Advanced Statistics: Alphergence - SP500 ETF
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 | -0.038 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | -0.552 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.541 | ||||
| df | 38.000 | ||||
| t | -0.995 | ||||
| p | 0.837 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.643 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.546 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.635 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.553 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.733 | ||||
| Upside Potential Ratio | 0.663 | ||||
| Upside part of mean | 0.035 | ||||
| Downside part of mean | -0.073 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.493 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.000 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.057 | ||||
| p(b) | 0.522 | ||||
| t(a) | -0.839 | ||||
| p(a) | 0.797 | ||||
| Lowerbound of 95% confidence interval for beta | -0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | 0.053 | ||||
| Treynor index (mean / b) | 15.941 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.041 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | -0.581 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.569 | ||||
| df | 38.000 | ||||
| t | -1.047 | ||||
| p | 0.849 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.672 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.518 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.664 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.525 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.747 | ||||
| Upside Potential Ratio | 0.617 | ||||
| Upside part of mean | 0.034 | ||||
| Downside part of mean | -0.074 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.448 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.014 | ||||
| p(b) | 0.506 | ||||
| t(a) | -0.920 | ||||
| p(a) | 0.818 | ||||
| Lowerbound of 95% confidence interval for beta | -0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.087 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.129 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | 66.007 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.075 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.051 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -29.373 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 1.229 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.100 | ||||
| Quartile 1 | 0.100 | ||||
| Median | 0.100 | ||||
| Quartile 3 | 0.100 | ||||
| Maximum | 0.100 | ||||
| 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) | 0.003 | ||||
| Compounded annual return (geometric extrapolation) | 0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.034 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.077 | ||||
| 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 | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.734 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.733 | ||||
| df | 853.000 | ||||
| t | -1.325 | ||||
| p | 0.907 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.820 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.352 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.819 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.353 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.080 | ||||
| Upside Potential Ratio | 2.440 | ||||
| Upside part of mean | 0.089 | ||||
| Downside part of mean | -0.128 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.036 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 826.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 854.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.001 | ||||
| r | 0.070 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 852.000 | ||||
| t(b) | 2.058 | ||||
| p(b) | 0.020 | ||||
| t(a) | -1.506 | ||||
| p(a) | 0.934 | ||||
| Lowerbound of 95% confidence interval for beta | 0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | -3.864 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.041 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.762 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.761 | ||||
| df | 853.000 | ||||
| t | -1.376 | ||||
| p | 0.915 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.848 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.324 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.848 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.325 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.109 | ||||
| Upside Potential Ratio | 2.397 | ||||
| Upside part of mean | 0.088 | ||||
| Downside part of mean | -0.128 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.037 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 826.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 854.000 | ||||
| Mean of predictor | 0.464 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.383 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.001 | ||||
| r | 0.068 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 852.000 | ||||
| t(b) | 1.983 | ||||
| p(b) | 0.024 | ||||
| t(a) | -1.523 | ||||
| p(a) | 0.936 | ||||
| Lowerbound of 95% confidence interval for beta | 0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.013 | ||||
| Treynor index (mean / b) | -4.308 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 854.000 | ||||
| Minimum | 0.973 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.039 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 26.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 28.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.911 | ||||
| VaR(95%) (moments method) | -0.011 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.611 | ||||
| VaR(95%) (regression method) | -0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.021 | ||||
| Maximum | 0.107 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.015 | ||||
| Mean of quarter 4 | 0.067 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.107 | ||||
| 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) | 0.003 | ||||
| Compounded annual return (geometric extrapolation) | 0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.032 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.050 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.488 | ||||
| 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 | 1.037 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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) | -8736666962018652.000 | ||||
| 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) | -546398138850813626994385068490752.000 | ||||
| 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 | ||||