Advanced Statistics: Z-2
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 | -0.022 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -0.340 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.336 | ||||
| df | 69.000 | ||||
| t | -0.821 | ||||
| p | 0.793 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.152 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.475 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.150 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.477 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.566 | ||||
| Upside Potential Ratio | 1.103 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.285 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | -0.000 | ||||
| r | -0.013 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.110 | ||||
| p(b) | 0.544 | ||||
| t(a) | -0.756 | ||||
| p(a) | 0.774 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.034 | ||||
| Treynor index (mean / b) | 7.590 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.062 | ||||
| Sharpe ratio (Glass type estimate) | -0.376 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.372 | ||||
| df | 69.000 | ||||
| t | -0.908 | ||||
| p | 0.816 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.189 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.439 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.186 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.442 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.602 | ||||
| Upside Potential Ratio | 1.043 | ||||
| Upside part of mean | 0.041 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.239 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.292 | ||||
| SD of criterion | 0.062 | ||||
| Covariance | -0.000 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.073 | ||||
| p(b) | 0.529 | ||||
| t(a) | -0.860 | ||||
| p(a) | 0.804 | ||||
| Lowerbound of 95% confidence interval for beta | -0.054 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.030 | ||||
| Treynor index (mean / b) | 12.384 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.941 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.095 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.100 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.129 | ||||
| Mean of outliers high | 1.030 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -9.732 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -1.034 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.065 | ||||
| Maximum | 0.071 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.059 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.071 | ||||
| Inter Quartile Range | 0.033 | ||||
| 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) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.293 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.293 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.541 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.279 | ||||
| Sharpe ratio (Glass type estimate) | 0.053 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.053 | ||||
| df | 1530.000 | ||||
| t | 0.129 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.757 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.864 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.757 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.864 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.082 | ||||
| Upside Potential Ratio | 2.647 | ||||
| Upside part of mean | 0.480 | ||||
| Downside part of mean | -0.465 | ||||
| Upside SD | 0.212 | ||||
| Downside SD | 0.181 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 1465.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1531.000 | ||||
| Mean of predictor | 0.432 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.614 | ||||
| SD of criterion | 0.279 | ||||
| Covariance | -0.077 | ||||
| r | -0.451 | ||||
| b (slope, estimate of beta) | -0.205 | ||||
| a (intercept, estimate of alpha) | 0.103 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 1529.000 | ||||
| t(b) | -19.748 | ||||
| p(b) | 0.777 | ||||
| t(a) | 1.002 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | -0.225 | ||||
| Upperbound of 95% confidence interval for beta | -0.185 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.306 | ||||
| Treynor index (mean / b) | -0.073 | ||||
| Jensen alpha (a) | 0.103 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.024 | ||||
| SD | 0.277 | ||||
| Sharpe ratio (Glass type estimate) | -0.085 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.085 | ||||
| df | 1530.000 | ||||
| t | -0.205 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.896 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.726 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.896 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.726 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.122 | ||||
| Upside Potential Ratio | 2.391 | ||||
| Upside part of mean | 0.459 | ||||
| Downside part of mean | -0.483 | ||||
| Upside SD | 0.199 | ||||
| Downside SD | 0.192 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 1465.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1531.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.606 | ||||
| SD of criterion | 0.277 | ||||
| Covariance | -0.077 | ||||
| r | -0.457 | ||||
| b (slope, estimate of beta) | -0.209 | ||||
| a (intercept, estimate of alpha) | 0.028 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 1529.000 | ||||
| t(b) | -20.071 | ||||
| p(b) | 0.780 | ||||
| t(a) | 0.277 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.229 | ||||
| Upperbound of 95% confidence interval for beta | -0.188 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.172 | ||||
| Upperbound of 95% confidence interval for alpha | 0.228 | ||||
| Treynor index (mean / b) | 0.113 | ||||
| Jensen alpha (a) | 0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| 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 | 1531.000 | ||||
| Minimum | 0.830 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.205 | ||||
| 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 | 0.000 | ||||
| Number outliers low | 88.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 95.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.030 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.735 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| 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 | 9.000 | ||||
| Minimum | 0.056 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.122 | ||||
| Quartile 3 | 0.170 | ||||
| Maximum | 0.204 | ||||
| Mean of quarter 1 | 0.069 | ||||
| Mean of quarter 2 | 0.120 | ||||
| Mean of quarter 3 | 0.147 | ||||
| Mean of quarter 4 | 0.194 | ||||
| Inter Quartile Range | 0.077 | ||||
| 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) | -2.090 | ||||
| VaR(95%) (moments method) | 0.201 | ||||
| Expected Shortfall (moments method) | 0.202 | ||||
| Extreme Value Index (regression method) | -0.280 | ||||
| VaR(95%) (regression method) | 0.211 | ||||
| Expected Shortfall (regression method) | 0.225 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.101 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.107 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.597 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.439 | ||||
| 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 | 0.864 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.439 | ||||
| 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) | -8735003922917795.000 | ||||
| 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) | 133359935079999101472667393327104.000 | ||||
| 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 | ||||