Advanced Statistics: SLCM Forex One
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 | -0.231 | ||||
| SD | 0.280 | ||||
| Sharpe ratio (Glass type estimate) | -0.824 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.812 | ||||
| df | 52.000 | ||||
| t | -1.732 | ||||
| p | 0.955 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.766 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.126 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.758 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.133 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.938 | ||||
| Upside Potential Ratio | 0.280 | ||||
| Upside part of mean | 0.069 | ||||
| Downside part of mean | -0.300 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.246 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | -0.231 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.280 | ||||
| Covariance | 0.012 | ||||
| r | 0.182 | ||||
| b (slope, estimate of beta) | 0.212 | ||||
| a (intercept, estimate of alpha) | -0.306 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 51.000 | ||||
| t(b) | 1.319 | ||||
| p(b) | 0.097 | ||||
| t(a) | -2.124 | ||||
| p(a) | 0.981 | ||||
| Lowerbound of 95% confidence interval for beta | -0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.534 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.596 | ||||
| Upperbound of 95% confidence interval for alpha | -0.017 | ||||
| Treynor index (mean / b) | -1.091 | ||||
| Jensen alpha (a) | -0.306 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.276 | ||||
| SD | 0.309 | ||||
| Sharpe ratio (Glass type estimate) | -0.895 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.882 | ||||
| df | 52.000 | ||||
| t | -1.881 | ||||
| p | 0.967 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.839 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.057 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.830 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.066 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.953 | ||||
| Upside Potential Ratio | 0.207 | ||||
| Upside part of mean | 0.060 | ||||
| Downside part of mean | -0.336 | ||||
| Upside SD | 0.126 | ||||
| Downside SD | 0.290 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.324 | ||||
| Mean of criterion | -0.276 | ||||
| SD of predictor | 0.228 | ||||
| SD of criterion | 0.309 | ||||
| Covariance | 0.014 | ||||
| r | 0.194 | ||||
| b (slope, estimate of beta) | 0.263 | ||||
| a (intercept, estimate of alpha) | -0.362 | ||||
| Mean Square Error | 0.094 | ||||
| DF error | 51.000 | ||||
| t(b) | 1.412 | ||||
| p(b) | 0.082 | ||||
| t(a) | -2.295 | ||||
| p(a) | 0.987 | ||||
| Lowerbound of 95% confidence interval for beta | -0.111 | ||||
| Upperbound of 95% confidence interval for beta | 0.637 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.678 | ||||
| Upperbound of 95% confidence interval for alpha | -0.045 | ||||
| Treynor index (mean / b) | -1.050 | ||||
| Jensen alpha (a) | -0.362 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.156 | ||||
| Expected Shortfall on VaR | 0.186 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.086 | ||||
| Expected Shortfall on VaR | 0.176 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.674 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.308 | ||||
| Mean of quarter 1 | 0.919 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.858 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.105 | ||||
| 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) | -0.842 | ||||
| VaR(95%) (regression method) | 0.101 | ||||
| Expected Shortfall (regression method) | 0.127 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.643 | ||||
| Quartile 1 | 0.643 | ||||
| Median | 0.643 | ||||
| Quartile 3 | 0.643 | ||||
| Maximum | 0.643 | ||||
| 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) | -0.145 | ||||
| Compounded annual return (geometric extrapolation) | -0.207 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.323 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.112 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.245 | ||||
| SD | 0.236 | ||||
| Sharpe ratio (Glass type estimate) | -1.037 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.036 | ||||
| df | 1173.000 | ||||
| t | -2.194 | ||||
| p | 0.541 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.963 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.110 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.963 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.109 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.340 | ||||
| Upside Potential Ratio | 2.362 | ||||
| Upside part of mean | 0.432 | ||||
| Downside part of mean | -0.676 | ||||
| Upside SD | 0.150 | ||||
| Downside SD | 0.183 | ||||
| N nonnegative terms | 89.000 | ||||
| N negative terms | 1085.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1174.000 | ||||
| Mean of predictor | 0.382 | ||||
| Mean of criterion | -0.245 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.236 | ||||
| Covariance | -0.000 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.243 | ||||
| Mean Square Error | 0.056 | ||||
| DF error | 1172.000 | ||||
| t(b) | -0.216 | ||||
| p(b) | 0.503 | ||||
| t(a) | -2.166 | ||||
| p(a) | 0.532 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.462 | ||||
| Upperbound of 95% confidence interval for alpha | -0.023 | ||||
| Treynor index (mean / b) | 44.457 | ||||
| Jensen alpha (a) | -0.243 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.273 | ||||
| SD | 0.238 | ||||
| Sharpe ratio (Glass type estimate) | -1.146 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.145 | ||||
| df | 1173.000 | ||||
| t | -2.425 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.073 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.218 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.072 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.218 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.432 | ||||
| Upside Potential Ratio | 2.208 | ||||
| Upside part of mean | 0.421 | ||||
| Downside part of mean | -0.694 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.191 | ||||
| N nonnegative terms | 89.000 | ||||
| N negative terms | 1085.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1174.000 | ||||
| Mean of predictor | 0.345 | ||||
| Mean of criterion | -0.273 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.238 | ||||
| Covariance | -0.000 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.271 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 1172.000 | ||||
| t(b) | -0.221 | ||||
| p(b) | 0.503 | ||||
| t(a) | -2.400 | ||||
| p(a) | 0.535 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.493 | ||||
| Upperbound of 95% confidence interval for alpha | -0.049 | ||||
| Treynor index (mean / b) | 48.509 | ||||
| Jensen alpha (a) | -0.271 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.019 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1174.000 | ||||
| Minimum | 0.858 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.173 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 121.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 89.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.924 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.274 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.042 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.383 | ||||
| Maximum | 0.695 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.695 | ||||
| Inter Quartile Range | 0.341 | ||||
| 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) | -0.143 | ||||
| Compounded annual return (geometric extrapolation) | -0.205 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.295 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.295 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.622 | ||||
| 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 | 0.929 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.821 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.466 | ||||
| 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) | -8747669202272436.000 | ||||
| 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) | 224701485114587496554847444926464.000 | ||||
| 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 | ||||