Advanced Statistics: FinFX
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 | -0.034 | ||||
| SD | 0.016 | ||||
| Sharpe ratio (Glass type estimate) | -2.160 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.104 | ||||
| df | 29.000 | ||||
| t | -3.416 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.502 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.787 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.456 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.751 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.725 | ||||
| Upside Potential Ratio | 0.680 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.013 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.634 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.016 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 28.000 | ||||
| t(b) | 0.002 | ||||
| p(b) | 0.499 | ||||
| t(a) | -2.827 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.021 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | -0.009 | ||||
| Treynor index (mean / b) | -1399.160 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.016 | ||||
| Sharpe ratio (Glass type estimate) | -2.190 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.133 | ||||
| df | 29.000 | ||||
| t | -3.462 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.535 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.813 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.488 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.777 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.734 | ||||
| Upside Potential Ratio | 0.672 | ||||
| Upside part of mean | 0.008 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.013 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.580 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.016 | ||||
| Covariance | 0.000 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 28.000 | ||||
| t(b) | 0.041 | ||||
| p(b) | 0.484 | ||||
| t(a) | -2.906 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.022 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | -77.689 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| 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 | 30.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.025 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.025 | ||||
| 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) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| 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 | 0.822 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -3.790 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.786 | ||||
| df | 668.000 | ||||
| t | -6.057 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.032 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.546 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.029 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.543 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -12.658 | ||||
| Upside Potential Ratio | 3.480 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 665.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 669.000 | ||||
| Mean of predictor | 0.642 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.356 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | 0.000 | ||||
| r | 0.024 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 667.000 | ||||
| t(b) | 0.622 | ||||
| p(b) | 0.267 | ||||
| t(a) | -6.086 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.024 | ||||
| Treynor index (mean / b) | -56.011 | ||||
| Jensen alpha (a) | -0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.034 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -3.812 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.808 | ||||
| df | 668.000 | ||||
| t | -6.092 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.054 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.567 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.051 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.564 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -12.673 | ||||
| Upside Potential Ratio | 3.465 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 665.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 669.000 | ||||
| Mean of predictor | 0.577 | ||||
| Mean of criterion | -0.034 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | 0.000 | ||||
| r | 0.024 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 667.000 | ||||
| t(b) | 0.623 | ||||
| p(b) | 0.267 | ||||
| t(a) | -6.121 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.024 | ||||
| Treynor index (mean / b) | -57.138 | ||||
| Jensen alpha (a) | -0.035 | ||||
| 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%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 669.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.010 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers high | 0.006 | ||||
| Mean of outliers high | 1.006 | ||||
| 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) | 0.010 | ||||
| Compounded annual return (geometric extrapolation) | 0.010 | ||||
| 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 | 7.588 | ||||
| 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 | 0.852 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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 | 0.745 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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) | -8756275819466857.000 | ||||
| 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) | -303238812093295403779685733105664.000 | ||||
| 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 | ||||