Advanced Statistics: System 33686814
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 | 0.161 | ||||
| SD | 0.673 | ||||
| Sharpe ratio (Glass type estimate) | 0.240 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.237 | ||||
| df | 64.000 | ||||
| t | 0.558 | ||||
| p | 0.289 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.604 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.082 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.606 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.080 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.475 | ||||
| Upside Potential Ratio | 1.309 | ||||
| Upside part of mean | 0.445 | ||||
| Downside part of mean | -0.283 | ||||
| Upside SD | 0.577 | ||||
| Downside SD | 0.340 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.309 | ||||
| Mean of criterion | 0.161 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.673 | ||||
| Covariance | -0.013 | ||||
| r | -0.062 | ||||
| b (slope, estimate of beta) | -0.135 | ||||
| a (intercept, estimate of alpha) | 0.203 | ||||
| Mean Square Error | 0.458 | ||||
| DF error | 63.000 | ||||
| t(b) | -0.495 | ||||
| p(b) | 0.689 | ||||
| t(a) | 0.671 | ||||
| p(a) | 0.252 | ||||
| Lowerbound of 95% confidence interval for beta | -0.681 | ||||
| Upperbound of 95% confidence interval for beta | 0.411 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.402 | ||||
| Upperbound of 95% confidence interval for alpha | 0.808 | ||||
| Treynor index (mean / b) | -1.193 | ||||
| Jensen alpha (a) | 0.203 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.627 | ||||
| Sharpe ratio (Glass type estimate) | -0.049 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.049 | ||||
| df | 64.000 | ||||
| t | -0.115 | ||||
| p | 0.546 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.891 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.793 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.891 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.065 | ||||
| Upside Potential Ratio | 0.720 | ||||
| Upside part of mean | 0.341 | ||||
| Downside part of mean | -0.372 | ||||
| Upside SD | 0.404 | ||||
| Downside SD | 0.473 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.259 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.627 | ||||
| Covariance | 0.008 | ||||
| r | 0.041 | ||||
| b (slope, estimate of beta) | 0.084 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.398 | ||||
| DF error | 63.000 | ||||
| t(b) | 0.323 | ||||
| p(b) | 0.374 | ||||
| t(a) | -0.189 | ||||
| p(a) | 0.575 | ||||
| Lowerbound of 95% confidence interval for beta | -0.437 | ||||
| Upperbound of 95% confidence interval for beta | 0.606 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.611 | ||||
| Upperbound of 95% confidence interval for alpha | 0.506 | ||||
| Treynor index (mean / b) | -0.367 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.259 | ||||
| Expected Shortfall on VaR | 0.312 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.158 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 65.000 | ||||
| Minimum | 0.417 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.202 | ||||
| Mean of quarter 1 | 0.921 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.154 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.154 | ||||
| Mean of outliers low | 0.865 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.246 | ||||
| Mean of outliers high | 1.154 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 3.019 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.890 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.636 | ||||
| Quartile 1 | 0.636 | ||||
| Median | 0.636 | ||||
| Quartile 3 | 0.636 | ||||
| Maximum | 0.636 | ||||
| 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) | 0.014 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.021 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.042 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.058 | ||||
| SD | 2.197 | ||||
| Sharpe ratio (Glass type estimate) | 0.936 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.936 | ||||
| df | 1436.000 | ||||
| t | 2.193 | ||||
| p | 0.471 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.099 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.774 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.098 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.774 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.023 | ||||
| Upside Potential Ratio | 4.272 | ||||
| Upside part of mean | 4.345 | ||||
| Downside part of mean | -2.287 | ||||
| Upside SD | 1.951 | ||||
| Downside SD | 1.017 | ||||
| N nonnegative terms | 239.000 | ||||
| N negative terms | 1198.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1437.000 | ||||
| Mean of predictor | 0.424 | ||||
| Mean of criterion | 2.058 | ||||
| SD of predictor | 0.534 | ||||
| SD of criterion | 2.197 | ||||
| Covariance | 0.075 | ||||
| r | 0.064 | ||||
| b (slope, estimate of beta) | 0.262 | ||||
| a (intercept, estimate of alpha) | 1.946 | ||||
| Mean Square Error | 4.811 | ||||
| DF error | 1435.000 | ||||
| t(b) | 2.421 | ||||
| p(b) | 0.459 | ||||
| t(a) | 2.076 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | 0.050 | ||||
| Upperbound of 95% confidence interval for beta | 0.475 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.107 | ||||
| Upperbound of 95% confidence interval for alpha | 3.786 | ||||
| Treynor index (mean / b) | 7.844 | ||||
| Jensen alpha (a) | 1.946 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 2.128 | ||||
| Sharpe ratio (Glass type estimate) | -0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.015 | ||||
| df | 1436.000 | ||||
| t | -0.034 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.851 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.822 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.851 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.822 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.018 | ||||
