Advanced Statistics: Schulenberg SSO/SDS/UWM/TWM (^SURE)
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 | 0.420 | ||||
| SD | 0.449 | ||||
| Sharpe ratio (Glass type estimate) | 0.934 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.922 | ||||
| df | 58.000 | ||||
| t | 2.072 | ||||
| p | 0.021 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.031 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.831 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.023 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.822 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.673 | ||||
| Upside Potential Ratio | 3.234 | ||||
| Upside part of mean | 0.812 | ||||
| Downside part of mean | -0.392 | ||||
| Upside SD | 0.388 | ||||
| Downside SD | 0.251 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 21.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | 0.420 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.449 | ||||
| Covariance | 0.065 | ||||
| r | 0.572 | ||||
| b (slope, estimate of beta) | 1.021 | ||||
| a (intercept, estimate of alpha) | 0.094 | ||||
| Mean Square Error | 0.138 | ||||
| DF error | 57.000 | ||||
| t(b) | 5.272 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.528 | ||||
| p(a) | 0.300 | ||||
| Lowerbound of 95% confidence interval for beta | 0.633 | ||||
| Upperbound of 95% confidence interval for beta | 1.408 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.263 | ||||
| Upperbound of 95% confidence interval for alpha | 0.452 | ||||
| Treynor index (mean / b) | 0.411 | ||||
| Jensen alpha (a) | 0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.316 | ||||
| SD | 0.446 | ||||
| Sharpe ratio (Glass type estimate) | 0.708 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.699 | ||||
| df | 58.000 | ||||
| t | 1.571 | ||||
| p | 0.061 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.188 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.599 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.194 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.592 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.084 | ||||
| Upside Potential Ratio | 2.553 | ||||
| Upside part of mean | 0.745 | ||||
| Downside part of mean | -0.429 | ||||
| Upside SD | 0.345 | ||||
| Downside SD | 0.292 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 21.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.284 | ||||
| Mean of criterion | 0.316 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.446 | ||||
| Covariance | 0.067 | ||||
| r | 0.611 | ||||
| b (slope, estimate of beta) | 1.114 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.127 | ||||
| DF error | 57.000 | ||||
| t(b) | 5.833 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.003 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.731 | ||||
| Upperbound of 95% confidence interval for beta | 1.496 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.340 | ||||
| Upperbound of 95% confidence interval for alpha | 0.339 | ||||
| Treynor index (mean / b) | 0.284 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.169 | ||||
| Expected Shortfall on VaR | 0.212 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.127 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.618 | ||||
| Quartile 1 | 0.954 | ||||
| Median | 1.039 | ||||
| Quartile 3 | 1.107 | ||||
| Maximum | 1.416 | ||||
| Mean of quarter 1 | 0.886 | ||||
| Mean of quarter 2 | 1.007 | ||||
| Mean of quarter 3 | 1.069 | ||||
| Mean of quarter 4 | 1.194 | ||||
| Inter Quartile Range | 0.153 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.017 | ||||
| Mean of outliers low | 0.618 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.017 | ||||
| Mean of outliers high | 1.416 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.301 | ||||
| VaR(95%) (moments method) | 0.121 | ||||
| Expected Shortfall (moments method) | 0.200 | ||||
| Extreme Value Index (regression method) | 0.411 | ||||
| VaR(95%) (regression method) | 0.133 | ||||
| Expected Shortfall (regression method) | 0.250 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.082 | ||||
| Median | 0.115 | ||||
| Quartile 3 | 0.190 | ||||
| Maximum | 0.415 | ||||
| Mean of quarter 1 | 0.042 | ||||
| Mean of quarter 2 | 0.096 | ||||
| Mean of quarter 3 | 0.152 | ||||
| Mean of quarter 4 | 0.286 | ||||
| Inter Quartile Range | 0.108 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.415 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.762 | ||||
| VaR(95%) (moments method) | 0.329 | ||||
| Expected Shortfall (moments method) | 0.368 | ||||
| Extreme Value Index (regression method) | 0.752 | ||||
| VaR(95%) (regression method) | 0.408 | ||||
