Advanced Statistics: SARF2!
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 | 0.078 | ||||
| SD | 0.531 | ||||
| Sharpe ratio (Glass type estimate) | 0.147 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.146 | ||||
| df | 92.000 | ||||
| t | 0.410 | ||||
| p | 0.342 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.558 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.851 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.850 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.285 | ||||
| Upside Potential Ratio | 1.087 | ||||
| Upside part of mean | 0.298 | ||||
| Downside part of mean | -0.220 | ||||
| Upside SD | 0.453 | ||||
| Downside SD | 0.274 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.148 | ||||
| Mean of criterion | 0.078 | ||||
| SD of predictor | 0.305 | ||||
| SD of criterion | 0.531 | ||||
| Covariance | -0.015 | ||||
| r | -0.095 | ||||
| b (slope, estimate of beta) | -0.165 | ||||
| a (intercept, estimate of alpha) | 0.103 | ||||
| Mean Square Error | 0.283 | ||||
| DF error | 91.000 | ||||
| t(b) | -0.906 | ||||
| p(b) | 0.816 | ||||
| t(a) | 0.532 | ||||
| p(a) | 0.298 | ||||
| Lowerbound of 95% confidence interval for beta | -0.526 | ||||
| Upperbound of 95% confidence interval for beta | 0.196 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.281 | ||||
| Upperbound of 95% confidence interval for alpha | 0.486 | ||||
| Treynor index (mean / b) | -0.475 | ||||
| Jensen alpha (a) | 0.103 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.047 | ||||
| SD | 0.507 | ||||
| Sharpe ratio (Glass type estimate) | -0.092 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.091 | ||||
| df | 92.000 | ||||
| t | -0.256 | ||||
| p | 0.601 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.796 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.612 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.795 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.613 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.122 | ||||
| Upside Potential Ratio | 0.601 | ||||
| Upside part of mean | 0.230 | ||||
| Downside part of mean | -0.277 | ||||
| Upside SD | 0.328 | ||||
| Downside SD | 0.383 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.101 | ||||
| Mean of criterion | -0.047 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.507 | ||||
| Covariance | -0.008 | ||||
| r | -0.050 | ||||
| b (slope, estimate of beta) | -0.083 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.260 | ||||
| DF error | 91.000 | ||||
| t(b) | -0.479 | ||||
| p(b) | 0.683 | ||||
| t(a) | -0.208 | ||||
| p(a) | 0.582 | ||||
| Lowerbound of 95% confidence interval for beta | -0.428 | ||||
| Upperbound of 95% confidence interval for beta | 0.262 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.403 | ||||
| Upperbound of 95% confidence interval for alpha | 0.327 | ||||
| Treynor index (mean / b) | 0.561 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.217 | ||||
| Expected Shortfall on VaR | 0.263 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.132 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 93.000 | ||||
| Minimum | 0.415 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.080 | ||||
| Mean of quarter 1 | 0.941 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.102 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.900 | ||||
| Number of outliers high | 23.000 | ||||
| Percentage of outliers high | 0.247 | ||||
| Mean of outliers high | 1.102 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.462 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.787 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.167 | ||||
| Quartile 1 | 0.278 | ||||
| Median | 0.390 | ||||
| Quartile 3 | 0.502 | ||||
| Maximum | 0.614 | ||||
| Mean of quarter 1 | 0.167 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.614 | ||||
| Inter Quartile Range | 0.224 | ||||
| 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) | -0.003 | ||||
| Compounded annual return (geometric extrapolation) | -0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.004 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.004 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.010 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.623 | ||||
| SD | 1.265 | ||||
| Sharpe ratio (Glass type estimate) | 0.492 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.492 | ||||
| df | 2050.000 | ||||
| t | 1.377 | ||||
| p | 0.084 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.208 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.193 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.209 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.193 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.024 | ||||
| Upside Potential Ratio | 3.336 | ||||
| Upside part of mean | 2.028 | ||||
| Downside part of mean | -1.405 | ||||
| Upside SD | 1.110 | ||||
| Downside SD | 0.608 | ||||
| N nonnegative terms | 310.000 | ||||
| N negative terms | 1741.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2051.000 | ||||
| Mean of predictor | 0.308 | ||||
| Mean of criterion | 0.623 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 1.265 | ||||
| Covariance | -0.118 | ||||
| r | -0.163 | ||||
| b (slope, estimate of beta) | -0.360 | ||||
| a (intercept, estimate of alpha) | 0.733 | ||||
| Mean Square Error | 1.558 | ||||
| DF error | 2049.000 | ||||
| t(b) | -7.486 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.643 | ||||
| p(a) | 0.050 | ||||
| Lowerbound of 95% confidence interval for beta | -0.454 | ||||
| Upperbound of 95% confidence interval for beta | -0.265 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.142 | ||||
| Upperbound of 95% confidence interval for alpha | 1.609 | ||||
| Treynor index (mean / b) | -1.732 | ||||
| Jensen alpha (a) | 0.733 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.047 | ||||
| SD | 1.162 | ||||
| Sharpe ratio (Glass type estimate) | -0.040 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.040 | ||||
| df | 2050.000 | ||||
| t | -0.112 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.741 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.660 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.741 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.660 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.054 | ||||
| Upside Potential Ratio | 1.916 | ||||
| Upside part of mean | 1.645 | ||||
| Downside part of mean | -1.691 | ||||
| Upside SD | 0.782 | ||||
| Downside SD | 0.858 | ||||
| N nonnegative terms | 310.000 | ||||
| N negative terms | 1741.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2051.000 | ||||
| Mean of predictor | 0.153 | ||||
| Mean of criterion | -0.047 | ||||
| SD of predictor | 0.550 | ||||
| SD of criterion | 1.162 | ||||
| Covariance | -0.091 | ||||
| r | -0.142 | ||||
| b (slope, estimate of beta) | -0.299 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 1.323 | ||||
| DF error | 2049.000 | ||||
| t(b) | -6.483 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.002 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.390 | ||||
| Upperbound of 95% confidence interval for beta | -0.209 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.807 | ||||
| Upperbound of 95% confidence interval for alpha | 0.805 | ||||
| Treynor index (mean / b) | 0.156 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.112 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2051.000 | ||||
| Minimum | 0.233 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.713 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 371.000 | ||||
| Percentage of outliers low | 0.181 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 409.000 | ||||
| Percentage of outliers high | 0.199 | ||||
| Mean of outliers high | 1.039 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.248 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.970 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.415 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.391 | ||||
| Median | 0.653 | ||||
| Quartile 3 | 0.807 | ||||
| Maximum | 0.874 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.520 | ||||
| Mean of quarter 3 | 0.785 | ||||
| Mean of quarter 4 | 0.874 | ||||
| Inter Quartile Range | 0.417 | ||||
| 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) | -0.003 | ||||
| Compounded annual return (geometric extrapolation) | -0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.003 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.003 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.019 | ||||
| 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 | 2.062 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.996 | ||||
| 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 | 1.653 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.861 | ||||
| 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) | -8738130389140021.000 | ||||
| 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) | 448516921712593408530048876544000.000 | ||||
| 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 | ||||