Advanced Statistics: punktrading
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 | -0.117 | ||||
| SD | 0.343 | ||||
| Sharpe ratio (Glass type estimate) | -0.342 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.335 | ||||
| df | 35.000 | ||||
| t | -0.592 | ||||
| p | 0.721 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.474 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.795 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.469 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.800 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.411 | ||||
| Upside Potential Ratio | 0.517 | ||||
| Upside part of mean | 0.147 | ||||
| Downside part of mean | -0.265 | ||||
| Upside SD | 0.185 | ||||
| Downside SD | 0.285 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.537 | ||||
| Mean of criterion | -0.117 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.343 | ||||
| Covariance | 0.012 | ||||
| r | 0.132 | ||||
| b (slope, estimate of beta) | 0.164 | ||||
| a (intercept, estimate of alpha) | -0.206 | ||||
| Mean Square Error | 0.119 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.774 | ||||
| p(b) | 0.222 | ||||
| t(a) | -0.896 | ||||
| p(a) | 0.812 | ||||
| Lowerbound of 95% confidence interval for beta | -0.267 | ||||
| Upperbound of 95% confidence interval for beta | 0.596 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.672 | ||||
| Upperbound of 95% confidence interval for alpha | 0.261 | ||||
| Treynor index (mean / b) | -0.714 | ||||
| Jensen alpha (a) | -0.206 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.189 | ||||
| SD | 0.410 | ||||
| Sharpe ratio (Glass type estimate) | -0.462 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.452 | ||||
| df | 35.000 | ||||
| t | -0.801 | ||||
| p | 0.786 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.678 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.589 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.684 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.508 | ||||
| Upside Potential Ratio | 0.355 | ||||
| Upside part of mean | 0.132 | ||||
| Downside part of mean | -0.322 | ||||
| Upside SD | 0.165 | ||||
| Downside SD | 0.373 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | -0.189 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 0.410 | ||||
| Covariance | 0.012 | ||||
| r | 0.108 | ||||
| b (slope, estimate of beta) | 0.167 | ||||
| a (intercept, estimate of alpha) | -0.271 | ||||
| Mean Square Error | 0.171 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.631 | ||||
| p(b) | 0.266 | ||||
| t(a) | -0.999 | ||||
| p(a) | 0.838 | ||||
| Lowerbound of 95% confidence interval for beta | -0.370 | ||||
| Upperbound of 95% confidence interval for beta | 0.703 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.823 | ||||
| Upperbound of 95% confidence interval for alpha | 0.280 | ||||
| Treynor index (mean / b) | -1.137 | ||||
| Jensen alpha (a) | -0.271 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.190 | ||||
| Expected Shortfall on VaR | 0.228 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.074 | ||||
| Expected Shortfall on VaR | 0.160 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.541 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.274 | ||||
| Mean of quarter 1 | 0.926 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.050 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.083 | ||||
| Mean of outliers low | 0.777 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.225 | ||||
| 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) | 0.604 | ||||
| VaR(95%) (regression method) | 0.131 | ||||
| Expected Shortfall (regression method) | 0.667 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.568 | ||||
| Quartile 1 | 0.568 | ||||
| Median | 0.568 | ||||
| Quartile 3 | 0.568 | ||||
| Maximum | 0.568 | ||||
| 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 | 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) | -0.118 | ||||
| Compounded annual return (geometric extrapolation) | -0.135 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.238 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.594 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.488 | ||||
| Sharpe ratio (Glass type estimate) | -0.136 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.136 | ||||
| df | 806.000 | ||||
| t | -0.238 | ||||
| p | 0.594 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.252 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.981 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.252 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.981 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.196 | ||||
| Upside Potential Ratio | 1.864 | ||||
| Upside part of mean | 0.630 | ||||
| Downside part of mean | -0.697 | ||||
| Upside SD | 0.351 | ||||
| Downside SD | 0.338 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 784.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 807.000 | ||||
| Mean of predictor | 0.583 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.344 | ||||
| SD of criterion | 0.488 | ||||
| Covariance | 0.006 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.049 | ||||
| a (intercept, estimate of alpha) | -0.095 | ||||
| Mean Square Error | 0.238 | ||||
| DF error | 805.000 | ||||
| t(b) | 0.987 | ||||
| p(b) | 0.162 | ||||
| t(a) | -0.339 | ||||
| p(a) | 0.633 | ||||
| Lowerbound of 95% confidence interval for beta | -0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.147 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.643 | ||||
| Upperbound of 95% confidence interval for alpha | 0.454 | ||||
| Treynor index (mean / b) | -1.343 | ||||
| Jensen alpha (a) | -0.095 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.186 | ||||
| SD | 0.493 | ||||
| Sharpe ratio (Glass type estimate) | -0.377 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.376 | ||||
| df | 806.000 | ||||
| t | -0.661 | ||||
| p | 0.746 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.494 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.740 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.493 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.741 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.483 | ||||
| Upside Potential Ratio | 1.505 | ||||
| Upside part of mean | 0.579 | ||||
| Downside part of mean | -0.764 | ||||
| Upside SD | 0.308 | ||||
| Downside SD | 0.384 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 784.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 807.000 | ||||
| Mean of predictor | 0.523 | ||||
| Mean of criterion | -0.186 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.493 | ||||
| Covariance | 0.006 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.048 | ||||
| a (intercept, estimate of alpha) | -0.211 | ||||
| Mean Square Error | 0.243 | ||||
| DF error | 805.000 | ||||
| t(b) | 0.939 | ||||
| p(b) | 0.174 | ||||
| t(a) | -0.746 | ||||
| p(a) | 0.772 | ||||
| Lowerbound of 95% confidence interval for beta | -0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.147 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.764 | ||||
| Upperbound of 95% confidence interval for alpha | 0.343 | ||||
| Treynor index (mean / b) | -3.903 | ||||
| Jensen alpha (a) | -0.211 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 807.000 | ||||
| Minimum | 0.721 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.434 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 24.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 0.916 | ||||
| Number of outliers high | 23.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.085 | ||||
| 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) | -0.214 | ||||
| VaR(95%) (regression method) | -0.033 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.080 | ||||
| Quartile 1 | 0.232 | ||||
| Median | 0.384 | ||||
| Quartile 3 | 0.536 | ||||
| Maximum | 0.688 | ||||
| Mean of quarter 1 | 0.080 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.688 | ||||
| Inter Quartile Range | 0.304 | ||||
| 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) | -0.115 | ||||
| Compounded annual return (geometric extrapolation) | -0.132 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.192 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.192 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.148 | ||||
| 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 | 0.972 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.476 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.474 | ||||
| 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) | -8744864398397434.000 | ||||
| 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) | 353300148808061992812714095804416.000 | ||||
| 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 | ||||