| Expected Shortfall (regression method) | 1.348 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.991 | ||||
| Compounded annual return (geometric extrapolation) | 0.433 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.045 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.516 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.045 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.523 | ||||
| SD | 0.555 | ||||
| Sharpe ratio (Glass type estimate) | 0.943 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.942 | ||||
| df | 1302.000 | ||||
| t | 2.103 | ||||
| p | 0.471 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.063 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.822 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.063 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.822 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.340 | ||||
| Upside Potential Ratio | 7.678 | ||||
| Upside part of mean | 2.998 | ||||
| Downside part of mean | -2.475 | ||||
| Upside SD | 0.395 | ||||
| Downside SD | 0.390 | ||||
| N nonnegative terms | 704.000 | ||||
| N negative terms | 599.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1303.000 | ||||
| Mean of predictor | 0.344 | ||||
| Mean of criterion | 0.523 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.555 | ||||
| Covariance | 0.100 | ||||
| r | 0.695 | ||||
| b (slope, estimate of beta) | 1.483 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.159 | ||||
| DF error | 1301.000 | ||||
| t(b) | 34.886 | ||||
| p(b) | 0.096 | ||||
| t(a) | 0.075 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 1.399 | ||||
| Upperbound of 95% confidence interval for beta | 1.566 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.339 | ||||
| Upperbound of 95% confidence interval for alpha | 0.366 | ||||
| Treynor index (mean / b) | 0.353 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.366 | ||||
| SD | 0.562 | ||||
| Sharpe ratio (Glass type estimate) | 0.652 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.652 | ||||
| df | 1302.000 | ||||
| t | 1.454 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.227 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.531 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.228 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.531 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.884 | ||||
| Upside Potential Ratio | 7.049 | ||||
| Upside part of mean | 2.923 | ||||
| Downside part of mean | -2.557 | ||||
| Upside SD | 0.380 | ||||
| Downside SD | 0.415 | ||||
| N nonnegative terms | 704.000 | ||||
| N negative terms | 599.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1303.000 | ||||
| Mean of predictor | 0.309 | ||||
| Mean of criterion | 0.366 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.562 | ||||
| Covariance | 0.103 | ||||
| r | 0.700 | ||||
| b (slope, estimate of beta) | 1.506 | ||||
| a (intercept, estimate of alpha) | -0.100 | ||||
| Mean Square Error | 0.161 | ||||
| DF error | 1301.000 | ||||
| t(b) | 35.363 | ||||
| p(b) | 0.094 | ||||
| t(a) | -0.552 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 1.423 | ||||
| Upperbound of 95% confidence interval for beta | 1.590 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.454 | ||||
| Upperbound of 95% confidence interval for alpha | 0.254 | ||||
| Treynor index (mean / b) | 0.243 | ||||
| Jensen alpha (a) | -0.100 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1303.000 | ||||
| Minimum | 0.729 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 1.181 | ||||
| Mean of quarter 1 | 0.965 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.039 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 80.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.920 | ||||
| Number of outliers high | 77.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.082 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.435 | ||||
| VaR(95%) (moments method) | 0.031 | ||||
| Expected Shortfall (moments method) | 0.064 | ||||
| Extreme Value Index (regression method) | 0.187 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.051 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 54.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.111 | ||||
| Maximum | 0.519 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.027 | ||||
| Mean of quarter 3 | 0.076 | ||||
| Mean of quarter 4 | 0.242 | ||||
| Inter Quartile Range | 0.093 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.357 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.028 | ||||
| VaR(95%) (moments method) | 0.239 | ||||
| Expected Shortfall (moments method) | 0.315 | ||||
| Extreme Value Index (regression method) | -0.406 | ||||
| VaR(95%) (regression method) | 0.266 | ||||
