Advanced Statistics: Quest for Yield
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 | 0.000 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | 0.005 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.005 | ||||
| df | 33.000 | ||||
| t | 0.009 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.159 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.170 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.159 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.170 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.007 | ||||
| Upside Potential Ratio | 1.874 | ||||
| Upside part of mean | 0.125 | ||||
| Downside part of mean | -0.125 | ||||
| Upside SD | 0.060 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.558 | ||||
| Mean of criterion | 0.000 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | 0.008 | ||||
| r | 0.324 | ||||
| b (slope, estimate of beta) | 0.114 | ||||
| a (intercept, estimate of alpha) | -0.063 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 32.000 | ||||
| t(b) | 1.936 | ||||
| p(b) | 0.031 | ||||
| t(a) | -1.023 | ||||
| p(a) | 0.843 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.233 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.189 | ||||
| Upperbound of 95% confidence interval for alpha | 0.062 | ||||
| Treynor index (mean / b) | 0.004 | ||||
| Jensen alpha (a) | -0.063 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.092 | ||||
| Sharpe ratio (Glass type estimate) | -0.039 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.038 | ||||
| df | 33.000 | ||||
| t | -0.065 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.203 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.126 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.202 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.126 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.052 | ||||
| Upside Potential Ratio | 1.804 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.514 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.092 | ||||
| Covariance | 0.008 | ||||
| r | 0.346 | ||||
| b (slope, estimate of beta) | 0.128 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 32.000 | ||||
| t(b) | 2.084 | ||||
| p(b) | 0.023 | ||||
| t(a) | -1.143 | ||||
| p(a) | 0.869 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.253 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | 0.054 | ||||
| Treynor index (mean / b) | -0.028 | ||||
| Jensen alpha (a) | -0.069 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.936 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.027 | ||||
| Maximum | 1.052 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 1.035 | ||||
| Inter Quartile Range | 0.038 | ||||
| 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) | -0.416 | ||||
| VaR(95%) (moments method) | 0.028 | ||||
| Expected Shortfall (moments method) | 0.034 | ||||
| Extreme Value Index (regression method) | -0.133 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.046 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.039 | ||||
| Quartile 1 | 0.059 | ||||
| Median | 0.078 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.088 | ||||
| Mean of quarter 1 | 0.039 | ||||
| Mean of quarter 2 | 0.078 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.088 | ||||
| Inter Quartile Range | 0.024 | ||||
| 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) | 0.041 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.469 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.469 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.775 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.108 | ||||
| Sharpe ratio (Glass type estimate) | 0.139 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.139 | ||||
| df | 760.000 | ||||
| t | 0.237 | ||||
| p | 0.406 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.011 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.289 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.011 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.289 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.176 | ||||
| Upside Potential Ratio | 5.927 | ||||
| Upside part of mean | 0.503 | ||||
| Downside part of mean | -0.488 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.085 | ||||
| N nonnegative terms | 389.000 | ||||
| N negative terms | 372.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 761.000 | ||||
| Mean of predictor | 0.626 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.108 | ||||
| Covariance | 0.024 | ||||
| r | 0.642 | ||||
| b (slope, estimate of beta) | 0.201 | ||||
| a (intercept, estimate of alpha) | -0.111 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 759.000 | ||||
| t(b) | 23.090 | ||||
| p(b) | -0.000 | ||||
| t(a) | -2.285 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | 0.184 | ||||
| Upperbound of 95% confidence interval for beta | 0.219 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.207 | ||||
| Upperbound of 95% confidence interval for alpha | -0.016 | ||||
| Treynor index (mean / b) | 0.074 | ||||
| Jensen alpha (a) | -0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.109 | ||||
| Sharpe ratio (Glass type estimate) | 0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.083 | ||||
| df | 760.000 | ||||
| t | 0.142 | ||||
| p | 0.443 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.067 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.233 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.067 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.233 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.105 | ||||
| Upside Potential Ratio | 5.768 | ||||
| Upside part of mean | 0.500 | ||||
| Downside part of mean | -0.491 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.087 | ||||
| N nonnegative terms | 389.000 | ||||
| N negative terms | 372.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 761.000 | ||||
