Advanced Statistics: Target 50 stopped trading 8-28-07
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 | 0.804 | ||||
| SD | 1.546 | ||||
| Sharpe ratio (Glass type estimate) | 0.520 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.516 | ||||
| df | 86.000 | ||||
| t | 1.401 | ||||
| p | 0.082 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.213 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.251 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.216 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.248 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.664 | ||||
| Upside Potential Ratio | 3.146 | ||||
| Upside part of mean | 1.520 | ||||
| Downside part of mean | -0.716 | ||||
| Upside SD | 1.478 | ||||
| Downside SD | 0.483 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.217 | ||||
| Mean of criterion | 0.804 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 1.546 | ||||
| Covariance | 0.339 | ||||
| r | 0.653 | ||||
| b (slope, estimate of beta) | 3.001 | ||||
| a (intercept, estimate of alpha) | 0.153 | ||||
| Mean Square Error | 1.388 | ||||
| DF error | 85.000 | ||||
| t(b) | 7.943 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.344 | ||||
| p(a) | 0.366 | ||||
| Lowerbound of 95% confidence interval for beta | 2.249 | ||||
| Upperbound of 95% confidence interval for beta | 3.752 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.732 | ||||
| Upperbound of 95% confidence interval for alpha | 1.038 | ||||
| Treynor index (mean / b) | 0.268 | ||||
| Jensen alpha (a) | 0.153 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.181 | ||||
| SD | 1.046 | ||||
| Sharpe ratio (Glass type estimate) | 0.173 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.172 | ||||
| df | 86.000 | ||||
| t | 0.466 | ||||
| p | 0.321 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.556 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.901 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.557 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.900 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.250 | ||||
| Upside Potential Ratio | 1.505 | ||||
| Upside part of mean | 1.090 | ||||
| Downside part of mean | -0.909 | ||||
| Upside SD | 0.747 | ||||
| Downside SD | 0.724 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.159 | ||||
| Mean of criterion | 0.181 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 1.046 | ||||
| Covariance | 0.289 | ||||
| r | 0.813 | ||||
| b (slope, estimate of beta) | 2.501 | ||||
| a (intercept, estimate of alpha) | -0.216 | ||||
| Mean Square Error | 0.376 | ||||
| DF error | 85.000 | ||||
| t(b) | 12.857 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.940 | ||||
| p(a) | 0.825 | ||||
| Lowerbound of 95% confidence interval for beta | 2.114 | ||||
| Upperbound of 95% confidence interval for beta | 2.887 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.673 | ||||
| Upperbound of 95% confidence interval for alpha | 0.241 | ||||
| Treynor index (mean / b) | 0.072 | ||||
| Jensen alpha (a) | -0.216 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.382 | ||||
| Expected Shortfall on VaR | 0.452 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.120 | ||||
| Expected Shortfall on VaR | 0.255 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 87.000 | ||||
| Minimum | 0.245 | ||||
| Quartile 1 | 0.947 | ||||
| Median | 1.024 | ||||
| Quartile 3 | 1.128 | ||||
| Maximum | 4.595 | ||||
| Mean of quarter 1 | 0.787 | ||||
| Mean of quarter 2 | 0.988 | ||||
| Mean of quarter 3 | 1.075 | ||||
| Mean of quarter 4 | 1.433 | ||||
| Inter Quartile Range | 0.182 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.416 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 2.254 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.245 | ||||
| VaR(95%) (moments method) | 0.179 | ||||
| Expected Shortfall (moments method) | 0.302 | ||||
| Extreme Value Index (regression method) | 0.356 | ||||
| VaR(95%) (regression method) | 0.221 | ||||
| Expected Shortfall (regression method) | 0.429 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.154 | ||||
| Quartile 3 | 0.267 | ||||
| Maximum | 0.937 | ||||
| Mean of quarter 1 | 0.050 | ||||
| Mean of quarter 2 | 0.118 | ||||
| Mean of quarter 3 | 0.222 | ||||
| Mean of quarter 4 | 0.659 | ||||
| Inter Quartile Range | 0.196 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.937 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.294 | ||||
| VaR(95%) (moments method) | 0.602 | ||||
| Expected Shortfall (moments method) | 0.741 | ||||
| Extreme Value Index (regression method) | 1.290 | ||||
| VaR(95%) (regression method) | 1.217 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.567 | ||||
