Advanced Statistics: SFX Tendance
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 | -0.042 | ||||
| SD | 0.075 | ||||
| Sharpe ratio (Glass type estimate) | -0.553 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.546 | ||||
| df | 61.000 | ||||
| t | -1.257 | ||||
| p | 0.893 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.419 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.317 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.414 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.322 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.819 | ||||
| Upside Potential Ratio | 0.597 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.359 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.075 | ||||
| Covariance | -0.009 | ||||
| r | -0.381 | ||||
| b (slope, estimate of beta) | -0.091 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 60.000 | ||||
| t(b) | -3.194 | ||||
| p(b) | 0.999 | ||||
| t(a) | -0.269 | ||||
| p(a) | 0.606 | ||||
| Lowerbound of 95% confidence interval for beta | -0.148 | ||||
| Upperbound of 95% confidence interval for beta | -0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.074 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 0.455 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | -0.596 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.588 | ||||
| df | 61.000 | ||||
| t | -1.354 | ||||
| p | 0.910 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.462 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.276 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.457 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.835 | ||||
| Upside Potential Ratio | 0.543 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.073 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.304 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | -0.010 | ||||
| r | -0.430 | ||||
| b (slope, estimate of beta) | -0.099 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 60.000 | ||||
| t(b) | -3.690 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.458 | ||||
| p(a) | 0.676 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | -0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.047 | ||||
| Treynor index (mean / b) | 0.446 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 62.000 | ||||
| Minimum | 0.901 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.126 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.097 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.081 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.248 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 1.174 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.145 | ||||
| Quartile 1 | 0.145 | ||||
| Median | 0.145 | ||||
| Quartile 3 | 0.145 | ||||
| Maximum | 0.145 | ||||
| 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) | -0.000 | ||||
| Compounded annual return (geometric extrapolation) | -0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.003 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.164 | ||||
| Sharpe ratio (Glass type estimate) | -0.189 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.189 | ||||
| df | 1363.000 | ||||
| t | -0.432 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.048 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.670 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.048 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.670 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.296 | ||||
| Upside Potential Ratio | 2.262 | ||||
| Upside part of mean | 0.237 | ||||
| Downside part of mean | -0.268 | ||||
| Upside SD | 0.126 | ||||
| Downside SD | 0.105 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 1310.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1364.000 | ||||
| Mean of predictor | 0.416 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.434 | ||||
| SD of criterion | 0.164 | ||||
| Covariance | -0.004 | ||||
| r | -0.062 | ||||
| b (slope, estimate of beta) | -0.023 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 1362.000 | ||||
| t(b) | -2.294 | ||||
| p(b) | 0.531 | ||||
| t(a) | -0.296 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | -0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.162 | ||||
| Upperbound of 95% confidence interval for alpha | 0.120 | ||||
| Treynor index (mean / b) | 1.324 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.162 | ||||
| Sharpe ratio (Glass type estimate) | -0.273 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.272 | ||||
| df | 1363.000 | ||||
| t | -0.622 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.132 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.587 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.131 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.587 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.406 | ||||
| Upside Potential Ratio | 2.110 | ||||
| Upside part of mean | 0.229 | ||||
| Downside part of mean | -0.274 | ||||
| Upside SD | 0.120 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 1310.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1364.000 | ||||
| Mean of predictor | 0.320 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.439 | ||||
| SD of criterion | 0.162 | ||||
| Covariance | -0.005 | ||||
| r | -0.068 | ||||
| b (slope, estimate of beta) | -0.025 | ||||
| a (intercept, estimate of alpha) | -0.036 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 1362.000 | ||||
| t(b) | -2.500 | ||||
| p(b) | 0.534 | ||||
| t(a) | -0.510 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | -0.045 | ||||
| Upperbound of 95% confidence interval for beta | -0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.175 | ||||
| Upperbound of 95% confidence interval for alpha | 0.103 | ||||
| Treynor index (mean / b) | 1.770 | ||||
| Jensen alpha (a) | -0.036 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1364.000 | ||||
| Minimum | 0.877 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.143 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 77.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 75.000 | ||||
| Percentage of outliers high | 0.055 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.325 | ||||
| VaR(95%) (moments method) | -0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.282 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.166 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.047 | ||||
| Mean of quarter 4 | 0.114 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.166 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.382 | ||||
| VaR(95%) (moments method) | 0.123 | ||||
| Expected Shortfall (moments method) | 0.217 | ||||
| Extreme Value Index (regression method) | 3.305 | ||||
| VaR(95%) (regression method) | 0.365 | ||||
| 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) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.006 | ||||
| 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 | 1.017 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| 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 | 0.912 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.455 | ||||
| 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) | -8732395393230779.000 | ||||
| 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) | -176419310728445057036651404984320.000 | ||||
| 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 | ||||