Advanced Statistics: OSL3
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 | 0.388 | ||||
| SD | 0.583 | ||||
| Sharpe ratio (Glass type estimate) | 0.666 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.649 | ||||
| df | 31.000 | ||||
| t | 1.087 | ||||
| p | 0.143 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.551 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.872 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.562 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.860 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.112 | ||||
| Upside Potential Ratio | 2.888 | ||||
| Upside part of mean | 1.008 | ||||
| Downside part of mean | -0.620 | ||||
| Upside SD | 0.469 | ||||
| Downside SD | 0.349 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.576 | ||||
| Mean of criterion | 0.388 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.583 | ||||
| Covariance | 0.052 | ||||
| r | 0.320 | ||||
| b (slope, estimate of beta) | 0.666 | ||||
| a (intercept, estimate of alpha) | 0.004 | ||||
| Mean Square Error | 0.315 | ||||
| DF error | 30.000 | ||||
| t(b) | 1.851 | ||||
| p(b) | 0.037 | ||||
| t(a) | 0.011 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | 1.401 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.816 | ||||
| Upperbound of 95% confidence interval for alpha | 0.824 | ||||
| Treynor index (mean / b) | 0.583 | ||||
| Jensen alpha (a) | 0.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.218 | ||||
| SD | 0.590 | ||||
| Sharpe ratio (Glass type estimate) | 0.370 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.361 | ||||
| df | 31.000 | ||||
| t | 0.604 | ||||
| p | 0.275 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.837 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.571 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.843 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.564 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.532 | ||||
| Upside Potential Ratio | 2.223 | ||||
| Upside part of mean | 0.911 | ||||
| Downside part of mean | -0.692 | ||||
| Upside SD | 0.416 | ||||
| Downside SD | 0.410 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | 0.218 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.590 | ||||
| Covariance | 0.041 | ||||
| r | 0.264 | ||||
| b (slope, estimate of beta) | 0.586 | ||||
| a (intercept, estimate of alpha) | -0.090 | ||||
| Mean Square Error | 0.335 | ||||
| DF error | 30.000 | ||||
| t(b) | 1.497 | ||||
| p(b) | 0.072 | ||||
| t(a) | -0.220 | ||||
| p(a) | 0.586 | ||||
| Lowerbound of 95% confidence interval for beta | -0.214 | ||||
| Upperbound of 95% confidence interval for beta | 1.385 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.927 | ||||
| Upperbound of 95% confidence interval for alpha | 0.747 | ||||
| Treynor index (mean / b) | 0.372 | ||||
| Jensen alpha (a) | -0.090 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.230 | ||||
| Expected Shortfall on VaR | 0.282 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.105 | ||||
| Expected Shortfall on VaR | 0.206 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.606 | ||||
| Quartile 1 | 0.904 | ||||
| Median | 1.023 | ||||
| Quartile 3 | 1.166 | ||||
| Maximum | 1.397 | ||||
| Mean of quarter 1 | 0.829 | ||||
| Mean of quarter 2 | 0.977 | ||||
| Mean of quarter 3 | 1.094 | ||||
| Mean of quarter 4 | 1.244 | ||||
| Inter Quartile Range | 0.261 | ||||
| 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) | 0.260 | ||||
| VaR(95%) (moments method) | 0.190 | ||||
| Expected Shortfall (moments method) | 0.284 | ||||
| Extreme Value Index (regression method) | 0.602 | ||||
| VaR(95%) (regression method) | 0.186 | ||||
| Expected Shortfall (regression method) | 0.388 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.244 | ||||
| Quartile 3 | 0.419 | ||||
| Maximum | 0.491 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.093 | ||||
| Mean of quarter 3 | 0.394 | ||||
| Mean of quarter 4 | 0.491 | ||||
| Inter Quartile Range | 0.349 | ||||
| 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) | 0.379 | ||||
| Compounded annual return (geometric extrapolation) | 0.300 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.610 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.610 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.063 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.283 | ||||
| SD | 0.535 | ||||
| Sharpe ratio (Glass type estimate) | 0.529 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.529 | ||||
| df | 716.000 | ||||
