Advanced Statistics: Canada Leveraged
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 | 0.055 | ||||
| SD | 0.626 | ||||
| Sharpe ratio (Glass type estimate) | 0.088 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.087 | ||||
| df | 50.000 | ||||
| t | 0.182 | ||||
| p | 0.428 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.863 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.039 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.864 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.038 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.108 | ||||
| Upside Potential Ratio | 1.446 | ||||
| Upside part of mean | 0.741 | ||||
| Downside part of mean | -0.686 | ||||
| Upside SD | 0.348 | ||||
| Downside SD | 0.513 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.440 | ||||
| Mean of criterion | 0.055 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.626 | ||||
| Covariance | 0.056 | ||||
| r | 0.336 | ||||
| b (slope, estimate of beta) | 0.796 | ||||
| a (intercept, estimate of alpha) | -0.295 | ||||
| Mean Square Error | 0.355 | ||||
| DF error | 49.000 | ||||
| t(b) | 2.499 | ||||
| p(b) | 0.008 | ||||
| t(a) | -0.919 | ||||
| p(a) | 0.819 | ||||
| Lowerbound of 95% confidence interval for beta | 0.156 | ||||
| Upperbound of 95% confidence interval for beta | 1.437 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.941 | ||||
| Upperbound of 95% confidence interval for alpha | 0.350 | ||||
| Treynor index (mean / b) | 0.069 | ||||
| Jensen alpha (a) | -0.295 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.403 | ||||
| SD | 1.284 | ||||
| Sharpe ratio (Glass type estimate) | -0.314 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.309 | ||||
| df | 50.000 | ||||
| t | -0.647 | ||||
| p | 0.740 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.265 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.640 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.262 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.644 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.326 | ||||
| Upside Potential Ratio | 0.554 | ||||
| Upside part of mean | 0.686 | ||||
| Downside part of mean | -1.088 | ||||
| Upside SD | 0.316 | ||||
| Downside SD | 1.237 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.399 | ||||
| Mean of criterion | -0.403 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 1.284 | ||||
| Covariance | 0.010 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.160 | ||||
| a (intercept, estimate of alpha) | -0.467 | ||||
| Mean Square Error | 1.680 | ||||
| DF error | 49.000 | ||||
| t(b) | 0.223 | ||||
| p(b) | 0.412 | ||||
| t(a) | -0.676 | ||||
| p(a) | 0.749 | ||||
| Lowerbound of 95% confidence interval for beta | -1.280 | ||||
| Upperbound of 95% confidence interval for beta | 1.601 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.855 | ||||
| Upperbound of 95% confidence interval for alpha | 0.921 | ||||
| Treynor index (mean / b) | -2.515 | ||||
| Jensen alpha (a) | -0.467 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.474 | ||||
| Expected Shortfall on VaR | 0.546 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.117 | ||||
| Expected Shortfall on VaR | 0.256 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 51.000 | ||||
| Minimum | 0.084 | ||||
| Quartile 1 | 0.933 | ||||
| Median | 1.017 | ||||
| Quartile 3 | 1.104 | ||||
| Maximum | 1.333 | ||||
| Mean of quarter 1 | 0.804 | ||||
| Mean of quarter 2 | 0.981 | ||||
| Mean of quarter 3 | 1.074 | ||||
| Mean of quarter 4 | 1.179 | ||||
| Inter Quartile Range | 0.172 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.020 | ||||
| Mean of outliers low | 0.084 | ||||
| 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) | 0.446 | ||||
| VaR(95%) (moments method) | 0.202 | ||||
| Expected Shortfall (moments method) | 0.406 | ||||
| Extreme Value Index (regression method) | 0.111 | ||||
| VaR(95%) (regression method) | 0.151 | ||||
| Expected Shortfall (regression method) | 0.209 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.047 | ||||
| Quartile 1 | 0.068 | ||||
| Median | 0.162 | ||||
| Quartile 3 | 0.348 | ||||
| Maximum | 0.916 | ||||
| Mean of quarter 1 | 0.053 | ||||
| Mean of quarter 2 | 0.099 | ||||
| Mean of quarter 3 | 0.265 | ||||
| Mean of quarter 4 | 0.654 | ||||
| Inter Quartile Range | 0.281 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.916 | ||||
| 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) | -0.184 | ||||
| Compounded annual return (geometric extrapolation) | -0.301 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.329 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.461 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.552 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.060 | ||||
