Advanced Statistics: BGP 558
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 | 0.159 | ||||
| SD | 0.627 | ||||
| Sharpe ratio (Glass type estimate) | 0.254 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.249 | ||||
| df | 40.000 | ||||
| t | 0.469 | ||||
| p | 0.321 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.809 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.314 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.813 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.311 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.796 | ||||
| Upside Potential Ratio | 1.881 | ||||
| Upside part of mean | 0.376 | ||||
| Downside part of mean | -0.217 | ||||
| Upside SD | 0.588 | ||||
| Downside SD | 0.200 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.448 | ||||
| Mean of criterion | 0.159 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.627 | ||||
| Covariance | -0.023 | ||||
| r | -0.131 | ||||
| b (slope, estimate of beta) | -0.288 | ||||
| a (intercept, estimate of alpha) | 0.288 | ||||
| Mean Square Error | 0.396 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.825 | ||||
| p(b) | 0.793 | ||||
| t(a) | 0.769 | ||||
| p(a) | 0.223 | ||||
| Lowerbound of 95% confidence interval for beta | -0.994 | ||||
| Upperbound of 95% confidence interval for beta | 0.418 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.470 | ||||
| Upperbound of 95% confidence interval for alpha | 1.046 | ||||
| Treynor index (mean / b) | -0.553 | ||||
| Jensen alpha (a) | 0.288 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.030 | ||||
| SD | 0.472 | ||||
| Sharpe ratio (Glass type estimate) | 0.063 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.062 | ||||
| df | 40.000 | ||||
| t | 0.116 | ||||
| p | 0.454 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.998 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.123 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.999 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.122 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.129 | ||||
| Upside Potential Ratio | 1.172 | ||||
| Upside part of mean | 0.270 | ||||
| Downside part of mean | -0.240 | ||||
| Upside SD | 0.405 | ||||
| Downside SD | 0.230 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | 0.030 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.472 | ||||
| Covariance | -0.014 | ||||
| r | -0.106 | ||||
| b (slope, estimate of beta) | -0.185 | ||||
| a (intercept, estimate of alpha) | 0.104 | ||||
| Mean Square Error | 0.226 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.666 | ||||
| p(b) | 0.745 | ||||
| t(a) | 0.371 | ||||
| p(a) | 0.356 | ||||
| Lowerbound of 95% confidence interval for beta | -0.746 | ||||
| Upperbound of 95% confidence interval for beta | 0.377 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.463 | ||||
| Upperbound of 95% confidence interval for alpha | 0.671 | ||||
| Treynor index (mean / b) | -0.161 | ||||
| Jensen alpha (a) | 0.104 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.199 | ||||
| Expected Shortfall on VaR | 0.242 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.127 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.708 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.069 | ||||
| Mean of quarter 1 | 0.945 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.130 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.880 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 1.432 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -21.767 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.193 | ||||
| VaR(95%) (regression method) | 0.133 | ||||
| Expected Shortfall (regression method) | 0.251 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.081 | ||||
| Quartile 1 | 0.139 | ||||
| Median | 0.198 | ||||
| Quartile 3 | 0.256 | ||||
| Maximum | 0.314 | ||||
| Mean of quarter 1 | 0.081 | ||||
| Mean of quarter 2 | 0.198 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.314 | ||||
| Inter Quartile Range | 0.117 | ||||
| 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) | 0.084 | ||||
| Compounded annual return (geometric extrapolation) | 0.077 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.244 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.244 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.316 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.060 | ||||
| SD | 0.259 | ||||
| Sharpe ratio (Glass type estimate) | 0.231 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.230 | ||||
| df | 914.000 | ||||
| t | 0.431 | ||||
| p | 0.333 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.818 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.279 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.818 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.279 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.446 | ||||
| Upside Potential Ratio | 3.867 | ||||
| Upside part of mean | 0.518 | ||||
| Downside part of mean | -0.459 | ||||
| Upside SD | 0.222 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 859.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 915.000 | ||||
| Mean of predictor | 0.498 | ||||
| Mean of criterion | 0.060 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.259 | ||||
| Covariance | -0.001 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | 0.063 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 913.000 | ||||
| t(b) | -0.225 | ||||
| p(b) | 0.589 | ||||
| t(a) | 0.451 | ||||
| p(a) | 0.326 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.211 | ||||
| Upperbound of 95% confidence interval for alpha | 0.337 | ||||
| Treynor index (mean / b) | -9.591 | ||||
| Jensen alpha (a) | 0.063 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.248 | ||||
| Sharpe ratio (Glass type estimate) | 0.113 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.113 | ||||
| df | 914.000 | ||||
| t | 0.212 | ||||
| p | 0.416 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.935 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.162 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.936 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.162 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.204 | ||||
| Upside Potential Ratio | 3.596 | ||||
| Upside part of mean | 0.496 | ||||
| Downside part of mean | -0.468 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.138 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 859.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 915.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.248 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | 0.030 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 913.000 | ||||
| t(b) | -0.157 | ||||
| p(b) | 0.562 | ||||
| t(a) | 0.225 | ||||
| p(a) | 0.411 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.232 | ||||
| Upperbound of 95% confidence interval for alpha | 0.292 | ||||
| Treynor index (mean / b) | -6.804 | ||||
| Jensen alpha (a) | 0.030 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 915.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.245 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 66.000 | ||||
| Percentage of outliers low | 0.072 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 57.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.032 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.722 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.080 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.123 | ||||
| Maximum | 0.367 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.096 | ||||
| Mean of quarter 4 | 0.251 | ||||
| Inter Quartile Range | 0.109 | ||||
| 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 | 0.367 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -10.592 | ||||
| VaR(95%) (moments method) | 0.251 | ||||
| Expected Shortfall (moments method) | 0.251 | ||||
| Extreme Value Index (regression method) | -1.225 | ||||
| VaR(95%) (regression method) | 0.430 | ||||
| Expected Shortfall (regression method) | 0.453 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.082 | ||||
| Compounded annual return (geometric extrapolation) | 0.075 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.204 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.299 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.412 | ||||
| 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 | 1.121 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.531 | ||||
| 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 | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.534 | ||||
| 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) | -8743673552534043.000 | ||||
| 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) | -345085562733348883828838246645760.000 | ||||
| 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 | ||||