Advanced Statistics: Blog.fallondpicks.com
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 | -0.004 | ||||
| SD | 0.090 | ||||
| Sharpe ratio (Glass type estimate) | -0.039 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.039 | ||||
| df | 95.000 | ||||
| t | -0.111 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.732 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.654 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.732 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.654 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.062 | ||||
| Upside Potential Ratio | 1.170 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.056 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.167 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.090 | ||||
| Covariance | 0.013 | ||||
| r | 0.532 | ||||
| b (slope, estimate of beta) | 0.178 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 94.000 | ||||
| t(b) | 6.098 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.213 | ||||
| p(a) | 0.886 | ||||
| Lowerbound of 95% confidence interval for beta | 0.120 | ||||
| Upperbound of 95% confidence interval for beta | 0.236 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.021 | ||||
| Treynor index (mean / b) | -0.020 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.088 | ||||
| Sharpe ratio (Glass type estimate) | -0.084 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 95.000 | ||||
| t | -0.237 | ||||
| p | 0.593 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.777 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.610 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.776 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.610 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.125 | ||||
| Upside Potential Ratio | 1.073 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.059 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.131 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.088 | ||||
| Covariance | 0.012 | ||||
| r | 0.508 | ||||
| b (slope, estimate of beta) | 0.170 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 94.000 | ||||
| t(b) | 5.713 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.087 | ||||
| p(a) | 0.860 | ||||
| Lowerbound of 95% confidence interval for beta | 0.111 | ||||
| Upperbound of 95% confidence interval for beta | 0.229 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | 0.024 | ||||
| Treynor index (mean / b) | -0.043 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 96.000 | ||||
| Minimum | 0.876 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.174 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.955 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.156 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.747 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.033 | ||||
| Extreme Value Index (regression method) | 0.747 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.043 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.124 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.018 | ||||
| Mean of quarter 3 | 0.070 | ||||
| Mean of quarter 4 | 0.124 | ||||
| Inter Quartile Range | 0.067 | ||||
| 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) | 0.043 | ||||
| Compounded annual return (geometric extrapolation) | 0.037 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.300 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.300 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.723 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.050 | ||||
| SD | 0.207 | ||||
| Sharpe ratio (Glass type estimate) | 0.240 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.240 | ||||
| df | 2100.000 | ||||
| t | 0.680 | ||||
| p | 0.248 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.452 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.932 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.452 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.932 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.358 | ||||
| Upside Potential Ratio | 2.846 | ||||
| Upside part of mean | 0.396 | ||||
| Downside part of mean | -0.346 | ||||
| Upside SD | 0.154 | ||||
| Downside SD | 0.139 | ||||
| N nonnegative terms | 866.000 | ||||
| N negative terms | 1235.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2101.000 | ||||
| Mean of predictor | 0.284 | ||||
| Mean of criterion | 0.050 | ||||
| SD of predictor | 0.499 | ||||
| SD of criterion | 0.207 | ||||
| Covariance | 0.049 | ||||
| r | 0.473 | ||||
| b (slope, estimate of beta) | 0.197 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 2099.000 | ||||
| t(b) | 24.578 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.093 | ||||
| p(a) | 0.537 | ||||
| Lowerbound of 95% confidence interval for beta | 0.181 | ||||
| Upperbound of 95% confidence interval for beta | 0.212 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.133 | ||||
| Upperbound of 95% confidence interval for alpha | 0.121 | ||||
| Treynor index (mean / b) | 0.253 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.208 | ||||
| Sharpe ratio (Glass type estimate) | 0.136 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.136 | ||||
| df | 2100.000 | ||||
| t | 0.385 | ||||
| p | 0.350 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.556 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.828 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.556 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.828 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.189 | ||||
| Upside Potential Ratio | 2.580 | ||||
| Upside part of mean | 0.385 | ||||
| Downside part of mean | -0.357 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.149 | ||||
| N nonnegative terms | 866.000 | ||||
| N negative terms | 1235.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2101.000 | ||||
| Mean of predictor | 0.159 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.499 | ||||
| SD of criterion | 0.208 | ||||
| Covariance | 0.049 | ||||
| r | 0.470 | ||||
