Advanced Statistics: bH NQ
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 | 0.039 | ||||
| SD | 0.213 | ||||
| Sharpe ratio (Glass type estimate) | 0.185 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.182 | ||||
| df | 53.000 | ||||
| t | 0.391 | ||||
| p | 0.349 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.741 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.108 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.743 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.107 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.323 | ||||
| Upside Potential Ratio | 1.861 | ||||
| Upside part of mean | 0.226 | ||||
| Downside part of mean | -0.187 | ||||
| Upside SD | 0.173 | ||||
| Downside SD | 0.122 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.348 | ||||
| Mean of criterion | 0.039 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.213 | ||||
| Covariance | 0.004 | ||||
| r | 0.075 | ||||
| b (slope, estimate of beta) | 0.062 | ||||
| a (intercept, estimate of alpha) | 0.018 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 52.000 | ||||
| t(b) | 0.544 | ||||
| p(b) | 0.294 | ||||
| t(a) | 0.164 | ||||
| p(a) | 0.435 | ||||
| Lowerbound of 95% confidence interval for beta | -0.166 | ||||
| Upperbound of 95% confidence interval for beta | 0.289 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.200 | ||||
| Upperbound of 95% confidence interval for alpha | 0.235 | ||||
| Treynor index (mean / b) | 0.637 | ||||
| Jensen alpha (a) | 0.018 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.207 | ||||
| Sharpe ratio (Glass type estimate) | 0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.084 | ||||
| df | 53.000 | ||||
| t | 0.182 | ||||
| p | 0.428 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.839 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.009 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.840 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.009 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.137 | ||||
| Upside Potential Ratio | 1.634 | ||||
| Upside part of mean | 0.212 | ||||
| Downside part of mean | -0.195 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.130 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.207 | ||||
| Covariance | 0.004 | ||||
| r | 0.087 | ||||
| b (slope, estimate of beta) | 0.076 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 52.000 | ||||
| t(b) | 0.630 | ||||
| p(b) | 0.266 | ||||
| t(a) | -0.059 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | -0.167 | ||||
| Upperbound of 95% confidence interval for beta | 0.320 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.218 | ||||
| Upperbound of 95% confidence interval for alpha | 0.205 | ||||
| Treynor index (mean / b) | 0.232 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.092 | ||||
| Expected Shortfall on VaR | 0.115 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 54.000 | ||||
| Minimum | 0.821 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.223 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.076 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.185 | ||||
| Mean of outliers low | 0.936 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 1.088 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.493 | ||||
| VaR(95%) (moments method) | 0.043 | ||||
| Expected Shortfall (moments method) | 0.102 | ||||
| Extreme Value Index (regression method) | 0.644 | ||||
| VaR(95%) (regression method) | 0.050 | ||||
| Expected Shortfall (regression method) | 0.159 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.083 | ||||
| Median | 0.154 | ||||
| Quartile 3 | 0.226 | ||||
| Maximum | 0.297 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.297 | ||||
| Inter Quartile Range | 0.143 | ||||
| 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) | 0.071 | ||||
| Compounded annual return (geometric extrapolation) | 0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.215 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.215 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.556 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.039 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | 0.189 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.189 | ||||
| df | 1180.000 | ||||
| t | 0.401 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.734 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.112 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.735 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.112 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.273 | ||||
| Upside Potential Ratio | 5.284 | ||||
| Upside part of mean | 0.754 | ||||
| Downside part of mean | -0.715 | ||||
| Upside SD | 0.149 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 224.000 | ||||
| N negative terms | 957.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1181.000 | ||||
| Mean of predictor | 0.346 | ||||
| Mean of criterion | 0.039 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | 0.004 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 0.048 | ||||
| a (intercept, estimate of alpha) | 0.022 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 1179.000 | ||||
| t(b) | 2.299 | ||||
| p(b) | 0.458 | ||||
| t(a) | 0.228 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | 0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.168 | ||||
| Upperbound of 95% confidence interval for alpha | 0.213 | ||||
| Treynor index (mean / b) | 0.804 | ||||
| Jensen alpha (a) | 0.022 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | 0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.086 | ||||
| df | 1180.000 | ||||
| t | 0.182 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.838 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.009 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.838 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.009 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.121 | ||||
| Upside Potential Ratio | 5.085 | ||||
| Upside part of mean | 0.743 | ||||
| Downside part of mean | -0.726 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 224.000 | ||||
| N negative terms | 957.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1181.000 | ||||
| Mean of predictor | 0.306 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | 0.004 | ||||
| r | 0.068 | ||||
| b (slope, estimate of beta) | 0.050 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 1179.000 | ||||
| t(b) | 2.333 | ||||
| p(b) | 0.457 | ||||
| t(a) | 0.026 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.188 | ||||
| Upperbound of 95% confidence interval for alpha | 0.193 | ||||
| Treynor index (mean / b) | 0.356 | ||||
| Jensen alpha (a) | 0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1181.000 | ||||
| Minimum | 0.907 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.100 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 208.000 | ||||
| Percentage of outliers low | 0.176 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 225.000 | ||||
| Percentage of outliers high | 0.191 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.227 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | -0.012 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.020 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.033 | ||||
| Maximum | 0.363 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.029 | ||||
| Mean of quarter 4 | 0.205 | ||||
| Inter Quartile Range | 0.025 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.363 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.996 | ||||
| VaR(95%) (moments method) | 0.188 | ||||
| Expected Shortfall (moments method) | 45.349 | ||||
| Extreme Value Index (regression method) | 3.638 | ||||
| VaR(95%) (regression method) | 1.118 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.071 | ||||
| Compounded annual return (geometric extrapolation) | 0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.175 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.311 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.460 | ||||
| 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 | 0.852 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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 | 0.744 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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) | -8756466616683288.000 | ||||
| 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) | 778574300094127019374807298867200.000 | ||||
| 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 | ||||