Advanced Statistics: PV Mix on hold
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 | 0.031 | ||||
| SD | 0.183 | ||||
| Sharpe ratio (Glass type estimate) | 0.168 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.167 | ||||
| df | 79.000 | ||||
| t | 0.435 | ||||
| p | 0.332 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.592 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.928 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.593 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.926 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.338 | ||||
| Upside Potential Ratio | 1.857 | ||||
| Upside part of mean | 0.169 | ||||
| Downside part of mean | -0.139 | ||||
| Upside SD | 0.157 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.214 | ||||
| Mean of criterion | 0.031 | ||||
| SD of predictor | 0.185 | ||||
| SD of criterion | 0.183 | ||||
| Covariance | -0.001 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | 0.037 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.262 | ||||
| p(b) | 0.603 | ||||
| t(a) | 0.493 | ||||
| p(a) | 0.312 | ||||
| Lowerbound of 95% confidence interval for beta | -0.252 | ||||
| Upperbound of 95% confidence interval for beta | 0.194 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.113 | ||||
| Upperbound of 95% confidence interval for alpha | 0.187 | ||||
| Treynor index (mean / b) | -1.050 | ||||
| Jensen alpha (a) | 0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.016 | ||||
| SD | 0.172 | ||||
| Sharpe ratio (Glass type estimate) | 0.090 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.090 | ||||
| df | 79.000 | ||||
| t | 0.234 | ||||
| p | 0.408 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.669 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.849 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.670 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.849 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.163 | ||||
| Upside Potential Ratio | 1.653 | ||||
| Upside part of mean | 0.158 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.142 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.196 | ||||
| Mean of criterion | 0.016 | ||||
| SD of predictor | 0.178 | ||||
| SD of criterion | 0.172 | ||||
| Covariance | -0.001 | ||||
| r | -0.023 | ||||
| b (slope, estimate of beta) | -0.023 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.207 | ||||
| p(b) | 0.582 | ||||
| t(a) | 0.284 | ||||
| p(a) | 0.389 | ||||
| Lowerbound of 95% confidence interval for beta | -0.241 | ||||
| Upperbound of 95% confidence interval for beta | 0.195 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | 0.160 | ||||
| Treynor index (mean / b) | -0.687 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.077 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.065 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.864 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.283 | ||||
| Mean of quarter 1 | 0.964 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.150 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.150 | ||||
| Mean of outliers high | 1.087 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.148 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.014 | ||||
| Extreme Value Index (regression method) | 0.142 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.066 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.136 | ||||
| Quartile 1 | 0.137 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.193 | ||||
| Maximum | 0.248 | ||||
| Mean of quarter 1 | 0.136 | ||||
| Mean of quarter 2 | 0.137 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.248 | ||||
| Inter Quartile Range | 0.056 | ||||
| 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) | 0.073 | ||||
| Compounded annual return (geometric extrapolation) | 0.061 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.247 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.247 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.639 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | 0.178 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.177 | ||||
| df | 1760.000 | ||||
| t | 0.460 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.578 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.934 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.579 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.933 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.269 | ||||
| Upside Potential Ratio | 5.168 | ||||
| Upside part of mean | 0.472 | ||||
| Downside part of mean | -0.447 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 532.000 | ||||
| N negative terms | 1229.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1761.000 | ||||
| Mean of predictor | 0.241 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | 0.001 | ||||
| r | 0.026 | ||||
| b (slope, estimate of beta) | 0.015 | ||||
| a (intercept, estimate of alpha) | 0.021 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 1759.000 | ||||
| t(b) | 1.088 | ||||
| p(b) | 0.483 | ||||
| t(a) | 0.392 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | 0.126 | ||||
| Treynor index (mean / b) | 1.641 | ||||
| Jensen alpha (a) | 0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | 0.110 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.110 | ||||
| df | 1760.000 | ||||
| t | 0.284 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.646 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.866 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.647 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.866 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.162 | ||||
| Upside Potential Ratio | 5.033 | ||||
| Upside part of mean | 0.467 | ||||
| Downside part of mean | -0.452 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 532.000 | ||||
| N negative terms | 1229.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1761.000 | ||||
| Mean of predictor | 0.214 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | 0.001 | ||||
| r | 0.026 | ||||
| b (slope, estimate of beta) | 0.015 | ||||
| a (intercept, estimate of alpha) | 0.012 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 1759.000 | ||||
| t(b) | 1.094 | ||||
| p(b) | 0.483 | ||||
| t(a) | 0.222 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.116 | ||||
| Treynor index (mean / b) | 0.985 | ||||
| Jensen alpha (a) | 0.012 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1761.000 | ||||
| Minimum | 0.936 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.090 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 283.000 | ||||
| Percentage of outliers low | 0.161 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 348.000 | ||||
| Percentage of outliers high | 0.198 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.598 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.013 | ||||
| Extreme Value Index (regression method) | 0.240 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 27.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.031 | ||||
| Maximum | 0.297 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.016 | ||||
| Mean of quarter 4 | 0.152 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.185 | ||||
| Mean of outliers high | 0.198 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.192 | ||||
| VaR(95%) (moments method) | 0.107 | ||||
| Expected Shortfall (moments method) | 0.115 | ||||
| Extreme Value Index (regression method) | -1.084 | ||||
| VaR(95%) (regression method) | 0.142 | ||||
| Expected Shortfall (regression method) | 0.154 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.073 | ||||
| Compounded annual return (geometric extrapolation) | 0.061 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.205 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.400 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.516 | ||||
| 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 | 1.091 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.437 | ||||
| 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 | 0.994 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.438 | ||||
| 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) | -8713875661584836.000 | ||||
| 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) | -222765755108796060431302227132416.000 | ||||
| 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 | ||||