Advanced Statistics: .
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 | 15.626 | ||||
| SD | 38.604 | ||||
| Sharpe ratio (Glass type estimate) | 0.405 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.400 | ||||
| df | 69.000 | ||||
| t | 0.978 | ||||
| p | 0.166 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.411 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.218 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.414 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.215 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 29.637 | ||||
| Upside Potential Ratio | 30.302 | ||||
| Upside part of mean | 15.977 | ||||
| Downside part of mean | -0.351 | ||||
| Upside SD | 38.589 | ||||
| Downside SD | 0.527 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.151 | ||||
| Mean of criterion | 15.626 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 38.604 | ||||
| Covariance | -0.271 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -5.084 | ||||
| a (intercept, estimate of alpha) | 16.393 | ||||
| Mean Square Error | 1510.823 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.251 | ||||
| p(b) | 0.599 | ||||
| t(a) | 1.001 | ||||
| p(a) | 0.160 | ||||
| Lowerbound of 95% confidence interval for beta | -45.562 | ||||
| Upperbound of 95% confidence interval for beta | 35.394 | ||||
| Lowerbound of 95% confidence interval for alpha | -16.296 | ||||
| Upperbound of 95% confidence interval for alpha | 49.081 | ||||
| Treynor index (mean / b) | -3.074 | ||||
| Jensen alpha (a) | 16.393 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 2.322 | ||||
| Sharpe ratio (Glass type estimate) | -0.019 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.019 | ||||
| df | 69.000 | ||||
| t | -0.046 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.830 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.793 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.830 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.033 | ||||
| Upside Potential Ratio | 0.584 | ||||
| Upside part of mean | 0.779 | ||||
| Downside part of mean | -0.823 | ||||
| Upside SD | 1.880 | ||||
| Downside SD | 1.334 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.123 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.230 | ||||
| SD of criterion | 2.322 | ||||
| Covariance | -0.023 | ||||
| r | -0.042 | ||||
| b (slope, estimate of beta) | -0.428 | ||||
| a (intercept, estimate of alpha) | 0.009 | ||||
| Mean Square Error | 5.463 | ||||
| DF error | 68.000 | ||||
| t(b) | -0.350 | ||||
| p(b) | 0.636 | ||||
| t(a) | 0.009 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -2.872 | ||||
| Upperbound of 95% confidence interval for beta | 2.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.946 | ||||
| Upperbound of 95% confidence interval for alpha | 1.963 | ||||
| Treynor index (mean / b) | 0.103 | ||||
| Jensen alpha (a) | 0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.669 | ||||
| Expected Shortfall on VaR | 0.743 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.101 | ||||
| Expected Shortfall on VaR | 0.223 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.093 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 94.204 | ||||
| Mean of quarter 1 | 0.900 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 6.178 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.104 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.014 | ||||
| Mean of outliers high | 94.204 | ||||
| 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) | -6.464 | ||||
| VaR(95%) (regression method) | -7.422 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.989 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 0.989 | ||||
| Quartile 3 | 0.989 | ||||
| Maximum | 0.989 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 48.462 | ||||
| SD | 117.306 | ||||
| Sharpe ratio (Glass type estimate) | 0.413 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.413 | ||||
| df | 1543.000 | ||||
| t | 1.003 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.394 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.221 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.395 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.220 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 68.550 | ||||
| Upside Potential Ratio | 70.355 | ||||
| Upside part of mean | 49.739 | ||||
| Downside part of mean | -1.276 | ||||
| Upside SD | 117.304 | ||||
| Downside SD | 0.707 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 1522.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1544.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | 48.462 | ||||
| SD of predictor | 0.578 | ||||
| SD of criterion | 117.306 | ||||
| Covariance | 7.336 | ||||
| r | 0.108 | ||||
| b (slope, estimate of beta) | 21.956 | ||||
| a (intercept, estimate of alpha) | 40.657 | ||||
| Mean Square Error | 13608.439 | ||||
| DF error | 1542.000 | ||||
| t(b) | 4.273 | ||||
| p(b) | 0.446 | ||||
| t(a) | 0.845 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | 11.878 | ||||
| Upperbound of 95% confidence interval for beta | 32.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -53.670 | ||||
| Upperbound of 95% confidence interval for alpha | 134.983 | ||||
| Treynor index (mean / b) | 2.207 | ||||
| Jensen alpha (a) | 40.657 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 2.747 | ||||
| Sharpe ratio (Glass type estimate) | -0.016 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.016 | ||||
| df | 1543.000 | ||||
| t | -0.039 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.823 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.791 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.823 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.791 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.037 | ||||
| Upside Potential Ratio | 1.453 | ||||
| Upside part of mean | 1.709 | ||||
| Downside part of mean | -1.753 | ||||
| Upside SD | 2.481 | ||||
| Downside SD | 1.176 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 1522.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1544.000 | ||||
| Mean of predictor | 0.191 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 2.747 | ||||
| Covariance | 0.141 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.428 | ||||
| a (intercept, estimate of alpha) | -0.126 | ||||
| Mean Square Error | 7.490 | ||||
| DF error | 1542.000 | ||||
| t(b) | 3.522 | ||||
| p(b) | 0.455 | ||||
| t(a) | -0.111 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.190 | ||||
| Upperbound of 95% confidence interval for beta | 0.666 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.337 | ||||
| Upperbound of 95% confidence interval for alpha | 2.086 | ||||
| Treynor index (mean / b) | -0.103 | ||||
| Jensen alpha (a) | -0.126 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.244 | ||||
| Expected Shortfall on VaR | 0.294 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1544.000 | ||||
| Minimum | 0.146 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 285.714 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.759 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 33.000 | ||||
| Percentage of outliers low | 0.021 | ||||
| Mean of outliers low | 0.780 | ||||
| Number of outliers high | 22.000 | ||||
| Percentage of outliers high | 0.014 | ||||
| Mean of outliers high | 14.324 | ||||
| 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) | 0.285 | ||||
| VaR(95%) (regression method) | -0.067 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.024 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.514 | ||||
| Maximum | 0.997 | ||||
| Mean of quarter 1 | 0.024 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.997 | ||||
| Inter Quartile Range | 0.486 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.674 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.662 | ||||
| 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 | 1.458 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.649 | ||||
| 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) | -8715630712982740.000 | ||||
| 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) | 1528618833591239248489674405052416.000 | ||||
| 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 | ||||