Advanced Statistics: Starlight EurUsd
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 | -0.043 | ||||
| SD | 0.147 | ||||
| Sharpe ratio (Glass type estimate) | -0.291 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.289 | ||||
| df | 84.000 | ||||
| t | -0.776 | ||||
| p | 0.780 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.447 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.027 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.449 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.485 | ||||
| Upside Potential Ratio | 0.575 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.093 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 83.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 85.000 | ||||
| Mean of predictor | 0.210 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.147 | ||||
| Covariance | -0.002 | ||||
| r | -0.046 | ||||
| b (slope, estimate of beta) | -0.026 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 83.000 | ||||
| t(b) | -0.424 | ||||
| p(b) | 0.664 | ||||
| t(a) | -0.657 | ||||
| p(a) | 0.743 | ||||
| Lowerbound of 95% confidence interval for beta | -0.147 | ||||
| Upperbound of 95% confidence interval for beta | 0.095 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | 1.657 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | -0.376 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.372 | ||||
| df | 84.000 | ||||
| t | -1.000 | ||||
| p | 0.840 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.113 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.364 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.111 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.366 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.548 | ||||
| Upside Potential Ratio | 0.467 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.097 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 83.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 85.000 | ||||
| Mean of predictor | 0.174 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | -0.002 | ||||
| r | -0.042 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 83.000 | ||||
| t(b) | -0.379 | ||||
| p(b) | 0.647 | ||||
| t(a) | -0.904 | ||||
| p(a) | 0.816 | ||||
| Lowerbound of 95% confidence interval for beta | -0.140 | ||||
| Upperbound of 95% confidence interval for beta | 0.095 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.156 | ||||
| Upperbound of 95% confidence interval for alpha | 0.058 | ||||
| Treynor index (mean / b) | 2.352 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 85.000 | ||||
| Minimum | 0.812 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.310 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.955 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 1.061 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.070 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 1.230 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.096 | ||||
| Median | 0.164 | ||||
| Quartile 3 | 0.232 | ||||
| Maximum | 0.300 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.300 | ||||
| Inter Quartile Range | 0.136 | ||||
| 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) | -0.008 | ||||
| Compounded annual return (geometric extrapolation) | -0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.028 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.028 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.102 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.058 | ||||
| SD | 0.485 | ||||
| Sharpe ratio (Glass type estimate) | 0.120 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.120 | ||||
| df | 1866.000 | ||||
| t | 0.322 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.855 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.614 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.855 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.197 | ||||
| Upside Potential Ratio | 2.045 | ||||
| Upside part of mean | 0.606 | ||||
| Downside part of mean | -0.548 | ||||
| Upside SD | 0.384 | ||||
| Downside SD | 0.296 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 1800.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1867.000 | ||||
| Mean of predictor | 0.299 | ||||
| Mean of criterion | 0.058 | ||||
| SD of predictor | 0.490 | ||||
| SD of criterion | 0.485 | ||||
| Covariance | 0.009 | ||||
| r | 0.039 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | 0.047 | ||||
| Mean Square Error | 0.235 | ||||
| DF error | 1865.000 | ||||
| t(b) | 1.671 | ||||
| p(b) | 0.475 | ||||
| t(a) | 0.259 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.309 | ||||
| Upperbound of 95% confidence interval for alpha | 0.403 | ||||
| Treynor index (mean / b) | 1.526 | ||||
| Jensen alpha (a) | 0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.474 | ||||
| Sharpe ratio (Glass type estimate) | -0.111 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.111 | ||||
| df | 1866.000 | ||||
| t | -0.296 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.845 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.623 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.845 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.623 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.145 | ||||
| Upside Potential Ratio | 1.526 | ||||
| Upside part of mean | 0.552 | ||||
| Downside part of mean | -0.604 | ||||
| Upside SD | 0.306 | ||||
| Downside SD | 0.362 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 1800.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1867.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.493 | ||||
| SD of criterion | 0.474 | ||||
| Covariance | 0.009 | ||||
| r | 0.037 | ||||
| b (slope, estimate of beta) | 0.035 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.224 | ||||
| DF error | 1865.000 | ||||
| t(b) | 1.584 | ||||
| p(b) | 0.477 | ||||
| t(a) | -0.331 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.407 | ||||
| Upperbound of 95% confidence interval for alpha | 0.289 | ||||
| Treynor index (mean / b) | -1.493 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1867.000 | ||||
| Minimum | 0.548 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.853 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 88.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.959 | ||||
| Number of outliers high | 98.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.732 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.083 | ||||
| Quartile 1 | 0.109 | ||||
| Median | 0.243 | ||||
| Quartile 3 | 0.317 | ||||
| Maximum | 0.585 | ||||
| Mean of quarter 1 | 0.096 | ||||
| Mean of quarter 2 | 0.243 | ||||
| Mean of quarter 3 | 0.317 | ||||
| Mean of quarter 4 | 0.585 | ||||
| Inter Quartile Range | 0.208 | ||||
| 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) | -0.008 | ||||
| Compounded annual return (geometric extrapolation) | -0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.014 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.014 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.144 | ||||
| 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 | 1.047 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.447 | ||||
| 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 | 0.947 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.445 | ||||
| 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) | -8724207457688631.000 | ||||
| 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) | -261409286980443268592039022821376.000 | ||||
| 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 | ||||