Advanced Statistics: The Systematic Trader
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 | -0.002 | ||||
| SD | 0.127 | ||||
| Sharpe ratio (Glass type estimate) | -0.020 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.019 | ||||
| df | 74.000 | ||||
| t | -0.049 | ||||
| p | 0.520 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.804 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.764 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.803 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.765 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.033 | ||||
| Upside Potential Ratio | 1.987 | ||||
| Upside part of mean | 0.149 | ||||
| Downside part of mean | -0.152 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.075 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.195 | ||||
| SD of criterion | 0.127 | ||||
| Covariance | 0.009 | ||||
| r | 0.347 | ||||
| b (slope, estimate of beta) | 0.226 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 73.000 | ||||
| t(b) | 3.166 | ||||
| p(b) | 0.001 | ||||
| t(a) | -1.148 | ||||
| p(a) | 0.873 | ||||
| Lowerbound of 95% confidence interval for beta | 0.084 | ||||
| Upperbound of 95% confidence interval for beta | 0.368 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.160 | ||||
| Upperbound of 95% confidence interval for alpha | 0.043 | ||||
| Treynor index (mean / b) | -0.011 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.010 | ||||
| SD | 0.124 | ||||
| Sharpe ratio (Glass type estimate) | -0.082 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.081 | ||||
| df | 74.000 | ||||
| t | -0.205 | ||||
| p | 0.581 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.866 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.702 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.865 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.703 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.133 | ||||
| Upside Potential Ratio | 1.874 | ||||
| Upside part of mean | 0.144 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.077 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.191 | ||||
| SD of criterion | 0.124 | ||||
| Covariance | 0.008 | ||||
| r | 0.355 | ||||
| b (slope, estimate of beta) | 0.231 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 73.000 | ||||
| t(b) | 3.240 | ||||
| p(b) | 0.001 | ||||
| t(a) | -1.266 | ||||
| p(a) | 0.895 | ||||
| Lowerbound of 95% confidence interval for beta | 0.089 | ||||
| Upperbound of 95% confidence interval for beta | 0.374 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.161 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -0.044 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.058 | ||||
| Expected Shortfall on VaR | 0.072 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 75.000 | ||||
| Minimum | 0.916 | ||||
| Quartile 1 | 0.984 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.126 | ||||
| Mean of quarter 1 | 0.965 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.052 | ||||
| Inter Quartile Range | 0.027 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 1.079 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.235 | ||||
| VaR(95%) (moments method) | 0.035 | ||||
| Expected Shortfall (moments method) | 0.043 | ||||
| Extreme Value Index (regression method) | 0.105 | ||||
| VaR(95%) (regression method) | 0.038 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.046 | ||||
| Quartile 3 | 0.092 | ||||
| Maximum | 0.206 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.039 | ||||
| Mean of quarter 3 | 0.054 | ||||
| Mean of quarter 4 | 0.155 | ||||
| Inter Quartile Range | 0.064 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.206 | ||||
| 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) | 0.038 | ||||
| Compounded annual return (geometric extrapolation) | 0.034 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.167 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.222 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.478 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.002 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | 0.013 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.013 | ||||
| df | 1658.000 | ||||
| t | 0.032 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.766 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.792 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.766 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.792 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.017 | ||||
| Upside Potential Ratio | 5.536 | ||||
| Upside part of mean | 0.647 | ||||
| Downside part of mean | -0.645 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.117 | ||||
| N nonnegative terms | 624.000 | ||||
| N negative terms | 1035.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1659.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | 0.013 | ||||
| r | 0.307 | ||||
| b (slope, estimate of beta) | 0.182 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1657.000 | ||||
| t(b) | 13.124 | ||||
| p(b) | 0.308 | ||||
| t(a) | -0.856 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | 0.154 | ||||
| Upperbound of 95% confidence interval for beta | 0.209 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.170 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | 0.011 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.011 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | -0.067 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.067 | ||||
| df | 1658.000 | ||||
| t | -0.168 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.712 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.846 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.712 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.089 | ||||
| Upside Potential Ratio | 5.385 | ||||
| Upside part of mean | 0.642 | ||||
| Downside part of mean | -0.652 | ||||
| Upside SD | 0.106 | ||||
| Downside SD | 0.119 | ||||
| N nonnegative terms | 624.000 | ||||
| N negative terms | 1035.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1659.000 | ||||
| Mean of predictor | 0.259 | ||||
| Mean of criterion | -0.011 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | 0.013 | ||||
| r | 0.306 | ||||
| b (slope, estimate of beta) | 0.180 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1657.000 | ||||
| t(b) | 13.106 | ||||
| p(b) | 0.308 | ||||
| t(a) | -0.948 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.207 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.176 | ||||
| Upperbound of 95% confidence interval for alpha | 0.061 | ||||
| Treynor index (mean / b) | -0.059 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1659.000 | ||||
| Minimum | 0.920 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.083 | ||||
| Mean of quarter 1 | 0.991 | ||||
| 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 | 179.000 | ||||
| Percentage of outliers low | 0.108 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 171.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.662 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.022 | ||||
| Extreme Value Index (regression method) | 0.306 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 21.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.072 | ||||
| Maximum | 0.231 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.051 | ||||
| Mean of quarter 4 | 0.131 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 0.205 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.399 | ||||
| VaR(95%) (moments method) | 0.149 | ||||
| Expected Shortfall (moments method) | 0.259 | ||||
| Extreme Value Index (regression method) | 0.985 | ||||
| VaR(95%) (regression method) | 0.139 | ||||
| Expected Shortfall (regression method) | 5.584 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.037 | ||||
| Compounded annual return (geometric extrapolation) | 0.034 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.147 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.259 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.687 | ||||
| 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 | 1.115 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.519 | ||||
| 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 | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.524 | ||||
| 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) | -8741540240989643.000 | ||||
| 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) | -181184710824955034442714803339264.000 | ||||
| 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 | ||||