Advanced Statistics: CTS Synergy System I
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 | 0.017 | ||||
| SD | 0.105 | ||||
| Sharpe ratio (Glass type estimate) | 0.162 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.161 | ||||
| df | 98.000 | ||||
| t | 0.466 | ||||
| p | 0.321 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.521 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.844 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.522 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.844 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.266 | ||||
| Upside Potential Ratio | 1.800 | ||||
| Upside part of mean | 0.115 | ||||
| Downside part of mean | -0.098 | ||||
| Upside SD | 0.083 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 99.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | 0.017 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.105 | ||||
| Covariance | 0.005 | ||||
| r | 0.173 | ||||
| b (slope, estimate of beta) | 0.070 | ||||
| a (intercept, estimate of alpha) | 0.005 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 97.000 | ||||
| t(b) | 1.726 | ||||
| p(b) | 0.044 | ||||
| t(a) | 0.125 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.150 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.069 | ||||
| Upperbound of 95% confidence interval for alpha | 0.078 | ||||
| Treynor index (mean / b) | 0.244 | ||||
| Jensen alpha (a) | 0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.012 | ||||
| SD | 0.104 | ||||
| Sharpe ratio (Glass type estimate) | 0.111 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.111 | ||||
| df | 98.000 | ||||
| t | 0.320 | ||||
| p | 0.375 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.571 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.794 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.572 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.175 | ||||
| Upside Potential Ratio | 1.688 | ||||
| Upside part of mean | 0.112 | ||||
| Downside part of mean | -0.100 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.066 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 99.000 | ||||
| Mean of predictor | 0.144 | ||||
| Mean of criterion | 0.012 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.104 | ||||
| Covariance | 0.005 | ||||
| r | 0.184 | ||||
| b (slope, estimate of beta) | 0.076 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 97.000 | ||||
| t(b) | 1.844 | ||||
| p(b) | 0.034 | ||||
| t(a) | 0.019 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.157 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | 0.153 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 99.000 | ||||
| Minimum | 0.904 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.093 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.141 | ||||
| Mean of outliers low | 0.962 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.172 | ||||
| Mean of outliers high | 1.055 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -18.017 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.069 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.044 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.095 | ||||
| Maximum | 0.142 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.090 | ||||
| Mean of quarter 4 | 0.121 | ||||
| Inter Quartile Range | 0.074 | ||||
| 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) | 0.071 | ||||
| Compounded annual return (geometric extrapolation) | 0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.404 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.474 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.968 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.060 | ||||
| SD | 0.314 | ||||
| Sharpe ratio (Glass type estimate) | 0.190 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.190 | ||||
| df | 2173.000 | ||||
| t | 0.547 | ||||
| p | 0.292 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.491 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.870 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.491 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.870 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.291 | ||||
| Upside Potential Ratio | 4.157 | ||||
| Upside part of mean | 0.853 | ||||
| Downside part of mean | -0.793 | ||||
| Upside SD | 0.238 | ||||
| Downside SD | 0.205 | ||||
| N nonnegative terms | 505.000 | ||||
| N negative terms | 1669.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2174.000 | ||||
| Mean of predictor | 0.322 | ||||
| Mean of criterion | 0.060 | ||||
| SD of predictor | 0.580 | ||||
| SD of criterion | 0.314 | ||||
| Covariance | 0.023 | ||||
| r | 0.124 | ||||
| b (slope, estimate of beta) | 0.067 | ||||
| a (intercept, estimate of alpha) | 0.038 | ||||
| Mean Square Error | 0.097 | ||||
| DF error | 2172.000 | ||||
| t(b) | 5.835 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.351 | ||||
| p(a) | 0.363 | ||||
| Lowerbound of 95% confidence interval for beta | 0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.174 | ||||
| Upperbound of 95% confidence interval for alpha | 0.251 | ||||
| Treynor index (mean / b) | 0.886 | ||||
| Jensen alpha (a) | 0.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.011 | ||||
| SD | 0.310 | ||||
| Sharpe ratio (Glass type estimate) | 0.036 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.036 | ||||
| df | 2173.000 | ||||
| t | 0.105 | ||||
| p | 0.458 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.644 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.717 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.644 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.717 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.052 | ||||
| Upside Potential Ratio | 3.845 | ||||
| Upside part of mean | 0.827 | ||||
| Downside part of mean | -0.815 | ||||
| Upside SD | 0.224 | ||||
| Downside SD | 0.215 | ||||
| N nonnegative terms | 505.000 | ||||
| N negative terms | 1669.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2174.000 | ||||
| Mean of predictor | 0.156 | ||||
| Mean of criterion | 0.011 | ||||
| SD of predictor | 0.576 | ||||
| SD of criterion | 0.310 | ||||
| Covariance | 0.022 | ||||
| r | 0.125 | ||||
| b (slope, estimate of beta) | 0.067 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.095 | ||||
| DF error | 2172.000 | ||||
| t(b) | 5.880 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.007 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.209 | ||||
| Upperbound of 95% confidence interval for alpha | 0.210 | ||||
| Treynor index (mean / b) | 0.167 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2174.000 | ||||
| Minimum | 0.835 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.314 | ||||
| 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 | 456.000 | ||||
| Percentage of outliers low | 0.210 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 512.000 | ||||
| Percentage of outliers high | 0.236 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.098 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.521 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 30.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.092 | ||||
| Maximum | 0.284 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.053 | ||||
| Mean of quarter 4 | 0.163 | ||||
| Inter Quartile Range | 0.083 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 0.263 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.062 | ||||
| VaR(95%) (moments method) | 0.177 | ||||
| Expected Shortfall (moments method) | 0.232 | ||||
| Extreme Value Index (regression method) | 0.670 | ||||
| VaR(95%) (regression method) | 0.172 | ||||
| Expected Shortfall (regression method) | 0.384 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.070 | ||||
| Compounded annual return (geometric extrapolation) | 0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.200 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.350 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.469 | ||||
| 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 | 0.497 | ||||
| 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 | 0.493 | ||||
| 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) | -8720324549762396.000 | ||||
| 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) | 195956621675717865782709426585600.000 | ||||
| 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 | ||||