Advanced Statistics: Alphergence - SP500
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 | -0.074 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -1.232 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.209 | ||||
| df | 40.000 | ||||
| t | -2.278 | ||||
| p | 0.986 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.319 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.131 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.302 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.116 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.299 | ||||
| Upside Potential Ratio | 0.354 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.094 | ||||
| Upside SD | 0.027 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.464 | ||||
| Mean of criterion | -0.074 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | -0.000 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.189 | ||||
| p(b) | 0.575 | ||||
| t(a) | -1.927 | ||||
| p(a) | 0.969 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.145 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | 10.999 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.075 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -1.237 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.214 | ||||
| df | 40.000 | ||||
| t | -2.286 | ||||
| p | 0.986 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.324 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.135 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.307 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.120 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.291 | ||||
| Upside Potential Ratio | 0.337 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.058 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.421 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | -0.000 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.166 | ||||
| p(b) | 0.566 | ||||
| t(a) | -1.964 | ||||
| p(a) | 0.972 | ||||
| Lowerbound of 95% confidence interval for beta | -0.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.071 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | 11.935 | ||||
| Jensen alpha (a) | -0.073 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.922 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.045 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.965 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.038 | ||||
| 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) | 0.756 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.101 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.050 | ||||
| Median | 0.084 | ||||
| Quartile 3 | 0.119 | ||||
| Maximum | 0.153 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.153 | ||||
| Inter Quartile Range | 0.069 | ||||
| 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) | -0.030 | ||||
| Compounded annual return (geometric extrapolation) | -0.031 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.202 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.202 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.743 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.923 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.923 | ||||
| df | 895.000 | ||||
| t | -1.708 | ||||
| p | 0.956 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.984 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.138 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.983 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.138 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.151 | ||||
| Upside Potential Ratio | 2.216 | ||||
| Upside part of mean | 0.139 | ||||
| Downside part of mean | -0.212 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 843.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 896.000 | ||||
| Mean of predictor | 0.530 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.372 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.003 | ||||
| r | 0.113 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.085 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 894.000 | ||||
| t(b) | 3.410 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.010 | ||||
| p(a) | 0.978 | ||||
| Lowerbound of 95% confidence interval for beta | 0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.168 | ||||
| Upperbound of 95% confidence interval for alpha | -0.002 | ||||
| Treynor index (mean / b) | -3.030 | ||||
| Jensen alpha (a) | -0.085 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.075 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.955 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.954 | ||||
| df | 895.000 | ||||
| t | -1.766 | ||||
| p | 0.961 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.016 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.106 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.015 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.106 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.178 | ||||
| Upside Potential Ratio | 2.158 | ||||
| Upside part of mean | 0.138 | ||||
| Downside part of mean | -0.214 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 843.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 896.000 | ||||
| Mean of predictor | 0.458 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.384 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.003 | ||||
| r | 0.110 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 894.000 | ||||
| t(b) | 3.302 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.014 | ||||
| p(a) | 0.978 | ||||
| Lowerbound of 95% confidence interval for beta | 0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.169 | ||||
| Upperbound of 95% confidence interval for alpha | -0.002 | ||||
| Treynor index (mean / b) | -3.340 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 896.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 51.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 53.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.776 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.246 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.026 | ||||
| Maximum | 0.166 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.079 | ||||
| Inter Quartile Range | 0.018 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.166 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.477 | ||||
| VaR(95%) (moments method) | 0.080 | ||||
| Expected Shortfall (moments method) | 0.183 | ||||
| Extreme Value Index (regression method) | 2.558 | ||||
| VaR(95%) (regression method) | 0.174 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.030 | ||||
| Compounded annual return (geometric extrapolation) | -0.031 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.187 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.391 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.005 | ||||
| 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 | 1.199 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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 | 1.076 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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) | -8719970726581191.000 | ||||
| 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) | 351137085086979600120944208642048.000 | ||||
| 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 | ||||