Advanced Statistics: Trendfriend
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 | -0.171 | ||||
| SD | 0.148 | ||||
| Sharpe ratio (Glass type estimate) | -1.151 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.124 | ||||
| df | 33.000 | ||||
| t | -1.937 | ||||
| p | 0.969 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.339 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.054 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.320 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.071 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.107 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.171 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.605 | ||||
| Mean of criterion | -0.171 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.148 | ||||
| Covariance | 0.003 | ||||
| r | 0.062 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | -0.190 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.352 | ||||
| p(b) | 0.364 | ||||
| t(a) | -1.808 | ||||
| p(a) | 0.960 | ||||
| Lowerbound of 95% confidence interval for beta | -0.155 | ||||
| Upperbound of 95% confidence interval for beta | 0.219 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.404 | ||||
| Upperbound of 95% confidence interval for alpha | 0.024 | ||||
| Treynor index (mean / b) | -5.275 | ||||
| Jensen alpha (a) | -0.190 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.183 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | -1.123 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.097 | ||||
| df | 33.000 | ||||
| t | -1.890 | ||||
| p | 0.966 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.310 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.081 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.291 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.097 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.083 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.183 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.169 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.552 | ||||
| Mean of criterion | -0.183 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | 0.003 | ||||
| r | 0.059 | ||||
| b (slope, estimate of beta) | 0.035 | ||||
| a (intercept, estimate of alpha) | -0.203 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.335 | ||||
| p(b) | 0.370 | ||||
| t(a) | -1.774 | ||||
| p(a) | 0.957 | ||||
| Lowerbound of 95% confidence interval for beta | -0.180 | ||||
| Upperbound of 95% confidence interval for beta | 0.250 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.436 | ||||
| Upperbound of 95% confidence interval for alpha | 0.030 | ||||
| Treynor index (mean / b) | -5.188 | ||||
| Jensen alpha (a) | -0.203 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.089 | ||||
| Expected Shortfall on VaR | 0.106 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.103 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.821 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.960 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.821 | ||||
| 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) | -8.789 | ||||
| VaR(95%) (regression method) | 1.422 | ||||
| Expected Shortfall (regression method) | 1.434 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.326 | ||||
| Quartile 1 | 0.326 | ||||
| Median | 0.326 | ||||
| Quartile 3 | 0.326 | ||||
| Maximum | 0.326 | ||||
| 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) | -0.115 | ||||
| Compounded annual return (geometric extrapolation) | -0.130 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.399 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.224 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.157 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | -0.728 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.727 | ||||
| df | 749.000 | ||||
| t | -1.232 | ||||
| p | 0.891 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.887 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.431 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.886 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.432 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.877 | ||||
| Upside Potential Ratio | 0.902 | ||||
| Upside part of mean | 0.162 | ||||
| Downside part of mean | -0.319 | ||||
| Upside SD | 0.121 | ||||
| Downside SD | 0.179 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 750.000 | ||||
| Mean of predictor | 0.637 | ||||
| Mean of criterion | -0.157 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | 0.001 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.163 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 748.000 | ||||
| t(b) | 0.348 | ||||
| p(b) | 0.364 | ||||
| t(a) | -1.264 | ||||
| p(a) | 0.897 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.054 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.415 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | -19.215 | ||||
| Jensen alpha (a) | -0.163 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.182 | ||||
| SD | 0.224 | ||||
| Sharpe ratio (Glass type estimate) | -0.811 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.810 | ||||
| df | 749.000 | ||||
| t | -1.372 | ||||
| p | 0.915 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.970 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.348 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.969 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.349 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.940 | ||||
| Upside Potential Ratio | 0.801 | ||||
| Upside part of mean | 0.155 | ||||
| Downside part of mean | -0.337 | ||||
| Upside SD | 0.114 | ||||
| Downside SD | 0.194 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 750.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -0.182 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.224 | ||||
| Covariance | 0.001 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.187 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 748.000 | ||||
| t(b) | 0.357 | ||||
| p(b) | 0.361 | ||||
| t(a) | -1.401 | ||||
| p(a) | 0.919 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.449 | ||||
| Upperbound of 95% confidence interval for alpha | 0.075 | ||||
| Treynor index (mean / b) | -21.153 | ||||
| Jensen alpha (a) | -0.187 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 750.000 | ||||
| Minimum | 0.839 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.167 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 13.000 | ||||
| Percentage of outliers low | 0.017 | ||||
| Mean of outliers low | 0.939 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.046 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.664 | ||||
| VaR(95%) (moments method) | -13.834 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.932 | ||||
| VaR(95%) (regression method) | -0.168 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.416 | ||||
| Quartile 1 | 0.416 | ||||
| Median | 0.416 | ||||
| Quartile 3 | 0.416 | ||||
| Maximum | 0.416 | ||||
| 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) | -0.114 | ||||
| Compounded annual return (geometric extrapolation) | -0.129 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.310 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.466 | ||||
| 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 | 1.122 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.504 | ||||
| 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 | 0.993 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8736058058761550.000 | ||||
| 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) | -121164124851772300197053971038208.000 | ||||
| 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 | ||||