio (Glass type estimate) | 0.203 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.202 | ||||
| df | 92.000 | ||||
| t | 0.566 | ||||
| p | 0.286 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.502 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.908 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.503 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.906 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.413 | ||||
| Upside Potential Ratio | 2.192 | ||||
| Upside part of mean | 0.072 | ||||
| Downside part of mean | -0.058 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.188 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.207 | ||||
| SD of criterion | 0.066 | ||||
| Covariance | 0.000 | ||||
| r | 0.006 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 91.000 | ||||
| t(b) | 0.059 | ||||
| p(b) | 0.477 | ||||
| t(a) | 0.530 | ||||
| p(a) | 0.299 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 0.062 | ||||
| Treynor index (mean / b) | 6.823 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 93.000 | ||||
| Minimum | 0.950 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.120 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.008 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.654 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.108 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.022 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.024 | ||||
| Maximum | 0.061 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.017 | ||||
| Mean of quarter 4 | 0.046 | ||||
| Inter Quartile Range | 0.024 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.061 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -60.553 | ||||
| VaR(95%) (moments method) | 0.046 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.729 | ||||
| VaR(95%) (regression method) | 0.086 | ||||
| Expected Shortfall (regression method) | 0.086 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.971 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.281 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.572 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | 0.246 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.246 | ||||
| df | 2050.000 | ||||
| t | 0.689 | ||||
| p | 0.245 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.454 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.947 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.454 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.947 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.409 | ||||
| Upside Potential Ratio | 5.072 | ||||
| Upside part of mean | 0.183 | ||||
| Downside part of mean | -0.168 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 364.000 | ||||
| N negative terms | 1687.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2051.000 | ||||
| Mean of predictor | 0.230 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 2049.000 | ||||
| t(b) | 0.094 | ||||
| p(b) | 0.462 | ||||
| t(a) | 0.683 | ||||
| p(a) | 0.247 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.027 | ||||
| Upperbound of 95% confidence interval for alpha | 0.057 | ||||
| Treynor index (mean / b) | 29.578 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | 0.217 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.217 | ||||
| df | 2050.000 | ||||
| t | 0.608 | ||||
| p | 0.272 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.483 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.918 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.483 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.918 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.356 | ||||
| Upside Potential Ratio | 4.999 | ||||
| Upside part of mean | 0.182 | ||||
| Downside part of mean | -0.169 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 364.000 | ||||
| N negative terms | 1687.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2051.000 | ||||
| Mean of predictor | 0.198 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 2049.000 | ||||
| t(b) | 0.069 | ||||
| p(b) | 0.473 | ||||
| t(a) | 0.604 | ||||
| p(a) | 0.273 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | 35.814 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2051.000 | ||||
| Minimum | 0.968 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.036 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 371.000 | ||||
| Percentage of outliers low | 0.181 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 396.000 | ||||
| Percentage of outliers high | 0.193 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.686 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.380 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.011 | ||||
| Maximum | 0.069 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.008 | ||||
| Mean of quarter 4 | 0.035 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.119 | ||||
| Mean of outliers high | 0.056 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.099 | ||||
| VaR(95%) (moments method) | 0.031 | ||||
| Expected Shortfall (moments method) | 0.045 | ||||
| Extreme Value Index (regression method) | -0.339 | ||||
| VaR(95%) (regression method) | 0.034 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.855 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.685 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.802 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.001 | ||||
| Sharpe ratio (Glass type estimate) | -70.593 | ||||
| Sharpe ratio (Hedges UMVUE) | -70.185 | ||||
| df | 130.000 | ||||
| t | -49.917 | ||||
| p | 0.987 | ||||
| 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) | -79.155 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -61.215 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -15.780 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.043 | ||||
| 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 | 1.086 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.001 | ||||
| Covariance | 0.000 | ||||
| r | 0.043 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.490 | ||||
| p(b) | 0.473 | ||||
| t(a) | -48.880 | ||||
| p(a) | 0.998 | ||||
| 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 | -0.045 | ||||
| Upperbound of 95% confidence interval for alpha | -0.041 | ||||
| Treynor index (mean / b) | -544.971 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.001 | ||||
| Sharpe ratio (Glass type estimate) | -70.587 | ||||
| Sharpe ratio (Hedges UMVUE) | -70.179 | ||||
| df | 130.000 | ||||
| t | -49.913 | ||||
| p | 0.987 | ||||
| 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) | -79.149 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -61.210 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -15.780 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.043 | ||||
| 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 | 1.029 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.001 | ||||
| Covariance | 0.000 | ||||
| r | 0.036 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.407 | ||||
| p(b) | 0.477 | ||||
| t(a) | -48.942 | ||||
| p(a) | 0.998 | ||||
| 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 | -0.045 | ||||
| Upperbound of 95% confidence interval for alpha | -0.041 | ||||
| Treynor index (mean / b) | -656.896 | ||||
| Jensen alpha (a) | -0.043 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 1.000 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.000 | ||||
| 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 | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.000 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 0.000 | ||||
| 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) | 0.001 | ||||
| Compounded annual return (geometric extrapolation) | 0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.976 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.521 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.033 | ||||