Advanced Statistics: Zen Fx
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 | 0.022 | ||||
| SD | 0.153 | ||||
| Sharpe ratio (Glass type estimate) | 0.145 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.142 | ||||
| df | 32.000 | ||||
| t | 0.241 | ||||
| p | 0.406 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.038 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.326 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.041 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.324 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.537 | ||||
| Upside Potential Ratio | 2.116 | ||||
| Upside part of mean | 0.088 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.599 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.153 | ||||
| Covariance | -0.008 | ||||
| r | -0.161 | ||||
| b (slope, estimate of beta) | -0.076 | ||||
| a (intercept, estimate of alpha) | 0.068 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.906 | ||||
| p(b) | 0.814 | ||||
| t(a) | 0.644 | ||||
| p(a) | 0.262 | ||||
| Lowerbound of 95% confidence interval for beta | -0.248 | ||||
| Upperbound of 95% confidence interval for beta | 0.096 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.147 | ||||
| Upperbound of 95% confidence interval for alpha | 0.283 | ||||
| Treynor index (mean / b) | -0.292 | ||||
| Jensen alpha (a) | 0.068 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.012 | ||||
| SD | 0.139 | ||||
| Sharpe ratio (Glass type estimate) | 0.088 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.086 | ||||
| df | 32.000 | ||||
| t | 0.146 | ||||
| p | 0.442 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.095 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.270 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.096 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.268 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.287 | ||||
| Upside Potential Ratio | 1.839 | ||||
| Upside part of mean | 0.078 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.130 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.537 | ||||
| Mean of criterion | 0.012 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.139 | ||||
| Covariance | -0.007 | ||||
| r | -0.159 | ||||
| b (slope, estimate of beta) | -0.072 | ||||
| a (intercept, estimate of alpha) | 0.051 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.896 | ||||
| p(b) | 0.812 | ||||
| t(a) | 0.540 | ||||
| p(a) | 0.297 | ||||
| Lowerbound of 95% confidence interval for beta | -0.236 | ||||
| Upperbound of 95% confidence interval for beta | 0.092 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.141 | ||||
| Upperbound of 95% confidence interval for alpha | 0.243 | ||||
| Treynor index (mean / b) | -0.170 | ||||
| Jensen alpha (a) | 0.051 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.078 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.245 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.245 | ||||
| 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 | 0.062 | ||||
| Quartile 1 | 0.062 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.062 | ||||
| Maximum | 0.062 | ||||
| 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) | 0.061 | ||||
| Compounded annual return (geometric extrapolation) | 0.058 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.930 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.740 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.016 | ||||
| SD | 0.092 | ||||
| Sharpe ratio (Glass type estimate) | 0.175 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.175 | ||||
| df | 724.000 | ||||
| t | 0.292 | ||||
| p | 0.385 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.003 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.354 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.003 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.353 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.261 | ||||
| Upside Potential Ratio | 2.421 | ||||
| Upside part of mean | 0.149 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 699.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 725.000 | ||||
| Mean of predictor | 0.627 | ||||
| Mean of criterion | 0.016 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.092 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 723.000 | ||||
| t(b) | -0.209 | ||||
| p(b) | 0.583 | ||||
| t(a) | 0.314 | ||||
| p(a) | 0.377 | ||||
| Lowerbound of 95% confidence interval for beta | -0.023 | ||||
| Upperbound of 95% confidence interval for beta | 0.018 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.127 | ||||
| Treynor index (mean / b) | -7.442 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.012 | ||||
| SD | 0.092 | ||||
| Sharpe ratio (Glass type estimate) | 0.129 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.128 | ||||
| df | 724.000 | ||||
| t | 0.214 | ||||
| p | 0.415 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.050 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.307 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.050 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.307 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.186 | ||||
| Upside Potential Ratio | 2.301 | ||||
| Upside part of mean | 0.147 | ||||
| Downside part of mean | -0.135 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 699.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 725.000 | ||||
| Mean of predictor | 0.572 | ||||
| Mean of criterion | 0.012 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.092 | ||||
| Covariance | -0.000 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 723.000 | ||||
| t(b) | -0.174 | ||||
| p(b) | 0.569 | ||||
| t(a) | 0.231 | ||||
| p(a) | 0.409 | ||||
| Lowerbound of 95% confidence interval for beta | -0.022 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.122 | ||||
| Treynor index (mean / b) | -6.563 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 725.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.074 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.022 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 26.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.754 | ||||
| VaR(95%) (moments method) | -0.023 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.753 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.151 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.023 | ||||
| Mean of quarter 4 | 0.091 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.151 | ||||
| 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) | 0.060 | ||||
| Compounded annual return (geometric extrapolation) | 0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.380 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.632 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.937 | ||||
| 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 | 1.033 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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) | -8734488728142967.000 | ||||
| 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) | -94552260902190455460374243180544.000 | ||||
| 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 | ||||