Advanced Statistics: Iron Box .618
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 | -0.498 | ||||
| SD | 1.004 | ||||
| Sharpe ratio (Glass type estimate) | -0.496 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.487 | ||||
| df | 40.000 | ||||
| t | -0.917 | ||||
| p | 0.818 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.559 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.573 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.552 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.579 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.653 | ||||
| Upside Potential Ratio | 0.562 | ||||
| Upside part of mean | 0.428 | ||||
| Downside part of mean | -0.926 | ||||
| Upside SD | 0.651 | ||||
| Downside SD | 0.762 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.507 | ||||
| Mean of criterion | -0.498 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 1.004 | ||||
| Covariance | -0.041 | ||||
| r | -0.130 | ||||
| b (slope, estimate of beta) | -0.421 | ||||
| a (intercept, estimate of alpha) | -0.284 | ||||
| Mean Square Error | 1.016 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.820 | ||||
| p(b) | 0.791 | ||||
| t(a) | -0.470 | ||||
| p(a) | 0.680 | ||||
| Lowerbound of 95% confidence interval for beta | -1.460 | ||||
| Upperbound of 95% confidence interval for beta | 0.618 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.506 | ||||
| Upperbound of 95% confidence interval for alpha | 0.938 | ||||
| Treynor index (mean / b) | 1.181 | ||||
| Jensen alpha (a) | -0.284 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.943 | ||||
| SD | 4.423 | ||||
| Sharpe ratio (Glass type estimate) | -0.665 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.653 | ||||
| df | 40.000 | ||||
| t | -1.230 | ||||
| p | 0.887 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.731 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.409 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.723 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.664 | ||||
| Upside Potential Ratio | 0.068 | ||||
| Upside part of mean | 0.301 | ||||
| Downside part of mean | -3.244 | ||||
| Upside SD | 0.440 | ||||
| Downside SD | 4.429 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.451 | ||||
| Mean of criterion | -2.943 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 4.423 | ||||
| Covariance | 0.038 | ||||
| r | 0.028 | ||||
| b (slope, estimate of beta) | 0.417 | ||||
| a (intercept, estimate of alpha) | -3.130 | ||||
| Mean Square Error | 20.049 | ||||
| DF error | 39.000 | ||||
| t(b) | 0.178 | ||||
| p(b) | 0.430 | ||||
| t(a) | -1.184 | ||||
| p(a) | 0.878 | ||||
| Lowerbound of 95% confidence interval for beta | -4.327 | ||||
| Upperbound of 95% confidence interval for beta | 5.160 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.476 | ||||
| Upperbound of 95% confidence interval for alpha | 2.215 | ||||
| Treynor index (mean / b) | -7.064 | ||||
| Jensen alpha (a) | -3.130 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.904 | ||||
| Expected Shortfall on VaR | 0.938 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.261 | ||||
| Expected Shortfall on VaR | 0.534 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.169 | ||||
| Mean of quarter 1 | 0.726 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.147 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.220 | ||||
| Mean of outliers low | 0.665 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.735 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -15.642 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.057 | ||||
| VaR(95%) (regression method) | 0.499 | ||||
| Expected Shortfall (regression method) | 0.877 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.293 | ||||
| Compounded annual return (geometric extrapolation) | -0.945 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.945 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.007 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.668 | ||||
| SD | 0.829 | ||||
| Sharpe ratio (Glass type estimate) | -0.806 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.805 | ||||
| df | 905.000 | ||||
| t | -1.499 | ||||
| p | 0.933 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.860 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.249 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.860 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.249 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.936 | ||||
| Upside Potential Ratio | 1.542 | ||||
| Upside part of mean | 1.100 | ||||
| Downside part of mean | -1.767 | ||||
| Upside SD | 0.423 | ||||
| Downside SD | 0.713 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 838.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 906.000 | ||||
| Mean of predictor | 0.531 | ||||
| Mean of criterion | -0.668 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.829 | ||||
| Covariance | -0.005 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | -0.645 | ||||
| Mean Square Error | 0.687 | ||||
| DF error | 904.000 | ||||
| t(b) | -0.522 | ||||
| p(b) | 0.699 | ||||
| t(a) | -1.439 | ||||
| p(a) | 0.925 | ||||
| Lowerbound of 95% confidence interval for beta | -0.206 | ||||
| Upperbound of 95% confidence interval for beta | 0.120 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.524 | ||||
| Upperbound of 95% confidence interval for alpha | 0.234 | ||||
| Treynor index (mean / b) | 15.421 | ||||
| Jensen alpha (a) | -0.645 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.908 | ||||
| SD | 4.365 | ||||
| Sharpe ratio (Glass type estimate) | -0.666 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.666 | ||||
| df | 905.000 | ||||
| t | -1.239 | ||||
| p | 0.892 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.720 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.388 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.720 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.389 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.668 | ||||
| Upside Potential Ratio | 0.235 | ||||
| Upside part of mean | 1.022 | ||||
| Downside part of mean | -3.930 | ||||
| Upside SD | 0.378 | ||||
| Downside SD | 4.350 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 838.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 906.000 | ||||
| Mean of predictor | 0.475 | ||||
| Mean of criterion | -2.908 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 4.365 | ||||
| Covariance | 0.023 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.201 | ||||
| a (intercept, estimate of alpha) | -3.003 | ||||
| Mean Square Error | 19.073 | ||||
| DF error | 904.000 | ||||
| t(b) | 0.467 | ||||
| p(b) | 0.320 | ||||
| t(a) | -1.274 | ||||
| p(a) | 0.898 | ||||
| Lowerbound of 95% confidence interval for beta | -0.644 | ||||
| Upperbound of 95% confidence interval for beta | 1.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -7.630 | ||||
| Upperbound of 95% confidence interval for alpha | 1.623 | ||||
| Treynor index (mean / b) | -14.480 | ||||
| Jensen alpha (a) | -3.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.365 | ||||
| Expected Shortfall on VaR | 0.430 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 906.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.446 | ||||
| Mean of quarter 1 | 0.974 | ||||
| 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 | 87.000 | ||||
| Percentage of outliers low | 0.096 | ||||
| Mean of outliers low | 0.931 | ||||
| Number of outliers high | 68.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.056 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.702 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.017 | ||||
| Extreme Value Index (regression method) | 0.504 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.066 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.289 | ||||
| Compounded annual return (geometric extrapolation) | -0.943 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.943 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.191 | ||||
| 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 | 1.050 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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 | 0.928 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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) | -8740565527495197.000 | ||||
| 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) | 98151572321337287102102918660096.000 | ||||
| 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 | ||||