Advanced Statistics: Test123
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 | 0.365 | ||||
| SD | 0.533 | ||||
| Sharpe ratio (Glass type estimate) | 0.685 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.670 | ||||
| df | 35.000 | ||||
| t | 1.187 | ||||
| p | 0.122 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.462 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.823 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.472 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.813 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.375 | ||||
| Upside Potential Ratio | 3.357 | ||||
| Upside part of mean | 0.891 | ||||
| Downside part of mean | -0.526 | ||||
| Upside SD | 0.466 | ||||
| Downside SD | 0.266 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 16.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.487 | ||||
| Mean of criterion | 0.365 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.533 | ||||
| Covariance | 0.009 | ||||
| r | 0.073 | ||||
| b (slope, estimate of beta) | 0.161 | ||||
| a (intercept, estimate of alpha) | 0.287 | ||||
| Mean Square Error | 0.291 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.427 | ||||
| p(b) | 0.336 | ||||
| t(a) | 0.793 | ||||
| p(a) | 0.217 | ||||
| Lowerbound of 95% confidence interval for beta | -0.605 | ||||
| Upperbound of 95% confidence interval for beta | 0.928 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.448 | ||||
| Upperbound of 95% confidence interval for alpha | 1.021 | ||||
| Treynor index (mean / b) | 2.267 | ||||
| Jensen alpha (a) | 0.287 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.235 | ||||
| SD | 0.499 | ||||
| Sharpe ratio (Glass type estimate) | 0.471 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.460 | ||||
| df | 35.000 | ||||
| t | 0.815 | ||||
| p | 0.210 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.670 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.604 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.676 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.597 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.819 | ||||
| Upside Potential Ratio | 2.783 | ||||
| Upside part of mean | 0.798 | ||||
| Downside part of mean | -0.563 | ||||
| Upside SD | 0.406 | ||||
| Downside SD | 0.287 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 16.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.450 | ||||
| Mean of criterion | 0.235 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 0.499 | ||||
| Covariance | 0.010 | ||||
| r | 0.088 | ||||
| b (slope, estimate of beta) | 0.196 | ||||
| a (intercept, estimate of alpha) | 0.147 | ||||
| Mean Square Error | 0.255 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.517 | ||||
| p(b) | 0.304 | ||||
| t(a) | 0.434 | ||||
| p(a) | 0.334 | ||||
| Lowerbound of 95% confidence interval for beta | -0.576 | ||||
| Upperbound of 95% confidence interval for beta | 0.968 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.540 | ||||
| Upperbound of 95% confidence interval for alpha | 0.833 | ||||
| Treynor index (mean / b) | 1.197 | ||||
| Jensen alpha (a) | 0.147 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.195 | ||||
| Expected Shortfall on VaR | 0.241 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.095 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.792 | ||||
| Quartile 1 | 0.925 | ||||
| Median | 1.019 | ||||
| Quartile 3 | 1.105 | ||||
| Maximum | 1.401 | ||||
| Mean of quarter 1 | 0.860 | ||||
| Mean of quarter 2 | 0.974 | ||||
| Mean of quarter 3 | 1.058 | ||||
| Mean of quarter 4 | 1.245 | ||||
| Inter Quartile Range | 0.181 | ||||
| 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 | 0.056 | ||||
| Mean of outliers high | 1.400 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.059 | ||||
| VaR(95%) (moments method) | 0.137 | ||||
| Expected Shortfall (moments method) | 0.137 | ||||
| Extreme Value Index (regression method) | -0.775 | ||||
| VaR(95%) (regression method) | 0.126 | ||||
| Expected Shortfall (regression method) | 0.133 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.116 | ||||
| Quartile 1 | 0.224 | ||||
| Median | 0.235 | ||||
| Quartile 3 | 0.265 | ||||
| Maximum | 0.332 | ||||
| Mean of quarter 1 | 0.170 | ||||
| Mean of quarter 2 | 0.235 | ||||
| Mean of quarter 3 | 0.265 | ||||
| Mean of quarter 4 | 0.332 | ||||
| Inter Quartile Range | 0.041 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.116 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.332 | ||||
| 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) | 0.436 | ||||
