Advanced Statistics: RR_AMCH
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 | 0.166 | ||||
| SD | 0.306 | ||||
| Sharpe ratio (Glass type estimate) | 0.542 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.531 | ||||
| df | 38.000 | ||||
| t | 0.977 | ||||
| p | 0.167 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.556 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.632 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.563 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.625 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.508 | ||||
| Upside Potential Ratio | 2.530 | ||||
| Upside part of mean | 0.279 | ||||
| Downside part of mean | -0.113 | ||||
| Upside SD | 0.286 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.504 | ||||
| Mean of criterion | 0.166 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 0.306 | ||||
| Covariance | -0.036 | ||||
| r | -0.444 | ||||
| b (slope, estimate of beta) | -0.514 | ||||
| a (intercept, estimate of alpha) | 0.425 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 37.000 | ||||
| t(b) | -3.015 | ||||
| p(b) | 0.998 | ||||
| t(a) | 2.407 | ||||
| p(a) | 0.011 | ||||
| Lowerbound of 95% confidence interval for beta | -0.860 | ||||
| Upperbound of 95% confidence interval for beta | -0.169 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.067 | ||||
| Upperbound of 95% confidence interval for alpha | 0.783 | ||||
| Treynor index (mean / b) | -0.323 | ||||
| Jensen alpha (a) | 0.425 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.125 | ||||
| SD | 0.275 | ||||
| Sharpe ratio (Glass type estimate) | 0.456 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.447 | ||||
| df | 38.000 | ||||
| t | 0.823 | ||||
| p | 0.208 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.639 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.545 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.645 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.539 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.039 | ||||
| Upside Potential Ratio | 2.025 | ||||
| Upside part of mean | 0.244 | ||||
| Downside part of mean | -0.119 | ||||
| Upside SD | 0.245 | ||||
| Downside SD | 0.121 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.461 | ||||
| Mean of criterion | 0.125 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.275 | ||||
| Covariance | -0.032 | ||||
| r | -0.462 | ||||
| b (slope, estimate of beta) | -0.505 | ||||
| a (intercept, estimate of alpha) | 0.358 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 37.000 | ||||
| t(b) | -3.167 | ||||
| p(b) | 0.998 | ||||
| t(a) | 2.304 | ||||
| p(a) | 0.013 | ||||
| Lowerbound of 95% confidence interval for beta | -0.828 | ||||
| Upperbound of 95% confidence interval for beta | -0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.043 | ||||
| Upperbound of 95% confidence interval for alpha | 0.673 | ||||
| Treynor index (mean / b) | -0.248 | ||||
| Jensen alpha (a) | 0.358 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.113 | ||||
| Expected Shortfall on VaR | 0.142 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.064 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.816 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.386 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.092 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.051 | ||||
| Mean of outliers low | 0.880 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.154 | ||||
| Mean of outliers high | 1.154 | ||||
| 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) | 0.180 | ||||
| VaR(95%) (regression method) | 0.044 | ||||
| Expected Shortfall (regression method) | 0.182 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.056 | ||||
| Quartile 1 | 0.088 | ||||
| Median | 0.120 | ||||
| Quartile 3 | 0.152 | ||||
| Maximum | 0.184 | ||||
| Mean of quarter 1 | 0.056 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.184 | ||||
| Inter Quartile Range | 0.064 | ||||
| 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) | 0.226 | ||||
| Compounded annual return (geometric extrapolation) | 0.185 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.001 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.303 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.149 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | 0.623 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.623 | ||||
| df | 859.000 | ||||
| t | 1.129 | ||||
| p | 0.130 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.459 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.460 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.705 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.408 | ||||
| Upside Potential Ratio | 4.012 | ||||
| Upside part of mean | 0.425 | ||||
| Downside part of mean | -0.276 | ||||
| Upside SD | 0.215 | ||||
| Downside SD | 0.106 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 801.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | 0.149 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | -0.008 | ||||
| r | -0.088 | ||||
| b (slope, estimate of beta) | -0.058 | ||||
| a (intercept, estimate of alpha) | 0.181 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 858.000 | ||||
| t(b) | -2.576 | ||||
| p(b) | 0.995 | ||||
| t(a) | 1.366 | ||||
| p(a) | 0.086 | ||||
| Lowerbound of 95% confidence interval for beta | -0.102 | ||||
| Upperbound of 95% confidence interval for beta | -0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.440 | ||||
| Treynor index (mean / b) | -2.577 | ||||
| Jensen alpha (a) | 0.181 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.124 | ||||
| SD | 0.220 | ||||
| Sharpe ratio (Glass type estimate) | 0.562 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.562 | ||||
| df | 859.000 | ||||
| t | 1.019 | ||||
| p | 0.154 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.520 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.644 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.520 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.644 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.123 | ||||
| Upside Potential Ratio | 3.682 | ||||
| Upside part of mean | 0.405 | ||||
| Downside part of mean | -0.282 | ||||
| Upside SD | 0.190 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 801.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 860.000 | ||||
| Mean of predictor | 0.476 | ||||
| Mean of criterion | 0.124 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.220 | ||||
| Covariance | -0.007 | ||||
| r | -0.082 | ||||
| b (slope, estimate of beta) | -0.048 | ||||
| a (intercept, estimate of alpha) | 0.146 | ||||
| Mean Square Error | 0.048 | ||||
| DF error | 858.000 | ||||
| t(b) | -2.398 | ||||
| p(b) | 0.992 | ||||
| t(a) | 1.206 | ||||
| p(a) | 0.114 | ||||
| Lowerbound of 95% confidence interval for beta | -0.087 | ||||
| Upperbound of 95% confidence interval for beta | -0.009 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.385 | ||||
| Treynor index (mean / b) | -2.588 | ||||
| Jensen alpha (a) | 0.146 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 860.000 | ||||
| Minimum | 0.880 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.345 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 36.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 61.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 1.023 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.352 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.140 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.020 | ||||
| Quartile 1 | 0.042 | ||||
| Median | 0.060 | ||||
| Quartile 3 | 0.096 | ||||
| Maximum | 0.203 | ||||
| Mean of quarter 1 | 0.030 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | 0.076 | ||||
| Mean of quarter 4 | 0.153 | ||||
| Inter Quartile Range | 0.054 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.203 | ||||
| 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) | 0.224 | ||||
| Compounded annual return (geometric extrapolation) | 0.183 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.898 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.194 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.721 | ||||
| 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 | 0.985 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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 | 0.867 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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) | -8746139490452362.000 | ||||
| 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) | -76205151824596236190898716672000.000 | ||||
| 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 | ||||