| Compounded annual return (geometric extrapolation) | 0.252 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.269 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.383 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.558 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.709 | ||||
| SD | 2.007 | ||||
| Sharpe ratio (Glass type estimate) | 0.851 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.851 | ||||
| df | 1918.000 | ||||
| t | 2.304 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.126 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.576 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.126 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.576 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.886 | ||||
| Upside Potential Ratio | 7.320 | ||||
| Upside part of mean | 6.634 | ||||
| Downside part of mean | -4.925 | ||||
| Upside SD | 1.794 | ||||
| Downside SD | 0.906 | ||||
| N nonnegative terms | 987.000 | ||||
| N negative terms | 932.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1919.000 | ||||
| Mean of predictor | 0.338 | ||||
| Mean of criterion | 1.709 | ||||
| SD of predictor | 0.558 | ||||
| SD of criterion | 2.007 | ||||
| Covariance | 0.755 | ||||
| r | 0.674 | ||||
| b (slope, estimate of beta) | 2.421 | ||||
| a (intercept, estimate of alpha) | 0.889 | ||||
| Mean Square Error | 2.203 | ||||
| DF error | 1917.000 | ||||
| t(b) | 39.894 | ||||
| p(b) | 0.106 | ||||
| t(a) | 1.621 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | 2.302 | ||||
| Upperbound of 95% confidence interval for beta | 2.540 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.187 | ||||
| Upperbound of 95% confidence interval for alpha | 1.966 | ||||
| Treynor index (mean / b) | 0.706 | ||||
| Jensen alpha (a) | 0.889 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.219 | ||||
| SD | 1.698 | ||||
| Sharpe ratio (Glass type estimate) | 0.129 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.129 | ||||
| df | 1918.000 | ||||
| t | 0.349 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.595 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.853 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.595 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.853 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.179 | ||||
| Upside Potential Ratio | 4.699 | ||||
| Upside part of mean | 5.743 | ||||
| Downside part of mean | -5.524 | ||||
| Upside SD | 1.179 | ||||
| Downside SD | 1.222 | ||||
| N nonnegative terms | 987.000 | ||||
| N negative terms | 932.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1919.000 | ||||
| Mean of predictor | 0.184 | ||||
| Mean of criterion | 0.219 | ||||
| SD of predictor | 0.556 | ||||
| SD of criterion | 1.698 | ||||
| Covariance | 0.702 | ||||
| r | 0.743 | ||||
| b (slope, estimate of beta) | 2.271 | ||||
| a (intercept, estimate of alpha) | -0.199 | ||||
| Mean Square Error | 1.291 | ||||
| DF error | 1917.000 | ||||
| t(b) | 48.650 | ||||
| p(b) | 0.075 | ||||
| t(a) | -0.473 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 2.179 | ||||
| Upperbound of 95% confidence interval for beta | 2.362 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.022 | ||||
| Upperbound of 95% confidence interval for alpha | 0.625 | ||||
| Treynor index (mean / b) | 0.096 | ||||
| Jensen alpha (a) | -0.199 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.158 | ||||
| Expected Shortfall on VaR | 0.193 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1919.000 | ||||
| Minimum | 0.231 | ||||
| Quartile 1 | 0.984 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 4.195 | ||||
| Mean of quarter 1 | 0.931 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.009 | ||||
| Mean of quarter 4 | 1.092 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 129.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.837 | ||||
| Number of outliers high | 121.000 | ||||
| Percentage of outliers high | 0.063 | ||||
| Mean of outliers high | 1.254 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.619 | ||||
| VaR(95%) (moments method) | 0.063 | ||||
| Expected Shortfall (moments method) | 0.185 | ||||
| Extreme Value Index (regression method) | 0.413 | ||||
| VaR(95%) (regression method) | 0.057 | ||||
| Expected Shortfall (regression method) | 0.118 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.049 | ||||
| Quartile 3 | 0.109 | ||||
| Maximum | 0.955 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | 0.066 | ||||
| Mean of quarter 4 | 0.309 | ||||
| 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 | 7.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 0.423 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.008 | ||||
