Advanced Statistics: System 69789319
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 | -0.665 | ||||
| SD | 0.758 | ||||
| Sharpe ratio (Glass type estimate) | -0.877 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.858 | ||||
| df | 36.000 | ||||
| t | -1.540 | ||||
| p | 0.934 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.005 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.263 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.992 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.275 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.889 | ||||
| Upside Potential Ratio | 0.146 | ||||
| Upside part of mean | 0.109 | ||||
| Downside part of mean | -0.774 | ||||
| Upside SD | 0.192 | ||||
| Downside SD | 0.748 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -0.665 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.758 | ||||
| Covariance | 0.021 | ||||
| r | 0.092 | ||||
| b (slope, estimate of beta) | 0.235 | ||||
| a (intercept, estimate of alpha) | -0.801 | ||||
| Mean Square Error | 0.586 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.549 | ||||
| p(b) | 0.293 | ||||
| t(a) | -1.597 | ||||
| p(a) | 0.940 | ||||
| Lowerbound of 95% confidence interval for beta | -0.634 | ||||
| Upperbound of 95% confidence interval for beta | 1.105 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.819 | ||||
| Upperbound of 95% confidence interval for alpha | 0.217 | ||||
| Treynor index (mean / b) | -2.825 | ||||
| Jensen alpha (a) | -0.801 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.518 | ||||
| SD | 6.954 | ||||
| Sharpe ratio (Glass type estimate) | -0.650 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.636 | ||||
| df | 36.000 | ||||
| t | -1.141 | ||||
| p | 0.869 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.771 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.481 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.762 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.490 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.647 | ||||
| Upside Potential Ratio | 0.013 | ||||
| Upside part of mean | 0.094 | ||||
| Downside part of mean | -4.612 | ||||
| Upside SD | 0.165 | ||||
| Downside SD | 6.981 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.525 | ||||
| Mean of criterion | -4.518 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 6.954 | ||||
| Covariance | 0.088 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 1.125 | ||||
| a (intercept, estimate of alpha) | -5.108 | ||||
| Mean Square Error | 49.642 | ||||
| DF error | 35.000 | ||||
| t(b) | 0.268 | ||||
| p(b) | 0.395 | ||||
| t(a) | -1.116 | ||||
| p(a) | 0.864 | ||||
| Lowerbound of 95% confidence interval for beta | -7.406 | ||||
| Upperbound of 95% confidence interval for beta | 9.656 | ||||
| Lowerbound of 95% confidence interval for alpha | -14.403 | ||||
| Upperbound of 95% confidence interval for alpha | 4.186 | ||||
| Treynor index (mean / b) | -4.017 | ||||
| Jensen alpha (a) | -5.108 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.975 | ||||
| Expected Shortfall on VaR | 0.987 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.221 | ||||
| Expected Shortfall on VaR | 0.467 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.340 | ||||
| Mean of quarter 1 | 0.775 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.135 | ||||
| Mean of outliers low | 0.549 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 1.340 | ||||
| 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) | 0.494 | ||||
| VaR(95%) (regression method) | 0.322 | ||||
| Expected Shortfall (regression method) | 1.049 | ||||
| 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) | -0.324 | ||||
| Compounded annual return (geometric extrapolation) | -0.989 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.989 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.002 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.039 | ||||
| SD | 1.317 | ||||
| Sharpe ratio (Glass type estimate) | -0.030 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.030 | ||||
| df | 807.000 | ||||
| t | -0.052 | ||||
| p | 0.521 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.146 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.086 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.146 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.086 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.052 | ||||
| Upside Potential Ratio | 2.361 | ||||
| Upside part of mean | 1.774 | ||||
| Downside part of mean | -1.813 | ||||
| Upside SD | 1.081 | ||||
| Downside SD | 0.752 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 756.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 808.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 1.317 | ||||
| Covariance | -0.003 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 1.737 | ||||
| DF error | 806.000 | ||||
| t(b) | -0.228 | ||||
| p(b) | 0.590 | ||||
| t(a) | -0.027 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.315 | ||||
| Upperbound of 95% confidence interval for beta | 0.249 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.502 | ||||
| Upperbound of 95% confidence interval for alpha | 1.462 | ||||
| Treynor index (mean / b) | 1.191 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.517 | ||||
| SD | 7.676 | ||||
| Sharpe ratio (Glass type estimate) | -0.589 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.588 | ||||
| df | 807.000 | ||||
| t | -1.034 | ||||
| p | 0.849 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.705 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.528 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.704 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.528 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.591 | ||||
| Upside Potential Ratio | 0.191 | ||||
| Upside part of mean | 1.460 | ||||
| Downside part of mean | -5.978 | ||||
| Upside SD | 0.686 | ||||
| Downside SD | 7.645 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 756.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 808.000 | ||||
| Mean of predictor | 0.525 | ||||
| Mean of criterion | -4.517 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 7.676 | ||||
| Covariance | 0.076 | ||||
| r | 0.030 | ||||
| b (slope, estimate of beta) | 0.714 | ||||
| a (intercept, estimate of alpha) | -4.892 | ||||
| Mean Square Error | 58.933 | ||||
| DF error | 806.000 | ||||
| t(b) | 0.859 | ||||
| p(b) | 0.195 | ||||
| t(a) | -1.113 | ||||
| p(a) | 0.867 | ||||
| Lowerbound of 95% confidence interval for beta | -0.916 | ||||
| Upperbound of 95% confidence interval for beta | 2.343 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.515 | ||||
| Upperbound of 95% confidence interval for alpha | 3.732 | ||||
| Treynor index (mean / b) | -6.330 | ||||
| Jensen alpha (a) | -4.892 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.549 | ||||
| Expected Shortfall on VaR | 0.625 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 808.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.764 | ||||
| Mean of quarter 1 | 0.973 | ||||
| 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 | 61.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.910 | ||||
| Number of outliers high | 52.000 | ||||
| Percentage of outliers high | 0.064 | ||||
| Mean of outliers high | 1.105 | ||||
| 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) | 0.442 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.100 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.258 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.255 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | -0.324 | ||||
| Compounded annual return (geometric extrapolation) | -0.989 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.989 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.989 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.582 | ||||
| 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 | 1.085 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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) | -8736262344084037.000 | ||||
| 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) | 505978266275397561495468820660224.000 | ||||
| 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 | ||||