| b (slope, estimate of beta) | 0.196 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 2099.000 | ||||
| t(b) | 24.415 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.046 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | 0.180 | ||||
| Upperbound of 95% confidence interval for beta | 0.212 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.124 | ||||
| Treynor index (mean / b) | 0.144 | ||||
| Jensen alpha (a) | -0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2101.000 | ||||
| Minimum | 0.824 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.189 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 197.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 237.000 | ||||
| Percentage of outliers high | 0.113 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.933 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.054 | ||||
| Extreme Value Index (regression method) | 0.750 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 20.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.178 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.017 | ||||
| Mean of quarter 4 | 0.110 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.129 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.528 | ||||
| VaR(95%) (moments method) | 0.084 | ||||
| Expected Shortfall (moments method) | 0.084 | ||||
| Extreme Value Index (regression method) | -0.899 | ||||
| VaR(95%) (regression method) | 0.097 | ||||
| Expected Shortfall (regression method) | 0.107 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.098 | ||||
| Compounded annual return (geometric extrapolation) | 0.075 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.422 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.684 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.878 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.119 | ||||
| SD | 0.332 | ||||
| Sharpe ratio (Glass type estimate) | 3.366 | ||||
| Sharpe ratio (Hedges UMVUE) | 3.347 | ||||
| df | 130.000 | ||||
| t | 2.380 | ||||
| p | 0.398 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.558 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 6.161 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.545 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 6.148 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 11.131 | ||||
| Upside Potential Ratio | 16.858 | ||||
| Upside part of mean | 1.695 | ||||
| Downside part of mean | -0.576 | ||||
| Upside SD | 0.323 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 77.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.893 | ||||
| Mean of criterion | 1.119 | ||||
| SD of predictor | 0.569 | ||||
| SD of criterion | 0.332 | ||||
| Covariance | 0.110 | ||||
| r | 0.581 | ||||
| b (slope, estimate of beta) | 0.339 | ||||
| a (intercept, estimate of alpha) | 0.477 | ||||
| Mean Square Error | 0.074 | ||||
| DF error | 129.000 | ||||
| t(b) | 8.099 | ||||
| p(b) | 0.152 | ||||
| t(a) | 1.215 | ||||
| p(a) | 0.432 | ||||
| Lowerbound of 95% confidence interval for beta | 0.257 | ||||
| Upperbound of 95% confidence interval for beta | 0.422 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.300 | ||||
| Upperbound of 95% confidence interval for alpha | 1.253 | ||||
| Treynor index (mean / b) | 3.297 | ||||
| Jensen alpha (a) | 0.477 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.065 | ||||
| SD | 0.317 | ||||
| Sharpe ratio (Glass type estimate) | 3.356 | ||||
| Sharpe ratio (Hedges UMVUE) | 3.337 | ||||
| df | 130.000 | ||||
| t | 2.373 | ||||
| p | 0.398 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.548 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 6.152 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.536 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 6.138 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 10.418 | ||||
| Upside Potential Ratio | 16.099 | ||||
| Upside part of mean | 1.646 | ||||
| Downside part of mean | -0.581 | ||||
| Upside SD | 0.306 | ||||
| Downside SD | 0.102 | ||||
| N nonnegative terms | 77.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.724 | ||||
| Mean of criterion | 1.065 | ||||
| SD of predictor | 0.573 | ||||
| SD of criterion | 0.317 | ||||
| Covariance | 0.107 | ||||
| r | 0.589 | ||||
| b (slope, estimate of beta) | 0.326 | ||||
| a (intercept, estimate of alpha) | 0.502 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 129.000 | ||||
| t(b) | 8.280 | ||||
| p(b) | 0.148 | ||||
| t(a) | 1.356 | ||||
| p(a) | 0.425 | ||||
| Lowerbound of 95% confidence interval for beta | 0.248 | ||||
| Upperbound of 95% confidence interval for beta | 0.404 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.231 | ||||
| Upperbound of 95% confidence interval for alpha | 1.235 | ||||
| Treynor index (mean / b) | 3.263 | ||||
| Jensen alpha (a) | 0.502 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.950 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.160 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.092 | ||||
| Mean of outliers high | 1.050 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.302 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.249 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.014 | ||||
| Maximum | 0.087 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.036 | ||||
| Inter Quartile Range | 0.012 | ||||
| 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 | 0.056 | ||||
| Mean of outliers high | 0.087 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.025 | ||||
| VaR(95%) (moments method) | 0.033 | ||||
| Expected Shortfall (moments method) | 0.047 | ||||
| Extreme Value Index (regression method) | 0.685 | ||||
| VaR(95%) (regression method) | 0.048 | ||||
| Expected Shortfall (regression method) | 0.158 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.482 | ||||
| Compounded annual return (geometric extrapolation) | 2.032 | ||||
| Calmar ratio (compounded annual return / max draw down) | 23.239 | ||||
| Compounded annual return / average of 25% largest draw downs | 57.043 | ||||
| Compounded annual return / Expected Shortfall lognormal | 56.915 | ||||