Advanced Statistics: FOREX Formula
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 | -0.024 | ||||
| SD | 0.177 | ||||
| Sharpe ratio (Glass type estimate) | -0.135 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.134 | ||||
| df | 94.000 | ||||
| t | -0.379 | ||||
| p | 0.647 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.831 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.562 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.831 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.563 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.242 | ||||
| Upside Potential Ratio | 1.014 | ||||
| Upside part of mean | 0.100 | ||||
| Downside part of mean | -0.124 | ||||
| Upside SD | 0.147 | ||||
| Downside SD | 0.099 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 89.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.192 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.177 | ||||
| Covariance | -0.006 | ||||
| r | -0.117 | ||||
| b (slope, estimate of beta) | -0.076 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 93.000 | ||||
| t(b) | -1.132 | ||||
| p(b) | 0.870 | ||||
| t(a) | -0.145 | ||||
| p(a) | 0.558 | ||||
| Lowerbound of 95% confidence interval for beta | -0.209 | ||||
| Upperbound of 95% confidence interval for beta | 0.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.137 | ||||
| Upperbound of 95% confidence interval for alpha | 0.118 | ||||
| Treynor index (mean / b) | 0.315 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.167 | ||||
| Sharpe ratio (Glass type estimate) | -0.228 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.227 | ||||
| df | 94.000 | ||||
| t | -0.643 | ||||
| p | 0.739 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.925 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.470 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.924 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.471 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.365 | ||||
| Upside Potential Ratio | 0.867 | ||||
| Upside part of mean | 0.091 | ||||
| Downside part of mean | -0.129 | ||||
| Upside SD | 0.130 | ||||
| Downside SD | 0.105 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 89.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.154 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.167 | ||||
| Covariance | -0.005 | ||||
| r | -0.102 | ||||
| b (slope, estimate of beta) | -0.063 | ||||
| a (intercept, estimate of alpha) | -0.028 | ||||
| Mean Square Error | 0.028 | ||||
| DF error | 93.000 | ||||
| t(b) | -0.990 | ||||
| p(b) | 0.838 | ||||
| t(a) | -0.472 | ||||
| p(a) | 0.681 | ||||
| Lowerbound of 95% confidence interval for beta | -0.190 | ||||
| Upperbound of 95% confidence interval for beta | 0.064 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | 0.603 | ||||
| Jensen alpha (a) | -0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 95.000 | ||||
| Minimum | 0.864 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.321 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 22.000 | ||||
| Percentage of outliers low | 0.232 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.308 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.113 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.184 | ||||
| Quartile 1 | 0.186 | ||||
| Median | 0.188 | ||||
| Quartile 3 | 0.217 | ||||
| Maximum | 0.247 | ||||
| Mean of quarter 1 | 0.184 | ||||
| Mean of quarter 2 | 0.188 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.247 | ||||
| Inter Quartile Range | 0.032 | ||||
| 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) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.024 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.024 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.060 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.007 | ||||
| SD | 0.303 | ||||
| Sharpe ratio (Glass type estimate) | 0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.022 | ||||
| df | 2084.000 | ||||
| t | 0.063 | ||||
| p | 0.475 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.672 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.717 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.672 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.717 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.034 | ||||
| Upside Potential Ratio | 2.351 | ||||
| Upside part of mean | 0.465 | ||||
| Downside part of mean | -0.458 | ||||
| Upside SD | 0.230 | ||||
| Downside SD | 0.198 | ||||
| N nonnegative terms | 216.000 | ||||
| N negative terms | 1869.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2085.000 | ||||
| Mean of predictor | 0.311 | ||||
| Mean of criterion | 0.007 | ||||
| SD of predictor | 0.544 | ||||
| SD of criterion | 0.303 | ||||
| Covariance | -0.022 | ||||
| r | -0.132 | ||||
| b (slope, estimate of beta) | -0.073 | ||||
| a (intercept, estimate of alpha) | 0.030 | ||||
| Mean Square Error | 0.090 | ||||
| DF error | 2083.000 | ||||
| t(b) | -6.066 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.278 | ||||
| p(a) | 0.390 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | -0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.179 | ||||
| Upperbound of 95% confidence interval for alpha | 0.239 | ||||
| Treynor index (mean / b) | -0.093 | ||||
| Jensen alpha (a) | 0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.300 | ||||
| Sharpe ratio (Glass type estimate) | -0.128 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.127 | ||||
| df | 2084.000 | ||||
| t | -0.360 | ||||
| p | 0.640 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.822 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.567 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.822 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.567 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.178 | ||||
| Upside Potential Ratio | 2.054 | ||||
| Upside part of mean | 0.441 | ||||
| Downside part of mean | -0.480 | ||||
| Upside SD | 0.209 | ||||
| Downside SD | 0.215 | ||||
| N nonnegative terms | 216.000 | ||||
| N negative terms | 1869.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2085.000 | ||||
| Mean of predictor | 0.165 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.541 | ||||
| SD of criterion | 0.300 | ||||
| Covariance | -0.021 | ||||
| r | -0.130 | ||||
| b (slope, estimate of beta) | -0.072 | ||||
| a (intercept, estimate of alpha) | -0.026 | ||||
| Mean Square Error | 0.088 | ||||
| DF error | 2083.000 | ||||
| t(b) | -5.990 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.250 | ||||
| p(a) | 0.599 | ||||
| Lowerbound of 95% confidence interval for beta | -0.096 | ||||
| Upperbound of 95% confidence interval for beta | -0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.233 | ||||
| Upperbound of 95% confidence interval for alpha | 0.180 | ||||
| Treynor index (mean / b) | 0.530 | ||||
| Jensen alpha (a) | -0.026 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2085.000 | ||||
| Minimum | 0.759 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.367 | ||||
| Mean of quarter 1 | 0.994 | ||||
| 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 | 342.000 | ||||
| Percentage of outliers low | 0.164 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 346.000 | ||||
| Percentage of outliers high | 0.166 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.265 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.619 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.046 | ||||
| Median | 0.139 | ||||
| Quartile 3 | 0.248 | ||||
| Maximum | 0.273 | ||||
| Mean of quarter 1 | 0.022 | ||||
| Mean of quarter 2 | 0.088 | ||||
| Mean of quarter 3 | 0.199 | ||||
| Mean of quarter 4 | 0.263 | ||||
| Inter Quartile Range | 0.201 | ||||
| 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) | -45.985 | ||||
| VaR(95%) (moments method) | 0.270 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.045 | ||||
| VaR(95%) (regression method) | 0.293 | ||||
| Expected Shortfall (regression method) | 0.293 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.021 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.022 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.155 | ||||
| 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 | 0.991 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.518 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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) | -8752461576260220.000 | ||||
| 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) | -309922657113909739886432718159872.000 | ||||
| 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 | ||||