Advanced Statistics: Bond Portfolio E9
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 | 0.004 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | 0.032 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.032 | ||||
| df | 63.000 | ||||
| t | 0.074 | ||||
| p | 0.471 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.817 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.881 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.817 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.880 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.043 | ||||
| Upside Potential Ratio | 1.159 | ||||
| Upside part of mean | 0.120 | ||||
| Downside part of mean | -0.116 | ||||
| Upside SD | 0.092 | ||||
| Downside SD | 0.104 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.321 | ||||
| Mean of criterion | 0.004 | ||||
| SD of predictor | 0.208 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | -0.004 | ||||
| r | -0.121 | ||||
| b (slope, estimate of beta) | -0.082 | ||||
| a (intercept, estimate of alpha) | 0.031 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 62.000 | ||||
| t(b) | -0.964 | ||||
| p(b) | 0.831 | ||||
| t(a) | 0.462 | ||||
| p(a) | 0.323 | ||||
| Lowerbound of 95% confidence interval for beta | -0.251 | ||||
| Upperbound of 95% confidence interval for beta | 0.088 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.102 | ||||
| Upperbound of 95% confidence interval for alpha | 0.164 | ||||
| Treynor index (mean / b) | -0.055 | ||||
| Jensen alpha (a) | 0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.006 | ||||
| SD | 0.146 | ||||
| Sharpe ratio (Glass type estimate) | -0.039 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.038 | ||||
| df | 63.000 | ||||
| t | -0.090 | ||||
| p | 0.536 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.887 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.810 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.887 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.810 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.049 | ||||
| Upside Potential Ratio | 1.007 | ||||
| Upside part of mean | 0.116 | ||||
| Downside part of mean | -0.122 | ||||
| Upside SD | 0.088 | ||||
| Downside SD | 0.115 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 49.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | -0.006 | ||||
| SD of predictor | 0.203 | ||||
| SD of criterion | 0.146 | ||||
| Covariance | -0.003 | ||||
| r | -0.093 | ||||
| b (slope, estimate of beta) | -0.067 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 62.000 | ||||
| t(b) | -0.735 | ||||
| p(b) | 0.767 | ||||
| t(a) | 0.205 | ||||
| p(a) | 0.419 | ||||
| Lowerbound of 95% confidence interval for beta | -0.249 | ||||
| Upperbound of 95% confidence interval for beta | 0.115 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.124 | ||||
| Upperbound of 95% confidence interval for alpha | 0.152 | ||||
| Treynor index (mean / b) | 0.085 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.783 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.146 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.203 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.234 | ||||
| Mean of outliers high | 1.046 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.609 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | 0.034 | ||||
| Extreme Value Index (regression method) | 0.846 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.165 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.135 | ||||
| Quartile 1 | 0.156 | ||||
| Median | 0.176 | ||||
| Quartile 3 | 0.196 | ||||
| Maximum | 0.217 | ||||
| Mean of quarter 1 | 0.135 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.217 | ||||
| Inter Quartile Range | 0.041 | ||||
| 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) | 0.043 | ||||
| Compounded annual return (geometric extrapolation) | 0.039 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.180 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.180 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.468 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.008 | ||||
| SD | 0.161 | ||||
| Sharpe ratio (Glass type estimate) | 0.049 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.049 | ||||
| df | 1402.000 | ||||
| t | 0.114 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.798 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.896 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.798 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.896 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.063 | ||||
| Upside Potential Ratio | 3.301 | ||||
| Upside part of mean | 0.418 | ||||
| Downside part of mean | -0.410 | ||||
| Upside SD | 0.100 | ||||
| Downside SD | 0.127 | ||||
| N nonnegative terms | 343.000 | ||||
| N negative terms | 1060.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1403.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | 0.008 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.161 | ||||
| Covariance | 0.002 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.020 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 1401.000 | ||||
| t(b) | 1.493 | ||||
| p(b) | 0.475 | ||||
| t(a) | 0.010 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.046 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.136 | ||||
| Upperbound of 95% confidence interval for alpha | 0.138 | ||||
| Treynor index (mean / b) | 0.403 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.006 | ||||
| SD | 0.168 | ||||
| Sharpe ratio (Glass type estimate) | -0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.035 | ||||
| df | 1402.000 | ||||
| t | -0.080 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.882 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.812 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.881 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.812 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.042 | ||||
| Upside Potential Ratio | 3.007 | ||||
| Upside part of mean | 0.413 | ||||
| Downside part of mean | -0.419 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.137 | ||||
| N nonnegative terms | 343.000 | ||||
| N negative terms | 1060.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1403.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | -0.006 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.168 | ||||
| Covariance | 0.003 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.028 | ||||
| DF error | 1401.000 | ||||
| t(b) | 1.970 | ||||
| p(b) | 0.467 | ||||
| t(a) | -0.192 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.157 | ||||
| Upperbound of 95% confidence interval for alpha | 0.129 | ||||
| Treynor index (mean / b) | -0.221 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1403.000 | ||||
| Minimum | 0.780 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.117 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 294.000 | ||||
| Percentage of outliers low | 0.210 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 305.000 | ||||
| Percentage of outliers high | 0.217 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.830 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.029 | ||||
| Extreme Value Index (regression method) | 0.529 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.049 | ||||
| Maximum | 0.230 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.132 | ||||
| Inter Quartile Range | 0.046 | ||||
| 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 | 0.118 | ||||
| Mean of outliers high | 0.194 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.016 | ||||
| VaR(95%) (moments method) | 0.114 | ||||
| Expected Shortfall (moments method) | 0.158 | ||||
| Extreme Value Index (regression method) | 0.502 | ||||
| VaR(95%) (regression method) | 0.161 | ||||
| Expected Shortfall (regression method) | 0.357 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.042 | ||||
| Compounded annual return (geometric extrapolation) | 0.039 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.169 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.296 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.832 | ||||
| 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 | 1.082 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.330 | ||||
| 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 | 1.026 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.330 | ||||
| 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) | -8640950576092030.000 | ||||
| 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) | -77257049902762023749431288922112.000 | ||||
| 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 | ||||