| Mean of predictor | 0.566 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.109 | ||||
| Covariance | 0.025 | ||||
| r | 0.651 | ||||
| b (slope, estimate of beta) | 0.203 | ||||
| a (intercept, estimate of alpha) | -0.106 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 759.000 | ||||
| t(b) | 23.649 | ||||
| p(b) | -0.000 | ||||
| t(a) | -2.172 | ||||
| p(a) | 0.985 | ||||
| Lowerbound of 95% confidence interval for beta | 0.186 | ||||
| Upperbound of 95% confidence interval for beta | 0.220 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.201 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | 0.045 | ||||
| Jensen alpha (a) | -0.106 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 761.000 | ||||
| Minimum | 0.923 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.042 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 32.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 24.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.403 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.012 | ||||
| Extreme Value Index (regression method) | 0.383 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 27.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.011 | ||||
| Maximum | 0.140 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.067 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.148 | ||||
| Mean of outliers high | 0.106 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.654 | ||||
| VaR(95%) (moments method) | 0.057 | ||||
| Expected Shortfall (moments method) | 0.195 | ||||
| Extreme Value Index (regression method) | -0.231 | ||||
| VaR(95%) (regression method) | 0.066 | ||||
| Expected Shortfall (regression method) | 0.089 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.057 | ||||
| Compounded annual return (geometric extrapolation) | 0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.389 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.814 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.973 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.156 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | 1.477 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.468 | ||||
| df | 130.000 | ||||
| t | 1.044 | ||||
| p | 0.454 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.303 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.252 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.309 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.246 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.197 | ||||
| Upside Potential Ratio | 10.014 | ||||
| Upside part of mean | 0.712 | ||||
| Downside part of mean | -0.556 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.071 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.101 | ||||
| Mean of criterion | 0.156 | ||||
| SD of predictor | 0.459 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.033 | ||||
| r | 0.678 | ||||
| b (slope, estimate of beta) | 0.156 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 129.000 | ||||
| t(b) | 10.477 | ||||
| p(b) | 0.104 | ||||
| t(a) | -0.142 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.127 | ||||
| Upperbound of 95% confidence interval for beta | 0.186 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.237 | ||||
| Upperbound of 95% confidence interval for alpha | 0.205 | ||||
| Treynor index (mean / b) | 0.999 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.151 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | 1.424 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.416 | ||||
| df | 130.000 | ||||
| t | 1.007 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.355 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.199 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.361 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.193 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.105 | ||||
| Upside Potential Ratio | 9.910 | ||||
| Upside part of mean | 0.709 | ||||
| Downside part of mean | -0.558 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.072 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.993 | ||||
| Mean of criterion | 0.151 | ||||
| SD of predictor | 0.461 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.033 | ||||
| r | 0.676 | ||||
| b (slope, estimate of beta) | 0.155 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 129.000 | ||||
| t(b) | 10.427 | ||||
| p(b) | 0.105 | ||||
| t(a) | -0.030 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | 0.126 | ||||
| Upperbound of 95% confidence interval for beta | 0.184 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.224 | ||||
| Upperbound of 95% confidence interval for alpha | 0.217 | ||||
| Treynor index (mean / b) | 0.972 | ||||
| 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%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.981 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.024 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.155 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.221 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.012 | ||||
| Maximum | 0.070 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.006 | ||||
| Mean of quarter 4 | 0.035 | ||||
| Inter Quartile Range | 0.009 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.070 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.643 | ||||
| VaR(95%) (moments method) | 0.042 | ||||
| Expected Shortfall (moments method) | 0.122 | ||||
| Extreme Value Index (regression method) | 4.631 | ||||
| VaR(95%) (regression method) | 0.136 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.204 | ||||
| Compounded annual return (geometric extrapolation) | 0.215 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.088 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.161 | ||||
| Compounded annual return / Expected Shortfall lognormal | 16.767 | ||||