Advanced Statistics: Gnome
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 | 0.082 | ||||
| SD | 0.135 | ||||
| Sharpe ratio (Glass type estimate) | 0.611 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.601 | ||||
| df | 47.000 | ||||
| t | 1.223 | ||||
| p | 0.114 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.380 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.596 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.386 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.589 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.314 | ||||
| Upside Potential Ratio | 3.066 | ||||
| Upside part of mean | 0.192 | ||||
| Downside part of mean | -0.110 | ||||
| Upside SD | 0.120 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 20.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.429 | ||||
| Mean of criterion | 0.082 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.135 | ||||
| Covariance | 0.011 | ||||
| r | 0.371 | ||||
| b (slope, estimate of beta) | 0.224 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 46.000 | ||||
| t(b) | 2.711 | ||||
| p(b) | 0.005 | ||||
| t(a) | -0.188 | ||||
| p(a) | 0.574 | ||||
| Lowerbound of 95% confidence interval for beta | 0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.390 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.160 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | 0.368 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.074 | ||||
| SD | 0.129 | ||||
| Sharpe ratio (Glass type estimate) | 0.571 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.562 | ||||
| df | 47.000 | ||||
| t | 1.143 | ||||
| p | 0.129 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.418 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.555 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.424 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.549 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.148 | ||||
| Upside Potential Ratio | 2.889 | ||||
| Upside part of mean | 0.185 | ||||
| Downside part of mean | -0.112 | ||||
| Upside SD | 0.112 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 20.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.398 | ||||
| Mean of criterion | 0.074 | ||||
| SD of predictor | 0.210 | ||||
| SD of criterion | 0.129 | ||||
| Covariance | 0.009 | ||||
| r | 0.334 | ||||
| b (slope, estimate of beta) | 0.204 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 46.000 | ||||
| t(b) | 2.400 | ||||
| p(b) | 0.010 | ||||
| t(a) | -0.109 | ||||
| p(a) | 0.543 | ||||
| Lowerbound of 95% confidence interval for beta | 0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.375 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.149 | ||||
| Upperbound of 95% confidence interval for alpha | 0.133 | ||||
| Treynor index (mean / b) | 0.361 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.932 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.009 | ||||
| Quartile 3 | 1.025 | ||||
| Maximum | 1.199 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.017 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.021 | ||||
| Mean of outliers low | 0.932 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.021 | ||||
| Mean of outliers high | 1.199 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.353 | ||||
| VaR(95%) (moments method) | 0.030 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | 0.226 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.039 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.022 | ||||
| Quartile 3 | 0.061 | ||||
| Maximum | 0.089 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.018 | ||||
| Mean of quarter 3 | 0.054 | ||||
| Mean of quarter 4 | 0.079 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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) | 0.150 | ||||
| Compounded annual return (geometric extrapolation) | 0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.395 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.588 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.835 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.081 | ||||
| SD | 0.137 | ||||
| Sharpe ratio (Glass type estimate) | 0.588 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.588 | ||||
| df | 1053.000 | ||||
| t | 1.180 | ||||
| p | 0.477 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.390 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.566 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.390 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.565 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.889 | ||||
| Upside Potential Ratio | 7.497 | ||||
| Upside part of mean | 0.680 | ||||
| Downside part of mean | -0.599 | ||||
| Upside SD | 0.103 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 531.000 | ||||
| N negative terms | 523.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1054.000 | ||||
| Mean of predictor | 0.463 | ||||
| Mean of criterion | 0.081 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.137 | ||||
| Covariance | 0.006 | ||||
| r | 0.159 | ||||
| b (slope, estimate of beta) | 0.075 | ||||
| a (intercept, estimate of alpha) | 0.046 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 1052.000 | ||||
| t(b) | 5.225 | ||||
| p(b) | 0.420 | ||||
| t(a) | 0.680 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | 0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.103 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | 0.179 | ||||
| Treynor index (mean / b) | 1.082 | ||||
| Jensen alpha (a) | 0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.071 | ||||
| SD | 0.137 | ||||
| Sharpe ratio (Glass type estimate) | 0.521 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.521 | ||||
| df | 1053.000 | ||||
