Advanced Statistics: Global Allocation
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.157 | ||||
| Sharpe ratio (Glass type estimate) | 0.179 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.178 | ||||
| df | 146.000 | ||||
| t | 0.627 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.381 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.739 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.382 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.739 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.328 | ||||
| Upside Potential Ratio | 1.764 | ||||
| Upside part of mean | 0.151 | ||||
| Downside part of mean | -0.123 | ||||
| Upside SD | 0.131 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 113.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 147.000 | ||||
| Mean of predictor | 0.123 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.206 | ||||
| SD of criterion | 0.157 | ||||
| Covariance | 0.001 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | 0.025 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 145.000 | ||||
| t(b) | 0.453 | ||||
| p(b) | 0.476 | ||||
| t(a) | 0.539 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.154 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.115 | ||||
| Treynor index (mean / b) | 0.982 | ||||
| Jensen alpha (a) | 0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.016 | ||||
| SD | 0.151 | ||||
| Sharpe ratio (Glass type estimate) | 0.109 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.108 | ||||
| df | 146.000 | ||||
| t | 0.381 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.452 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.669 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.452 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.668 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.183 | ||||
| Upside Potential Ratio | 1.594 | ||||
| Upside part of mean | 0.143 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.121 | ||||
| Downside SD | 0.090 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 113.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 147.000 | ||||
| Mean of predictor | 0.102 | ||||
| Mean of criterion | 0.016 | ||||
| SD of predictor | 0.204 | ||||
| SD of criterion | 0.151 | ||||
| Covariance | 0.001 | ||||
| r | 0.029 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 145.000 | ||||
| t(b) | 0.349 | ||||
| p(b) | 0.482 | ||||
| t(a) | 0.325 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | -0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.143 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.101 | ||||
| Treynor index (mean / b) | 0.764 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 147.000 | ||||
| Minimum | 0.878 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.254 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 25.000 | ||||
| Percentage of outliers low | 0.170 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 33.000 | ||||
| Percentage of outliers high | 0.224 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.754 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.043 | ||||
| Extreme Value Index (regression method) | -0.172 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | 0.046 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.018 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.099 | ||||
| Quartile 3 | 0.154 | ||||
| Maximum | 0.290 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | 0.099 | ||||
| Mean of quarter 3 | 0.154 | ||||
| Mean of quarter 4 | 0.290 | ||||
| Inter Quartile Range | 0.096 | ||||
| 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) | 0.090 | ||||
| Compounded annual return (geometric extrapolation) | 0.062 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.215 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.215 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.735 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.113 | ||||
| SD | 0.441 | ||||
| Sharpe ratio (Glass type estimate) | 0.256 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.256 | ||||
| df | 3216.000 | ||||
| t | 0.897 | ||||
| p | 0.185 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.303 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.815 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.304 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.815 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.399 | ||||
| Upside Potential Ratio | 3.577 | ||||
| Upside part of mean | 1.012 | ||||
| Downside part of mean | -0.899 | ||||
| Upside SD | 0.338 | ||||
| Downside SD | 0.283 | ||||
| N nonnegative terms | 770.000 | ||||
| N negative terms | 2447.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 3217.000 | ||||
| Mean of predictor | 0.179 | ||||
| Mean of criterion | 0.113 | ||||
| SD of predictor | 0.406 | ||||
| SD of criterion | 0.441 | ||||
| Covariance | -0.037 | ||||
| r | -0.206 | ||||
| b (slope, estimate of beta) | -0.224 | ||||
| a (intercept, estimate of alpha) | 0.153 | ||||
| Mean Square Error | 0.186 | ||||
| DF error | 3215.000 | ||||
| t(b) | -11.946 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.242 | ||||
| p(a) | 0.107 | ||||
| Lowerbound of 95% confidence interval for beta | -0.261 | ||||
| Upperbound of 95% confidence interval for beta | -0.187 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.089 | ||||
| Upperbound of 95% confidence interval for alpha | 0.394 | ||||
| Treynor index (mean / b) | -0.503 | ||||
| Jensen alpha (a) | 0.153 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.016 | ||||
| SD | 0.442 | ||||
| Sharpe ratio (Glass type estimate) | 0.037 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.037 | ||||
| df | 3216.000 | ||||
| t | 0.129 | ||||
| p | 0.449 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.522 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.596 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.522 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.596 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.050 | ||||
| Upside Potential Ratio | 2.979 | ||||
| Upside part of mean | 0.963 | ||||
| Downside part of mean | -0.946 | ||||
| Upside SD | 0.301 | ||||
| Downside SD | 0.323 | ||||
| N nonnegative terms | 770.000 | ||||
| N negative terms | 2447.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 3217.000 | ||||
| Mean of predictor | 0.100 | ||||
| Mean of criterion | 0.016 | ||||
| SD of predictor | 0.395 | ||||
| SD of criterion | 0.442 | ||||
| Covariance | -0.036 | ||||
| r | -0.207 | ||||
| b (slope, estimate of beta) | -0.231 | ||||
| a (intercept, estimate of alpha) | 0.039 | ||||
| Mean Square Error | 0.187 | ||||
| DF error | 3215.000 | ||||
| t(b) | -11.969 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.319 | ||||
| p(a) | 0.375 | ||||
| Lowerbound of 95% confidence interval for beta | -0.269 | ||||
| Upperbound of 95% confidence interval for beta | -0.193 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.202 | ||||
| Upperbound of 95% confidence interval for alpha | 0.281 | ||||
| Treynor index (mean / b) | -0.071 | ||||
| Jensen alpha (a) | 0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 3217.000 | ||||
| Minimum | 0.625 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.477 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 630.000 | ||||
| Percentage of outliers low | 0.196 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 647.000 | ||||
| Percentage of outliers high | 0.201 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.841 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.044 | ||||
| Extreme Value Index (regression method) | 0.530 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.031 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.030 | ||||
| Median | 0.109 | ||||
| Quartile 3 | 0.287 | ||||
| Maximum | 0.385 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.070 | ||||
| Mean of quarter 3 | 0.196 | ||||
| Mean of quarter 4 | 0.336 | ||||
| Inter Quartile Range | 0.257 | ||||
| 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) | -0.593 | ||||
| VaR(95%) (moments method) | 0.363 | ||||
| Expected Shortfall (moments method) | 0.379 | ||||
| Extreme Value Index (regression method) | -0.158 | ||||
| VaR(95%) (regression method) | 0.365 | ||||
| Expected Shortfall (regression method) | 0.394 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.089 | ||||
| Compounded annual return (geometric extrapolation) | 0.062 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.162 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.185 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.139 | ||||
| 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 | 0.170 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.148 | ||||
| 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 | 0.159 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.148 | ||||
| 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) | -8780366317586568.000 | ||||
| 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) | 158441549710309492666172681748480.000 | ||||
| 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 | ||||