Advanced Statistics: Equinox
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 | -0.044 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -4.888 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.828 | ||||
| df | 62.000 | ||||
| t | -11.199 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -3.666 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.034 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.623 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.977 | ||||
| Upside Potential Ratio | 0.141 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.348 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.151 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 61.000 | ||||
| t(b) | -1.193 | ||||
| p(b) | 0.881 | ||||
| t(a) | -10.313 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | 10.056 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.009 | ||||
| Sharpe ratio (Glass type estimate) | -4.884 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.824 | ||||
| df | 62.000 | ||||
| t | -11.190 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -3.662 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.030 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.619 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.974 | ||||
| Upside Potential Ratio | 0.139 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.298 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.009 | ||||
| Covariance | -0.000 | ||||
| r | -0.149 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 61.000 | ||||
| t(b) | -1.178 | ||||
| p(b) | 0.878 | ||||
| t(a) | -10.446 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.051 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | 9.745 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.986 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.015 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.016 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.007 | ||||
| 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 | 0.014 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.014 | ||||
| Maximum | 0.014 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.804 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.803 | ||||
| df | 1379.000 | ||||
| t | -1.844 | ||||
| p | 0.532 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.658 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.051 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.658 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.051 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.071 | ||||
| Upside Potential Ratio | 1.027 | ||||
| Upside part of mean | 0.041 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 1363.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1380.000 | ||||
| Mean of predictor | 0.442 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.509 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | -0.005 | ||||
| r | -0.178 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1378.000 | ||||
| t(b) | -6.719 | ||||
| p(b) | 0.589 | ||||
| t(a) | -1.511 | ||||
| p(a) | 0.520 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | -0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | 2.299 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.827 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.826 | ||||
| df | 1379.000 | ||||
| t | -1.897 | ||||
| p | 0.532 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.681 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.028 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.681 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.028 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.079 | ||||
| Upside Potential Ratio | 0.987 | ||||
| Upside part of mean | 0.040 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 1363.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1380.000 | ||||
| Mean of predictor | 0.311 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | -0.005 | ||||
| r | -0.177 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1378.000 | ||||
| t(b) | -6.666 | ||||
| p(b) | 0.588 | ||||
| t(a) | -1.675 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | -0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.007 | ||||
| Treynor index (mean / b) | 2.393 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1380.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.065 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.007 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.780 | ||||
| VaR(95%) (moments method) | -4.964 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.009 | ||||
| VaR(95%) (regression method) | -0.037 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.037 | ||||
| Quartile 3 | 0.062 | ||||
| Maximum | 0.066 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.037 | ||||
| Mean of quarter 3 | 0.062 | ||||
| Mean of quarter 4 | 0.066 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.655 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.553 | ||||
| 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 | 1.499 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.550 | ||||
| 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) | -8676718457562903.000 | ||||
| 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) | 313660832265731573617913212436480.000 | ||||
| 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 | ||||