Advanced Statistics: System 22811602
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 | -0.231 | ||||
| SD | 0.323 | ||||
| Sharpe ratio (Glass type estimate) | -0.717 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.711 | ||||
| df | 83.000 | ||||
| t | -1.897 | ||||
| p | 0.969 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.464 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.034 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.459 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.038 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.812 | ||||
| Upside Potential Ratio | 0.259 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.305 | ||||
| Upside SD | 0.162 | ||||
| Downside SD | 0.285 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.218 | ||||
| Mean of criterion | -0.231 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.323 | ||||
| Covariance | -0.003 | ||||
| r | -0.036 | ||||
| b (slope, estimate of beta) | -0.045 | ||||
| a (intercept, estimate of alpha) | -0.222 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.329 | ||||
| p(b) | 0.628 | ||||
| t(a) | -1.756 | ||||
| p(a) | 0.959 | ||||
| Lowerbound of 95% confidence interval for beta | -0.317 | ||||
| Upperbound of 95% confidence interval for beta | 0.227 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.473 | ||||
| Upperbound of 95% confidence interval for alpha | 0.029 | ||||
| Treynor index (mean / b) | 5.151 | ||||
| Jensen alpha (a) | -0.222 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.295 | ||||
| SD | 0.370 | ||||
| Sharpe ratio (Glass type estimate) | -0.795 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.788 | ||||
| df | 83.000 | ||||
| t | -2.104 | ||||
| p | 0.981 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.544 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.042 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.539 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.038 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.835 | ||||
| Upside Potential Ratio | 0.179 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.358 | ||||
| Upside SD | 0.135 | ||||
| Downside SD | 0.353 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.183 | ||||
| Mean of criterion | -0.295 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 0.370 | ||||
| Covariance | -0.003 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.044 | ||||
| a (intercept, estimate of alpha) | -0.287 | ||||
| Mean Square Error | 0.139 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.274 | ||||
| p(b) | 0.608 | ||||
| t(a) | -1.993 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.362 | ||||
| Upperbound of 95% confidence interval for beta | 0.274 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.573 | ||||
| Upperbound of 95% confidence interval for alpha | -0.001 | ||||
| Treynor index (mean / b) | 6.726 | ||||
| Jensen alpha (a) | -0.287 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.182 | ||||
| Expected Shortfall on VaR | 0.217 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.175 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.542 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.425 | ||||
| Mean of quarter 1 | 0.911 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 19.000 | ||||
| Percentage of outliers low | 0.226 | ||||
| Mean of outliers low | 0.901 | ||||
| Number of outliers high | 19.000 | ||||
| Percentage of outliers high | 0.226 | ||||
| Mean of outliers high | 1.030 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.279 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.188 | ||||
| VaR(95%) (regression method) | 0.052 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.847 | ||||
| Quartile 1 | 0.847 | ||||
| Median | 0.847 | ||||
| Quartile 3 | 0.847 | ||||
| Maximum | 0.847 | ||||
| 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) | -0.118 | ||||
| Compounded annual return (geometric extrapolation) | -0.222 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.262 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.023 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.422 | ||||
| SD | 1.538 | ||||
| Sharpe ratio (Glass type estimate) | 0.274 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.274 | ||||
| df | 1841.000 | ||||
| t | 0.727 | ||||
| p | 0.489 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.465 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.013 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.465 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.013 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.757 | ||||
| Upside Potential Ratio | 3.116 | ||||
| Upside part of mean | 1.735 | ||||
| Downside part of mean | -1.314 | ||||
| Upside SD | 1.434 | ||||
| Downside SD | 0.557 | ||||
| N nonnegative terms | 240.000 | ||||
| N negative terms | 1602.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1842.000 | ||||
| Mean of predictor | 0.327 | ||||
| Mean of criterion | 0.422 | ||||
| SD of predictor | 0.513 | ||||
| SD of criterion | 1.538 | ||||
| Covariance | -0.061 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.230 | ||||
| a (intercept, estimate of alpha) | 0.497 | ||||
| Mean Square Error | 2.353 | ||||
| DF error | 1840.000 | ||||
| t(b) | -3.302 | ||||
| p(b) | 0.538 | ||||
| t(a) | 0.858 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | -0.367 | ||||
| Upperbound of 95% confidence interval for beta | -0.093 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.639 | ||||
| Upperbound of 95% confidence interval for alpha | 1.632 | ||||
| Treynor index (mean / b) | -1.833 | ||||
| Jensen alpha (a) | 0.497 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.294 | ||||
| SD | 1.127 | ||||
