Advanced Statistics: Montex
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 | -0.027 | ||||
| SD | 0.201 | ||||
| Sharpe ratio (Glass type estimate) | -0.132 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.130 | ||||
| df | 65.000 | ||||
| t | -0.309 | ||||
| p | 0.621 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.967 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.966 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.706 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.269 | ||||
| Upside Potential Ratio | 0.752 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.101 | ||||
| Upside SD | 0.174 | ||||
| Downside SD | 0.099 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 66.000 | ||||
| Mean of predictor | 0.346 | ||||
| Mean of criterion | -0.027 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.201 | ||||
| Covariance | -0.024 | ||||
| r | -0.396 | ||||
| b (slope, estimate of beta) | -0.263 | ||||
| a (intercept, estimate of alpha) | 0.065 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 64.000 | ||||
| t(b) | -3.452 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.773 | ||||
| p(a) | 0.221 | ||||
| Lowerbound of 95% confidence interval for beta | -0.416 | ||||
| Upperbound of 95% confidence interval for beta | -0.111 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.102 | ||||
| Upperbound of 95% confidence interval for alpha | 0.232 | ||||
| Treynor index (mean / b) | 0.101 | ||||
| Jensen alpha (a) | 0.065 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.181 | ||||
| Sharpe ratio (Glass type estimate) | -0.241 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.238 | ||||
| df | 65.000 | ||||
| t | -0.565 | ||||
| p | 0.713 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.077 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.597 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.075 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.599 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.408 | ||||
| Upside Potential Ratio | 0.579 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.107 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 66.000 | ||||
| Mean of predictor | 0.297 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.181 | ||||
| Covariance | -0.023 | ||||
| r | -0.427 | ||||
| b (slope, estimate of beta) | -0.261 | ||||
| a (intercept, estimate of alpha) | 0.034 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 64.000 | ||||
| t(b) | -3.778 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.460 | ||||
| p(a) | 0.324 | ||||
| Lowerbound of 95% confidence interval for beta | -0.398 | ||||
| Upperbound of 95% confidence interval for beta | -0.123 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.113 | ||||
| Upperbound of 95% confidence interval for alpha | 0.180 | ||||
| Treynor index (mean / b) | 0.168 | ||||
| Jensen alpha (a) | 0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.086 | ||||
| Expected Shortfall on VaR | 0.105 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 66.000 | ||||
| Minimum | 0.836 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.411 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.084 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.718 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.695 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.156 | ||||
| Quartile 1 | 0.158 | ||||
| Median | 0.160 | ||||
| Quartile 3 | 0.162 | ||||
| Maximum | 0.164 | ||||
| Mean of quarter 1 | 0.156 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.164 | ||||
| Inter Quartile Range | 0.004 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.002 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.002 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.003 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.086 | ||||
| SD | 0.511 | ||||
| Sharpe ratio (Glass type estimate) | 0.168 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.168 | ||||
| df | 1441.000 | ||||
| t | 0.393 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.668 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.003 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.668 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.003 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.257 | ||||
| Upside Potential Ratio | 2.459 | ||||
| Upside part of mean | 0.819 | ||||
| Downside part of mean | -0.734 | ||||
| Upside SD | 0.387 | ||||
| Downside SD | 0.333 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 1370.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1442.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | 0.086 | ||||
| SD of predictor | 0.593 | ||||
| SD of criterion | 0.511 | ||||
| Covariance | -0.147 | ||||
| r | -0.483 | ||||
| b (slope, estimate of beta) | -0.416 | ||||
| a (intercept, estimate of alpha) | 0.281 | ||||
| Mean Square Error | 0.200 | ||||
| DF error | 1440.000 | ||||
| t(b) | -20.945 | ||||
| p(b) | 0.742 | ||||
| t(a) | 1.469 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | -0.455 | ||||
| Upperbound of 95% confidence interval for beta | -0.377 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.094 | ||||
| Upperbound of 95% confidence interval for alpha | 0.655 | ||||
| Treynor index (mean / b) | -0.206 | ||||
| Jensen alpha (a) | 0.281 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.510 | ||||
| Sharpe ratio (Glass type estimate) | -0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.086 | ||||
| df | 1441.000 | ||||
| t | -0.201 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.921 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.750 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.921 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.750 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.117 | ||||
| Upside Potential Ratio | 2.014 | ||||
| Upside part of mean | 0.755 | ||||
| Downside part of mean | -0.798 | ||||
| Upside SD | 0.346 | ||||
| Downside SD | 0.375 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 1370.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1442.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.587 | ||||
| SD of criterion | 0.510 | ||||
| Covariance | -0.146 | ||||
| r | -0.488 | ||||
| b (slope, estimate of beta) | -0.424 | ||||
| a (intercept, estimate of alpha) | 0.082 | ||||
| Mean Square Error | 0.199 | ||||
| DF error | 1440.000 | ||||
| t(b) | -21.211 | ||||
| p(b) | 0.744 | ||||
| t(a) | 0.429 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.464 | ||||
| Upperbound of 95% confidence interval for beta | -0.385 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.291 | ||||
| Upperbound of 95% confidence interval for alpha | 0.454 | ||||
| Treynor index (mean / b) | 0.103 | ||||
| Jensen alpha (a) | 0.082 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1442.000 | ||||
| Minimum | 0.687 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.450 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 83.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 87.000 | ||||
| Percentage of outliers high | 0.060 | ||||
| Mean of outliers high | 1.052 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.034 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 | 6.000 | ||||
| Minimum | 0.039 | ||||
| Quartile 1 | 0.188 | ||||
| Median | 0.265 | ||||
| Quartile 3 | 0.313 | ||||
| Maximum | 0.436 | ||||
| Mean of quarter 1 | 0.109 | ||||
| Mean of quarter 2 | 0.218 | ||||
| Mean of quarter 3 | 0.313 | ||||
| Mean of quarter 4 | 0.375 | ||||
| Inter Quartile Range | 0.125 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.005 | ||||
| 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 | 0.980 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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) | -8748429027286585.000 | ||||
| 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) | 96467626284176441732039289339904.000 | ||||
| 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 | ||||