| SD | 0.644 | ||||
| Sharpe ratio (Glass type estimate) | 0.093 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.093 | ||||
| df | 1125.000 | ||||
| t | 0.193 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.852 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.039 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.852 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.039 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.109 | ||||
| Upside Potential Ratio | 4.838 | ||||
| Upside part of mean | 2.665 | ||||
| Downside part of mean | -2.605 | ||||
| Upside SD | 0.333 | ||||
| Downside SD | 0.551 | ||||
| N nonnegative terms | 566.000 | ||||
| N negative terms | 560.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1126.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | 0.060 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.644 | ||||
| Covariance | 0.095 | ||||
| r | 0.469 | ||||
| b (slope, estimate of beta) | 0.961 | ||||
| a (intercept, estimate of alpha) | -0.389 | ||||
| Mean Square Error | 0.324 | ||||
| DF error | 1124.000 | ||||
| t(b) | 17.826 | ||||
| p(b) | 0.265 | ||||
| t(a) | -1.413 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | 0.855 | ||||
| Upperbound of 95% confidence interval for beta | 1.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.930 | ||||
| Upperbound of 95% confidence interval for alpha | 0.151 | ||||
| Treynor index (mean / b) | 0.063 | ||||
| Jensen alpha (a) | -0.389 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.408 | ||||
| SD | 1.272 | ||||
| Sharpe ratio (Glass type estimate) | -0.321 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.320 | ||||
| df | 1125.000 | ||||
| t | -0.665 | ||||
| p | 0.513 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.266 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.625 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.266 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.625 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.331 | ||||
| Upside Potential Ratio | 2.123 | ||||
| Upside part of mean | 2.612 | ||||
| Downside part of mean | -3.020 | ||||
| Upside SD | 0.322 | ||||
| Downside SD | 1.231 | ||||
| N nonnegative terms | 566.000 | ||||
| N negative terms | 560.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1126.000 | ||||
| Mean of predictor | 0.418 | ||||
| Mean of criterion | -0.408 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 1.272 | ||||
| Covariance | 0.110 | ||||
| r | 0.274 | ||||
| b (slope, estimate of beta) | 1.100 | ||||
| a (intercept, estimate of alpha) | -0.867 | ||||
| Mean Square Error | 1.499 | ||||
| DF error | 1124.000 | ||||
| t(b) | 9.539 | ||||
| p(b) | 0.363 | ||||
| t(a) | -1.464 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | 0.874 | ||||
| Upperbound of 95% confidence interval for beta | 1.326 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.030 | ||||
| Upperbound of 95% confidence interval for alpha | 0.295 | ||||
| Treynor index (mean / b) | -0.371 | ||||
| Jensen alpha (a) | -0.867 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.123 | ||||
| Expected Shortfall on VaR | 0.151 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1126.000 | ||||
| Minimum | 0.086 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 1.165 | ||||
| Mean of quarter 1 | 0.964 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.025 | ||||
| Number outliers low | 49.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 39.000 | ||||
| Percentage of outliers high | 0.035 | ||||
| Mean of outliers high | 1.077 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.339 | ||||
| VaR(95%) (moments method) | 0.033 | ||||
| Expected Shortfall (moments method) | 0.059 | ||||
| Extreme Value Index (regression method) | 0.214 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.050 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.071 | ||||
| Maximum | 0.930 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.042 | ||||
| Mean of quarter 4 | 0.319 | ||||
| Inter Quartile Range | 0.061 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.429 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.112 | ||||
| VaR(95%) (moments method) | 0.224 | ||||
| Expected Shortfall (moments method) | 0.308 | ||||
| Extreme Value Index (regression method) | 0.060 | ||||
| VaR(95%) (regression method) | 0.411 | ||||
| Expected Shortfall (regression method) | 0.649 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.184 | ||||
