Advanced Statistics: Fibz
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 | 0.072 | ||||
| SD | 0.406 | ||||
| Sharpe ratio (Glass type estimate) | 0.178 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.174 | ||||
| df | 38.000 | ||||
| t | 0.321 | ||||
| p | 0.375 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.911 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.265 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.914 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.262 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.344 | ||||
| Upside Potential Ratio | 1.489 | ||||
| Upside part of mean | 0.312 | ||||
| Downside part of mean | -0.240 | ||||
| Upside SD | 0.342 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.547 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.406 | ||||
| Covariance | 0.010 | ||||
| r | 0.074 | ||||
| b (slope, estimate of beta) | 0.089 | ||||
| a (intercept, estimate of alpha) | 0.023 | ||||
| Mean Square Error | 0.168 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.452 | ||||
| p(b) | 0.327 | ||||
| t(a) | 0.093 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | -0.311 | ||||
| Upperbound of 95% confidence interval for beta | 0.490 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.487 | ||||
| Upperbound of 95% confidence interval for alpha | 0.534 | ||||
| Treynor index (mean / b) | 0.808 | ||||
| Jensen alpha (a) | 0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.001 | ||||
| SD | 0.380 | ||||
| Sharpe ratio (Glass type estimate) | -0.002 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.002 | ||||
| df | 38.000 | ||||
| t | -0.003 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.089 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.085 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.089 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.085 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.003 | ||||
| Upside Potential Ratio | 1.096 | ||||
| Upside part of mean | 0.265 | ||||
| Downside part of mean | -0.266 | ||||
| Upside SD | 0.287 | ||||
| Downside SD | 0.242 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.484 | ||||
| Mean of criterion | -0.001 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.380 | ||||
| Covariance | 0.011 | ||||
| r | 0.096 | ||||
| b (slope, estimate of beta) | 0.116 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.147 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.586 | ||||
| p(b) | 0.281 | ||||
| t(a) | -0.243 | ||||
| p(a) | 0.595 | ||||
| Lowerbound of 95% confidence interval for beta | -0.284 | ||||
| Upperbound of 95% confidence interval for beta | 0.515 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.529 | ||||
| Upperbound of 95% confidence interval for alpha | 0.416 | ||||
| Treynor index (mean / b) | -0.006 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.165 | ||||
| Expected Shortfall on VaR | 0.202 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.136 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.697 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.459 | ||||
| Mean of quarter 1 | 0.935 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.103 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.154 | ||||
| Mean of outliers low | 0.891 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 1.257 | ||||
| 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) | 0.598 | ||||
| VaR(95%) (regression method) | 0.067 | ||||
| Expected Shortfall (regression method) | 0.257 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.145 | ||||
| Quartile 1 | 0.185 | ||||
| Median | 0.224 | ||||
| Quartile 3 | 0.264 | ||||
| Maximum | 0.303 | ||||
| Mean of quarter 1 | 0.145 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.303 | ||||
| Inter Quartile Range | 0.079 | ||||
| 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) | 0.046 | ||||
| Compounded annual return (geometric extrapolation) | 0.044 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.146 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.146 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.219 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.031 | ||||
| SD | 0.253 | ||||
| Sharpe ratio (Glass type estimate) | 0.121 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.121 | ||||
| df | 852.000 | ||||
| t | 0.218 | ||||
| p | 0.414 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.966 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.207 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.966 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.207 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.193 | ||||
| Upside Potential Ratio | 4.475 | ||||
| Upside part of mean | 0.709 | ||||
| Downside part of mean | -0.678 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.158 | ||||
| N nonnegative terms | 98.000 | ||||
| N negative terms | 755.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 853.000 | ||||
| Mean of predictor | 0.535 | ||||
| Mean of criterion | 0.031 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.253 | ||||
| Covariance | 0.011 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.104 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.063 | ||||
| DF error | 851.000 | ||||
| t(b) | 3.981 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.179 | ||||
| p(a) | 0.571 | ||||
| Lowerbound of 95% confidence interval for beta | 0.053 | ||||
| Upperbound of 95% confidence interval for beta | 0.155 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 0.249 | ||||
| Treynor index (mean / b) | 0.294 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.001 | ||||
| SD | 0.249 | ||||
| Sharpe ratio (Glass type estimate) | -0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.003 | ||||
| df | 852.000 | ||||
| t | -0.006 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.089 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.083 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.089 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.083 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.005 | ||||
| Upside Potential Ratio | 4.240 | ||||
| Upside part of mean | 0.690 | ||||
| Downside part of mean | -0.691 | ||||
| Upside SD | 0.189 | ||||
| Downside SD | 0.163 | ||||
| N nonnegative terms | 98.000 | ||||
| N negative terms | 755.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 853.000 | ||||
| Mean of predictor | 0.480 | ||||
| Mean of criterion | -0.001 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.249 | ||||
| Covariance | 0.011 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.101 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 851.000 | ||||
| t(b) | 3.968 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.359 | ||||
| p(a) | 0.640 | ||||
| Lowerbound of 95% confidence interval for beta | 0.051 | ||||
| Upperbound of 95% confidence interval for beta | 0.151 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.319 | ||||
| Upperbound of 95% confidence interval for alpha | 0.221 | ||||
| Treynor index (mean / b) | -0.008 | ||||
| Jensen alpha (a) | -0.049 | ||||
| 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%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 853.000 | ||||
| Minimum | 0.909 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.179 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 99.000 | ||||
| Percentage of outliers low | 0.116 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 101.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 1.023 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.779 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.037 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.041 | ||||
| Quartile 3 | 0.254 | ||||
| Maximum | 0.396 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | 0.204 | ||||
| Mean of quarter 4 | 0.349 | ||||
| Inter Quartile Range | 0.235 | ||||
| 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) | 0.046 | ||||
| Compounded annual return (geometric extrapolation) | 0.044 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.112 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.126 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.413 | ||||
| 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 | 0.951 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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 | 0.832 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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) | -8750466828894253.000 | ||||
| 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) | 99107798722248000706025546055680.000 | ||||
| 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 | ||||