Advanced Statistics: CYCLE
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 | 0.132 | ||||
| SD | 0.191 | ||||
| Sharpe ratio (Glass type estimate) | 0.693 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.675 | ||||
| df | 30.000 | ||||
| t | 1.113 | ||||
| p | 0.137 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.545 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.919 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.556 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.907 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.549 | ||||
| Upside Potential Ratio | 3.493 | ||||
| Upside part of mean | 0.299 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.172 | ||||
| Downside SD | 0.085 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 16.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.685 | ||||
| Mean of criterion | 0.132 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.191 | ||||
| Covariance | 0.056 | ||||
| r | 0.861 | ||||
| b (slope, estimate of beta) | 0.481 | ||||
| a (intercept, estimate of alpha) | -0.197 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 29.000 | ||||
| t(b) | 9.113 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.762 | ||||
| p(a) | 0.995 | ||||
| Lowerbound of 95% confidence interval for beta | 0.373 | ||||
| Upperbound of 95% confidence interval for beta | 0.590 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.343 | ||||
| Upperbound of 95% confidence interval for alpha | -0.051 | ||||
| Treynor index (mean / b) | 0.275 | ||||
| Jensen alpha (a) | -0.197 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.115 | ||||
| SD | 0.184 | ||||
| Sharpe ratio (Glass type estimate) | 0.624 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.608 | ||||
| df | 30.000 | ||||
| t | 1.003 | ||||
| p | 0.162 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.610 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.849 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.621 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.838 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.308 | ||||
| Upside Potential Ratio | 3.238 | ||||
| Upside part of mean | 0.284 | ||||
| Downside part of mean | -0.169 | ||||
| Upside SD | 0.161 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 16.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.616 | ||||
| Mean of criterion | 0.115 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.184 | ||||
| Covariance | 0.048 | ||||
| r | 0.844 | ||||
| b (slope, estimate of beta) | 0.503 | ||||
| a (intercept, estimate of alpha) | -0.195 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 29.000 | ||||
| t(b) | 8.465 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.701 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | 0.382 | ||||
| Upperbound of 95% confidence interval for beta | 0.625 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.343 | ||||
| Upperbound of 95% confidence interval for alpha | -0.047 | ||||
| Treynor index (mean / b) | 0.228 | ||||
| Jensen alpha (a) | -0.195 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.075 | ||||
| Expected Shortfall on VaR | 0.095 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.925 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.043 | ||||
| Maximum | 1.186 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.091 | ||||
| Inter Quartile Range | 0.059 | ||||
| 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 | 0.032 | ||||
| Mean of outliers high | 1.186 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.204 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.060 | ||||
| Extreme Value Index (regression method) | 0.105 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.068 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | 0.034 | ||||
| Mean of quarter 4 | 0.118 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.135 | ||||
| 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) | 0.196 | ||||
| Compounded annual return (geometric extrapolation) | 0.172 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.272 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.457 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.814 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.131 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | 0.607 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.606 | ||||
| df | 677.000 | ||||
| t | 0.976 | ||||
| p | 0.165 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.612 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.826 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.612 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.825 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.833 | ||||
| Upside Potential Ratio | 6.753 | ||||
| Upside part of mean | 1.061 | ||||
| Downside part of mean | -0.930 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.157 | ||||
| N nonnegative terms | 342.000 | ||||
| N negative terms | 336.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 678.000 | ||||
| Mean of predictor | 0.681 | ||||
| Mean of criterion | 0.131 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | 0.050 | ||||
| r | 0.666 | ||||
| b (slope, estimate of beta) | 0.412 | ||||
| a (intercept, estimate of alpha) | -0.150 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 676.000 | ||||
| t(b) | 23.211 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.485 | ||||
| p(a) | 0.931 | ||||
| Lowerbound of 95% confidence interval for beta | 0.377 | ||||
| Upperbound of 95% confidence interval for beta | 0.447 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.348 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | 0.318 | ||||
| Jensen alpha (a) | -0.150 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.107 | ||||
| SD | 0.219 | ||||
| Sharpe ratio (Glass type estimate) | 0.490 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.489 | ||||
| df | 677.000 | ||||
| t | 0.788 | ||||
| p | 0.216 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.729 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.708 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.708 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.655 | ||||
| Upside Potential Ratio | 6.414 | ||||
| Upside part of mean | 1.051 | ||||
| Downside part of mean | -0.943 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.164 | ||||
