Advanced Statistics: Momentum and Volatility Trading
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 | -0.014 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -0.330 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.323 | ||||
| df | 33.000 | ||||
| t | -0.556 | ||||
| p | 0.709 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.495 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.839 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.490 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.844 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.163 | ||||
| Upside Potential Ratio | 2.197 | ||||
| Upside part of mean | 0.027 | ||||
| Downside part of mean | -0.042 | ||||
| Upside SD | 0.041 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.570 | ||||
| Mean of criterion | -0.014 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | -0.002 | ||||
| r | -0.179 | ||||
| b (slope, estimate of beta) | -0.030 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 32.000 | ||||
| t(b) | -1.030 | ||||
| p(b) | 0.845 | ||||
| t(a) | 0.088 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | -0.089 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.060 | ||||
| Upperbound of 95% confidence interval for alpha | 0.065 | ||||
| Treynor index (mean / b) | 0.479 | ||||
| Jensen alpha (a) | 0.003 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.015 | ||||
| SD | 0.042 | ||||
| Sharpe ratio (Glass type estimate) | -0.362 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.354 | ||||
| df | 33.000 | ||||
| t | -0.609 | ||||
| p | 0.727 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.527 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.808 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.521 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.814 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.233 | ||||
| Upside Potential Ratio | 2.128 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.041 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.525 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.042 | ||||
| Covariance | -0.002 | ||||
| r | -0.179 | ||||
| b (slope, estimate of beta) | -0.031 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 32.000 | ||||
| t(b) | -1.030 | ||||
| p(b) | 0.845 | ||||
| t(a) | 0.029 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | -0.091 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.061 | ||||
| Treynor index (mean / b) | 0.497 | ||||
| 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%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| 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 | 34.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.073 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.042 | ||||
| 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) | 0.030 | ||||
| Compounded annual return (geometric extrapolation) | 0.029 | ||||
| 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 | 1.128 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.015 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -0.506 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.505 | ||||
| df | 745.000 | ||||
| t | -0.854 | ||||
| p | 0.803 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.668 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.656 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.667 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.656 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.011 | ||||
| Upside Potential Ratio | 3.714 | ||||
| Upside part of mean | 0.055 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 719.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 746.000 | ||||
| Mean of predictor | 0.591 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | -0.000 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.012 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 744.000 | ||||
| t(b) | -1.329 | ||||
| p(b) | 0.908 | ||||
| t(a) | -0.701 | ||||
| p(a) | 0.758 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | 0.022 | ||||
| Treynor index (mean / b) | 3.404 | ||||
| Jensen alpha (a) | -0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.015 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -0.523 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.523 | ||||
| df | 745.000 | ||||
| t | -0.883 | ||||
| p | 0.811 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.685 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.639 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.685 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.639 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.036 | ||||
| Upside Potential Ratio | 3.676 | ||||
| Upside part of mean | 0.054 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 719.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 746.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | -0.000 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 744.000 | ||||
| t(b) | -1.296 | ||||
| p(b) | 0.902 | ||||
| t(a) | -0.751 | ||||
| p(a) | 0.773 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | 0.021 | ||||
| Treynor index (mean / b) | 3.666 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 746.000 | ||||
| Minimum | 0.988 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.025 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 15.000 | ||||
| Percentage of outliers low | 0.020 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 27.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.653 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.316 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.008 | ||||
| Maximum | 0.040 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.008 | ||||
| Mean of quarter 4 | 0.040 | ||||
| Inter Quartile Range | 0.006 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.040 | ||||
| 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) | 0.030 | ||||
| Compounded annual return (geometric extrapolation) | 0.029 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.720 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.720 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.685 | ||||
| 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 | 1.043 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.465 | ||||
| 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 | 0.932 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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) | -8734219683934208.000 | ||||
| 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) | 134109601236979846360218237665280.000 | ||||
| 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 | ||||