| t | 0.875 | ||||
| p | 0.191 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.656 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.714 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.657 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.714 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.754 | ||||
| Upside Potential Ratio | 8.571 | ||||
| Upside part of mean | 3.220 | ||||
| Downside part of mean | -2.937 | ||||
| Upside SD | 0.381 | ||||
| Downside SD | 0.376 | ||||
| N nonnegative terms | 371.000 | ||||
| N negative terms | 346.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.658 | ||||
| Mean of criterion | 0.283 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.535 | ||||
| Covariance | 0.080 | ||||
| r | 0.439 | ||||
| b (slope, estimate of beta) | 0.694 | ||||
| a (intercept, estimate of alpha) | -0.173 | ||||
| Mean Square Error | 0.232 | ||||
| DF error | 715.000 | ||||
| t(b) | 13.063 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.591 | ||||
| p(a) | 0.723 | ||||
| Lowerbound of 95% confidence interval for beta | 0.590 | ||||
| Upperbound of 95% confidence interval for beta | 0.798 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.749 | ||||
| Upperbound of 95% confidence interval for alpha | 0.402 | ||||
| Treynor index (mean / b) | 0.408 | ||||
| Jensen alpha (a) | -0.173 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.140 | ||||
| SD | 0.537 | ||||
| Sharpe ratio (Glass type estimate) | 0.260 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.260 | ||||
| df | 716.000 | ||||
| t | 0.430 | ||||
| p | 0.334 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.925 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.445 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.925 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.444 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.358 | ||||
| Upside Potential Ratio | 8.083 | ||||
| Upside part of mean | 3.150 | ||||
| Downside part of mean | -3.010 | ||||
| Upside SD | 0.369 | ||||
| Downside SD | 0.390 | ||||
| N nonnegative terms | 371.000 | ||||
| N negative terms | 346.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.599 | ||||
| Mean of criterion | 0.140 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.537 | ||||
| Covariance | 0.080 | ||||
| r | 0.439 | ||||
| b (slope, estimate of beta) | 0.691 | ||||
| a (intercept, estimate of alpha) | -0.275 | ||||
| Mean Square Error | 0.233 | ||||
| DF error | 715.000 | ||||
| t(b) | 13.065 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.935 | ||||
| p(a) | 0.825 | ||||
| Lowerbound of 95% confidence interval for beta | 0.587 | ||||
| Upperbound of 95% confidence interval for beta | 0.795 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.851 | ||||
| Upperbound of 95% confidence interval for alpha | 0.302 | ||||
| Treynor index (mean / b) | 0.202 | ||||
| Jensen alpha (a) | -0.275 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 717.000 | ||||
| Minimum | 0.861 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 1.150 | ||||
| Mean of quarter 1 | 0.961 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.009 | ||||
| Mean of quarter 4 | 1.040 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.907 | ||||
| Number of outliers high | 20.000 | ||||
| Percentage of outliers high | 0.028 | ||||
| Mean of outliers high | 1.090 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.236 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.062 | ||||
| Extreme Value Index (regression method) | -0.047 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.047 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.085 | ||||
| Maximum | 0.565 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.023 | ||||
| Mean of quarter 3 | 0.058 | ||||
| Mean of quarter 4 | 0.305 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.558 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.182 | ||||
| VaR(95%) (moments method) | 0.253 | ||||
| Expected Shortfall (moments method) | 0.335 | ||||
| Extreme Value Index (regression method) | -1.752 | ||||
| VaR(95%) (regression method) | 0.382 | ||||
| Expected Shortfall (regression method) | 0.393 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.238 | ||||
| Compounded annual return (geometric extrapolation) | 0.201 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.357 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.660 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.072 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.154 | ||||
