Advanced Statistics: Silver Alpha
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 | 0.511 | ||||
| SD | 1.335 | ||||
| Sharpe ratio (Glass type estimate) | 0.383 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.376 | ||||
| df | 44.000 | ||||
| t | 0.741 | ||||
| p | 0.231 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.635 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.396 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.639 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.391 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.788 | ||||
| Upside Potential Ratio | 1.694 | ||||
| Upside part of mean | 1.099 | ||||
| Downside part of mean | -0.588 | ||||
| Upside SD | 1.159 | ||||
| Downside SD | 0.649 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | 0.511 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 1.335 | ||||
| Covariance | -0.062 | ||||
| r | -0.177 | ||||
| b (slope, estimate of beta) | -0.902 | ||||
| a (intercept, estimate of alpha) | 0.916 | ||||
| Mean Square Error | 1.767 | ||||
| DF error | 43.000 | ||||
| t(b) | -1.181 | ||||
| p(b) | 0.878 | ||||
| t(a) | 1.193 | ||||
| p(a) | 0.120 | ||||
| Lowerbound of 95% confidence interval for beta | -2.443 | ||||
| Upperbound of 95% confidence interval for beta | 0.639 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.632 | ||||
| Upperbound of 95% confidence interval for alpha | 2.463 | ||||
| Treynor index (mean / b) | -0.566 | ||||
| Jensen alpha (a) | 0.916 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.467 | ||||
| SD | 1.647 | ||||
| Sharpe ratio (Glass type estimate) | -0.284 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.279 | ||||
| df | 44.000 | ||||
| t | -0.549 | ||||
| p | 0.707 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.296 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.732 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.293 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.735 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.321 | ||||
| Upside Potential Ratio | 0.500 | ||||
| Upside part of mean | 0.728 | ||||
| Downside part of mean | -1.196 | ||||
| Upside SD | 0.739 | ||||
| Downside SD | 1.457 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | -0.467 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 1.647 | ||||
| Covariance | -0.027 | ||||
| r | -0.065 | ||||
| b (slope, estimate of beta) | -0.424 | ||||
| a (intercept, estimate of alpha) | -0.294 | ||||
| Mean Square Error | 2.763 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.428 | ||||
| p(b) | 0.665 | ||||
| t(a) | -0.310 | ||||
| p(a) | 0.621 | ||||
| Lowerbound of 95% confidence interval for beta | -2.422 | ||||
| Upperbound of 95% confidence interval for beta | 1.574 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.208 | ||||
| Upperbound of 95% confidence interval for alpha | 1.619 | ||||
| Treynor index (mean / b) | 1.102 | ||||
| Jensen alpha (a) | -0.294 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.560 | ||||
| Expected Shortfall on VaR | 0.634 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.161 | ||||
| Expected Shortfall on VaR | 0.349 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.130 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.710 | ||||
| Mean of quarter 1 | 0.829 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.376 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.089 | ||||
| Mean of outliers low | 0.487 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.089 | ||||
| Mean of outliers high | 2.034 | ||||
| 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) | -1.995 | ||||
| VaR(95%) (regression method) | 0.473 | ||||
| Expected Shortfall (regression method) | 0.557 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.056 | ||||
| Quartile 1 | 0.283 | ||||
| Median | 0.509 | ||||
| Quartile 3 | 0.736 | ||||
| Maximum | 0.962 | ||||
| Mean of quarter 1 | 0.056 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.962 | ||||
| Inter Quartile Range | 0.453 | ||||
| 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) | -0.212 | ||||
| Compounded annual return (geometric extrapolation) | -0.345 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.358 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.358 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.544 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.167 | ||||
| SD | 1.134 | ||||
| Sharpe ratio (Glass type estimate) | 0.147 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.147 | ||||
| df | 988.000 | ||||
| t | 0.286 | ||||
| p | 0.387 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.861 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.156 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.862 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.156 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.247 | ||||
| Upside Potential Ratio | 3.062 | ||||
| Upside part of mean | 2.069 | ||||
| Downside part of mean | -1.902 | ||||
| Upside SD | 0.910 | ||||
| Downside SD | 0.676 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 918.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 989.000 | ||||
| Mean of predictor | 0.461 | ||||
| Mean of criterion | 0.167 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 1.134 | ||||
| Covariance | -0.021 | ||||
| r | -0.058 | ||||
| b (slope, estimate of beta) | -0.207 | ||||
| a (intercept, estimate of alpha) | 0.263 | ||||
| Mean Square Error | 1.282 | ||||
| DF error | 987.000 | ||||
| t(b) | -1.818 | ||||
| p(b) | 0.965 | ||||
| t(a) | 0.449 | ||||
| p(a) | 0.327 | ||||
| Lowerbound of 95% confidence interval for beta | -0.431 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.886 | ||||
| Upperbound of 95% confidence interval for alpha | 1.411 | ||||
| Treynor index (mean / b) | -0.807 | ||||
| Jensen alpha (a) | 0.263 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.464 | ||||
| SD | 1.168 | ||||
| Sharpe ratio (Glass type estimate) | -0.398 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.397 | ||||
| df | 988.000 | ||||
| t | -0.772 | ||||
| p | 0.780 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.406 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.611 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.406 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.612 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.493 | ||||
| Upside Potential Ratio | 1.894 | ||||
| Upside part of mean | 1.785 | ||||
| Downside part of mean | -2.249 | ||||
| Upside SD | 0.689 | ||||
| Downside SD | 0.943 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 918.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 989.000 | ||||
| Mean of predictor | 0.410 | ||||
| Mean of criterion | -0.464 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 1.168 | ||||
| Covariance | -0.013 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.130 | ||||
| a (intercept, estimate of alpha) | -0.411 | ||||
| Mean Square Error | 1.364 | ||||
| DF error | 987.000 | ||||
| t(b) | -1.109 | ||||
| p(b) | 0.866 | ||||
| t(a) | -0.682 | ||||
| p(a) | 0.752 | ||||
| Lowerbound of 95% confidence interval for beta | -0.359 | ||||
| Upperbound of 95% confidence interval for beta | 0.100 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.594 | ||||
| Upperbound of 95% confidence interval for alpha | 0.772 | ||||
| Treynor index (mean / b) | 3.583 | ||||
| Jensen alpha (a) | -0.411 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.113 | ||||
| Expected Shortfall on VaR | 0.140 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 989.000 | ||||
| Minimum | 0.267 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.163 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 68.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.897 | ||||
| Number of outliers high | 71.000 | ||||
| Percentage of outliers high | 0.072 | ||||
| Mean of outliers high | 1.110 | ||||
| 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) | 0.427 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.084 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.073 | ||||
| Median | 0.148 | ||||
| Quartile 3 | 0.242 | ||||
| Maximum | 0.966 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | 0.115 | ||||
| Mean of quarter 3 | 0.177 | ||||
| Mean of quarter 4 | 0.524 | ||||
| Inter Quartile Range | 0.169 | ||||
| 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 | 0.966 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.023 | ||||
| VaR(95%) (moments method) | 0.552 | ||||
| Expected Shortfall (moments method) | 0.773 | ||||
| Extreme Value Index (regression method) | 1.727 | ||||
| VaR(95%) (regression method) | 1.205 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.211 | ||||
| Compounded annual return (geometric extrapolation) | -0.343 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.355 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.655 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.460 | ||||
| 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 | 0.949 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.466 | ||||
| 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 | 0.838 | ||||
| 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) | -8746856903954401.000 | ||||
| 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) | 201636475933996409609579434868736.000 | ||||
| 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 | ||||