Advanced Statistics: CTS CLC System
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 | 0.049 | ||||
| SD | 0.212 | ||||
| Sharpe ratio (Glass type estimate) | 0.231 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.229 | ||||
| df | 100.000 | ||||
| t | 0.671 | ||||
| p | 0.252 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.446 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.907 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.447 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.906 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.543 | ||||
| Upside Potential Ratio | 1.845 | ||||
| Upside part of mean | 0.166 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.191 | ||||
| Downside SD | 0.090 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 101.000 | ||||
| Mean of predictor | 0.172 | ||||
| Mean of criterion | 0.049 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.212 | ||||
| Covariance | -0.013 | ||||
| r | -0.225 | ||||
| b (slope, estimate of beta) | -0.182 | ||||
| a (intercept, estimate of alpha) | 0.080 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 99.000 | ||||
| t(b) | -2.297 | ||||
| p(b) | 0.988 | ||||
| t(a) | 1.101 | ||||
| p(a) | 0.137 | ||||
| Lowerbound of 95% confidence interval for beta | -0.338 | ||||
| Upperbound of 95% confidence interval for beta | -0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.225 | ||||
| Treynor index (mean / b) | -0.270 | ||||
| Jensen alpha (a) | 0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.030 | ||||
| SD | 0.190 | ||||
| Sharpe ratio (Glass type estimate) | 0.156 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.155 | ||||
| df | 100.000 | ||||
| t | 0.452 | ||||
| p | 0.326 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.521 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.831 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.521 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.830 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.312 | ||||
| Upside Potential Ratio | 1.590 | ||||
| Upside part of mean | 0.151 | ||||
| Downside part of mean | -0.121 | ||||
| Upside SD | 0.164 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 101.000 | ||||
| Mean of predictor | 0.136 | ||||
| Mean of criterion | 0.030 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.190 | ||||
| Covariance | -0.010 | ||||
| r | -0.211 | ||||
| b (slope, estimate of beta) | -0.154 | ||||
| a (intercept, estimate of alpha) | 0.051 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 99.000 | ||||
| t(b) | -2.150 | ||||
| p(b) | 0.983 | ||||
| t(a) | 0.777 | ||||
| p(a) | 0.220 | ||||
| Lowerbound of 95% confidence interval for beta | -0.296 | ||||
| Upperbound of 95% confidence interval for beta | -0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.180 | ||||
| Treynor index (mean / b) | -0.193 | ||||
| Jensen alpha (a) | 0.051 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.084 | ||||
| Expected Shortfall on VaR | 0.105 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 101.000 | ||||
| Minimum | 0.869 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.456 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.119 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.178 | ||||
| Mean of outliers high | 1.080 | ||||
| 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) | 0.051 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.046 | ||||
| Quartile 1 | 0.094 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.131 | ||||
| Maximum | 0.164 | ||||
| Mean of quarter 1 | 0.070 | ||||
| Mean of quarter 2 | 0.098 | ||||
| Mean of quarter 3 | 0.131 | ||||
| Mean of quarter 4 | 0.164 | ||||
| Inter Quartile Range | 0.037 | ||||
| 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) | 0.102 | ||||
| Compounded annual return (geometric extrapolation) | 0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.466 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.466 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.730 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.277 | ||||
| SD | 0.743 | ||||
| Sharpe ratio (Glass type estimate) | 0.372 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.372 | ||||
| df | 2225.000 | ||||
| t | 1.085 | ||||
| p | 0.139 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.300 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.045 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.300 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.667 | ||||
| Upside Potential Ratio | 3.530 | ||||
| Upside part of mean | 1.464 | ||||
| Downside part of mean | -1.187 | ||||
| Upside SD | 0.617 | ||||
| Downside SD | 0.415 | ||||
| N nonnegative terms | 288.000 | ||||
| N negative terms | 1938.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2226.000 | ||||
| Mean of predictor | 0.340 | ||||
| Mean of criterion | 0.277 | ||||
| SD of predictor | 0.615 | ||||
| SD of criterion | 0.743 | ||||
| Covariance | -0.084 | ||||
| r | -0.184 | ||||
| b (slope, estimate of beta) | -0.223 | ||||
| a (intercept, estimate of alpha) | 0.352 | ||||
| Mean Square Error | 0.534 | ||||
| DF error | 2224.000 | ||||
| t(b) | -8.845 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.405 | ||||
| p(a) | 0.080 | ||||
| Lowerbound of 95% confidence interval for beta | -0.272 | ||||
| Upperbound of 95% confidence interval for beta | -0.173 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.140 | ||||
| Upperbound of 95% confidence interval for alpha | 0.844 | ||||
| Treynor index (mean / b) | -1.241 | ||||
| Jensen alpha (a) | 0.352 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.697 | ||||
| Sharpe ratio (Glass type estimate) | 0.042 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.042 | ||||
| df | 2225.000 | ||||
| t | 0.121 | ||||
| p | 0.452 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.631 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.714 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.631 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.714 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.059 | ||||
| Upside Potential Ratio | 2.707 | ||||
| Upside part of mean | 1.322 | ||||
| Downside part of mean | -1.293 | ||||
| Upside SD | 0.497 | ||||
| Downside SD | 0.488 | ||||
| N nonnegative terms | 288.000 | ||||
| N negative terms | 1938.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2226.000 | ||||
| Mean of predictor | 0.155 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.607 | ||||
| SD of criterion | 0.697 | ||||
| Covariance | -0.081 | ||||
| r | -0.192 | ||||
| b (slope, estimate of beta) | -0.220 | ||||
| a (intercept, estimate of alpha) | 0.063 | ||||
| Mean Square Error | 0.468 | ||||
| DF error | 2224.000 | ||||
| t(b) | -9.224 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.269 | ||||
| p(a) | 0.394 | ||||
| Lowerbound of 95% confidence interval for beta | -0.267 | ||||
| Upperbound of 95% confidence interval for beta | -0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.397 | ||||
| Upperbound of 95% confidence interval for alpha | 0.523 | ||||
| Treynor index (mean / b) | -0.131 | ||||
| Jensen alpha (a) | 0.063 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2226.000 | ||||
| Minimum | 0.467 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.141 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 244.000 | ||||
| Percentage of outliers low | 0.110 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 293.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.578 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| 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 | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.114 | ||||
| Quartile 3 | 0.143 | ||||
| Maximum | 0.551 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.075 | ||||
| Mean of quarter 3 | 0.120 | ||||
| Mean of quarter 4 | 0.261 | ||||
| Inter Quartile Range | 0.126 | ||||
| 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 | 0.071 | ||||
| Mean of outliers high | 0.551 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.585 | ||||
| VaR(95%) (moments method) | 0.329 | ||||
| Expected Shortfall (moments method) | 0.769 | ||||
| Extreme Value Index (regression method) | 2.747 | ||||
| VaR(95%) (regression method) | 0.452 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.101 | ||||
| Compounded annual return (geometric extrapolation) | 0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.137 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.290 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.893 | ||||
| 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 | 1.044 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.465 | ||||
| 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 | 0.935 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.466 | ||||
| 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) | -8732446807933460.000 | ||||
| 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) | 3150243724293350893279179379310592.000 | ||||
| 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 | ||||