Advanced Statistics: Cletus Forex
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 | -0.046 | ||||
| SD | 0.003 | ||||
| Sharpe ratio (Glass type estimate) | -13.399 | ||||
| Sharpe ratio (Hedges UMVUE) | -13.133 | ||||
| df | 38.000 | ||||
| t | -24.156 | ||||
| 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) | -16.279 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -9.986 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.357 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.493 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.003 | ||||
| Covariance | 0.000 | ||||
| r | 0.084 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.515 | ||||
| p(b) | 0.305 | ||||
| t(a) | -21.207 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | -0.042 | ||||
| Treynor index (mean / b) | -41.553 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.003 | ||||
| Sharpe ratio (Glass type estimate) | -13.336 | ||||
| Sharpe ratio (Hedges UMVUE) | -13.071 | ||||
| df | 38.000 | ||||
| t | -24.042 | ||||
| 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) | -16.204 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -9.938 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.356 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.450 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.003 | ||||
| Covariance | 0.000 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.483 | ||||
| p(b) | 0.316 | ||||
| t(a) | -21.326 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | -0.042 | ||||
| Treynor index (mean / b) | -42.567 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.994 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 0.051 | ||||
| Mean of outliers low | 0.997 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.007 | ||||
| Maximum | 0.007 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.308 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.352 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -7.045 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.039 | ||||
| df | 864.000 | ||||
| t | -12.800 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -5.914 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -8.167 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.910 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -7.117 | ||||
| Upside Potential Ratio | 0.502 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.049 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.006 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 860.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 865.000 | ||||
| Mean of predictor | 0.525 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 863.000 | ||||
| t(b) | -0.405 | ||||
| p(b) | 0.657 | ||||
| t(a) | -12.683 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.053 | ||||
| Upperbound of 95% confidence interval for alpha | -0.039 | ||||
| Treynor index (mean / b) | 159.257 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -7.033 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.027 | ||||
| df | 864.000 | ||||
| t | -12.778 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -5.902 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -8.155 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.898 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -7.101 | ||||
| Upside Potential Ratio | 0.500 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.049 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.006 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 860.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 865.000 | ||||
| Mean of predictor | 0.476 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 863.000 | ||||
| t(b) | -0.408 | ||||
| p(b) | 0.658 | ||||
| t(a) | -12.679 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.053 | ||||
| Upperbound of 95% confidence interval for alpha | -0.039 | ||||
| Treynor index (mean / b) | 159.094 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 865.000 | ||||
| Minimum | 0.993 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.004 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.007 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.007 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -18.849 | ||||
| VaR(95%) (moments method) | -10762962665494370304.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.657 | ||||
| VaR(95%) (regression method) | -5.135 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.012 | ||||
| Maximum | 0.016 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.016 | ||||
| Inter Quartile Range | 0.008 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.125 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.125 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.020 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.488 | ||||
| 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 | 0.931 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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) | -8739542836594534.000 | ||||
| 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) | -388205662317198108452230977814528.000 | ||||
| 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 | ||||