Advanced Statistics: R.N. Trading
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 | -0.739 | ||||
| SD | 0.713 | ||||
| Sharpe ratio (Glass type estimate) | -1.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.012 | ||||
| df | 33.000 | ||||
| t | -1.743 | ||||
| p | 0.955 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.219 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.163 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.201 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.178 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.056 | ||||
| Upside Potential Ratio | 0.317 | ||||
| Upside part of mean | 0.222 | ||||
| Downside part of mean | -0.960 | ||||
| Upside SD | 0.224 | ||||
| Downside SD | 0.699 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 26.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.587 | ||||
| Mean of criterion | -0.739 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.713 | ||||
| Covariance | -0.081 | ||||
| r | -0.331 | ||||
| b (slope, estimate of beta) | -0.688 | ||||
| a (intercept, estimate of alpha) | -0.335 | ||||
| Mean Square Error | 0.467 | ||||
| DF error | 32.000 | ||||
| t(b) | -1.986 | ||||
| p(b) | 0.972 | ||||
| t(a) | -0.737 | ||||
| p(a) | 0.767 | ||||
| Lowerbound of 95% confidence interval for beta | -1.394 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.260 | ||||
| Upperbound of 95% confidence interval for alpha | 0.590 | ||||
| Treynor index (mean / b) | 1.073 | ||||
| Jensen alpha (a) | -0.335 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.107 | ||||
| SD | 6.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.676 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.660 | ||||
| df | 33.000 | ||||
| t | -1.137 | ||||
| p | 0.868 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.505 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.836 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.515 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.673 | ||||
| Upside Potential Ratio | 0.033 | ||||
| Upside part of mean | 0.200 | ||||
| Downside part of mean | -4.307 | ||||
| Upside SD | 0.198 | ||||
| Downside SD | 6.101 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 26.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | -4.107 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 6.078 | ||||
| Covariance | -0.524 | ||||
| r | -0.270 | ||||
| b (slope, estimate of beta) | -5.134 | ||||
| a (intercept, estimate of alpha) | -1.432 | ||||
| Mean Square Error | 35.317 | ||||
| DF error | 32.000 | ||||
| t(b) | -1.586 | ||||
| p(b) | 0.939 | ||||
| t(a) | -0.366 | ||||
| p(a) | 0.642 | ||||
| Lowerbound of 95% confidence interval for beta | -11.728 | ||||
| Upperbound of 95% confidence interval for beta | 1.459 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.402 | ||||
| Upperbound of 95% confidence interval for alpha | 6.538 | ||||
| Treynor index (mean / b) | 0.800 | ||||
| Jensen alpha (a) | -1.432 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.960 | ||||
| Expected Shortfall on VaR | 0.978 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.237 | ||||
| Expected Shortfall on VaR | 0.480 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.949 | ||||
| Median | 0.980 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.313 | ||||
| Mean of quarter 1 | 0.744 | ||||
| Mean of quarter 2 | 0.964 | ||||
| Mean of quarter 3 | 0.996 | ||||
| Mean of quarter 4 | 1.073 | ||||
| Inter Quartile Range | 0.052 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.147 | ||||
| Mean of outliers low | 0.595 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.263 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.834 | ||||
| VaR(95%) (moments method) | 0.255 | ||||
| Expected Shortfall (moments method) | 1.655 | ||||
| Extreme Value Index (regression method) | 1.141 | ||||
| VaR(95%) (regression method) | 0.317 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.353 | ||||
| Compounded annual return (geometric extrapolation) | -0.983 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.983 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.005 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.771 | ||||
| SD | 0.690 | ||||
| Sharpe ratio (Glass type estimate) | -1.117 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.116 | ||||
| df | 753.000 | ||||
| t | -1.895 | ||||
| p | 0.971 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.274 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.040 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.273 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.041 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.206 | ||||
| Upside Potential Ratio | 1.575 | ||||
| Upside part of mean | 1.007 | ||||
| Downside part of mean | -1.779 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.640 | ||||
| N nonnegative terms | 241.000 | ||||
| N negative terms | 513.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 754.000 | ||||
| Mean of predictor | 0.605 | ||||
| Mean of criterion | -0.771 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.690 | ||||
| Covariance | -0.047 | ||||
| r | -0.201 | ||||
| b (slope, estimate of beta) | -0.412 | ||||
| a (intercept, estimate of alpha) | -0.522 | ||||
| Mean Square Error | 0.458 | ||||
| DF error | 752.000 | ||||
| t(b) | -5.635 | ||||
| p(b) | 1.000 | ||||
| t(a) | -1.301 | ||||
| p(a) | 0.903 | ||||
| Lowerbound of 95% confidence interval for beta | -0.556 | ||||
| Upperbound of 95% confidence interval for beta | -0.269 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.310 | ||||
| Upperbound of 95% confidence interval for alpha | 0.266 | ||||
| Treynor index (mean / b) | 1.872 | ||||
| Jensen alpha (a) | -0.522 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.044 | ||||
| SD | 6.044 | ||||
| Sharpe ratio (Glass type estimate) | -0.669 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.669 | ||||
| df | 753.000 | ||||
| t | -1.135 | ||||
| p | 0.872 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.825 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.487 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.824 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.487 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.670 | ||||