| t | 1.045 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.456 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.498 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.457 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.498 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.769 | ||||
| Upside Potential Ratio | 7.283 | ||||
| Upside part of mean | 0.675 | ||||
| Downside part of mean | -0.604 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 531.000 | ||||
| N negative terms | 523.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1054.000 | ||||
| Mean of predictor | 0.420 | ||||
| Mean of criterion | 0.071 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.137 | ||||
| Covariance | 0.006 | ||||
| r | 0.159 | ||||
| b (slope, estimate of beta) | 0.074 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 1052.000 | ||||
| t(b) | 5.237 | ||||
| p(b) | 0.420 | ||||
| t(a) | 0.596 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | 0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.173 | ||||
| Treynor index (mean / b) | 0.966 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1054.000 | ||||
| Minimum | 0.903 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.110 | ||||
| Mean of quarter 1 | 0.992 | ||||
| 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 | 32.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 42.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.314 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.013 | ||||
| Extreme Value Index (regression method) | 0.245 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.153 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.015 | ||||
| Mean of quarter 4 | 0.056 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 0.129 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.676 | ||||
| VaR(95%) (moments method) | 0.069 | ||||
| Expected Shortfall (moments method) | 0.201 | ||||
| Extreme Value Index (regression method) | 2.979 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.147 | ||||
| Compounded annual return (geometric extrapolation) | 0.122 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.800 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.174 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.185 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.308 | ||||
| SD | 0.297 | ||||
| Sharpe ratio (Glass type estimate) | 1.038 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.032 | ||||
| df | 130.000 | ||||
| t | 0.734 | ||||
| p | 0.468 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.738 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.811 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.742 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.807 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.588 | ||||
| Upside Potential Ratio | 8.058 | ||||
| Upside part of mean | 1.565 | ||||
| Downside part of mean | -1.257 | ||||
| Upside SD | 0.224 | ||||
| Downside SD | 0.194 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.048 | ||||
| Mean of criterion | 0.308 | ||||
| SD of predictor | 0.503 | ||||
| SD of criterion | 0.297 | ||||
| Covariance | 0.031 | ||||
| r | 0.208 | ||||
| b (slope, estimate of beta) | 0.123 | ||||
| a (intercept, estimate of alpha) | 0.179 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.418 | ||||
| p(b) | 0.368 | ||||
| t(a) | 0.431 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | 0.022 | ||||
| Upperbound of 95% confidence interval for beta | 0.224 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.643 | ||||
| Upperbound of 95% confidence interval for alpha | 1.002 | ||||
| Treynor index (mean / b) | 2.506 | ||||
| Jensen alpha (a) | 0.179 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.265 | ||||
| SD | 0.296 | ||||
| Sharpe ratio (Glass type estimate) | 0.894 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.889 | ||||
| df | 130.000 | ||||
| t | 0.632 | ||||
| p | 0.472 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.881 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.667 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.885 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.663 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.320 | ||||
| Upside Potential Ratio | 7.685 | ||||
| Upside part of mean | 1.541 | ||||
| Downside part of mean | -1.276 | ||||
| Upside SD | 0.217 | ||||
| Downside SD | 0.201 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.919 | ||||
| Mean of criterion | 0.265 | ||||
| SD of predictor | 0.507 | ||||
| SD of criterion | 0.296 | ||||
| Covariance | 0.032 | ||||
| r | 0.212 | ||||
| b (slope, estimate of beta) | 0.124 | ||||
| a (intercept, estimate of alpha) | 0.151 | ||||
| Mean Square Error | 0.084 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.465 | ||||
| p(b) | 0.366 | ||||
| t(a) | 0.365 | ||||
| p(a) | 0.480 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.223 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.667 | ||||
| Upperbound of 95% confidence interval for alpha | 0.969 | ||||
| Treynor index (mean / b) | 2.139 | ||||
| Jensen alpha (a) | 0.151 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.903 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.110 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.055 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.422 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | 0.033 | ||||
| Extreme Value Index (regression method) | 0.325 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.094 | ||||
| Maximum | 0.129 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.065 | ||||
| Mean of quarter 4 | 0.117 | ||||
| Inter Quartile Range | 0.086 | ||||
| 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) | 0.334 | ||||
| Compounded annual return (geometric extrapolation) | 0.362 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.797 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.103 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.041 | ||||