| Sharpe ratio (Glass type estimate) | -0.260 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.260 | ||||
| df | 1841.000 | ||||
| t | -0.691 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.000 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.479 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.479 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.374 | ||||
| Upside Potential Ratio | 1.608 | ||||
| Upside part of mean | 1.261 | ||||
| Downside part of mean | -1.555 | ||||
| Upside SD | 0.809 | ||||
| Downside SD | 0.784 | ||||
| N nonnegative terms | 240.000 | ||||
| N negative terms | 1602.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1842.000 | ||||
| Mean of predictor | 0.195 | ||||
| Mean of criterion | -0.294 | ||||
| SD of predictor | 0.514 | ||||
| SD of criterion | 1.127 | ||||
| Covariance | -0.046 | ||||
| r | -0.080 | ||||
| b (slope, estimate of beta) | -0.175 | ||||
| a (intercept, estimate of alpha) | -0.259 | ||||
| Mean Square Error | 1.263 | ||||
| DF error | 1840.000 | ||||
| t(b) | -3.434 | ||||
| p(b) | 0.540 | ||||
| t(a) | -0.612 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | -0.275 | ||||
| Upperbound of 95% confidence interval for beta | -0.075 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.091 | ||||
| Upperbound of 95% confidence interval for alpha | 0.572 | ||||
| Treynor index (mean / b) | 1.678 | ||||
| Jensen alpha (a) | -0.259 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.109 | ||||
| Expected Shortfall on VaR | 0.134 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1842.000 | ||||
| Minimum | 0.358 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.540 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 313.000 | ||||
| Percentage of outliers low | 0.170 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 315.000 | ||||
| Percentage of outliers high | 0.171 | ||||
| Mean of outliers high | 1.039 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.900 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| 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 | 4.000 | ||||
| Minimum | 0.156 | ||||
| Quartile 1 | 0.572 | ||||
| Median | 0.711 | ||||
| Quartile 3 | 0.747 | ||||
| Maximum | 0.854 | ||||
| Mean of quarter 1 | 0.156 | ||||
| Mean of quarter 2 | 0.711 | ||||
| Mean of quarter 3 | 0.712 | ||||
| Mean of quarter 4 | 0.854 | ||||
| Inter Quartile Range | 0.175 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.250 | ||||
| Mean of outliers low | 0.156 | ||||
| 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) | -0.118 | ||||
| Compounded annual return (geometric extrapolation) | -0.221 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.259 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.259 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.642 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.099 | ||||
| SD | 0.101 | ||||
| Sharpe ratio (Glass type estimate) | 0.980 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.975 | ||||
| df | 130.000 | ||||
| t | 0.693 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.796 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.753 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.800 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.749 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 36.700 | ||||
| Upside Potential Ratio | 52.825 | ||||
| Upside part of mean | 0.143 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.188 | ||||
| Mean of criterion | 0.099 | ||||
| SD of predictor | 0.499 | ||||
| SD of criterion | 0.101 | ||||
| Covariance | -0.002 | ||||
| r | -0.046 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.111 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.526 | ||||
| p(b) | 0.529 | ||||
| t(a) | 0.761 | ||||
| p(a) | 0.457 | ||||
| Lowerbound of 95% confidence interval for beta | -0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.177 | ||||
| Upperbound of 95% confidence interval for alpha | 0.398 | ||||
| Treynor index (mean / b) | -10.553 | ||||
| Jensen alpha (a) | 0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.095 | ||||
| SD | 0.098 | ||||
| Sharpe ratio (Glass type estimate) | 0.965 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.959 | ||||
| df | 130.000 | ||||
| t | 0.682 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.811 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.737 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.815 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.734 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 34.892 | ||||
| Upside Potential Ratio | 51.016 | ||||
| Upside part of mean | 0.138 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.098 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 130.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.060 | ||||
| Mean of criterion | 0.095 | ||||
| SD of predictor | 0.504 | ||||
| SD of criterion | 0.098 | ||||
| Covariance | -0.002 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.104 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.508 | ||||
| p(b) | 0.528 | ||||
| t(a) | 0.740 | ||||
| p(a) | 0.459 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.173 | ||||
| Upperbound of 95% confidence interval for alpha | 0.381 | ||||
| Treynor index (mean / b) | -10.887 | ||||
| Jensen alpha (a) | 0.104 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| 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 | 1.072 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.072 | ||||
| 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) | 0.143 | ||||
| Compounded annual return (geometric extrapolation) | 0.149 | ||||
| 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 | 12.334 | ||||