Advanced Statistics: ALWA
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 | -0.002 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -0.070 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.070 | ||||
| df | 60.000 | ||||
| t | -0.159 | ||||
| p | 0.563 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.940 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.799 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.939 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.800 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.181 | ||||
| Upside Potential Ratio | 2.938 | ||||
| Upside part of mean | 0.033 | ||||
| Downside part of mean | -0.036 | ||||
| Upside SD | 0.027 | ||||
| Downside SD | 0.011 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.443 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | -0.000 | ||||
| r | -0.041 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | 0.000 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.313 | ||||
| p(b) | 0.622 | ||||
| t(a) | 0.013 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.030 | ||||
| Upperbound of 95% confidence interval for alpha | 0.030 | ||||
| Treynor index (mean / b) | 0.405 | ||||
| Jensen alpha (a) | 0.000 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -0.085 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.084 | ||||
| df | 60.000 | ||||
| t | -0.193 | ||||
| p | 0.576 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.955 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.784 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.954 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.785 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.217 | ||||
| Upside Potential Ratio | 2.902 | ||||
| Upside part of mean | 0.033 | ||||
| Downside part of mean | -0.035 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.011 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.408 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | -0.000 | ||||
| r | -0.031 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.236 | ||||
| p(b) | 0.593 | ||||
| t(a) | -0.059 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | -0.037 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.030 | ||||
| Upperbound of 95% confidence interval for alpha | 0.028 | ||||
| Treynor index (mean / b) | 0.625 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.041 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 1.000 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.230 | ||||
| Mean of outliers high | 1.015 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.000 | ||||
| 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 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) | 0.046 | ||||
| Compounded annual return (geometric extrapolation) | 0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | 85.148 | ||||
| Compounded annual return / average of 25% largest draw downs | 85.148 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.466 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.001 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.022 | ||||
| df | 1334.000 | ||||
| t | -0.049 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.890 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.890 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.846 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.033 | ||||
| Upside Potential Ratio | 3.629 | ||||
| Upside part of mean | 0.126 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 149.000 | ||||
| N negative terms | 1186.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1335.000 | ||||
| Mean of predictor | 0.474 | ||||
| Mean of criterion | -0.001 | ||||
| SD of predictor | 0.353 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.005 | ||||
| r | 0.263 | ||||
| b (slope, estimate of beta) | 0.040 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1333.000 | ||||
| t(b) | 9.944 | ||||
| p(b) | 0.335 | ||||
| t(a) | -0.875 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | 0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.047 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | 0.025 | ||||
| Treynor index (mean / b) | -0.029 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.003 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.048 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.048 | ||||
| df | 1334.000 | ||||
| t | -0.109 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.917 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.820 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.917 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.820 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.073 | ||||
| Upside Potential Ratio | 3.566 | ||||
| Upside part of mean | 0.125 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 149.000 | ||||
| N negative terms | 1186.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1335.000 | ||||
| Mean of predictor | 0.412 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.005 | ||||
| r | 0.261 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1333.000 | ||||
| t(b) | 9.876 | ||||
| p(b) | 0.336 | ||||
| t(a) | -0.828 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | 0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.047 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.063 | ||||
| Upperbound of 95% confidence interval for alpha | 0.026 | ||||
| Treynor index (mean / b) | -0.065 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1335.000 | ||||
| Minimum | 0.962 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 128.000 | ||||
| Percentage of outliers low | 0.096 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 183.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.811 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| 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 | 43.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.010 | ||||
| Maximum | 0.038 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.019 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 0.030 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.036 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.025 | ||||
| Extreme Value Index (regression method) | -0.170 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.029 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.046 | ||||
| Compounded annual return (geometric extrapolation) | 0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.120 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.255 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.284 | ||||
| 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 | 1.246 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.367 | ||||
| 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 | 1.176 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.367 | ||||
| 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) | -8630849152872847.000 | ||||
| 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) | 53907710588621284209882447216640.000 | ||||
| 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 | ||||