Advanced Statistics: US Realized Income-Dividend System
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 | -0.790 | ||||
| SD | 0.748 | ||||
| Sharpe ratio (Glass type estimate) | -1.057 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.040 | ||||
| df | 45.000 | ||||
| t | -2.070 | ||||
| p | 0.978 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.076 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.027 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.063 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.064 | ||||
| Upside Potential Ratio | 0.354 | ||||
| Upside part of mean | 0.263 | ||||
| Downside part of mean | -1.054 | ||||
| Upside SD | 0.216 | ||||
| Downside SD | 0.743 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.399 | ||||
| Mean of criterion | -0.790 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.748 | ||||
| Covariance | 0.004 | ||||
| r | 0.020 | ||||
| b (slope, estimate of beta) | 0.055 | ||||
| a (intercept, estimate of alpha) | -0.812 | ||||
| Mean Square Error | 0.571 | ||||
| DF error | 44.000 | ||||
| t(b) | 0.134 | ||||
| p(b) | 0.447 | ||||
| t(a) | -1.938 | ||||
| p(a) | 0.970 | ||||
| Lowerbound of 95% confidence interval for beta | -0.769 | ||||
| Upperbound of 95% confidence interval for beta | 0.879 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.657 | ||||
| Upperbound of 95% confidence interval for alpha | 0.032 | ||||
| Treynor index (mean / b) | -14.386 | ||||
| Jensen alpha (a) | -0.812 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.867 | ||||
| SD | 4.052 | ||||
| Sharpe ratio (Glass type estimate) | -0.707 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.696 | ||||
| df | 45.000 | ||||
| t | -1.385 | ||||
| p | 0.914 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.715 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.308 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.707 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.316 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.701 | ||||
| Upside Potential Ratio | 0.059 | ||||
| Upside part of mean | 0.242 | ||||
| Downside part of mean | -3.109 | ||||
| Upside SD | 0.192 | ||||
| Downside SD | 4.087 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.360 | ||||
| Mean of criterion | -2.867 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 4.052 | ||||
| Covariance | 0.066 | ||||
| r | 0.067 | ||||
| b (slope, estimate of beta) | 1.109 | ||||
| a (intercept, estimate of alpha) | -3.266 | ||||
| Mean Square Error | 16.715 | ||||
| DF error | 44.000 | ||||
| t(b) | 0.443 | ||||
| p(b) | 0.330 | ||||
| t(a) | -1.436 | ||||
| p(a) | 0.921 | ||||
| Lowerbound of 95% confidence interval for beta | -3.942 | ||||
| Upperbound of 95% confidence interval for beta | 6.161 | ||||
| Lowerbound of 95% confidence interval for alpha | -7.851 | ||||
| Upperbound of 95% confidence interval for alpha | 1.319 | ||||
| Treynor index (mean / b) | -2.584 | ||||
| Jensen alpha (a) | -3.266 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.885 | ||||
| Expected Shortfall on VaR | 0.924 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.251 | ||||
| Expected Shortfall on VaR | 0.505 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.922 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 1.335 | ||||
| Mean of quarter 1 | 0.700 | ||||
| Mean of quarter 2 | 0.971 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.087 | ||||
| Inter Quartile Range | 0.092 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.087 | ||||
| Mean of outliers low | 0.356 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.264 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.689 | ||||
| VaR(95%) (moments method) | 0.317 | ||||
| Expected Shortfall (moments method) | 1.105 | ||||
| Extreme Value Index (regression method) | 0.683 | ||||
| VaR(95%) (regression method) | 0.228 | ||||
| Expected Shortfall (regression method) | 0.693 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.063 | ||||
| Quartile 3 | 0.331 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.107 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.316 | ||||
| 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) | -0.261 | ||||
| Compounded annual return (geometric extrapolation) | -0.941 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.941 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.941 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.018 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.371 | ||||
| SD | 1.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.351 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.351 | ||||
| df | 1012.000 | ||||
| t | -0.691 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.348 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.646 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.348 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.646 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.478 | ||||
| Upside Potential Ratio | 2.814 | ||||
| Upside part of mean | 2.186 | ||||
| Downside part of mean | -2.557 | ||||
| Upside SD | 0.714 | ||||
| Downside SD | 0.777 | ||||
| N nonnegative terms | 367.000 | ||||
| N negative terms | 646.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1013.000 | ||||
| Mean of predictor | 0.426 | ||||
| Mean of criterion | -0.371 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 1.056 | ||||
| Covariance | -0.068 | ||||
| r | -0.217 | ||||
| b (slope, estimate of beta) | -0.775 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 1.063 | ||||
| DF error | 1011.000 | ||||
| t(b) | -7.064 | ||||
| p(b) | 0.637 | ||||
| t(a) | -0.077 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.991 | ||||
| Upperbound of 95% confidence interval for beta | -0.560 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.992 | ||||
| Treynor index (mean / b) | 0.478 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.842 | ||||
| SD | 4.592 | ||||
| Sharpe ratio (Glass type estimate) | -0.619 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.618 | ||||
| df | 1012.000 | ||||
| t | -1.217 | ||||
| p | 0.519 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.616 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.378 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.616 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.379 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.624 | ||||
| Upside Potential Ratio | 0.438 | ||||
| Upside part of mean | 1.997 | ||||
| Downside part of mean | -4.840 | ||||
| Upside SD | 0.571 | ||||
| Downside SD | 4.558 | ||||
| N nonnegative terms | 367.000 | ||||
| N negative terms | 646.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1013.000 | ||||
| Mean of predictor | 0.382 | ||||
| Mean of criterion | -2.842 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 4.592 | ||||
| Covariance | -0.276 | ||||
| r | -0.203 | ||||
| b (slope, estimate of beta) | -3.147 | ||||
| a (intercept, estimate of alpha) | -1.640 | ||||
| Mean Square Error | 20.241 | ||||
| DF error | 1011.000 | ||||
| t(b) | -6.593 | ||||
| p(b) | 0.628 | ||||
| t(a) | -0.714 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -4.083 | ||||
| Upperbound of 95% confidence interval for beta | -2.210 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.144 | ||||
| Upperbound of 95% confidence interval for alpha | 2.864 | ||||
| Treynor index (mean / b) | 0.903 | ||||
| Jensen alpha (a) | -1.640 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.380 | ||||
| Expected Shortfall on VaR | 0.446 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.058 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1013.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.970 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 104.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.924 | ||||
| Number of outliers high | 87.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 1.079 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.905 | ||||
| VaR(95%) (moments method) | 0.029 | ||||
| Expected Shortfall (moments method) | 0.324 | ||||
| Extreme Value Index (regression method) | 0.682 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.094 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.013 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.300 | ||||
| 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 | 0.176 | ||||
| Mean of outliers high | 0.395 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.688 | ||||
| VaR(95%) (moments method) | 0.211 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.687 | ||||
| VaR(95%) (regression method) | 0.591 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.259 | ||||
| Compounded annual return (geometric extrapolation) | -0.939 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.939 | ||||
| Compounded annual return / average of 25% largest draw downs | -3.134 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.105 | ||||
| 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 | 1.449 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.528 | ||||
| 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 | 1.306 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.533 | ||||
| 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) | -8700021356553364.000 | ||||
| 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) | -1000060948748613447119019574296576.000 | ||||
| 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 | ||||