| Expected Shortfall (regression method) | 0.313 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.348 | ||||
| Compounded annual return (geometric extrapolation) | 0.508 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.978 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.095 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.493 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.352 | ||||
| SD | 1.039 | ||||
| Sharpe ratio (Glass type estimate) | 1.301 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.294 | ||||
| df | 130.000 | ||||
| t | 0.920 | ||||
| p | 0.460 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.477 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.075 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.482 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.070 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.899 | ||||
| Upside Potential Ratio | 10.220 | ||||
| Upside part of mean | 7.277 | ||||
| Downside part of mean | -5.925 | ||||
| Upside SD | 0.756 | ||||
| Downside SD | 0.712 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.977 | ||||
| Mean of criterion | 1.352 | ||||
| SD of predictor | 0.469 | ||||
| SD of criterion | 1.039 | ||||
| Covariance | 0.450 | ||||
| r | 0.924 | ||||
| b (slope, estimate of beta) | 2.047 | ||||
| a (intercept, estimate of alpha) | -0.648 | ||||
| Mean Square Error | 0.159 | ||||
| DF error | 129.000 | ||||
| t(b) | 27.427 | ||||
| p(b) | 0.012 | ||||
| t(a) | -1.139 | ||||
| p(a) | 0.563 | ||||
| Lowerbound of 95% confidence interval for beta | 1.899 | ||||
| Upperbound of 95% confidence interval for beta | 2.194 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.774 | ||||
| Upperbound of 95% confidence interval for alpha | 0.478 | ||||
| Treynor index (mean / b) | 0.661 | ||||
| Jensen alpha (a) | -0.648 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.810 | ||||
| SD | 1.046 | ||||
| Sharpe ratio (Glass type estimate) | 0.775 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.770 | ||||
| df | 130.000 | ||||
| t | 0.548 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.000 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.547 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.003 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.544 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.075 | ||||
| Upside Potential Ratio | 9.295 | ||||
| Upside part of mean | 7.008 | ||||
| Downside part of mean | -6.198 | ||||
| Upside SD | 0.721 | ||||
| Downside SD | 0.754 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.867 | ||||
| Mean of criterion | 0.810 | ||||
| SD of predictor | 0.468 | ||||
| SD of criterion | 1.046 | ||||
| Covariance | 0.453 | ||||
| r | 0.924 | ||||
| b (slope, estimate of beta) | 2.064 | ||||
| a (intercept, estimate of alpha) | -0.979 | ||||
| Mean Square Error | 0.160 | ||||
| DF error | 129.000 | ||||
| t(b) | 27.528 | ||||
| p(b) | 0.012 | ||||
| t(a) | -1.717 | ||||
| p(a) | 0.595 | ||||
| Lowerbound of 95% confidence interval for beta | 1.916 | ||||
| Upperbound of 95% confidence interval for beta | 2.213 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.107 | ||||
| Upperbound of 95% confidence interval for alpha | 0.149 | ||||
| Treynor index (mean / b) | 0.393 | ||||
| Jensen alpha (a) | -0.979 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 0.966 | ||||
| Median | 1.010 | ||||
| Quartile 3 | 1.041 | ||||
| Maximum | 1.181 | ||||
| Mean of quarter 1 | 0.922 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.027 | ||||
| Mean of quarter 4 | 1.084 | ||||
| Inter Quartile Range | 0.076 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.823 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.181 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.251 | ||||
| VaR(95%) (moments method) | 0.077 | ||||
| Expected Shortfall (moments method) | 0.094 | ||||
| Extreme Value Index (regression method) | -0.532 | ||||
| VaR(95%) (regression method) | 0.077 | ||||
| Expected Shortfall (regression method) | 0.087 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.041 | ||||
| Quartile 1 | 0.092 | ||||
| Median | 0.146 | ||||
| Quartile 3 | 0.292 | ||||
| Maximum | 0.490 | ||||
| Mean of quarter 1 | 0.066 | ||||
| Mean of quarter 2 | 0.146 | ||||
| Mean of quarter 3 | 0.292 | ||||
| Mean of quarter 4 | 0.490 | ||||
| Inter Quartile Range | 0.200 | ||||
| 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) | 1.066 | ||||
| Compounded annual return (geometric extrapolation) | 1.350 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.752 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.752 | ||||
| Compounded annual return / Expected Shortfall lognormal | 11.080 | ||||