Advanced Statistics: Theta SPY Swing System
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 | -0.022 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -0.771 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.760 | ||||
| df | 53.000 | ||||
| t | -1.635 | ||||
| p | 0.946 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.703 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.168 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.695 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.175 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.734 | ||||
| Upside Potential Ratio | 1.567 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.042 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.344 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | -0.001 | ||||
| r | -0.093 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 52.000 | ||||
| t(b) | -0.676 | ||||
| p(b) | 0.749 | ||||
| t(a) | -1.261 | ||||
| p(a) | 0.893 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.011 | ||||
| Treynor index (mean / b) | 2.078 | ||||
| Jensen alpha (a) | -0.018 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.028 | ||||
| Sharpe ratio (Glass type estimate) | -0.800 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.789 | ||||
| df | 53.000 | ||||
| t | -1.697 | ||||
| p | 0.952 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.733 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.140 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.725 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.147 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.763 | ||||
| Upside Potential Ratio | 1.538 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.042 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.028 | ||||
| Covariance | -0.001 | ||||
| r | -0.092 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 52.000 | ||||
| t(b) | -0.670 | ||||
| p(b) | 0.747 | ||||
| t(a) | -1.337 | ||||
| p(a) | 0.907 | ||||
| Lowerbound of 95% confidence interval for beta | -0.044 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | 2.043 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 54.000 | ||||
| Minimum | 0.997 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.054 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.125 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.189 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.003 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.003 | ||||
| Maximum | 0.003 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.003 | ||||
| Inter Quartile Range | 0.001 | ||||
| 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) | 0.023 | ||||
| Compounded annual return (geometric extrapolation) | 0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | 6.488 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.488 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.182 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -0.563 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.563 | ||||
| df | 1194.000 | ||||
| t | -1.203 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.481 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.355 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.481 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.355 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.918 | ||||
| Upside Potential Ratio | 3.148 | ||||
| Upside part of mean | 0.075 | ||||
| Downside part of mean | -0.098 | ||||
| Upside SD | 0.031 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 1134.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1195.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | 0.000 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.024 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 1193.000 | ||||
| t(b) | 1.555 | ||||
| p(b) | 0.471 | ||||
| t(a) | -1.325 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.060 | ||||
| Upperbound of 95% confidence interval for alpha | 0.012 | ||||
| Treynor index (mean / b) | -3.472 | ||||
| Jensen alpha (a) | -0.024 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -0.584 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.584 | ||||
| df | 1194.000 | ||||
| t | -1.248 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.502 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.334 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.502 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.334 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.943 | ||||
| Upside Potential Ratio | 3.107 | ||||
| Upside part of mean | 0.075 | ||||
| Downside part of mean | -0.098 | ||||
| Upside SD | 0.031 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 1134.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1195.000 | ||||
| Mean of predictor | 0.326 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | 0.000 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 1193.000 | ||||
| t(b) | 1.547 | ||||
| p(b) | 0.472 | ||||
| t(a) | -1.357 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.061 | ||||
| Upperbound of 95% confidence interval for alpha | 0.011 | ||||
| Treynor index (mean / b) | -3.638 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1195.000 | ||||
| Minimum | 0.977 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.032 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 42.000 | ||||
| Percentage of outliers low | 0.035 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 63.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.456 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.037 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.018 | ||||
| Maximum | 0.057 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.015 | ||||
| Mean of quarter 4 | 0.034 | ||||
| Inter Quartile Range | 0.008 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.057 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.783 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.044 | ||||
| Extreme Value Index (regression method) | 0.819 | ||||
| VaR(95%) (regression method) | 0.064 | ||||
| Expected Shortfall (regression method) | 0.341 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.375 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.631 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.263 | ||||
| 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 | 1.002 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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 | 0.869 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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) | -8751909250090533.000 | ||||
| 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) | -341690157042239545130047781208064.000 | ||||
| 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 | ||||