Advanced Statistics: bahar
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.011 | ||||
| Sharpe ratio (Glass type estimate) | -3.503 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.417 | ||||
| df | 31.000 | ||||
| t | -5.720 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.965 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.003 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.888 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.946 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.996 | ||||
| Upside Potential Ratio | 0.414 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.008 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.602 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.011 | ||||
| Covariance | -0.000 | ||||
| r | -0.034 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.188 | ||||
| p(b) | 0.574 | ||||
| t(a) | -4.755 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.053 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | 30.656 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.011 | ||||
| Sharpe ratio (Glass type estimate) | -3.531 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.445 | ||||
| df | 31.000 | ||||
| t | -5.766 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.997 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.027 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.920 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.970 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.999 | ||||
| Upside Potential Ratio | 0.410 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.008 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.546 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.011 | ||||
| Covariance | -0.000 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.147 | ||||
| p(b) | 0.558 | ||||
| t(a) | -4.888 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | -0.022 | ||||
| Treynor index (mean / b) | 37.906 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.018 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.018 | ||||
| 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) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.007 | ||||
| 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 | 0.694 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.010 | ||||
| Sharpe ratio (Glass type estimate) | -3.948 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.944 | ||||
| df | 702.000 | ||||
| t | -6.467 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.161 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.733 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.158 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.730 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -13.812 | ||||
| Upside Potential Ratio | 2.351 | ||||
| Upside part of mean | 0.006 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 701.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 703.000 | ||||
| Mean of predictor | 0.682 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.397 | ||||
| SD of criterion | 0.010 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 701.000 | ||||
| t(b) | -0.056 | ||||
| p(b) | 0.522 | ||||
| t(a) | -6.421 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.049 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | 743.475 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -3.983 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.978 | ||||
| df | 702.000 | ||||
| t | -6.524 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.196 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.767 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.193 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.764 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -13.828 | ||||
| Upside Potential Ratio | 2.335 | ||||
| Upside part of mean | 0.006 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 701.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 703.000 | ||||
| Mean of predictor | 0.599 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.411 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 701.000 | ||||
| t(b) | -0.040 | ||||
| p(b) | 0.516 | ||||
| t(a) | -6.489 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.049 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | 1084.895 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| 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 | 703.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.015 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.003 | ||||
| Mean of outliers high | 1.009 | ||||
| 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) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| 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 | 4.826 | ||||
| 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 | 1.006 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.524 | ||||
| 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 | 0.869 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.522 | ||||
| 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) | -8753300833873833.000 | ||||
| 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) | -148037734425697374200986368737280.000 | ||||
| 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 | ||||