Advanced Statistics: US Stock Trader
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 | 0.195 | ||||
| SD | 0.171 | ||||
| Sharpe ratio (Glass type estimate) | 1.142 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.133 | ||||
| df | 91.000 | ||||
| t | 3.163 | ||||
| p | 0.001 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.413 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.867 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.406 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.860 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.854 | ||||
| Upside Potential Ratio | 4.361 | ||||
| Upside part of mean | 0.298 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.165 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 92.000 | ||||
| Mean of predictor | 0.206 | ||||
| Mean of criterion | 0.195 | ||||
| SD of predictor | 0.188 | ||||
| SD of criterion | 0.171 | ||||
| Covariance | 0.005 | ||||
| r | 0.161 | ||||
| b (slope, estimate of beta) | 0.146 | ||||
| a (intercept, estimate of alpha) | 0.165 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 90.000 | ||||
| t(b) | 1.547 | ||||
| p(b) | 0.063 | ||||
| t(a) | 2.572 | ||||
| p(a) | 0.006 | ||||
| Lowerbound of 95% confidence interval for beta | -0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.333 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.038 | ||||
| Upperbound of 95% confidence interval for alpha | 0.293 | ||||
| Treynor index (mean / b) | 1.338 | ||||
| Jensen alpha (a) | 0.165 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.179 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | 1.100 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.090 | ||||
| df | 91.000 | ||||
| t | 3.045 | ||||
| p | 0.002 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.371 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.822 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.365 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.816 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.551 | ||||
| Upside Potential Ratio | 4.044 | ||||
| Upside part of mean | 0.285 | ||||
| Downside part of mean | -0.105 | ||||
| Upside SD | 0.155 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 92.000 | ||||
| Mean of predictor | 0.187 | ||||
| Mean of criterion | 0.179 | ||||
| SD of predictor | 0.179 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | 0.005 | ||||
| r | 0.185 | ||||
| b (slope, estimate of beta) | 0.169 | ||||
| a (intercept, estimate of alpha) | 0.148 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 90.000 | ||||
| t(b) | 1.790 | ||||
| p(b) | 0.038 | ||||
| t(a) | 2.428 | ||||
| p(a) | 0.009 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.357 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.027 | ||||
| Upperbound of 95% confidence interval for alpha | 0.269 | ||||
| Treynor index (mean / b) | 1.060 | ||||
| Jensen alpha (a) | 0.148 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 92.000 | ||||
| Minimum | 0.911 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.004 | ||||
| Quartile 3 | 1.043 | ||||
| Maximum | 1.241 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.019 | ||||
| Mean of quarter 4 | 1.087 | ||||
| Inter Quartile Range | 0.043 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.022 | ||||
| Mean of outliers low | 0.917 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.065 | ||||
| Mean of outliers high | 1.141 | ||||
| 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) | -0.060 | ||||
| VaR(95%) (regression method) | 0.033 | ||||
| Expected Shortfall (regression method) | 0.052 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.088 | ||||
| Maximum | 0.137 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.045 | ||||
| Mean of quarter 4 | 0.116 | ||||
| Inter Quartile Range | 0.077 | ||||
| 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) | -2.143 | ||||
| VaR(95%) (moments method) | 0.131 | ||||
| Expected Shortfall (moments method) | 0.132 | ||||
| Extreme Value Index (regression method) | -0.243 | ||||
| VaR(95%) (regression method) | 0.143 | ||||
| Expected Shortfall (regression method) | 0.160 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.593 | ||||
| Compounded annual return (geometric extrapolation) | 0.250 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.821 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.152 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.178 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.188 | ||||
| SD | 0.133 | ||||
| Sharpe ratio (Glass type estimate) | 1.410 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.409 | ||||
| df | 2015.000 | ||||
| t | 3.911 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.702 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.118 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.701 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.117 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.298 | ||||
| Upside Potential Ratio | 8.499 | ||||
| Upside part of mean | 0.694 | ||||
| Downside part of mean | -0.506 | ||||
| Upside SD | 0.106 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 751.000 | ||||
| N negative terms | 1265.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2016.000 | ||||
| Mean of predictor | 0.228 | ||||
| Mean of criterion | 0.188 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.133 | ||||
| Covariance | 0.003 | ||||
| r | 0.087 | ||||
| b (slope, estimate of beta) | 0.050 | ||||
| a (intercept, estimate of alpha) | 0.176 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 2014.000 | ||||
| t(b) | 3.921 | ||||
| p(b) | 0.000 | ||||
| t(a) | 3.680 | ||||
| p(a) | 0.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.075 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.082 | ||||
| Upperbound of 95% confidence interval for alpha | 0.270 | ||||
| Treynor index (mean / b) | 3.749 | ||||
| Jensen alpha (a) | 0.176 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.179 | ||||
| SD | 0.132 | ||||
| Sharpe ratio (Glass type estimate) | 1.349 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.348 | ||||
| df | 2015.000 | ||||
| t | 3.741 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.641 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.056 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.640 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.056 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.163 | ||||
| Upside Potential Ratio | 8.331 | ||||
| Upside part of mean | 0.688 | ||||
| Downside part of mean | -0.509 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.083 | ||||
| N nonnegative terms | 751.000 | ||||
| N negative terms | 1265.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2016.000 | ||||
| Mean of predictor | 0.200 | ||||
| Mean of criterion | 0.179 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.132 | ||||
| Covariance | 0.003 | ||||
| r | 0.087 | ||||
| b (slope, estimate of beta) | 0.048 | ||||
| a (intercept, estimate of alpha) | 0.169 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 2014.000 | ||||
| t(b) | 3.903 | ||||
| p(b) | 0.000 | ||||
| t(a) | 3.546 | ||||
| p(a) | 0.000 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.262 | ||||
| Treynor index (mean / b) | 3.688 | ||||
| Jensen alpha (a) | 0.169 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| 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 | 2016.000 | ||||
| Minimum | 0.942 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.082 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 159.000 | ||||
| Percentage of outliers low | 0.079 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 210.000 | ||||
| Percentage of outliers high | 0.104 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.227 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.114 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.034 | ||||
| Maximum | 0.177 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.020 | ||||
| Mean of quarter 4 | 0.071 | ||||
| Inter Quartile Range | 0.031 | ||||
| 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 | 0.070 | ||||
| Mean of outliers high | 0.128 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.246 | ||||
| VaR(95%) (moments method) | 0.076 | ||||
| Expected Shortfall (moments method) | 0.119 | ||||
| Extreme Value Index (regression method) | -0.007 | ||||
| VaR(95%) (regression method) | 0.076 | ||||
| Expected Shortfall (regression method) | 0.101 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.591 | ||||
| Compounded annual return (geometric extrapolation) | 0.249 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.406 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.497 | ||||
| Compounded annual return / Expected Shortfall lognormal | 15.525 | ||||
| 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 | 1.310 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.392 | ||||
| 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 | 1.230 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.393 | ||||
| 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) | -8638675482162985.000 | ||||
| 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) | 249183282235565420363871437193216.000 | ||||
| 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 | ||||