Advanced Statistics: TrendDeviator
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 | -0.015 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.189 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.185 | ||||
| df | 31.000 | ||||
| t | -0.309 | ||||
| p | 0.620 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.389 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.013 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.386 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.404 | ||||
| Upside Potential Ratio | 1.256 | ||||
| Upside part of mean | 0.046 | ||||
| Downside part of mean | -0.061 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.037 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.606 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.001 | ||||
| r | 0.027 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.148 | ||||
| p(b) | 0.442 | ||||
| t(a) | -0.336 | ||||
| p(a) | 0.630 | ||||
| Lowerbound of 95% confidence interval for beta | -0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.116 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.100 | ||||
| Treynor index (mean / b) | -1.908 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | -0.234 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.228 | ||||
| df | 31.000 | ||||
| t | -0.382 | ||||
| p | 0.647 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.434 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.970 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.430 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.974 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.469 | ||||
| Upside Potential Ratio | 1.167 | ||||
| Upside part of mean | 0.044 | ||||
| Downside part of mean | -0.062 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.558 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | 0.001 | ||||
| r | 0.037 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.024 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.201 | ||||
| p(b) | 0.421 | ||||
| t(a) | -0.425 | ||||
| p(a) | 0.663 | ||||
| Lowerbound of 95% confidence interval for beta | -0.101 | ||||
| Upperbound of 95% confidence interval for beta | 0.123 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | -1.613 | ||||
| Jensen alpha (a) | -0.024 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.947 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.114 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.066 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.053 | ||||
| Quartile 1 | 0.053 | ||||
| Median | 0.053 | ||||
| Quartile 3 | 0.053 | ||||
| Maximum | 0.053 | ||||
| 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 | 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.500 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.585 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.015 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | -0.178 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.178 | ||||
| df | 712.000 | ||||
| t | -0.294 | ||||
| p | 0.615 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.366 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.010 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.366 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.010 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.263 | ||||
| Upside Potential Ratio | 2.790 | ||||
| Upside part of mean | 0.157 | ||||
| Downside part of mean | -0.172 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.056 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 688.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 713.000 | ||||
| Mean of predictor | 0.645 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | 0.001 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 711.000 | ||||
| t(b) | 1.055 | ||||
| p(b) | 0.146 | ||||
| t(a) | -0.414 | ||||
| p(a) | 0.661 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | 0.079 | ||||
| Treynor index (mean / b) | -1.538 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | -0.220 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.219 | ||||
| df | 712.000 | ||||
| t | -0.362 | ||||
| p | 0.641 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.408 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.969 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.408 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.969 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.320 | ||||
| Upside Potential Ratio | 2.715 | ||||
| Upside part of mean | 0.155 | ||||
| Downside part of mean | -0.173 | ||||
| Upside SD | 0.060 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 688.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 713.000 | ||||
| Mean of predictor | 0.585 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | 0.001 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.024 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 711.000 | ||||
| t(b) | 1.058 | ||||
| p(b) | 0.145 | ||||
| t(a) | -0.471 | ||||
| p(a) | 0.681 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.123 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | -1.910 | ||||
| Jensen alpha (a) | -0.024 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 713.000 | ||||
| Minimum | 0.951 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 23.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 25.000 | ||||
| Percentage of outliers high | 0.035 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.045 | ||||
| VaR(95%) (moments method) | -0.012 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.145 | ||||
| VaR(95%) (regression method) | -0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.078 | ||||
| Maximum | 0.090 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.072 | ||||
| Mean of quarter 4 | 0.087 | ||||
| Inter Quartile Range | 0.060 | ||||
| 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.289 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.300 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.459 | ||||
| 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 | 1.030 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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 | 0.896 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.514 | ||||
| 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) | -8748822247427749.000 | ||||
| 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) | 219394760719300638825205567848448.000 | ||||
| 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 | ||||