| N nonnegative terms | 342.000 | ||||
| N negative terms | 336.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 678.000 | ||||
| Mean of predictor | 0.619 | ||||
| Mean of criterion | 0.107 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.219 | ||||
| Covariance | 0.053 | ||||
| r | 0.679 | ||||
| b (slope, estimate of beta) | 0.419 | ||||
| a (intercept, estimate of alpha) | -0.152 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 676.000 | ||||
| t(b) | 24.025 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.512 | ||||
| p(a) | 0.935 | ||||
| Lowerbound of 95% confidence interval for beta | 0.385 | ||||
| Upperbound of 95% confidence interval for beta | 0.454 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.350 | ||||
| Upperbound of 95% confidence interval for alpha | 0.045 | ||||
| Treynor index (mean / b) | 0.256 | ||||
| Jensen alpha (a) | -0.152 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 678.000 | ||||
| Minimum | 0.849 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.071 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 32.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 38.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.331 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| Extreme Value Index (regression method) | 0.382 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 29.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.043 | ||||
| Maximum | 0.159 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.032 | ||||
| Mean of quarter 4 | 0.091 | ||||
| Inter Quartile Range | 0.038 | ||||
| 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 | 0.069 | ||||
| Mean of outliers high | 0.151 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.113 | ||||
| VaR(95%) (moments method) | 0.088 | ||||
| Expected Shortfall (moments method) | 0.112 | ||||
| Extreme Value Index (regression method) | -0.161 | ||||
| VaR(95%) (regression method) | 0.095 | ||||
| Expected Shortfall (regression method) | 0.118 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.185 | ||||
| Compounded annual return (geometric extrapolation) | 0.163 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.030 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.795 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.023 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.401 | ||||
| SD | 0.336 | ||||
| Sharpe ratio (Glass type estimate) | 1.193 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.186 | ||||
| df | 130.000 | ||||
| t | 0.844 | ||||
| p | 0.463 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.585 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.966 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.589 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.962 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.778 | ||||
| Upside Potential Ratio | 9.419 | ||||
| Upside part of mean | 2.123 | ||||
| Downside part of mean | -1.722 | ||||
| Upside SD | 0.248 | ||||
| Downside SD | 0.225 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.417 | ||||
| Mean of criterion | 0.401 | ||||
| SD of predictor | 0.512 | ||||
| SD of criterion | 0.336 | ||||
| Covariance | 0.113 | ||||
| r | 0.659 | ||||
| b (slope, estimate of beta) | 0.432 | ||||
| a (intercept, estimate of alpha) | -0.211 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 129.000 | ||||
| t(b) | 9.946 | ||||
| p(b) | 0.113 | ||||
| t(a) | -0.580 | ||||
| p(a) | 0.532 | ||||
| Lowerbound of 95% confidence interval for beta | 0.346 | ||||
| Upperbound of 95% confidence interval for beta | 0.518 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.931 | ||||
| Upperbound of 95% confidence interval for alpha | 0.509 | ||||
| Treynor index (mean / b) | 0.928 | ||||
| Jensen alpha (a) | -0.211 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.344 | ||||
| SD | 0.336 | ||||
| Sharpe ratio (Glass type estimate) | 1.025 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.019 | ||||
| df | 130.000 | ||||
| t | 0.725 | ||||
| p | 0.468 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.751 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.798 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.755 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.794 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.493 | ||||
| Upside Potential Ratio | 9.070 | ||||
| Upside part of mean | 2.093 | ||||
| Downside part of mean | -1.748 | ||||
| Upside SD | 0.243 | ||||
| Downside SD | 0.231 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.282 | ||||
| Mean of criterion | 0.344 | ||||
| SD of predictor | 0.514 | ||||
| SD of criterion | 0.336 | ||||
| Covariance | 0.115 | ||||
| r | 0.664 | ||||
| b (slope, estimate of beta) | 0.434 | ||||
| a (intercept, estimate of alpha) | -0.212 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 129.000 | ||||
| t(b) | 10.095 | ||||
| p(b) | 0.111 | ||||
| t(a) | -0.589 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | 0.349 | ||||
| Upperbound of 95% confidence interval for beta | 0.519 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.926 | ||||
| Upperbound of 95% confidence interval for alpha | 0.501 | ||||
| Treynor index (mean / b) | 0.793 | ||||
| Jensen alpha (a) | -0.212 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.071 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.943 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.280 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.038 | ||||
| Extreme Value Index (regression method) | 0.165 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.044 | ||||
| Maximum | 0.144 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.027 | ||||
| Mean of quarter 4 | 0.087 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.100 | ||||
| Mean of outliers high | 0.144 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.541 | ||||
| VaR(95%) (moments method) | 0.101 | ||||
| Expected Shortfall (moments method) | 0.117 | ||||
| Extreme Value Index (regression method) | 1.011 | ||||
| VaR(95%) (regression method) | 0.162 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.429 | ||||
| Compounded annual return (geometric extrapolation) | 0.475 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.303 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.464 | ||||
| Compounded annual return / Expected Shortfall lognormal | 11.685 | ||||