Advanced Statistics: HPW- High Probability Winning
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 | -0.005 | ||||
| SD | 0.150 | ||||
| Sharpe ratio (Glass type estimate) | -0.033 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.033 | ||||
| df | 93.000 | ||||
| t | -0.094 | ||||
| p | 0.537 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.734 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.667 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.734 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.667 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.046 | ||||
| Upside Potential Ratio | 1.162 | ||||
| Upside part of mean | 0.127 | ||||
| Downside part of mean | -0.132 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 67.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 94.000 | ||||
| Mean of predictor | 0.201 | ||||
| Mean of criterion | -0.005 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.150 | ||||
| Covariance | 0.015 | ||||
| r | 0.368 | ||||
| b (slope, estimate of beta) | 0.205 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 92.000 | ||||
| t(b) | 3.791 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.904 | ||||
| p(a) | 0.816 | ||||
| Lowerbound of 95% confidence interval for beta | 0.098 | ||||
| Upperbound of 95% confidence interval for beta | 0.313 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | -0.024 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.016 | ||||
| SD | 0.152 | ||||
| Sharpe ratio (Glass type estimate) | -0.107 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.106 | ||||
| df | 93.000 | ||||
| t | -0.299 | ||||
| p | 0.617 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.807 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.594 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.807 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.594 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.138 | ||||
| Upside Potential Ratio | 1.029 | ||||
| Upside part of mean | 0.122 | ||||
| Downside part of mean | -0.138 | ||||
| Upside SD | 0.095 | ||||
| Downside SD | 0.119 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 67.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 94.000 | ||||
| Mean of predictor | 0.164 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.152 | ||||
| Covariance | 0.015 | ||||
| r | 0.382 | ||||
| b (slope, estimate of beta) | 0.221 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 92.000 | ||||
| t(b) | 3.959 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.024 | ||||
| p(a) | 0.846 | ||||
| Lowerbound of 95% confidence interval for beta | 0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.333 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 0.049 | ||||
| Treynor index (mean / b) | -0.074 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 94.000 | ||||
| Minimum | 0.796 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.009 | ||||
| Maximum | 1.208 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.045 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.117 | ||||
| Mean of outliers low | 0.931 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.181 | ||||
| Mean of outliers high | 1.058 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.665 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.028 | ||||
| Extreme Value Index (regression method) | 0.650 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.146 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.038 | ||||
| Quartile 3 | 0.121 | ||||
| Maximum | 0.204 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | 0.056 | ||||
| Mean of quarter 4 | 0.173 | ||||
| Inter Quartile Range | 0.114 | ||||
| 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) | 0.031 | ||||
| Compounded annual return (geometric extrapolation) | 0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.138 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.162 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.320 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.043 | ||||
| SD | 0.343 | ||||
| Sharpe ratio (Glass type estimate) | 0.125 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.125 | ||||
| df | 2053.000 | ||||
| t | 0.349 | ||||
| p | 0.364 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.575 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.825 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.575 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.825 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.180 | ||||
| Upside Potential Ratio | 4.173 | ||||
| Upside part of mean | 0.991 | ||||
| Downside part of mean | -0.948 | ||||
| Upside SD | 0.247 | ||||
| Downside SD | 0.237 | ||||
| N nonnegative terms | 454.000 | ||||
| N negative terms | 1600.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2054.000 | ||||
| Mean of predictor | 0.346 | ||||
| Mean of criterion | 0.043 | ||||
| SD of predictor | 0.605 | ||||
| SD of criterion | 0.343 | ||||
| Covariance | 0.044 | ||||
| r | 0.214 | ||||
| b (slope, estimate of beta) | 0.121 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.112 | ||||
| DF error | 2052.000 | ||||
| t(b) | 9.911 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.007 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.145 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.234 | ||||
| Upperbound of 95% confidence interval for alpha | 0.236 | ||||
| Treynor index (mean / b) | 0.353 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.016 | ||||
| SD | 0.345 | ||||
| Sharpe ratio (Glass type estimate) | -0.047 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.047 | ||||
| df | 2053.000 | ||||
| t | -0.133 | ||||
| p | 0.553 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.747 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.653 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.747 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.653 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.065 | ||||
| Upside Potential Ratio | 3.836 | ||||
| Upside part of mean | 0.962 | ||||
| Downside part of mean | -0.978 | ||||
| Upside SD | 0.236 | ||||
| Downside SD | 0.251 | ||||
| N nonnegative terms | 454.000 | ||||
| N negative terms | 1600.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2054.000 | ||||
| Mean of predictor | 0.170 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.589 | ||||
| SD of criterion | 0.345 | ||||
| Covariance | 0.043 | ||||
| r | 0.210 | ||||
| b (slope, estimate of beta) | 0.123 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.114 | ||||
| DF error | 2052.000 | ||||
| t(b) | 9.723 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.309 | ||||
| p(a) | 0.621 | ||||
| Lowerbound of 95% confidence interval for beta | 0.098 | ||||
| Upperbound of 95% confidence interval for beta | 0.148 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.273 | ||||
| Upperbound of 95% confidence interval for alpha | 0.199 | ||||
| Treynor index (mean / b) | -0.133 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2054.000 | ||||
| Minimum | 0.783 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.152 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 425.000 | ||||
| Percentage of outliers low | 0.207 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 490.000 | ||||
| Percentage of outliers high | 0.239 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.908 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.082 | ||||
| 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 | 15.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.073 | ||||
| Median | 0.112 | ||||
| Quartile 3 | 0.145 | ||||
| Maximum | 0.263 | ||||
| Mean of quarter 1 | 0.045 | ||||
| Mean of quarter 2 | 0.098 | ||||
| Mean of quarter 3 | 0.123 | ||||
| Mean of quarter 4 | 0.209 | ||||
| Inter Quartile Range | 0.071 | ||||
| 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 | 0.067 | ||||
| Mean of outliers high | 0.263 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5.304 | ||||
| VaR(95%) (moments method) | 0.224 | ||||
| Expected Shortfall (moments method) | 0.224 | ||||
| Extreme Value Index (regression method) | -1.256 | ||||
| VaR(95%) (regression method) | 0.275 | ||||
| Expected Shortfall (regression method) | 0.286 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.031 | ||||
| Compounded annual return (geometric extrapolation) | 0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.107 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.134 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.653 | ||||
| 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 | 1.136 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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 | 1.007 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.506 | ||||
| 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) | -8733374179591797.000 | ||||
| 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) | -927794762780329149323321370738688.000 | ||||
| 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 | ||||