Advanced Statistics: EZV-180
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 | 0.023 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | 0.275 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.269 | ||||
| df | 36.000 | ||||
| t | 0.482 | ||||
| p | 0.316 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.845 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.849 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.387 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.707 | ||||
| Upside Potential Ratio | 2.415 | ||||
| Upside part of mean | 0.078 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.547 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | -0.002 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.030 | ||||
| a (intercept, estimate of alpha) | 0.039 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 35.000 | ||||
| t(b) | -0.619 | ||||
| p(b) | 0.730 | ||||
| t(a) | 0.719 | ||||
| p(a) | 0.238 | ||||
| Lowerbound of 95% confidence interval for beta | -0.129 | ||||
| Upperbound of 95% confidence interval for beta | 0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.151 | ||||
| Treynor index (mean / b) | -0.757 | ||||
| Jensen alpha (a) | 0.039 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.020 | ||||
| SD | 0.081 | ||||
| Sharpe ratio (Glass type estimate) | 0.242 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.237 | ||||
| df | 36.000 | ||||
| t | 0.425 | ||||
| p | 0.337 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.877 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.358 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.881 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.354 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.592 | ||||
| Upside Potential Ratio | 2.276 | ||||
| Upside part of mean | 0.075 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.073 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.498 | ||||
| Mean of criterion | 0.020 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.081 | ||||
| Covariance | -0.002 | ||||
| r | -0.100 | ||||
| b (slope, estimate of beta) | -0.030 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 35.000 | ||||
| t(b) | -0.593 | ||||
| p(b) | 0.722 | ||||
| t(a) | 0.654 | ||||
| p(a) | 0.259 | ||||
| Lowerbound of 95% confidence interval for beta | -0.133 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.142 | ||||
| Treynor index (mean / b) | -0.647 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.951 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.091 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.951 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.108 | ||||
| Mean of outliers high | 1.064 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.049 | ||||
| Quartile 1 | 0.049 | ||||
| Median | 0.049 | ||||
| Quartile 3 | 0.049 | ||||
| Maximum | 0.049 | ||||
| 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 | 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) | 0.070 | ||||
| Compounded annual return (geometric extrapolation) | 0.066 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.333 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.446 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.021 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | 0.335 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.334 | ||||
| df | 809.000 | ||||
| t | 0.589 | ||||
| p | 0.278 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.780 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.450 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.780 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.449 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.576 | ||||
| Upside Potential Ratio | 3.401 | ||||
| Upside part of mean | 0.127 | ||||
| Downside part of mean | -0.105 | ||||
| Upside SD | 0.052 | ||||
| Downside SD | 0.037 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 773.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 810.000 | ||||
| Mean of predictor | 0.561 | ||||
| Mean of criterion | 0.021 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | 0.000 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 808.000 | ||||
| t(b) | 0.309 | ||||
| p(b) | 0.379 | ||||
| t(a) | 0.551 | ||||
| p(a) | 0.291 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | 0.092 | ||||
| Treynor index (mean / b) | 9.787 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.019 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | 0.304 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.304 | ||||
| df | 809.000 | ||||
| t | 0.534 | ||||
| p | 0.297 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.811 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.419 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.811 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.418 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.512 | ||||
| Upside Potential Ratio | 3.308 | ||||
| Upside part of mean | 0.125 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 773.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 810.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | 0.019 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | 0.000 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | 0.018 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 808.000 | ||||
| t(b) | 0.328 | ||||
| p(b) | 0.372 | ||||
| t(a) | 0.499 | ||||
| p(a) | 0.309 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.053 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | 8.443 | ||||
| Jensen alpha (a) | 0.018 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 810.000 | ||||
| Minimum | 0.953 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.041 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 26.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 37.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.885 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.738 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.019 | ||||
| Maximum | 0.088 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.013 | ||||
| Mean of quarter 4 | 0.055 | ||||
| Inter Quartile Range | 0.015 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.088 | ||||
| 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) | 0.070 | ||||
| Compounded annual return (geometric extrapolation) | 0.065 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.740 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.189 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.160 | ||||
| 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 | 1.174 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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 | 1.049 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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) | -8725869298288166.000 | ||||
| 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) | -53065583677888834065803232935936.000 | ||||
| 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 | ||||