| Upside Potential Ratio | 0.162 | ||||
| Upside part of mean | 0.977 | ||||
| Downside part of mean | -5.021 | ||||
| Upside SD | 0.241 | ||||
| Downside SD | 6.040 | ||||
| N nonnegative terms | 241.000 | ||||
| N negative terms | 513.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 754.000 | ||||
| Mean of predictor | 0.547 | ||||
| Mean of criterion | -4.044 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 6.044 | ||||
| Covariance | -0.089 | ||||
| r | -0.043 | ||||
| b (slope, estimate of beta) | -0.763 | ||||
| a (intercept, estimate of alpha) | -3.627 | ||||
| Mean Square Error | 36.506 | ||||
| DF error | 752.000 | ||||
| t(b) | -1.182 | ||||
| p(b) | 0.881 | ||||
| t(a) | -1.013 | ||||
| p(a) | 0.844 | ||||
| Lowerbound of 95% confidence interval for beta | -2.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.504 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.653 | ||||
| Upperbound of 95% confidence interval for alpha | 3.399 | ||||
| Treynor index (mean / b) | 5.300 | ||||
| Jensen alpha (a) | -3.627 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.467 | ||||
| Expected Shortfall on VaR | 0.540 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 754.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.320 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 102.000 | ||||
| Percentage of outliers low | 0.135 | ||||
| Mean of outliers low | 0.959 | ||||
| Number of outliers high | 93.000 | ||||
| Percentage of outliers high | 0.123 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.745 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.082 | ||||
| Extreme Value Index (regression method) | 0.544 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.047 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.047 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.313 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.062 | ||||
| Mean of quarter 3 | 0.083 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.265 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | -0.347 | ||||
| Compounded annual return (geometric extrapolation) | -0.982 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.982 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.982 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.818 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.047 | ||||
| SD | 1.414 | ||||
| Sharpe ratio (Glass type estimate) | -1.447 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.439 | ||||
| df | 130.000 | ||||
| t | -1.023 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.222 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.333 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.216 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.339 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.447 | ||||
| Upside Potential Ratio | 0.004 | ||||
| Upside part of mean | 0.006 | ||||
| Downside part of mean | -2.053 | ||||
| Upside SD | 0.002 | ||||
| Downside SD | 1.414 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 116.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.106 | ||||
| Mean of criterion | -2.047 | ||||
| SD of predictor | 0.470 | ||||
| SD of criterion | 1.414 | ||||
| Covariance | -0.023 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.105 | ||||
| a (intercept, estimate of alpha) | -1.930 | ||||
| Mean Square Error | 2.013 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.397 | ||||
| p(b) | 0.522 | ||||
| t(a) | -0.952 | ||||
| p(a) | 0.553 | ||||
| Lowerbound of 95% confidence interval for beta | -0.629 | ||||
| Upperbound of 95% confidence interval for beta | 0.419 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.942 | ||||
| Upperbound of 95% confidence interval for alpha | 2.081 | ||||
| Treynor index (mean / b) | 19.488 | ||||
| Jensen alpha (a) | -1.930 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -20.520 | ||||
| SD | 14.477 | ||||
| Sharpe ratio (Glass type estimate) | -1.417 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.409 | ||||
| df | 130.000 | ||||
| t | -1.002 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.192 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.362 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.186 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.368 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.417 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.006 | ||||
| Downside part of mean | -20.526 | ||||
| Upside SD | 0.002 | ||||
| Downside SD | 14.477 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 116.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.993 | ||||
| Mean of criterion | -20.520 | ||||
| SD of predictor | 0.473 | ||||
| SD of criterion | 14.477 | ||||
| Covariance | -0.233 | ||||
| r | -0.034 | ||||
| b (slope, estimate of beta) | -1.043 | ||||
| a (intercept, estimate of alpha) | -19.484 | ||||
| Mean Square Error | 210.961 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.387 | ||||
| p(b) | 0.522 | ||||
| t(a) | -0.941 | ||||
| p(a) | 0.552 | ||||
| Lowerbound of 95% confidence interval for beta | -6.372 | ||||
| Upperbound of 95% confidence interval for beta | 4.286 | ||||
| Lowerbound of 95% confidence interval for alpha | -60.468 | ||||
| Upperbound of 95% confidence interval for alpha | 21.499 | ||||
| Treynor index (mean / b) | 19.672 | ||||
| Jensen alpha (a) | -19.484 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.788 | ||||
| Expected Shortfall on VaR | 0.847 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.058 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.001 | ||||
| Mean of quarter 1 | 0.969 | ||||
| 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 | 11.000 | ||||
| Percentage of outliers low | 0.084 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.099 | ||||
| Mean of outliers high | 1.000 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.250 | ||||
| Median | 0.500 | ||||
| Quartile 3 | 0.750 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.500 | ||||
| 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) | -2.000 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.000 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.181 | ||||