Advanced Statistics: System 25480083
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 | -0.126 | ||||
| SD | 0.184 | ||||
| Sharpe ratio (Glass type estimate) | -0.686 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.680 | ||||
| df | 78.000 | ||||
| t | -1.761 | ||||
| p | 0.959 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.456 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.087 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.451 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.091 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.770 | ||||
| Upside Potential Ratio | 0.272 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.171 | ||||
| Upside SD | 0.089 | ||||
| Downside SD | 0.164 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 79.000 | ||||
| Mean of predictor | 0.235 | ||||
| Mean of criterion | -0.126 | ||||
| SD of predictor | 0.348 | ||||
| SD of criterion | 0.184 | ||||
| Covariance | -0.003 | ||||
| r | -0.055 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | -0.120 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 77.000 | ||||
| t(b) | -0.479 | ||||
| p(b) | 0.683 | ||||
| t(a) | -1.628 | ||||
| p(a) | 0.946 | ||||
| Lowerbound of 95% confidence interval for beta | -0.149 | ||||
| Upperbound of 95% confidence interval for beta | 0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.266 | ||||
| Upperbound of 95% confidence interval for alpha | 0.027 | ||||
| Treynor index (mean / b) | 4.376 | ||||
| Jensen alpha (a) | -0.120 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.145 | ||||
| SD | 0.199 | ||||
| Sharpe ratio (Glass type estimate) | -0.730 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.723 | ||||
| df | 78.000 | ||||
| t | -1.874 | ||||
| p | 0.968 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.501 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.044 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.496 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.049 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.784 | ||||
| Upside Potential Ratio | 0.221 | ||||
| Upside part of mean | 0.041 | ||||
| Downside part of mean | -0.186 | ||||
| Upside SD | 0.081 | ||||
| Downside SD | 0.185 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 79.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | -0.145 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.199 | ||||
| Covariance | -0.004 | ||||
| r | -0.058 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | -0.139 | ||||
| Mean Square Error | 0.040 | ||||
| DF error | 77.000 | ||||
| t(b) | -0.511 | ||||
| p(b) | 0.695 | ||||
| t(a) | -1.762 | ||||
| p(a) | 0.959 | ||||
| Lowerbound of 95% confidence interval for beta | -0.174 | ||||
| Upperbound of 95% confidence interval for beta | 0.103 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.296 | ||||
| Upperbound of 95% confidence interval for alpha | 0.018 | ||||
| Treynor index (mean / b) | 4.086 | ||||
| Jensen alpha (a) | -0.139 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.101 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.103 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 79.000 | ||||
| Minimum | 0.743 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.216 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.089 | ||||
| Mean of outliers low | 0.879 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.051 | ||||
| Mean of outliers high | 1.075 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -53.553 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -1.428 | ||||
| VaR(95%) (regression method) | 0.104 | ||||
| Expected Shortfall (regression method) | 0.182 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.578 | ||||
| Quartile 1 | 0.578 | ||||
| Median | 0.578 | ||||
| Quartile 3 | 0.578 | ||||
| Maximum | 0.578 | ||||
| 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) | -0.074 | ||||
| Compounded annual return (geometric extrapolation) | -0.096 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.167 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.788 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.602 | ||||
| Sharpe ratio (Glass type estimate) | -0.004 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.004 | ||||
| df | 1741.000 | ||||
| t | -0.010 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.764 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.756 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.764 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.756 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.008 | ||||
| Upside Potential Ratio | 2.341 | ||||
| Upside part of mean | 0.685 | ||||
| Downside part of mean | -0.687 | ||||
| Upside SD | 0.525 | ||||
| Downside SD | 0.293 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 1691.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1742.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.599 | ||||
| SD of criterion | 0.602 | ||||
| Covariance | -0.017 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.047 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.361 | ||||
| DF error | 1740.000 | ||||
| t(b) | -1.969 | ||||
| p(b) | 0.524 | ||||
| t(a) | 0.065 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.094 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.442 | ||||
| Upperbound of 95% confidence interval for alpha | 0.473 | ||||
| Treynor index (mean / b) | 0.051 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.144 | ||||
| SD | 0.510 | ||||
