Advanced Statistics: Simple SPY
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 | 112.871 | ||||
| SD | 239.384 | ||||
| Sharpe ratio (Glass type estimate) | 0.472 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.465 | ||||
| df | 52.000 | ||||
| t | 0.991 | ||||
| p | 0.163 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.468 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.406 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.472 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.402 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 132.667 | ||||
| Upside Potential Ratio | 134.076 | ||||
| Upside part of mean | 114.069 | ||||
| Downside part of mean | -1.198 | ||||
| Upside SD | 239.341 | ||||
| Downside SD | 0.851 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.413 | ||||
| Mean of criterion | 112.871 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 239.384 | ||||
| Covariance | -10.974 | ||||
| r | -0.185 | ||||
| b (slope, estimate of beta) | -178.732 | ||||
| a (intercept, estimate of alpha) | 186.699 | ||||
| Mean Square Error | 56428.322 | ||||
| DF error | 51.000 | ||||
| t(b) | -1.344 | ||||
| p(b) | 0.908 | ||||
| t(a) | 1.486 | ||||
| p(a) | 0.072 | ||||
| Lowerbound of 95% confidence interval for beta | -445.628 | ||||
| Upperbound of 95% confidence interval for beta | 88.164 | ||||
| Lowerbound of 95% confidence interval for alpha | -65.585 | ||||
| Upperbound of 95% confidence interval for alpha | 438.984 | ||||
| Treynor index (mean / b) | -0.632 | ||||
| Jensen alpha (a) | 186.699 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.129 | ||||
| SD | 5.063 | ||||
| Sharpe ratio (Glass type estimate) | -0.421 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.414 | ||||
| df | 52.000 | ||||
| t | -0.884 | ||||
| p | 0.810 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.355 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.518 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.350 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.522 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.520 | ||||
| Upside Potential Ratio | 0.385 | ||||
| Upside part of mean | 1.576 | ||||
| Downside part of mean | -3.705 | ||||
| Upside SD | 2.964 | ||||
| Downside SD | 4.092 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.376 | ||||
| Mean of criterion | -2.129 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 5.063 | ||||
| Covariance | -0.220 | ||||
| r | -0.181 | ||||
| b (slope, estimate of beta) | -3.793 | ||||
| a (intercept, estimate of alpha) | -0.702 | ||||
| Mean Square Error | 25.288 | ||||
| DF error | 51.000 | ||||
| t(b) | -1.311 | ||||
| p(b) | 0.902 | ||||
| t(a) | -0.267 | ||||
| p(a) | 0.605 | ||||
| Lowerbound of 95% confidence interval for beta | -9.603 | ||||
| Upperbound of 95% confidence interval for beta | 2.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.980 | ||||
| Upperbound of 95% confidence interval for alpha | 4.577 | ||||
| Treynor index (mean / b) | 0.561 | ||||
| Jensen alpha (a) | -0.702 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.924 | ||||
| Expected Shortfall on VaR | 0.954 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.315 | ||||
| Expected Shortfall on VaR | 0.626 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.936 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 504.000 | ||||
| Mean of quarter 1 | 0.657 | ||||
| Mean of quarter 2 | 0.975 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 39.757 | ||||
| Inter Quartile Range | 0.064 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.170 | ||||
| Mean of outliers low | 0.521 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 126.913 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.452 | ||||
| VaR(95%) (moments method) | 0.269 | ||||
| Expected Shortfall (moments method) | 0.599 | ||||
| Extreme Value Index (regression method) | -0.789 | ||||
| VaR(95%) (regression method) | 0.396 | ||||
| Expected Shortfall (regression method) | 0.451 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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 | 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) | -0.226 | ||||
| Compounded annual return (geometric extrapolation) | -0.876 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.876 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.918 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 584.009 | ||||
| SD | 635.536 | ||||
| Sharpe ratio (Glass type estimate) | 0.919 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.918 | ||||
| df | 1160.000 | ||||
| t | 1.934 | ||||
| p | 0.472 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.013 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.851 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.013 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.850 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 299.450 | ||||
| Upside Potential Ratio | 303.116 | ||||
| Upside part of mean | 591.158 | ||||
| Downside part of mean | -7.149 | ||||
| Upside SD | 636.283 | ||||
| Downside SD | 1.950 | ||||
| N nonnegative terms | 301.000 | ||||
| N negative terms | 860.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1161.000 | ||||
| Mean of predictor | 0.443 | ||||
| Mean of criterion | 584.009 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 635.536 | ||||
| Covariance | -33.815 | ||||
| r | -0.164 | ||||
| b (slope, estimate of beta) | -322.088 | ||||
| a (intercept, estimate of alpha) | 726.695 | ||||
| Mean Square Error | 393353.213 | ||||
| DF error | 1159.000 | ||||
| t(b) | -5.667 | ||||
| p(b) | 0.604 | ||||
| t(a) | 2.430 | ||||
| p(a) | 0.455 | ||||
| Lowerbound of 95% confidence interval for beta | -433.593 | ||||
| Upperbound of 95% confidence interval for beta | -210.582 | ||||
| Lowerbound of 95% confidence interval for alpha | 140.054 | ||||
| Upperbound of 95% confidence interval for alpha | 1313.337 | ||||
| Treynor index (mean / b) | -1.813 | ||||
| Jensen alpha (a) | 726.695 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.122 | ||||
| SD | 10.883 | ||||
| Sharpe ratio (Glass type estimate) | -0.195 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.195 | ||||
| df | 1160.000 | ||||
| t | -0.411 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.126 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.736 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.126 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.736 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.280 | ||||
| Upside Potential Ratio | 2.018 | ||||
| Upside part of mean | 15.278 | ||||
| Downside part of mean | -17.400 | ||||
| Upside SD | 7.812 | ||||
| Downside SD | 7.571 | ||||
| N nonnegative terms | 301.000 | ||||
| N negative terms | 860.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1161.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | -2.122 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 10.883 | ||||
| Covariance | -0.583 | ||||
| r | -0.163 | ||||
| b (slope, estimate of beta) | -5.376 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 115.406 | ||||
| DF error | 1159.000 | ||||
| t(b) | -5.612 | ||||
| p(b) | 0.603 | ||||
| t(a) | -0.006 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -7.256 | ||||
| Upperbound of 95% confidence interval for beta | -3.497 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.070 | ||||
| Upperbound of 95% confidence interval for alpha | 10.009 | ||||
| Treynor index (mean / b) | 0.395 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.672 | ||||
| Expected Shortfall on VaR | 0.745 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.078 | ||||
| Expected Shortfall on VaR | 0.176 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1161.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1210.000 | ||||
| Mean of quarter 1 | 0.892 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 10.033 | ||||
| Inter Quartile Range | 0.008 | ||||
| Number outliers low | 202.000 | ||||
| Percentage of outliers low | 0.174 | ||||
| Mean of outliers low | 0.850 | ||||
| Number of outliers high | 172.000 | ||||
| Percentage of outliers high | 0.148 | ||||
| Mean of outliers high | 16.226 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.262 | ||||
| VaR(95%) (moments method) | 0.069 | ||||
| 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 | 4.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.047 | ||||
| Quartile 3 | 0.317 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.089 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.312 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | -0.226 | ||||
| Compounded annual return (geometric extrapolation) | -0.875 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.875 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.875 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.174 | ||||
| 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 | 1.292 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.333 | ||||
| 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 | 1.234 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.332 | ||||
| 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) | -8574279442470672.000 | ||||
| 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) | -72316091194875267342367713132544.000 | ||||
| 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 | ||||