Advanced Statistics: EA Test Portfolio 17
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 | 0.493 | ||||
| SD | 1.134 | ||||
| Sharpe ratio (Glass type estimate) | 0.434 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.427 | ||||
| df | 42.000 | ||||
| t | 0.822 | ||||
| p | 0.208 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.608 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.471 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.613 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.466 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.054 | ||||
| Upside Potential Ratio | 1.943 | ||||
| Upside part of mean | 0.908 | ||||
| Downside part of mean | -0.416 | ||||
| Upside SD | 1.028 | ||||
| Downside SD | 0.467 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.438 | ||||
| Mean of criterion | 0.493 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 1.134 | ||||
| Covariance | 0.012 | ||||
| r | 0.039 | ||||
| b (slope, estimate of beta) | 0.166 | ||||
| a (intercept, estimate of alpha) | 0.420 | ||||
| Mean Square Error | 1.315 | ||||
| DF error | 41.000 | ||||
| t(b) | 0.248 | ||||
| p(b) | 0.403 | ||||
| t(a) | 0.624 | ||||
| p(a) | 0.268 | ||||
| Lowerbound of 95% confidence interval for beta | -1.188 | ||||
| Upperbound of 95% confidence interval for beta | 1.521 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.940 | ||||
| Upperbound of 95% confidence interval for alpha | 1.779 | ||||
| Treynor index (mean / b) | 2.962 | ||||
| Jensen alpha (a) | 0.420 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 1.066 | ||||
| Sharpe ratio (Glass type estimate) | -0.024 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.024 | ||||
| df | 42.000 | ||||
| t | -0.046 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.060 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.011 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.059 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.011 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.032 | ||||
| Upside Potential Ratio | 0.748 | ||||
| Upside part of mean | 0.617 | ||||
| Downside part of mean | -0.643 | ||||
| Upside SD | 0.655 | ||||
| Downside SD | 0.825 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.398 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 1.066 | ||||
| Covariance | 0.025 | ||||
| r | 0.093 | ||||
| b (slope, estimate of beta) | 0.399 | ||||
| a (intercept, estimate of alpha) | -0.185 | ||||
| Mean Square Error | 1.154 | ||||
| DF error | 41.000 | ||||
| t(b) | 0.597 | ||||
| p(b) | 0.277 | ||||
| t(a) | -0.295 | ||||
| p(a) | 0.615 | ||||
| Lowerbound of 95% confidence interval for beta | -0.949 | ||||
| Upperbound of 95% confidence interval for beta | 1.747 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.450 | ||||
| Upperbound of 95% confidence interval for alpha | 1.080 | ||||
| Treynor index (mean / b) | -0.065 | ||||
| Jensen alpha (a) | -0.185 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.398 | ||||
| Expected Shortfall on VaR | 0.468 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.110 | ||||
| Expected Shortfall on VaR | 0.240 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.230 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.586 | ||||
| Mean of quarter 1 | 0.877 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.298 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.070 | ||||
| Mean of outliers low | 0.549 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 1.546 | ||||
| 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) | -0.336 | ||||
| VaR(95%) (regression method) | 0.297 | ||||
| Expected Shortfall (regression method) | 0.634 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.224 | ||||
| Quartile 1 | 0.381 | ||||
| Median | 0.538 | ||||
| Quartile 3 | 0.696 | ||||
| Maximum | 0.853 | ||||
| Mean of quarter 1 | 0.224 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.853 | ||||
| Inter Quartile Range | 0.314 | ||||
| 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) | 0.019 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.021 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.021 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.039 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.669 | ||||
| SD | 1.235 | ||||
| Sharpe ratio (Glass type estimate) | 0.542 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.541 | ||||
| df | 957.000 | ||||
| t | 1.035 | ||||
| p | 0.150 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.484 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.567 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.484 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.566 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.987 | ||||
| Upside Potential Ratio | 3.799 | ||||
| Upside part of mean | 2.573 | ||||
| Downside part of mean | -1.904 | ||||
| Upside SD | 1.033 | ||||
| Downside SD | 0.677 | ||||
| N nonnegative terms | 98.000 | ||||
| N negative terms | 860.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 958.000 | ||||
| Mean of predictor | 0.496 | ||||
| Mean of criterion | 0.669 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 1.235 | ||||
| Covariance | 0.027 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 0.250 | ||||
| a (intercept, estimate of alpha) | 0.545 | ||||
| Mean Square Error | 1.520 | ||||
| DF error | 956.000 | ||||
| t(b) | 2.078 | ||||
| p(b) | 0.019 | ||||
| t(a) | 0.841 | ||||
| p(a) | 0.200 | ||||
| Lowerbound of 95% confidence interval for beta | 0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.486 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.726 | ||||
| Upperbound of 95% confidence interval for alpha | 1.815 | ||||
| Treynor index (mean / b) | 2.673 | ||||
| Jensen alpha (a) | 0.545 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 1.188 | ||||
| Sharpe ratio (Glass type estimate) | -0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.022 | ||||
| df | 957.000 | ||||
| t | -0.043 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.047 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.003 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.047 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.003 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.030 | ||||
| Upside Potential Ratio | 2.487 | ||||
| Upside part of mean | 2.202 | ||||
| Downside part of mean | -2.228 | ||||
| Upside SD | 0.791 | ||||
| Downside SD | 0.885 | ||||
| N nonnegative terms | 98.000 | ||||
| N negative terms | 860.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 958.000 | ||||
| Mean of predictor | 0.441 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 1.188 | ||||
| Covariance | 0.028 | ||||
| r | 0.072 | ||||
| b (slope, estimate of beta) | 0.260 | ||||
| a (intercept, estimate of alpha) | -0.141 | ||||
| Mean Square Error | 1.405 | ||||
| DF error | 956.000 | ||||
| t(b) | 2.230 | ||||
| p(b) | 0.013 | ||||
| t(a) | -0.227 | ||||
| p(a) | 0.590 | ||||
| Lowerbound of 95% confidence interval for beta | 0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.489 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.362 | ||||
| Upperbound of 95% confidence interval for alpha | 1.080 | ||||
| Treynor index (mean / b) | -0.102 | ||||
| Jensen alpha (a) | -0.141 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.114 | ||||
| Expected Shortfall on VaR | 0.140 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 958.000 | ||||
| Minimum | 0.355 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.262 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.039 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 78.000 | ||||
| Percentage of outliers low | 0.081 | ||||
| Mean of outliers low | 0.913 | ||||
| Number of outliers high | 98.000 | ||||
| Percentage of outliers high | 0.102 | ||||
| Mean of outliers high | 1.096 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.856 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.035 | ||||
| Extreme Value Index (regression method) | 0.467 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.094 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.022 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.173 | ||||
| Maximum | 0.952 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.039 | ||||
| Mean of quarter 3 | 0.077 | ||||
| Mean of quarter 4 | 0.684 | ||||
| Inter Quartile Range | 0.151 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.684 | ||||
| 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) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.019 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.026 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.126 | ||||
| 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 | 1.143 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8733674005517795.000 | ||||
| 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) | -941802013088313751033952528760832.000 | ||||
| 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 | ||||