| Compounded annual return (geometric extrapolation) | 0.322 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.971 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.971 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.333 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.557 | ||||
| SD | 0.921 | ||||
| Sharpe ratio (Glass type estimate) | 0.604 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.604 | ||||
| df | 805.000 | ||||
| t | 1.060 | ||||
| p | 0.145 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.514 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.722 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.514 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.722 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.408 | ||||
| Upside Potential Ratio | 9.869 | ||||
| Upside part of mean | 3.902 | ||||
| Downside part of mean | -3.345 | ||||
| Upside SD | 0.832 | ||||
| Downside SD | 0.395 | ||||
| N nonnegative terms | 368.000 | ||||
| N negative terms | 438.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 806.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | 0.557 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.921 | ||||
| Covariance | -0.058 | ||||
| r | -0.198 | ||||
| b (slope, estimate of beta) | -0.573 | ||||
| a (intercept, estimate of alpha) | 0.878 | ||||
| Mean Square Error | 0.816 | ||||
| DF error | 804.000 | ||||
| t(b) | -5.718 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.695 | ||||
| p(a) | 0.045 | ||||
| Lowerbound of 95% confidence interval for beta | -0.770 | ||||
| Upperbound of 95% confidence interval for beta | -0.376 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 1.895 | ||||
| Treynor index (mean / b) | -0.971 | ||||
| Jensen alpha (a) | 0.878 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.234 | ||||
| SD | 0.760 | ||||
| Sharpe ratio (Glass type estimate) | 0.309 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.308 | ||||
| df | 805.000 | ||||
| t | 0.541 | ||||
| p | 0.294 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.809 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.426 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.809 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.426 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.573 | ||||
| Upside Potential Ratio | 8.946 | ||||
| Upside part of mean | 3.661 | ||||
| Downside part of mean | -3.427 | ||||
| Upside SD | 0.640 | ||||
| Downside SD | 0.409 | ||||
| N nonnegative terms | 368.000 | ||||
| N negative terms | 438.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 806.000 | ||||
| Mean of predictor | 0.509 | ||||
| Mean of criterion | 0.234 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 0.760 | ||||
| Covariance | -0.058 | ||||
| r | -0.235 | ||||
| b (slope, estimate of beta) | -0.552 | ||||
| a (intercept, estimate of alpha) | 0.516 | ||||
| Mean Square Error | 0.546 | ||||
| DF error | 804.000 | ||||
| t(b) | -6.866 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.218 | ||||
| p(a) | 0.112 | ||||
| Lowerbound of 95% confidence interval for beta | -0.710 | ||||
| Upperbound of 95% confidence interval for beta | -0.394 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.315 | ||||
| Upperbound of 95% confidence interval for alpha | 1.346 | ||||
| Treynor index (mean / b) | -0.425 | ||||
| Jensen alpha (a) | 0.516 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.091 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.058 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 806.000 | ||||
| Minimum | 0.872 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 2.189 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.053 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 21.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.906 | ||||
| Number of outliers high | 32.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.145 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.195 | ||||
| VaR(95%) (moments method) | 0.043 | ||||
| Expected Shortfall (moments method) | 0.065 | ||||
| Extreme Value Index (regression method) | 0.039 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.050 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.083 | ||||
| Median | 0.198 | ||||
| Quartile 3 | 0.302 | ||||
| Maximum | 0.538 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | 0.119 | ||||
| Mean of quarter 3 | 0.256 | ||||
| Mean of quarter 4 | 0.418 | ||||
| Inter Quartile Range | 0.219 | ||||
| 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) | -3.098 | ||||
| VaR(95%) (moments method) | 0.474 | ||||
