Advanced Statistics: MultiTrader
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 | -0.014 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | -0.166 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.164 | ||||
| df | 60.000 | ||||
| t | -0.374 | ||||
| p | 0.645 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.035 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.034 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.706 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.249 | ||||
| Upside Potential Ratio | 1.785 | ||||
| Upside part of mean | 0.103 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.058 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.403 | ||||
| Mean of criterion | -0.014 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | -0.000 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.012 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.120 | ||||
| p(b) | 0.548 | ||||
| t(a) | -0.276 | ||||
| p(a) | 0.608 | ||||
| Lowerbound of 95% confidence interval for beta | -0.103 | ||||
| Upperbound of 95% confidence interval for beta | 0.092 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.075 | ||||
| Treynor index (mean / b) | 2.452 | ||||
| Jensen alpha (a) | -0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.086 | ||||
| Sharpe ratio (Glass type estimate) | -0.210 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.207 | ||||
| df | 60.000 | ||||
| t | -0.472 | ||||
| p | 0.681 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.079 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.661 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.077 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.663 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.306 | ||||
| Upside Potential Ratio | 1.717 | ||||
| Upside part of mean | 0.101 | ||||
| Downside part of mean | -0.119 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.059 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.371 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.086 | ||||
| Covariance | -0.000 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.133 | ||||
| p(b) | 0.553 | ||||
| t(a) | -0.365 | ||||
| p(a) | 0.642 | ||||
| Lowerbound of 95% confidence interval for beta | -0.106 | ||||
| Upperbound of 95% confidence interval for beta | 0.093 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.101 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | 2.715 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 1.100 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.016 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.016 | ||||
| Mean of outliers high | 1.100 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.304 | ||||
| VaR(95%) (moments method) | 0.028 | ||||
| Expected Shortfall (moments method) | 0.044 | ||||
| Extreme Value Index (regression method) | 0.418 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | 0.040 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.048 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.108 | ||||
| Maximum | 0.134 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.083 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.134 | ||||
| Inter Quartile Range | 0.060 | ||||
| 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) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.197 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.197 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.517 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.000 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | -0.001 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.001 | ||||
| df | 1333.000 | ||||
| t | -0.003 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.870 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.867 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.870 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.867 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.002 | ||||
| Upside Potential Ratio | 5.027 | ||||
| Upside part of mean | 0.675 | ||||
| Downside part of mean | -0.675 | ||||
| Upside SD | 0.129 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 643.000 | ||||
| N negative terms | 691.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1334.000 | ||||
| Mean of predictor | 0.428 | ||||
| Mean of criterion | -0.000 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | 0.017 | ||||
| r | 0.293 | ||||
| b (slope, estimate of beta) | 0.172 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 1332.000 | ||||
| t(b) | 11.189 | ||||
| p(b) | 0.353 | ||||
| t(a) | -0.931 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | 0.142 | ||||
| Upperbound of 95% confidence interval for beta | 0.202 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.229 | ||||
| Upperbound of 95% confidence interval for alpha | 0.082 | ||||
| Treynor index (mean / b) | -0.001 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.190 | ||||
| Sharpe ratio (Glass type estimate) | -0.095 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.095 | ||||
| df | 1333.000 | ||||
| t | -0.214 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.963 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.774 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.963 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.774 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.126 | ||||
| Upside Potential Ratio | 4.661 | ||||
| Upside part of mean | 0.667 | ||||
| Downside part of mean | -0.685 | ||||
| Upside SD | 0.124 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 643.000 | ||||
| N negative terms | 691.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1334.000 | ||||
| Mean of predictor | 0.377 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 0.190 | ||||
| Covariance | 0.018 | ||||
| r | 0.293 | ||||
| b (slope, estimate of beta) | 0.175 | ||||
| a (intercept, estimate of alpha) | -0.084 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 1332.000 | ||||
| t(b) | 11.200 | ||||
| p(b) | 0.353 | ||||
| t(a) | -1.038 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | 0.144 | ||||
| Upperbound of 95% confidence interval for beta | 0.205 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.242 | ||||
| Upperbound of 95% confidence interval for alpha | 0.074 | ||||
| Treynor index (mean / b) | -0.103 | ||||
| Jensen alpha (a) | -0.084 | ||||
| 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%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1334.000 | ||||
| Minimum | 0.798 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.136 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 36.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.024 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.468 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| Extreme Value Index (regression method) | 0.447 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 25.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.049 | ||||
| Maximum | 0.202 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.035 | ||||
| Mean of quarter 4 | 0.117 | ||||
| Inter Quartile Range | 0.041 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 0.178 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.159 | ||||
| VaR(95%) (moments method) | 0.110 | ||||
| Expected Shortfall (moments method) | 0.116 | ||||
| Extreme Value Index (regression method) | -0.196 | ||||
| VaR(95%) (regression method) | 0.104 | ||||
| Expected Shortfall (regression method) | 0.127 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.130 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.226 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.101 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.010 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.164 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.163 | ||||
| df | 130.000 | ||||
| t | -0.116 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.936 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.608 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.935 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.609 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.223 | ||||
| Upside Potential Ratio | 6.600 | ||||
| Upside part of mean | 0.309 | ||||
| Downside part of mean | -0.319 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 84.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.088 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.348 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | 0.010 | ||||
| r | 0.435 | ||||
| b (slope, estimate of beta) | 0.079 | ||||
| a (intercept, estimate of alpha) | -0.097 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.482 | ||||
| p(b) | 0.232 | ||||
| t(a) | -1.168 | ||||
| p(a) | 0.565 | ||||
| Lowerbound of 95% confidence interval for beta | 0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.260 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | -0.131 | ||||
| Jensen alpha (a) | -0.097 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.012 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -0.195 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.194 | ||||
| df | 130.000 | ||||
| t | -0.138 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.967 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.577 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.966 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.578 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.264 | ||||
| Upside Potential Ratio | 6.532 | ||||
| Upside part of mean | 0.308 | ||||
| Downside part of mean | -0.320 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 84.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.025 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | 0.010 | ||||
| r | 0.436 | ||||
| b (slope, estimate of beta) | 0.079 | ||||
| a (intercept, estimate of alpha) | -0.094 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.496 | ||||
| p(b) | 0.232 | ||||
| t(a) | -1.134 | ||||
| p(a) | 0.563 | ||||
| Lowerbound of 95% confidence interval for beta | 0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.257 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | -0.156 | ||||
| Jensen alpha (a) | -0.094 | ||||
| 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%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.976 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.013 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.247 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.017 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.006 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.008 | ||||
| Maximum | 0.043 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.005 | ||||
| Mean of quarter 4 | 0.023 | ||||
| Inter Quartile Range | 0.006 | ||||
| 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 | 0.043 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.028 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.031 | ||||
| Extreme Value Index (regression method) | 1.627 | ||||
| VaR(95%) (regression method) | 0.047 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.032 | ||||
| Compounded annual return (geometric extrapolation) | 0.032 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.750 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.426 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.954 | ||||