| Upside Potential Ratio | 1.927 | ||||
| Upside part of mean | 3.244 | ||||
| Downside part of mean | -3.275 | ||||
| Upside SD | 1.301 | ||||
| Downside SD | 1.683 | ||||
| N nonnegative terms | 239.000 | ||||
| N negative terms | 1198.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1437.000 | ||||
| Mean of predictor | 0.284 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.527 | ||||
| SD of criterion | 2.128 | ||||
| Covariance | 0.076 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 0.272 | ||||
| a (intercept, estimate of alpha) | -0.108 | ||||
| Mean Square Error | 4.511 | ||||
| DF error | 1435.000 | ||||
| t(b) | 2.557 | ||||
| p(b) | 0.457 | ||||
| t(a) | -0.119 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | 0.063 | ||||
| Upperbound of 95% confidence interval for beta | 0.480 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.888 | ||||
| Upperbound of 95% confidence interval for alpha | 1.672 | ||||
| Treynor index (mean / b) | -0.114 | ||||
| Jensen alpha (a) | -0.108 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.195 | ||||
| Expected Shortfall on VaR | 0.237 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1437.000 | ||||
| Minimum | 0.129 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.719 | ||||
| Mean of quarter 1 | 0.966 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.066 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 179.000 | ||||
| Percentage of outliers low | 0.125 | ||||
| Mean of outliers low | 0.931 | ||||
| Number of outliers high | 250.000 | ||||
| Percentage of outliers high | 0.174 | ||||
| Mean of outliers high | 1.095 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.303 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.463 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.458 | ||||
| Median | 0.605 | ||||
| Quartile 3 | 0.708 | ||||
| Maximum | 0.886 | ||||
| Mean of quarter 1 | 0.153 | ||||
| Mean of quarter 2 | 0.550 | ||||
| Mean of quarter 3 | 0.651 | ||||
| Mean of quarter 4 | 0.838 | ||||
| Inter Quartile Range | 0.249 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.125 | ||||
| Mean of outliers low | 0.012 | ||||
| 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) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.015 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.016 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.055 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.860 | ||||
| SD | 0.639 | ||||
| Sharpe ratio (Glass type estimate) | 1.345 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.338 | ||||
| df | 130.000 | ||||
| t | 0.951 | ||||
| p | 0.458 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.434 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.119 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.439 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.114 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 317.546 | ||||
| Upside Potential Ratio | 333.670 | ||||
| Upside part of mean | 0.904 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.639 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.112 | ||||
| Mean of criterion | 0.860 | ||||
| SD of predictor | 0.515 | ||||
| SD of criterion | 0.639 | ||||
| Covariance | -0.026 | ||||
| r | -0.079 | ||||
| b (slope, estimate of beta) | -0.099 | ||||
| a (intercept, estimate of alpha) | 0.970 | ||||
| Mean Square Error | 0.409 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.905 | ||||
| p(b) | 0.551 | ||||
| t(a) | 1.062 | ||||
| p(a) | 0.441 | ||||
| Lowerbound of 95% confidence interval for beta | -0.314 | ||||
| Upperbound of 95% confidence interval for beta | 0.117 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.836 | ||||
| Upperbound of 95% confidence interval for alpha | 2.776 | ||||
| Treynor index (mean / b) | -8.722 | ||||
| Jensen alpha (a) | 0.970 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.702 | ||||
| SD | 0.528 | ||||
| Sharpe ratio (Glass type estimate) | 1.331 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.323 | ||||
| df | 130.000 | ||||
| t | 0.941 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.448 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.105 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.453 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.100 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 259.170 | ||||
| Upside Potential Ratio | 275.294 | ||||
| Upside part of mean | 0.746 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.527 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.977 | ||||
| Mean of criterion | 0.702 | ||||
| SD of predictor | 0.519 | ||||
| SD of criterion | 0.528 | ||||
| Covariance | -0.021 | ||||
| r | -0.078 | ||||
| b (slope, estimate of beta) | -0.080 | ||||
| a (intercept, estimate of alpha) | 0.780 | ||||
| Mean Square Error | 0.279 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.891 | ||||
| p(b) | 0.550 | ||||
| t(a) | 1.037 | ||||
| p(a) | 0.442 | ||||
| Lowerbound of 95% confidence interval for beta | -0.256 | ||||
| Upperbound of 95% confidence interval for beta | 0.097 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.708 | ||||
| Upperbound of 95% confidence interval for alpha | 2.267 | ||||
| Treynor index (mean / b) | -8.823 | ||||
| Jensen alpha (a) | 0.780 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| 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 | 1.452 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.452 | ||||
| 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) | 0.904 | ||||
| Compounded annual return (geometric extrapolation) | 1.109 | ||||
| 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 | 17.756 | ||||