| Compounded annual return (geometric extrapolation) | -0.305 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.328 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.956 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.025 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.519 | ||||
| SD | 1.471 | ||||
| Sharpe ratio (Glass type estimate) | -1.032 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.026 | ||||
| df | 130.000 | ||||
| t | -0.730 | ||||
| p | 0.532 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.805 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.745 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.801 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.749 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.099 | ||||
| Upside Potential Ratio | 2.915 | ||||
| Upside part of mean | 4.029 | ||||
| Downside part of mean | -5.548 | ||||
| Upside SD | 0.497 | ||||
| Downside SD | 1.382 | ||||
| N nonnegative terms | 63.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.102 | ||||
| Mean of criterion | -1.519 | ||||
| SD of predictor | 0.515 | ||||
| SD of criterion | 1.471 | ||||
| Covariance | 0.283 | ||||
| r | 0.373 | ||||
| b (slope, estimate of beta) | 1.065 | ||||
| a (intercept, estimate of alpha) | -2.692 | ||||
| Mean Square Error | 1.879 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.564 | ||||
| p(b) | 0.268 | ||||
| t(a) | -1.377 | ||||
| p(a) | 0.576 | ||||
| Lowerbound of 95% confidence interval for beta | 0.603 | ||||
| Upperbound of 95% confidence interval for beta | 1.526 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.561 | ||||
| Upperbound of 95% confidence interval for alpha | 1.177 | ||||
| Treynor index (mean / b) | -1.426 | ||||
| Jensen alpha (a) | -2.692 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.836 | ||||
| SD | 3.536 | ||||
| Sharpe ratio (Glass type estimate) | -1.368 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.360 | ||||
| df | 130.000 | ||||
| t | -0.967 | ||||
| p | 0.542 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.142 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.412 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.137 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.381 | ||||
| Upside Potential Ratio | 1.117 | ||||
| Upside part of mean | 3.911 | ||||
| Downside part of mean | -8.747 | ||||
| Upside SD | 0.478 | ||||
| Downside SD | 3.502 | ||||
| N nonnegative terms | 63.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.966 | ||||
| Mean of criterion | -4.836 | ||||
| SD of predictor | 0.522 | ||||
| SD of criterion | 3.536 | ||||
| Covariance | 0.417 | ||||
| r | 0.226 | ||||
| b (slope, estimate of beta) | 1.528 | ||||
| a (intercept, estimate of alpha) | -6.312 | ||||
| Mean Square Error | 11.957 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.631 | ||||
| p(b) | 0.358 | ||||
| t(a) | -1.282 | ||||
| p(a) | 0.571 | ||||
| Lowerbound of 95% confidence interval for beta | 0.379 | ||||
| Upperbound of 95% confidence interval for beta | 2.677 | ||||
| Lowerbound of 95% confidence interval for alpha | -16.051 | ||||
| Upperbound of 95% confidence interval for alpha | 3.427 | ||||
| Treynor index (mean / b) | -3.165 | ||||
| Jensen alpha (a) | -6.312 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.315 | ||||
| Expected Shortfall on VaR | 0.372 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.111 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.086 | ||||
| Quartile 1 | 0.982 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.018 | ||||
| Maximum | 1.115 | ||||
| Mean of quarter 1 | 0.923 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.753 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.084 | ||||
| Mean of outliers high | 1.088 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.635 | ||||
| VaR(95%) (moments method) | 0.067 | ||||
| Expected Shortfall (moments method) | 0.202 | ||||
| Extreme Value Index (regression method) | 0.536 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.148 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.074 | ||||
| Quartile 3 | 0.318 | ||||
| Maximum | 0.930 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.074 | ||||
| Mean of quarter 3 | 0.318 | ||||
| Mean of quarter 4 | 0.930 | ||||
| Inter Quartile Range | 0.301 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.930 | ||||
| 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) | -1.818 | ||||
| Compounded annual return (geometric extrapolation) | -0.992 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.067 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.067 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.663 | ||||