Advanced Statistics: System 28959109
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.027 | ||||
| SD | 0.370 | ||||
| Sharpe ratio (Glass type estimate) | -0.074 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.073 | ||||
| df | 72.000 | ||||
| t | -0.183 | ||||
| p | 0.572 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.869 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.721 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.868 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.721 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.113 | ||||
| Upside Potential Ratio | 0.659 | ||||
| Upside part of mean | 0.160 | ||||
| Downside part of mean | -0.188 | ||||
| Upside SD | 0.276 | ||||
| Downside SD | 0.243 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | -0.027 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.370 | ||||
| Covariance | -0.015 | ||||
| r | -0.145 | ||||
| b (slope, estimate of beta) | -0.195 | ||||
| a (intercept, estimate of alpha) | 0.024 | ||||
| Mean Square Error | 0.136 | ||||
| DF error | 71.000 | ||||
| t(b) | -1.234 | ||||
| p(b) | 0.889 | ||||
| t(a) | 0.152 | ||||
| p(a) | 0.440 | ||||
| Lowerbound of 95% confidence interval for beta | -0.510 | ||||
| Upperbound of 95% confidence interval for beta | 0.120 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.286 | ||||
| Upperbound of 95% confidence interval for alpha | 0.333 | ||||
| Treynor index (mean / b) | 0.141 | ||||
| Jensen alpha (a) | 0.024 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 0.410 | ||||
| Sharpe ratio (Glass type estimate) | -0.249 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.246 | ||||
| df | 72.000 | ||||
| t | -0.614 | ||||
| p | 0.729 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.044 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.548 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.042 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.549 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.298 | ||||
| Upside Potential Ratio | 0.383 | ||||
| Upside part of mean | 0.131 | ||||
| Downside part of mean | -0.234 | ||||
| Upside SD | 0.222 | ||||
| Downside SD | 0.343 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.220 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.410 | ||||
| Covariance | -0.015 | ||||
| r | -0.128 | ||||
| b (slope, estimate of beta) | -0.187 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.168 | ||||
| DF error | 71.000 | ||||
| t(b) | -1.083 | ||||
| p(b) | 0.859 | ||||
| t(a) | -0.357 | ||||
| p(a) | 0.639 | ||||
| Lowerbound of 95% confidence interval for beta | -0.532 | ||||
| Upperbound of 95% confidence interval for beta | 0.157 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.401 | ||||
| Upperbound of 95% confidence interval for alpha | 0.279 | ||||
| Treynor index (mean / b) | 0.545 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.184 | ||||
| Expected Shortfall on VaR | 0.223 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.446 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.593 | ||||
| Mean of quarter 1 | 0.953 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.055 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.096 | ||||
| Mean of outliers low | 0.873 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.164 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.065 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 1.214 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.130 | ||||
| Median | 0.252 | ||||
| Quartile 3 | 0.416 | ||||
| Maximum | 0.579 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.252 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.579 | ||||
| Inter Quartile Range | 0.286 | ||||
| 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) | -0.049 | ||||
| Compounded annual return (geometric extrapolation) | -0.056 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.097 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.097 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.254 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.101 | ||||
| SD | 0.634 | ||||
| Sharpe ratio (Glass type estimate) | 0.159 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.159 | ||||
| df | 1596.000 | ||||
| t | 0.393 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.635 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.953 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.635 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.953 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.247 | ||||
| Upside Potential Ratio | 2.521 | ||||
| Upside part of mean | 1.029 | ||||
| Downside part of mean | -0.929 | ||||
| Upside SD | 0.484 | ||||
| Downside SD | 0.408 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 1510.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1597.000 | ||||
| Mean of predictor | 0.385 | ||||
| Mean of criterion | 0.101 | ||||
| SD of predictor | 0.556 | ||||
| SD of criterion | 0.634 | ||||
| Covariance | -0.037 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.118 | ||||
| a (intercept, estimate of alpha) | 0.146 | ||||
| Mean Square Error | 0.397 | ||||
| DF error | 1595.000 | ||||
| t(b) | -4.174 | ||||
| p(b) | 0.566 | ||||
| t(a) | 0.573 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -0.174 | ||||
| Upperbound of 95% confidence interval for beta | -0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.355 | ||||
| Upperbound of 95% confidence interval for alpha | 0.648 | ||||
| Treynor index (mean / b) | -0.852 | ||||
| Jensen alpha (a) | 0.146 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 0.648 | ||||
