Advanced Statistics: Engleman Invest
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 | 0.482 | ||||
| SD | 0.712 | ||||
| Sharpe ratio (Glass type estimate) | 0.677 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.664 | ||||
| df | 40.000 | ||||
| t | 1.251 | ||||
| p | 0.109 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.398 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.743 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.406 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.734 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.138 | ||||
| Upside Potential Ratio | 4.066 | ||||
| Upside part of mean | 0.916 | ||||
| Downside part of mean | -0.434 | ||||
| Upside SD | 0.680 | ||||
| Downside SD | 0.225 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.487 | ||||
| Mean of criterion | 0.482 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.712 | ||||
| Covariance | 0.044 | ||||
| r | 0.228 | ||||
| b (slope, estimate of beta) | 0.594 | ||||
| a (intercept, estimate of alpha) | 0.193 | ||||
| Mean Square Error | 0.493 | ||||
| DF error | 39.000 | ||||
| t(b) | 1.459 | ||||
| p(b) | 0.076 | ||||
| t(a) | 0.450 | ||||
| p(a) | 0.328 | ||||
| Lowerbound of 95% confidence interval for beta | -0.229 | ||||
| Upperbound of 95% confidence interval for beta | 1.418 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.674 | ||||
| Upperbound of 95% confidence interval for alpha | 1.059 | ||||
| Treynor index (mean / b) | 0.811 | ||||
| Jensen alpha (a) | 0.193 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.297 | ||||
| SD | 0.563 | ||||
| Sharpe ratio (Glass type estimate) | 0.528 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.518 | ||||
| df | 40.000 | ||||
| t | 0.976 | ||||
| p | 0.168 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.542 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.591 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.549 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.584 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.201 | ||||
| Upside Potential Ratio | 3.067 | ||||
| Upside part of mean | 0.759 | ||||
| Downside part of mean | -0.461 | ||||
| Upside SD | 0.505 | ||||
| Downside SD | 0.247 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.441 | ||||
| Mean of criterion | 0.297 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.563 | ||||
| Covariance | 0.034 | ||||
| r | 0.225 | ||||
| b (slope, estimate of beta) | 0.476 | ||||
| a (intercept, estimate of alpha) | 0.087 | ||||
| Mean Square Error | 0.308 | ||||
| DF error | 39.000 | ||||
| t(b) | 1.444 | ||||
| p(b) | 0.078 | ||||
| t(a) | 0.262 | ||||
| p(a) | 0.398 | ||||
| Lowerbound of 95% confidence interval for beta | -0.191 | ||||
| Upperbound of 95% confidence interval for beta | 1.142 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.588 | ||||
| Upperbound of 95% confidence interval for alpha | 0.762 | ||||
| Treynor index (mean / b) | 0.625 | ||||
| Jensen alpha (a) | 0.087 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.215 | ||||
| Expected Shortfall on VaR | 0.266 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.088 | ||||
| Expected Shortfall on VaR | 0.157 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.733 | ||||
| Quartile 1 | 0.952 | ||||
| Median | 0.993 | ||||
| Quartile 3 | 1.091 | ||||
| Maximum | 2.045 | ||||
| Mean of quarter 1 | 0.896 | ||||
| Mean of quarter 2 | 0.974 | ||||
| Mean of quarter 3 | 1.040 | ||||
| Mean of quarter 4 | 1.279 | ||||
| Inter Quartile Range | 0.139 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.024 | ||||
| Mean of outliers low | 0.733 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.784 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.263 | ||||
| VaR(95%) (moments method) | 0.105 | ||||
| Expected Shortfall (moments method) | 0.128 | ||||
| Extreme Value Index (regression method) | 0.036 | ||||
| VaR(95%) (regression method) | 0.123 | ||||
| Expected Shortfall (regression method) | 0.171 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.054 | ||||
| Quartile 1 | 0.056 | ||||
| Median | 0.129 | ||||
| Quartile 3 | 0.262 | ||||
| Maximum | 0.412 | ||||
| Mean of quarter 1 | 0.055 | ||||
| Mean of quarter 2 | 0.129 | ||||
| Mean of quarter 3 | 0.262 | ||||
| Mean of quarter 4 | 0.412 | ||||
| Inter Quartile Range | 0.206 | ||||
| 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) | 0.646 | ||||
| Compounded annual return (geometric extrapolation) | 0.407 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.988 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.988 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.531 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.385 | ||||
| SD | 0.428 | ||||
| Sharpe ratio (Glass type estimate) | 0.899 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.898 | ||||
| df | 901.000 | ||||
| t | 1.668 | ||||
| p | 0.048 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.158 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.956 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.159 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.956 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.446 | ||||
| Upside Potential Ratio | 9.574 | ||||
| Upside part of mean | 2.549 | ||||
| Downside part of mean | -2.164 | ||||
| Upside SD | 0.336 | ||||
| Downside SD | 0.266 | ||||
| N nonnegative terms | 441.000 | ||||
| N negative terms | 461.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 902.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | 0.385 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.428 | ||||
| Covariance | -0.020 | ||||
| r | -0.154 | ||||
| b (slope, estimate of beta) | -0.221 | ||||
| a (intercept, estimate of alpha) | 0.498 | ||||
| Mean Square Error | 0.179 | ||||
| DF error | 900.000 | ||||
| t(b) | -4.685 | ||||
| p(b) | 1.000 | ||||
| t(a) | 2.171 | ||||
| p(a) | 0.015 | ||||
| Lowerbound of 95% confidence interval for beta | -0.314 | ||||
| Upperbound of 95% confidence interval for beta | -0.128 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.948 | ||||
| Treynor index (mean / b) | -1.741 | ||||
| Jensen alpha (a) | 0.498 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.295 | ||||
| SD | 0.424 | ||||
| Sharpe ratio (Glass type estimate) | 0.695 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.695 | ||||
| df | 901.000 | ||||
| t | 1.290 | ||||
| p | 0.099 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.362 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.752 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.362 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.751 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.079 | ||||
