Advanced Statistics: UltraPro (3X) SPX Timer
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 | -0.077 | ||||
| SD | 0.133 | ||||
| Sharpe ratio (Glass type estimate) | -0.576 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.568 | ||||
| df | 51.000 | ||||
| t | -1.200 | ||||
| p | 0.882 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.522 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.374 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.516 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.380 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.831 | ||||
| Upside Potential Ratio | 1.160 | ||||
| Upside part of mean | 0.107 | ||||
| Downside part of mean | -0.184 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.092 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.335 | ||||
| Mean of criterion | -0.077 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 0.133 | ||||
| Covariance | 0.002 | ||||
| r | 0.081 | ||||
| b (slope, estimate of beta) | 0.048 | ||||
| a (intercept, estimate of alpha) | -0.093 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.574 | ||||
| p(b) | 0.284 | ||||
| t(a) | -1.322 | ||||
| p(a) | 0.904 | ||||
| Lowerbound of 95% confidence interval for beta | -0.121 | ||||
| Upperbound of 95% confidence interval for beta | 0.218 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.234 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | -1.583 | ||||
| Jensen alpha (a) | -0.093 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.085 | ||||
| SD | 0.130 | ||||
| Sharpe ratio (Glass type estimate) | -0.653 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.643 | ||||
| df | 51.000 | ||||
| t | -1.360 | ||||
| p | 0.910 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.600 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.300 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.593 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.306 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.896 | ||||
| Upside Potential Ratio | 1.078 | ||||
| Upside part of mean | 0.102 | ||||
| Downside part of mean | -0.188 | ||||
| Upside SD | 0.091 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.307 | ||||
| Mean of criterion | -0.085 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.130 | ||||
| Covariance | 0.002 | ||||
| r | 0.087 | ||||
| b (slope, estimate of beta) | 0.054 | ||||
| a (intercept, estimate of alpha) | -0.102 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 50.000 | ||||
| t(b) | 0.616 | ||||
| p(b) | 0.270 | ||||
| t(a) | -1.484 | ||||
| p(a) | 0.928 | ||||
| Lowerbound of 95% confidence interval for beta | -0.121 | ||||
| Upperbound of 95% confidence interval for beta | 0.229 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.239 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -1.585 | ||||
| Jensen alpha (a) | -0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.078 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.912 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.168 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.017 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.096 | ||||
| Mean of outliers low | 0.932 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 1.064 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.050 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.053 | ||||
| Extreme Value Index (regression method) | -0.243 | ||||
| VaR(95%) (regression method) | 0.052 | ||||
| Expected Shortfall (regression method) | 0.067 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.099 | ||||
| Median | 0.197 | ||||
| Quartile 3 | 0.294 | ||||
| Maximum | 0.392 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.392 | ||||
| Inter Quartile Range | 0.195 | ||||
| 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) | -0.038 | ||||
| Compounded annual return (geometric extrapolation) | -0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.103 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.103 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.497 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.117 | ||||
| Sharpe ratio (Glass type estimate) | -0.664 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.663 | ||||
| df | 1149.000 | ||||
| t | -1.390 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.599 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.272 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.599 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.273 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.935 | ||||
| Upside Potential Ratio | 5.379 | ||||
| Upside part of mean | 0.447 | ||||
| Downside part of mean | -0.525 | ||||
| Upside SD | 0.083 | ||||
| Downside SD | 0.083 | ||||
| N nonnegative terms | 319.000 | ||||
| N negative terms | 831.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1150.000 | ||||
| Mean of predictor | 0.347 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.117 | ||||
| Covariance | 0.001 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | -0.085 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 1148.000 | ||||
| t(b) | 1.604 | ||||
| p(b) | 0.476 | ||||
| t(a) | -1.520 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.195 | ||||
| Upperbound of 95% confidence interval for alpha | 0.025 | ||||
| Treynor index (mean / b) | -3.609 | ||||
| Jensen alpha (a) | -0.085 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.085 | ||||
| SD | 0.117 | ||||
| Sharpe ratio (Glass type estimate) | -0.723 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.723 | ||||
| df | 1149.000 | ||||
| t | -1.515 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.659 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.213 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.659 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.213 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.007 | ||||
| Upside Potential Ratio | 5.282 | ||||
| Upside part of mean | 0.444 | ||||
| Downside part of mean | -0.528 | ||||
| Upside SD | 0.082 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 319.000 | ||||
| N negative terms | 831.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1150.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | -0.085 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.117 | ||||
| Covariance | 0.001 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.091 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 1148.000 | ||||
| t(b) | 1.592 | ||||
| p(b) | 0.477 | ||||
| t(a) | -1.630 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.047 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.201 | ||||
| Upperbound of 95% confidence interval for alpha | 0.019 | ||||
| Treynor index (mean / b) | -4.014 | ||||
| Jensen alpha (a) | -0.091 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1150.000 | ||||
| Minimum | 0.954 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.052 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 199.000 | ||||
| Percentage of outliers low | 0.173 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 191.000 | ||||
| Percentage of outliers high | 0.166 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.158 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.029 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.052 | ||||
| Maximum | 0.426 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.023 | ||||
| Mean of quarter 4 | 0.153 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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 | 0.071 | ||||
| Mean of outliers high | 0.426 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.894 | ||||
| VaR(95%) (moments method) | 0.184 | ||||
| Expected Shortfall (moments method) | 1.619 | ||||
| Extreme Value Index (regression method) | 4.637 | ||||
| VaR(95%) (regression method) | 0.328 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.037 | ||||
| Compounded annual return (geometric extrapolation) | -0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.093 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.260 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.632 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.847 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.744 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8754648264555237.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 175760898557837839179808996589568.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| 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 for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||