| VaR(95%) (moments method) | 0.262 | ||||
| Expected Shortfall (moments method) | 0.358 | ||||
| Extreme Value Index (regression method) | -0.078 | ||||
| VaR(95%) (regression method) | 0.307 | ||||
| Expected Shortfall (regression method) | 0.411 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.801 | ||||
| Compounded annual return (geometric extrapolation) | 0.301 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.315 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.974 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.556 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.676 | ||||
| SD | 0.682 | ||||
| Sharpe ratio (Glass type estimate) | 0.992 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.986 | ||||
| df | 130.000 | ||||
| t | 0.701 | ||||
| p | 0.469 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.785 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.764 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.788 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.760 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.508 | ||||
| Upside Potential Ratio | 9.577 | ||||
| Upside part of mean | 4.294 | ||||
| Downside part of mean | -3.617 | ||||
| Upside SD | 0.512 | ||||
| Downside SD | 0.448 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.043 | ||||
| Mean of criterion | 0.676 | ||||
| SD of predictor | 0.510 | ||||
| SD of criterion | 0.682 | ||||
| Covariance | 0.277 | ||||
| r | 0.796 | ||||
| b (slope, estimate of beta) | 1.064 | ||||
| a (intercept, estimate of alpha) | -0.434 | ||||
| Mean Square Error | 0.171 | ||||
| DF error | 129.000 | ||||
| t(b) | 14.961 | ||||
| p(b) | 0.053 | ||||
| t(a) | -0.736 | ||||
| p(a) | 0.541 | ||||
| Lowerbound of 95% confidence interval for beta | 0.923 | ||||
| Upperbound of 95% confidence interval for beta | 1.205 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.601 | ||||
| Upperbound of 95% confidence interval for alpha | 0.733 | ||||
| Treynor index (mean / b) | 0.635 | ||||
| Jensen alpha (a) | -0.434 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.447 | ||||
| SD | 0.678 | ||||
| Sharpe ratio (Glass type estimate) | 0.658 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.655 | ||||
| df | 130.000 | ||||
| t | 0.466 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.116 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.430 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.118 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.427 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.959 | ||||
| Upside Potential Ratio | 8.956 | ||||
| Upside part of mean | 4.169 | ||||
| Downside part of mean | -3.723 | ||||
| Upside SD | 0.491 | ||||
| Downside SD | 0.465 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.912 | ||||
| Mean of criterion | 0.447 | ||||
| SD of predictor | 0.513 | ||||
| SD of criterion | 0.678 | ||||
| Covariance | 0.278 | ||||
| r | 0.799 | ||||
| b (slope, estimate of beta) | 1.058 | ||||
| a (intercept, estimate of alpha) | -0.518 | ||||
| Mean Square Error | 0.167 | ||||
| DF error | 129.000 | ||||
| t(b) | 15.116 | ||||
| p(b) | 0.052 | ||||
| t(a) | -0.890 | ||||
| p(a) | 0.550 | ||||
| Lowerbound of 95% confidence interval for beta | 0.920 | ||||
| Upperbound of 95% confidence interval for beta | 1.197 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.669 | ||||
| Upperbound of 95% confidence interval for alpha | 0.634 | ||||
| Treynor index (mean / b) | 0.422 | ||||
| Jensen alpha (a) | -0.518 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.892 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 1.162 | ||||
| Mean of quarter 1 | 0.952 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.045 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.903 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.132 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.036 | ||||
| VaR(95%) (moments method) | 0.044 | ||||
| Expected Shortfall (moments method) | 0.059 | ||||
| Extreme Value Index (regression method) | -0.259 | ||||
| VaR(95%) (regression method) | 0.047 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.046 | ||||
| Quartile 3 | 0.184 | ||||
| Maximum | 0.320 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.030 | ||||
| Mean of quarter 3 | 0.061 | ||||
| Mean of quarter 4 | 0.272 | ||||
| Inter Quartile Range | 0.167 | ||||
| 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) | 0.556 | ||||
| Compounded annual return (geometric extrapolation) | 0.633 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.978 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.324 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.805 | ||||