| Sharpe ratio (Glass type estimate) | -0.158 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.157 | ||||
| df | 1596.000 | ||||
| t | -0.389 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.951 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.636 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.951 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.636 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.206 | ||||
| Upside Potential Ratio | 1.882 | ||||
| Upside part of mean | 0.934 | ||||
| Downside part of mean | -1.036 | ||||
| Upside SD | 0.416 | ||||
| Downside SD | 0.496 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 1510.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1597.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.554 | ||||
| SD of criterion | 0.648 | ||||
| Covariance | -0.037 | ||||
| r | -0.102 | ||||
| b (slope, estimate of beta) | -0.119 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.415 | ||||
| DF error | 1595.000 | ||||
| t(b) | -4.100 | ||||
| p(b) | 0.565 | ||||
| t(a) | -0.285 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.177 | ||||
| Upperbound of 95% confidence interval for beta | -0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.587 | ||||
| Upperbound of 95% confidence interval for alpha | 0.438 | ||||
| Treynor index (mean / b) | 0.854 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.064 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1597.000 | ||||
| Minimum | 0.462 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.615 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 97.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.944 | ||||
| Number of outliers high | 109.000 | ||||
| Percentage of outliers high | 0.068 | ||||
| Mean of outliers high | 1.058 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.609 | ||||
| VaR(95%) (moments method) | -0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.167 | ||||
| VaR(95%) (regression method) | -0.009 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.036 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.104 | ||||
| Quartile 3 | 0.324 | ||||
| Maximum | 0.618 | ||||
| Mean of quarter 1 | 0.046 | ||||
| Mean of quarter 2 | 0.070 | ||||
| Mean of quarter 3 | 0.139 | ||||
| Mean of quarter 4 | 0.502 | ||||
| Inter Quartile Range | 0.264 | ||||
| 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) | -0.049 | ||||
| Compounded annual return (geometric extrapolation) | -0.056 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.091 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.112 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.709 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.063 | ||||
| SD | 0.076 | ||||
| Sharpe ratio (Glass type estimate) | 0.835 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.830 | ||||
| df | 130.000 | ||||
| t | 0.590 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.940 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.607 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.944 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.604 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 23.417 | ||||
| Upside Potential Ratio | 39.542 | ||||
| Upside part of mean | 0.107 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.076 | ||||
| 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 | 1.050 | ||||
| Mean of criterion | 0.063 | ||||
| SD of predictor | 0.475 | ||||
| SD of criterion | 0.076 | ||||
| Covariance | -0.004 | ||||
| r | -0.121 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.084 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.387 | ||||
| p(b) | 0.577 | ||||
| t(a) | 0.775 | ||||
| p(a) | 0.457 | ||||
| Lowerbound of 95% confidence interval for beta | -0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.298 | ||||
| Treynor index (mean / b) | -3.271 | ||||
| Jensen alpha (a) | 0.084 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.061 | ||||
| SD | 0.074 | ||||
| Sharpe ratio (Glass type estimate) | 0.820 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.815 | ||||
| df | 130.000 | ||||
| t | 0.579 | ||||
| p | 0.475 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.956 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.592 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.959 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.588 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 22.392 | ||||
| Upside Potential Ratio | 38.516 | ||||
| Upside part of mean | 0.104 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.074 | ||||
| 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 | 0.934 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.481 | ||||
| SD of criterion | 0.074 | ||||
| Covariance | -0.004 | ||||
| r | -0.120 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.078 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.378 | ||||
| p(b) | 0.576 | ||||
| t(a) | 0.742 | ||||
| p(a) | 0.459 | ||||
| Lowerbound of 95% confidence interval for beta | -0.045 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.286 | ||||
| Treynor index (mean / b) | -3.271 | ||||
| Jensen alpha (a) | 0.078 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| 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 | 1.054 | ||||
| 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 | 1.054 | ||||
| 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) | 0.107 | ||||
| Compounded annual return (geometric extrapolation) | 0.110 | ||||
| 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 | 12.051 | ||||