Advanced Statistics: Gen 3 - 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 | -0.043 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.787 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.779 | ||||
| df | 76.000 | ||||
| t | -1.994 | ||||
| p | 0.975 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.568 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.001 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.563 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.004 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.982 | ||||
| Upside Potential Ratio | 0.588 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 77.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.216 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | -0.003 | ||||
| r | -0.217 | ||||
| b (slope, estimate of beta) | -0.055 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 75.000 | ||||
| t(b) | -1.929 | ||||
| p(b) | 0.971 | ||||
| t(a) | -1.275 | ||||
| p(a) | 0.897 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.016 | ||||
| Treynor index (mean / b) | 0.780 | ||||
| Jensen alpha (a) | -0.029 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.808 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.800 | ||||
| df | 76.000 | ||||
| t | -2.046 | ||||
| p | 0.978 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.590 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.021 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.584 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.984 | ||||
| Upside Potential Ratio | 0.556 | ||||
| Upside part of mean | 0.025 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.033 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 77.000 | ||||
| Mean of predictor | 0.236 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.207 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | -0.003 | ||||
| r | -0.222 | ||||
| b (slope, estimate of beta) | -0.059 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 75.000 | ||||
| t(b) | -1.971 | ||||
| p(b) | 0.974 | ||||
| t(a) | -1.362 | ||||
| p(a) | 0.911 | ||||
| Lowerbound of 95% confidence interval for beta | -0.118 | ||||
| Upperbound of 95% confidence interval for beta | 0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | 0.755 | ||||
| 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%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 77.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.070 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.104 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.091 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.826 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.523 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.060 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.033 | ||||
| Median | 0.049 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.085 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | 0.049 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.085 | ||||
| Inter Quartile Range | 0.034 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.005 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.005 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.012 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | -0.253 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.253 | ||||
| df | 1690.000 | ||||
| t | -0.644 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.025 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.518 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.025 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.518 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.369 | ||||
| Upside Potential Ratio | 2.687 | ||||
| Upside part of mean | 0.255 | ||||
| Downside part of mean | -0.290 | ||||
| Upside SD | 0.100 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 103.000 | ||||
| N negative terms | 1588.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1691.000 | ||||
| Mean of predictor | 0.290 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 1689.000 | ||||
| t(b) | 0.724 | ||||
| p(b) | 0.489 | ||||
| t(a) | -0.687 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -4.142 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | -0.323 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.323 | ||||
| df | 1690.000 | ||||
| t | -0.820 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.094 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.449 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.094 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.449 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.455 | ||||
| Upside Potential Ratio | 2.559 | ||||
| Upside part of mean | 0.250 | ||||
| Downside part of mean | -0.294 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.098 | ||||
| N nonnegative terms | 103.000 | ||||
| N negative terms | 1588.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1691.000 | ||||
| Mean of predictor | 0.249 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 1689.000 | ||||
| t(b) | 0.726 | ||||
| p(b) | 0.489 | ||||
| t(a) | -0.857 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.153 | ||||
| Upperbound of 95% confidence interval for alpha | 0.060 | ||||
| Treynor index (mean / b) | -5.220 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1691.000 | ||||
| Minimum | 0.900 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.121 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 118.000 | ||||
| Percentage of outliers low | 0.070 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 110.000 | ||||
| Percentage of outliers high | 0.065 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.509 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.291 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.025 | ||||
| Quartile 1 | 0.030 | ||||
| Median | 0.067 | ||||
| Quartile 3 | 0.102 | ||||
| Maximum | 0.194 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.040 | ||||
| Mean of quarter 3 | 0.094 | ||||
| Mean of quarter 4 | 0.150 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.002 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.003 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.024 | ||||
| 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 | 0.983 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.480 | ||||
| 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 | 0.866 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.480 | ||||
| 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) | -8745213296018733.000 | ||||
| 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) | 669502222767770511133418018832384.000 | ||||
| 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 | ||||