| Sharpe ratio (Glass type estimate) | -0.283 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.283 | ||||
| df | 1741.000 | ||||
| t | -0.730 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.043 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.477 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.043 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.477 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.443 | ||||
| Upside Potential Ratio | 1.820 | ||||
| Upside part of mean | 0.592 | ||||
| Downside part of mean | -0.737 | ||||
| Upside SD | 0.392 | ||||
| Downside SD | 0.326 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 1691.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1742.000 | ||||
| Mean of predictor | 0.200 | ||||
| Mean of criterion | -0.144 | ||||
| SD of predictor | 0.584 | ||||
| SD of criterion | 0.510 | ||||
| Covariance | -0.013 | ||||
| r | -0.043 | ||||
| b (slope, estimate of beta) | -0.037 | ||||
| a (intercept, estimate of alpha) | -0.137 | ||||
| Mean Square Error | 0.259 | ||||
| DF error | 1740.000 | ||||
| t(b) | -1.787 | ||||
| p(b) | 0.521 | ||||
| t(a) | -0.693 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.524 | ||||
| Upperbound of 95% confidence interval for alpha | 0.251 | ||||
| Treynor index (mean / b) | 3.864 | ||||
| Jensen alpha (a) | -0.137 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1742.000 | ||||
| Minimum | 0.672 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.118 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 84.000 | ||||
| Percentage of outliers low | 0.048 | ||||
| Mean of outliers low | 0.949 | ||||
| Number of outliers high | 78.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 1.059 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -7.101 | ||||
| VaR(95%) (moments method) | -0.127 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.181 | ||||
| VaR(95%) (regression method) | -0.027 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.073 | ||||
| Quartile 1 | 0.191 | ||||
| Median | 0.279 | ||||
| Quartile 3 | 0.434 | ||||
| Maximum | 0.754 | ||||
| Mean of quarter 1 | 0.073 | ||||
| Mean of quarter 2 | 0.230 | ||||
| Mean of quarter 3 | 0.328 | ||||
| Mean of quarter 4 | 0.754 | ||||
| Inter Quartile Range | 0.243 | ||||
| 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) | -0.073 | ||||
| Compounded annual return (geometric extrapolation) | -0.095 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.126 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.126 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.506 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.133 | ||||
| SD | 0.063 | ||||
| Sharpe ratio (Glass type estimate) | -2.111 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.098 | ||||
| df | 130.000 | ||||
| t | -1.492 | ||||
| p | 0.565 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.890 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.677 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.882 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.685 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.101 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.064 | ||||
| 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 | 0.957 | ||||
| Mean of criterion | -0.133 | ||||
| SD of predictor | 0.429 | ||||
| SD of criterion | 0.063 | ||||
| Covariance | 0.002 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.143 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.764 | ||||
| p(b) | 0.457 | ||||
| t(a) | -1.581 | ||||
| p(a) | 0.587 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.322 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -13.475 | ||||
| Jensen alpha (a) | -0.143 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.135 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | -2.095 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.083 | ||||
| df | 130.000 | ||||
| t | -1.481 | ||||
| p | 0.564 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.874 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.692 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.866 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.701 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.085 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.135 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.065 | ||||
| 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 | 0.864 | ||||
| Mean of criterion | -0.135 | ||||
| SD of predictor | 0.430 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | 0.002 | ||||
| r | 0.066 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.144 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.754 | ||||
| p(b) | 0.458 | ||||
| t(a) | -1.561 | ||||
| p(a) | 0.586 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.327 | ||||
| Upperbound of 95% confidence interval for alpha | 0.039 | ||||
| Treynor index (mean / b) | -13.604 | ||||
| Jensen alpha (a) | -0.144 | ||||
| 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%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.955 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.955 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.045 | ||||
| Quartile 1 | 0.045 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.045 | ||||
| Maximum | 0.045 | ||||
| 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) | -0.089 | ||||
| Compounded annual return (geometric extrapolation) | -0.087 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.955 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -10.024 | ||||