| SD | 0.714 | ||||
| Sharpe ratio (Glass type estimate) | -0.215 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.214 | ||||
| df | 130.000 | ||||
| t | -0.152 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.987 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.557 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.986 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.558 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.293 | ||||
| Upside Potential Ratio | 7.610 | ||||
| Upside part of mean | 4.000 | ||||
| Downside part of mean | -4.154 | ||||
| Upside SD | 0.479 | ||||
| Downside SD | 0.526 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.092 | ||||
| Mean of criterion | -0.154 | ||||
| SD of predictor | 0.476 | ||||
| SD of criterion | 0.714 | ||||
| Covariance | 0.119 | ||||
| r | 0.349 | ||||
| b (slope, estimate of beta) | 0.523 | ||||
| a (intercept, estimate of alpha) | -0.725 | ||||
| Mean Square Error | 0.451 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.232 | ||||
| p(b) | 0.282 | ||||
| t(a) | -0.756 | ||||
| p(a) | 0.542 | ||||
| Lowerbound of 95% confidence interval for beta | 0.279 | ||||
| Upperbound of 95% confidence interval for beta | 0.768 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.624 | ||||
| Upperbound of 95% confidence interval for alpha | 1.173 | ||||
| Treynor index (mean / b) | -0.294 | ||||
| Jensen alpha (a) | -0.725 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.411 | ||||
| SD | 0.722 | ||||
| Sharpe ratio (Glass type estimate) | -0.569 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.565 | ||||
| df | 130.000 | ||||
| t | -0.402 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.340 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.205 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.338 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.207 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.743 | ||||
| Upside Potential Ratio | 7.040 | ||||
| Upside part of mean | 3.891 | ||||
| Downside part of mean | -4.301 | ||||
| Upside SD | 0.461 | ||||
| Downside SD | 0.553 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.977 | ||||
| Mean of criterion | -0.411 | ||||
| SD of predictor | 0.477 | ||||
| SD of criterion | 0.722 | ||||
| Covariance | 0.123 | ||||
| r | 0.358 | ||||
| b (slope, estimate of beta) | 0.541 | ||||
| a (intercept, estimate of alpha) | -0.939 | ||||
| Mean Square Error | 0.458 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.352 | ||||
| p(b) | 0.277 | ||||
| t(a) | -0.973 | ||||
| p(a) | 0.554 | ||||
| Lowerbound of 95% confidence interval for beta | 0.295 | ||||
| Upperbound of 95% confidence interval for beta | 0.787 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.848 | ||||
| Upperbound of 95% confidence interval for alpha | 0.970 | ||||
| Treynor index (mean / b) | -0.759 | ||||
| Jensen alpha (a) | -0.939 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.072 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.861 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.150 | ||||
| Mean of quarter 1 | 0.946 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.041 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.881 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.136 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.250 | ||||
| VaR(95%) (moments method) | 0.054 | ||||
| Expected Shortfall (moments method) | 0.087 | ||||
| Extreme Value Index (regression method) | 0.025 | ||||
| VaR(95%) (regression method) | 0.054 | ||||
| Expected Shortfall (regression method) | 0.075 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.037 | ||||
| Median | 0.057 | ||||
| Quartile 3 | 0.085 | ||||
| Maximum | 0.565 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.048 | ||||
| Mean of quarter 3 | 0.061 | ||||
| Mean of quarter 4 | 0.269 | ||||
| Inter Quartile Range | 0.049 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.565 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.553 | ||||
| VaR(95%) (moments method) | 0.299 | ||||
| Expected Shortfall (moments method) | 0.766 | ||||
| Extreme Value Index (regression method) | 2.866 | ||||
| VaR(95%) (regression method) | 0.747 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.335 | ||||
| Compounded annual return (geometric extrapolation) | -0.307 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.543 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.140 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.440 | ||||