Advanced Statistics: Gen 2 - Mini S&P Only
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 | 0.002 | ||||
| SD | 0.214 | ||||
| Sharpe ratio (Glass type estimate) | 0.008 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.008 | ||||
| df | 88.000 | ||||
| t | 0.023 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.711 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.728 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.711 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.728 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.016 | ||||
| Upside Potential Ratio | 1.281 | ||||
| Upside part of mean | 0.145 | ||||
| Downside part of mean | -0.143 | ||||
| Upside SD | 0.180 | ||||
| Downside SD | 0.113 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.214 | ||||
| Covariance | 0.006 | ||||
| r | 0.112 | ||||
| b (slope, estimate of beta) | 0.097 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 87.000 | ||||
| t(b) | 1.048 | ||||
| p(b) | 0.149 | ||||
| t(a) | -0.276 | ||||
| p(a) | 0.608 | ||||
| Lowerbound of 95% confidence interval for beta | -0.086 | ||||
| Upperbound of 95% confidence interval for beta | 0.280 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.186 | ||||
| Upperbound of 95% confidence interval for alpha | 0.140 | ||||
| Treynor index (mean / b) | 0.019 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.019 | ||||
| SD | 0.200 | ||||
| Sharpe ratio (Glass type estimate) | -0.094 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.093 | ||||
| df | 88.000 | ||||
| t | -0.256 | ||||
| p | 0.601 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.813 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.626 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.813 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.627 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.153 | ||||
| Upside Potential Ratio | 1.068 | ||||
| Upside part of mean | 0.131 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.157 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.221 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.200 | ||||
| Covariance | 0.006 | ||||
| r | 0.127 | ||||
| b (slope, estimate of beta) | 0.108 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.040 | ||||
| DF error | 87.000 | ||||
| t(b) | 1.196 | ||||
| p(b) | 0.117 | ||||
| t(a) | -0.560 | ||||
| p(a) | 0.712 | ||||
| Lowerbound of 95% confidence interval for beta | -0.071 | ||||
| Upperbound of 95% confidence interval for beta | 0.286 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.194 | ||||
| Upperbound of 95% confidence interval for alpha | 0.109 | ||||
| Treynor index (mean / b) | -0.175 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.092 | ||||
| Expected Shortfall on VaR | 0.114 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.078 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 89.000 | ||||
| Minimum | 0.789 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.398 | ||||
| Mean of quarter 1 | 0.966 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.945 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.124 | ||||
| Mean of outliers high | 1.101 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.477 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.235 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | 0.110 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.211 | ||||
| Quartile 1 | 0.242 | ||||
| Median | 0.273 | ||||
| Quartile 3 | 0.303 | ||||
| Maximum | 0.334 | ||||
| Mean of quarter 1 | 0.211 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.334 | ||||
| Inter Quartile Range | 0.061 | ||||
| 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) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.076 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.076 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.225 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.047 | ||||
| SD | 0.370 | ||||
| Sharpe ratio (Glass type estimate) | 0.126 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.126 | ||||
| df | 1944.000 | ||||
| t | 0.344 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.593 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.593 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.846 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.204 | ||||
| Upside Potential Ratio | 3.704 | ||||
| Upside part of mean | 0.852 | ||||
| Downside part of mean | -0.805 | ||||
| Upside SD | 0.290 | ||||
| Downside SD | 0.230 | ||||
| N nonnegative terms | 247.000 | ||||
| N negative terms | 1698.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1945.000 | ||||
| Mean of predictor | 0.289 | ||||
| Mean of criterion | 0.047 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.370 | ||||
| Covariance | 0.007 | ||||
| r | 0.057 | ||||
| b (slope, estimate of beta) | 0.061 | ||||
| a (intercept, estimate of alpha) | 0.029 | ||||
| Mean Square Error | 0.137 | ||||
| DF error | 1943.000 | ||||
| t(b) | 2.515 | ||||
| p(b) | 0.464 | ||||
| t(a) | 0.215 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.108 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.237 | ||||
| Upperbound of 95% confidence interval for alpha | 0.296 | ||||
| Treynor index (mean / b) | 0.769 | ||||
| Jensen alpha (a) | 0.029 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.019 | ||||
| SD | 0.360 | ||||
| Sharpe ratio (Glass type estimate) | -0.052 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.052 | ||||
| df | 1944.000 | ||||
| t | -0.143 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.772 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.667 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.772 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.667 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.077 | ||||
| Upside Potential Ratio | 3.312 | ||||
| Upside part of mean | 0.815 | ||||
| Downside part of mean | -0.834 | ||||
| Upside SD | 0.262 | ||||
| Downside SD | 0.246 | ||||
| N nonnegative terms | 247.000 | ||||
| N negative terms | 1698.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1945.000 | ||||
| Mean of predictor | 0.228 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.360 | ||||
| Covariance | 0.008 | ||||
| r | 0.060 | ||||
| b (slope, estimate of beta) | 0.063 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.129 | ||||
| DF error | 1943.000 | ||||
| t(b) | 2.668 | ||||
| p(b) | 0.462 | ||||
| t(a) | -0.251 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.292 | ||||
| Upperbound of 95% confidence interval for alpha | 0.226 | ||||
| Treynor index (mean / b) | -0.300 | ||||
| Jensen alpha (a) | -0.033 | ||||
| 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 | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1945.000 | ||||
| Minimum | 0.788 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.447 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 255.000 | ||||
| Percentage of outliers low | 0.131 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 250.000 | ||||
| Percentage of outliers high | 0.129 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.172 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.373 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.030 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.070 | ||||
| Quartile 3 | 0.193 | ||||
| Maximum | 0.396 | ||||
| Mean of quarter 1 | 0.019 | ||||
| Mean of quarter 2 | 0.037 | ||||
| Mean of quarter 3 | 0.135 | ||||
| Mean of quarter 4 | 0.321 | ||||
| Inter Quartile Range | 0.163 | ||||
| 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) | -43.143 | ||||
| VaR(95%) (moments method) | 0.337 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.645 | ||||
| VaR(95%) (regression method) | 0.512 | ||||
| Expected Shortfall (regression method) | 0.516 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.064 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.079 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.569 | ||||
| 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 | 1.144 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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 | 1.017 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| 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) | -8731229250307685.000 | ||||
| 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) | -107711485466332519854116517707776.000 | ||||
| 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 | ||||