Advanced Statistics: Gold Pairs
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 | -0.092 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | -1.248 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.219 | ||||
| df | 33.000 | ||||
| t | -2.100 | ||||
| p | 0.978 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.441 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.036 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.420 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.018 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.189 | ||||
| Upside Potential Ratio | 0.003 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.610 | ||||
| Mean of criterion | -0.092 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | 0.002 | ||||
| r | 0.080 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.106 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.457 | ||||
| p(b) | 0.326 | ||||
| t(a) | -1.968 | ||||
| p(a) | 0.971 | ||||
| Lowerbound of 95% confidence interval for beta | -0.079 | ||||
| Upperbound of 95% confidence interval for beta | 0.125 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.216 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | -4.024 | ||||
| Jensen alpha (a) | -0.106 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -1.207 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.179 | ||||
| df | 33.000 | ||||
| t | -2.032 | ||||
| p | 0.975 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.398 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.002 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.378 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.019 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.155 | ||||
| Upside Potential Ratio | 0.003 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.001 | ||||
| r | 0.076 | ||||
| b (slope, estimate of beta) | 0.025 | ||||
| a (intercept, estimate of alpha) | -0.109 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.432 | ||||
| p(b) | 0.334 | ||||
| t(a) | -1.898 | ||||
| p(a) | 0.967 | ||||
| Lowerbound of 95% confidence interval for beta | -0.093 | ||||
| Upperbound of 95% confidence interval for beta | 0.143 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.226 | ||||
| Upperbound of 95% confidence interval for alpha | 0.008 | ||||
| Treynor index (mean / b) | -3.816 | ||||
| Jensen alpha (a) | -0.109 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.876 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.004 | ||||
| Mean of quarter 1 | 0.984 | ||||
| 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 | 0.059 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.004 | ||||
| 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) | 1.620 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.135 | ||||
| Quartile 1 | 0.135 | ||||
| Median | 0.135 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.135 | ||||
| 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) | -0.048 | ||||
| Compounded annual return (geometric extrapolation) | -0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.370 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.934 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.094 | ||||
| SD | 0.042 | ||||
| Sharpe ratio (Glass type estimate) | -2.254 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.252 | ||||
| df | 744.000 | ||||
| t | -3.801 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.421 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.086 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.420 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.084 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.305 | ||||
| Upside Potential Ratio | 0.558 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.010 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 728.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 745.000 | ||||
| Mean of predictor | 0.628 | ||||
| Mean of criterion | -0.094 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.042 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.093 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 743.000 | ||||
| t(b) | -0.373 | ||||
| p(b) | 0.645 | ||||
| t(a) | -3.729 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.142 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 54.185 | ||||
| Jensen alpha (a) | -0.093 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 0.042 | ||||
| Sharpe ratio (Glass type estimate) | -2.239 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.237 | ||||
| df | 744.000 | ||||
| t | -3.775 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.406 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.070 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.404 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.069 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.287 | ||||
| Upside Potential Ratio | 0.547 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.118 | ||||
| Upside SD | 0.010 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 728.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 745.000 | ||||
| Mean of predictor | 0.573 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.042 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.094 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 743.000 | ||||
| t(b) | -0.387 | ||||
| p(b) | 0.651 | ||||
| t(a) | -3.710 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 51.988 | ||||
| Jensen alpha (a) | -0.094 | ||||
| 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%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 745.000 | ||||
| Minimum | 0.951 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.008 | ||||
| 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 | 25.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.039 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.528 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.030 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.091 | ||||
| Quartile 3 | 0.122 | ||||
| Maximum | 0.153 | ||||
| Mean of quarter 1 | 0.030 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.153 | ||||
| Inter Quartile Range | 0.062 | ||||
| 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) | -0.047 | ||||
| Compounded annual return (geometric extrapolation) | -0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.325 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.325 | ||||
| Compounded annual return / Expected Shortfall lognormal | -8.638 | ||||
| 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 | 1.043 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| 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 | 0.917 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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) | -8743342729719560.000 | ||||
| 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) | 76298581537760121903780215128064.000 | ||||
| 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 | ||||