| Upside Potential Ratio | 9.136 | ||||
| Upside part of mean | 2.495 | ||||
| Downside part of mean | -2.200 | ||||
| Upside SD | 0.324 | ||||
| Downside SD | 0.273 | ||||
| N nonnegative terms | 441.000 | ||||
| N negative terms | 461.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 902.000 | ||||
| Mean of predictor | 0.465 | ||||
| Mean of criterion | 0.295 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 0.424 | ||||
| Covariance | -0.020 | ||||
| r | -0.157 | ||||
| b (slope, estimate of beta) | -0.218 | ||||
| a (intercept, estimate of alpha) | 0.396 | ||||
| Mean Square Error | 0.175 | ||||
| DF error | 900.000 | ||||
| t(b) | -4.758 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.747 | ||||
| p(a) | 0.040 | ||||
| Lowerbound of 95% confidence interval for beta | -0.308 | ||||
| Upperbound of 95% confidence interval for beta | -0.128 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.049 | ||||
| Upperbound of 95% confidence interval for alpha | 0.841 | ||||
| Treynor index (mean / b) | -1.349 | ||||
| Jensen alpha (a) | 0.396 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 902.000 | ||||
| Minimum | 0.890 | ||||
| Quartile 1 | 0.988 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.152 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.025 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.021 | ||||
| Mean of outliers low | 0.931 | ||||
| Number of outliers high | 33.000 | ||||
| Percentage of outliers high | 0.037 | ||||
| Mean of outliers high | 1.082 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.030 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | 0.036 | ||||
| Extreme Value Index (regression method) | 0.084 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 22.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.069 | ||||
| Maximum | 0.531 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.039 | ||||
| Mean of quarter 4 | 0.240 | ||||
| Inter Quartile Range | 0.063 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.182 | ||||
| Mean of outliers high | 0.313 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.189 | ||||
| VaR(95%) (moments method) | 0.205 | ||||
| Expected Shortfall (moments method) | 0.220 | ||||
| Extreme Value Index (regression method) | 0.016 | ||||
| VaR(95%) (regression method) | 0.351 | ||||
| Expected Shortfall (regression method) | 0.525 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.641 | ||||
| Compounded annual return (geometric extrapolation) | 0.403 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.758 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.676 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.830 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.216 | ||||
| SD | 0.322 | ||||
| Sharpe ratio (Glass type estimate) | 0.671 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.667 | ||||
| df | 130.000 | ||||
| t | 0.474 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.104 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.442 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.106 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.440 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.022 | ||||
| Upside Potential Ratio | 8.636 | ||||
| Upside part of mean | 1.824 | ||||
| Downside part of mean | -1.608 | ||||
| Upside SD | 0.241 | ||||
| Downside SD | 0.211 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.122 | ||||
| Mean of criterion | 0.216 | ||||
| SD of predictor | 0.444 | ||||
| SD of criterion | 0.322 | ||||
| Covariance | -0.043 | ||||
| r | -0.301 | ||||
| b (slope, estimate of beta) | -0.218 | ||||
| a (intercept, estimate of alpha) | 0.460 | ||||
| Mean Square Error | 0.095 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.581 | ||||
| p(b) | 0.689 | ||||
| t(a) | 1.044 | ||||
| p(a) | 0.442 | ||||
| Lowerbound of 95% confidence interval for beta | -0.339 | ||||
| Upperbound of 95% confidence interval for beta | -0.098 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.412 | ||||
| Upperbound of 95% confidence interval for alpha | 1.333 | ||||
| Treynor index (mean / b) | -0.989 | ||||
| Jensen alpha (a) | 0.460 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.165 | ||||
| SD | 0.320 | ||||
| Sharpe ratio (Glass type estimate) | 0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.511 | ||||
| df | 130.000 | ||||
| t | 0.364 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.259 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.286 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.261 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.284 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.764 | ||||
| Upside Potential Ratio | 8.330 | ||||
| Upside part of mean | 1.795 | ||||
| Downside part of mean | -1.631 | ||||
| Upside SD | 0.235 | ||||
| Downside SD | 0.216 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.022 | ||||
| Mean of criterion | 0.165 | ||||
| SD of predictor | 0.443 | ||||
| SD of criterion | 0.320 | ||||
| Covariance | -0.043 | ||||
| r | -0.304 | ||||
| b (slope, estimate of beta) | -0.219 | ||||
| a (intercept, estimate of alpha) | 0.389 | ||||
| Mean Square Error | 0.094 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.619 | ||||
| p(b) | 0.690 | ||||
| t(a) | 0.889 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | -0.339 | ||||
| Upperbound of 95% confidence interval for beta | -0.099 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.477 | ||||
| Upperbound of 95% confidence interval for alpha | 1.254 | ||||
| Treynor index (mean / b) | -0.751 | ||||
| Jensen alpha (a) | 0.389 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.925 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.102 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.959 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.053 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.147 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | -0.154 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.064 | ||||
| Maximum | 0.147 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.020 | ||||
| Mean of quarter 3 | 0.045 | ||||
| Mean of quarter 4 | 0.123 | ||||
| Inter Quartile Range | 0.054 | ||||
| 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 | 0.147 | ||||
| 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) | 0.220 | ||||
| Compounded annual return (geometric extrapolation) | 0.232 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.583 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.890 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.899 | ||||