Advanced Statistics: Index Spreads
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 | 0.020 | ||||
| SD | 0.261 | ||||
| Sharpe ratio (Glass type estimate) | 0.077 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.077 | ||||
| df | 116.000 | ||||
| t | 0.241 | ||||
| p | 0.489 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.551 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.551 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.704 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.092 | ||||
| Upside Potential Ratio | 1.231 | ||||
| Upside part of mean | 0.269 | ||||
| Downside part of mean | -0.249 | ||||
| Upside SD | 0.141 | ||||
| Downside SD | 0.218 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 117.000 | ||||
| Mean of predictor | 0.175 | ||||
| Mean of criterion | 0.020 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.261 | ||||
| Covariance | -0.015 | ||||
| r | -0.237 | ||||
| b (slope, estimate of beta) | -0.256 | ||||
| a (intercept, estimate of alpha) | 0.065 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 115.000 | ||||
| t(b) | -2.612 | ||||
| p(b) | 0.649 | ||||
| t(a) | 0.778 | ||||
| p(a) | 0.454 | ||||
| Lowerbound of 95% confidence interval for beta | -0.450 | ||||
| Upperbound of 95% confidence interval for beta | -0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.230 | ||||
| Treynor index (mean / b) | -0.079 | ||||
| Jensen alpha (a) | 0.065 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | -0.068 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.068 | ||||
| df | 116.000 | ||||
| t | -0.213 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.696 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.560 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.696 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.560 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.076 | ||||
| Upside Potential Ratio | 0.952 | ||||
| Upside part of mean | 0.259 | ||||
| Downside part of mean | -0.280 | ||||
| Upside SD | 0.133 | ||||
| Downside SD | 0.272 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 117.000 | ||||
| Mean of predictor | 0.145 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | -0.017 | ||||
| r | -0.232 | ||||
| b (slope, estimate of beta) | -0.298 | ||||
| a (intercept, estimate of alpha) | 0.023 | ||||
| Mean Square Error | 0.088 | ||||
| DF error | 115.000 | ||||
| t(b) | -2.553 | ||||
| p(b) | 0.646 | ||||
| t(a) | 0.234 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.530 | ||||
| Upperbound of 95% confidence interval for beta | -0.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.169 | ||||
| Upperbound of 95% confidence interval for alpha | 0.214 | ||||
| Treynor index (mean / b) | 0.070 | ||||
| Jensen alpha (a) | 0.023 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.136 | ||||
| Expected Shortfall on VaR | 0.167 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.103 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 117.000 | ||||
| Minimum | 0.510 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.006 | ||||
| Quartile 3 | 1.041 | ||||
| Maximum | 1.214 | ||||
| Mean of quarter 1 | 0.926 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.027 | ||||
| Mean of quarter 4 | 1.071 | ||||
| Inter Quartile Range | 0.041 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.848 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.169 | ||||
| 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) | 0.163 | ||||
| VaR(95%) (regression method) | 0.090 | ||||
| Expected Shortfall (regression method) | 0.175 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.077 | ||||
| Quartile 1 | 0.102 | ||||
| Median | 0.246 | ||||
| Quartile 3 | 0.408 | ||||
| Maximum | 0.490 | ||||
| Mean of quarter 1 | 0.077 | ||||
| Mean of quarter 2 | 0.111 | ||||
| Mean of quarter 3 | 0.381 | ||||
| Mean of quarter 4 | 0.490 | ||||
| Inter Quartile Range | 0.306 | ||||
| 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) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.024 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.048 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.048 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.141 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.057 | ||||
| SD | 0.394 | ||||
| Sharpe ratio (Glass type estimate) | 0.146 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.146 | ||||
| df | 2562.000 | ||||
| t | 0.457 | ||||
| p | 0.324 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.481 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.773 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.481 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.773 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.208 | ||||
| Upside Potential Ratio | 4.578 | ||||
| Upside part of mean | 1.261 | ||||
| Downside part of mean | -1.204 | ||||
| Upside SD | 0.281 | ||||
| Downside SD | 0.276 | ||||
| N nonnegative terms | 868.000 | ||||
| N negative terms | 1695.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2563.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | 0.057 | ||||
| SD of predictor | 0.452 | ||||
| SD of criterion | 0.394 | ||||
| Covariance | -0.008 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -0.038 | ||||
| a (intercept, estimate of alpha) | 0.067 | ||||
| Mean Square Error | 0.155 | ||||
| DF error | 2561.000 | ||||
| t(b) | -2.206 | ||||
| p(b) | 0.986 | ||||
| t(a) | 0.533 | ||||
| p(a) | 0.297 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | -0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | 0.314 | ||||
| Treynor index (mean / b) | -1.515 | ||||
| Jensen alpha (a) | 0.067 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.398 | ||||
| Sharpe ratio (Glass type estimate) | -0.052 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.052 | ||||
| df | 2562.000 | ||||
| t | -0.164 | ||||
| p | 0.565 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.679 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.574 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.679 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.574 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.070 | ||||
| Upside Potential Ratio | 4.097 | ||||
| Upside part of mean | 1.225 | ||||
| Downside part of mean | -1.246 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.299 | ||||
| N nonnegative terms | 868.000 | ||||
| N negative terms | 1695.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2563.000 | ||||
| Mean of predictor | 0.153 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.446 | ||||
| SD of criterion | 0.398 | ||||
| Covariance | -0.009 | ||||
| r | -0.048 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.158 | ||||
| DF error | 2561.000 | ||||
| t(b) | -2.442 | ||||
| p(b) | 0.993 | ||||
| t(a) | -0.112 | ||||
| p(a) | 0.545 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | -0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.264 | ||||
| Upperbound of 95% confidence interval for alpha | 0.235 | ||||
| Treynor index (mean / b) | 0.485 | ||||
| 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%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2563.000 | ||||
| Minimum | 0.646 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.334 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 411.000 | ||||
| Percentage of outliers low | 0.160 | ||||
| Mean of outliers low | 0.973 | ||||
| Number of outliers high | 429.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.884 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.082 | ||||
| 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 | 52.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.024 | ||||
| Maximum | 0.513 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.127 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 0.208 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.999 | ||||
| VaR(95%) (moments method) | 0.126 | ||||
| Expected Shortfall (moments method) | 212.431 | ||||
| Extreme Value Index (regression method) | 1.319 | ||||
| VaR(95%) (regression method) | 0.110 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.046 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.185 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.473 | ||||
| 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 | 1.194 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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 | 1.060 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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) | -8728885577995431.000 | ||||
| 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) | -855052255178561609681719345020928.000 | ||||
| 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 | ||||