| Expected Shortfall (moments method) | 0.477 | ||||
| Extreme Value Index (regression method) | -0.477 | ||||
| VaR(95%) (regression method) | 0.557 | ||||
| Expected Shortfall (regression method) | 0.630 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.441 | ||||
| Compounded annual return (geometric extrapolation) | 0.321 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.597 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.767 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.516 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.756 | ||||
| SD | 0.408 | ||||
| Sharpe ratio (Glass type estimate) | 1.852 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.841 | ||||
| df | 130.000 | ||||
| t | 1.309 | ||||
| p | 0.443 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.933 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.629 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.940 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.622 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.122 | ||||
| Upside Potential Ratio | 11.265 | ||||
| Upside part of mean | 2.727 | ||||
| Downside part of mean | -1.971 | ||||
| Upside SD | 0.330 | ||||
| Downside SD | 0.242 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.131 | ||||
| Mean of criterion | 0.756 | ||||
| SD of predictor | 0.442 | ||||
| SD of criterion | 0.408 | ||||
| Covariance | -0.044 | ||||
| r | -0.243 | ||||
| b (slope, estimate of beta) | -0.224 | ||||
| a (intercept, estimate of alpha) | 1.009 | ||||
| Mean Square Error | 0.158 | ||||
| DF error | 129.000 | ||||
| t(b) | -2.845 | ||||
| p(b) | 0.653 | ||||
| t(a) | 1.773 | ||||
| p(a) | 0.402 | ||||
| Lowerbound of 95% confidence interval for beta | -0.380 | ||||
| Upperbound of 95% confidence interval for beta | -0.068 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.117 | ||||
| Upperbound of 95% confidence interval for alpha | 2.135 | ||||
| Treynor index (mean / b) | -3.371 | ||||
| Jensen alpha (a) | 1.009 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.673 | ||||
| SD | 0.405 | ||||
| Sharpe ratio (Glass type estimate) | 1.661 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.651 | ||||
| df | 130.000 | ||||
| t | 1.174 | ||||
| p | 0.449 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.121 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.437 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.128 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.430 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.723 | ||||
| Upside Potential Ratio | 10.819 | ||||
| Upside part of mean | 2.674 | ||||
| Downside part of mean | -2.001 | ||||
| Upside SD | 0.322 | ||||
| Downside SD | 0.247 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.031 | ||||
| Mean of criterion | 0.673 | ||||
| SD of predictor | 0.445 | ||||
| SD of criterion | 0.405 | ||||
| Covariance | -0.044 | ||||
| r | -0.247 | ||||
| b (slope, estimate of beta) | -0.224 | ||||
| a (intercept, estimate of alpha) | 0.904 | ||||
| Mean Square Error | 0.155 | ||||
| DF error | 129.000 | ||||
| t(b) | -2.891 | ||||
| p(b) | 0.655 | ||||
| t(a) | 1.606 | ||||
| p(a) | 0.411 | ||||
| Lowerbound of 95% confidence interval for beta | -0.378 | ||||
| Upperbound of 95% confidence interval for beta | -0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.210 | ||||
| Upperbound of 95% confidence interval for alpha | 2.018 | ||||
| Treynor index (mean / b) | -2.999 | ||||
| Jensen alpha (a) | 0.904 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.923 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.066 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.539 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.029 | ||||
| Extreme Value Index (regression method) | -0.175 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.038 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.037 | ||||
| Median | 0.047 | ||||
| Quartile 3 | 0.076 | ||||
| Maximum | 0.174 | ||||
| Mean of quarter 1 | 0.033 | ||||
| Mean of quarter 2 | 0.043 | ||||
| Mean of quarter 3 | 0.054 | ||||
| Mean of quarter 4 | 0.136 | ||||
| Inter Quartile Range | 0.039 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.174 | ||||
| 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) | 0.862 | ||||
| Compounded annual return (geometric extrapolation) | 1.048 | ||||
| Calmar ratio (compounded annual return / max draw down) | 6.029 | ||||
| Compounded annual return / average of 25% largest draw downs | 7.690 | ||||
| Compounded annual return / Expected Shortfall lognormal | 21.910 | ||||