Advanced Statistics: LBTI
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 | -0.046 | ||||
| SD | 0.059 | ||||
| Sharpe ratio (Glass type estimate) | -0.786 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.776 | ||||
| df | 59.000 | ||||
| t | -1.758 | ||||
| p | 0.958 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.671 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.105 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.664 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.111 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.215 | ||||
| Upside Potential Ratio | 0.542 | ||||
| Upside part of mean | 0.021 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.015 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.059 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 58.000 | ||||
| t(b) | -0.012 | ||||
| p(b) | 0.505 | ||||
| t(a) | -1.743 | ||||
| p(a) | 0.957 | ||||
| Lowerbound of 95% confidence interval for beta | -0.063 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.007 | ||||
| Treynor index (mean / b) | 127.902 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.048 | ||||
| SD | 0.057 | ||||
| Sharpe ratio (Glass type estimate) | -0.832 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.821 | ||||
| df | 59.000 | ||||
| t | -1.860 | ||||
| p | 0.966 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.718 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.061 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.710 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.068 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.225 | ||||
| Upside Potential Ratio | 0.502 | ||||
| Upside part of mean | 0.020 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | -0.017 | ||||
| Mean of criterion | -0.048 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.057 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 58.000 | ||||
| t(b) | -0.028 | ||||
| p(b) | 0.511 | ||||
| t(a) | -1.844 | ||||
| p(a) | 0.965 | ||||
| Lowerbound of 95% confidence interval for beta | -0.059 | ||||
| Upperbound of 95% confidence interval for beta | 0.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | 59.302 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.933 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.083 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -27.415 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.148 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.040 | ||||
| Median | 0.058 | ||||
| Quartile 3 | 0.076 | ||||
| Maximum | 0.094 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.094 | ||||
| Inter Quartile Range | 0.036 | ||||
| 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) | -0.004 | ||||
| Compounded annual return (geometric extrapolation) | -0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.040 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.040 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.100 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -0.754 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.754 | ||||
| df | 1727.000 | ||||
| t | -1.690 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.629 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.121 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.628 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.121 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.098 | ||||
| Upside Potential Ratio | 2.365 | ||||
| Upside part of mean | 0.099 | ||||
| Downside part of mean | -0.145 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 42.000 | ||||
| N negative terms | 1686.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1728.000 | ||||
| Mean of predictor | 0.036 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1726.000 | ||||
| t(b) | -0.065 | ||||
| p(b) | 0.501 | ||||
| t(a) | -1.689 | ||||
| p(a) | 0.520 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.007 | ||||
| Treynor index (mean / b) | 130.842 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.048 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -0.786 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.785 | ||||
| df | 1727.000 | ||||
| t | -1.761 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.660 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.089 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.660 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.090 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.130 | ||||
| Upside Potential Ratio | 2.316 | ||||
| Upside part of mean | 0.098 | ||||
| Downside part of mean | -0.146 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 42.000 | ||||
| N negative terms | 1686.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1728.000 | ||||
| Mean of predictor | -0.000 | ||||
| Mean of criterion | -0.048 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1726.000 | ||||
| t(b) | -0.071 | ||||
| p(b) | 0.501 | ||||
| t(a) | -1.760 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.101 | ||||
| Upperbound of 95% confidence interval for alpha | 0.005 | ||||
| Treynor index (mean / b) | 123.841 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1728.000 | ||||
| Minimum | 0.964 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.044 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 77.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 74.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.549 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.143 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.042 | ||||
| Maximum | 0.119 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.090 | ||||
| Inter Quartile Range | 0.024 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.119 | ||||
| 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) | -0.004 | ||||
| Compounded annual return (geometric extrapolation) | -0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.031 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.042 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.542 | ||||
| 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) | -3053.384 | ||||
| Sharpe ratio (Hedges UMVUE) | -3039.973 | ||||
| df | 171.000 | ||||
| t | -2159.069 | ||||
| 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) | -3362.169 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2717.776 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.653 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.063 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 170.000 | ||||
| t(b) | -0.822 | ||||
| p(b) | 0.531 | ||||
| t(a) | -2138.079 | ||||
| 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) | 12868.145 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -3053.204 | ||||
| Sharpe ratio (Hedges UMVUE) | -3039.794 | ||||
| df | 171.000 | ||||
| t | -2158.942 | ||||
| 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) | -3361.971 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2717.616 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.617 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.063 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 170.000 | ||||
| t(b) | -0.821 | ||||
| p(b) | 0.531 | ||||
| t(a) | -2139.808 | ||||
| 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) | 12845.497 | ||||
| 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 | 172.000 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.006 | ||||
| Mean of outliers high | 1.000 | ||||
| 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 | 0.157 | ||||
