Advanced Statistics: YM Superior
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 | 0.217 | ||||
| SD | 0.859 | ||||
| Sharpe ratio (Glass type estimate) | 0.253 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.251 | ||||
| df | 93.000 | ||||
| t | 0.709 | ||||
| p | 0.240 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.449 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.954 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.450 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.952 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.011 | ||||
| Upside Potential Ratio | 1.858 | ||||
| Upside part of mean | 0.399 | ||||
| Downside part of mean | -0.182 | ||||
| Upside SD | 0.829 | ||||
| Downside SD | 0.215 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 89.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 94.000 | ||||
| Mean of predictor | 0.115 | ||||
| Mean of criterion | 0.217 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.859 | ||||
| Covariance | -0.031 | ||||
| r | -0.160 | ||||
| b (slope, estimate of beta) | -0.619 | ||||
| a (intercept, estimate of alpha) | 0.288 | ||||
| Mean Square Error | 0.726 | ||||
| DF error | 92.000 | ||||
| t(b) | -1.559 | ||||
| p(b) | 0.939 | ||||
| t(a) | 0.936 | ||||
| p(a) | 0.176 | ||||
| Lowerbound of 95% confidence interval for beta | -1.407 | ||||
| Upperbound of 95% confidence interval for beta | 0.169 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.323 | ||||
| Upperbound of 95% confidence interval for alpha | 0.900 | ||||
| Treynor index (mean / b) | -0.351 | ||||
| Jensen alpha (a) | 0.288 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.036 | ||||
| SD | 0.526 | ||||
| Sharpe ratio (Glass type estimate) | 0.068 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.067 | ||||
| df | 93.000 | ||||
| t | 0.189 | ||||
| p | 0.425 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.633 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.768 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.633 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.767 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.130 | ||||
| Upside Potential Ratio | 0.912 | ||||
| Upside part of mean | 0.248 | ||||
| Downside part of mean | -0.213 | ||||
| Upside SD | 0.447 | ||||
| Downside SD | 0.272 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 89.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 94.000 | ||||
| Mean of predictor | 0.089 | ||||
| Mean of criterion | 0.036 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.526 | ||||
| Covariance | -0.020 | ||||
| r | -0.173 | ||||
| b (slope, estimate of beta) | -0.409 | ||||
| a (intercept, estimate of alpha) | 0.072 | ||||
| Mean Square Error | 0.271 | ||||
| DF error | 92.000 | ||||
| t(b) | -1.686 | ||||
| p(b) | 0.952 | ||||
| t(a) | 0.384 | ||||
| p(a) | 0.351 | ||||
| Lowerbound of 95% confidence interval for beta | -0.890 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.300 | ||||
| Upperbound of 95% confidence interval for alpha | 0.444 | ||||
| Treynor index (mean / b) | -0.087 | ||||
| Jensen alpha (a) | 0.072 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.219 | ||||
| Expected Shortfall on VaR | 0.266 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.111 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 94.000 | ||||
| Minimum | 0.533 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.278 | ||||
| Mean of quarter 1 | 0.954 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.131 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.780 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.629 | ||||
| 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) | -0.006 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.207 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.172 | ||||
| Median | 0.329 | ||||
| Quartile 3 | 0.467 | ||||
| Maximum | 0.604 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.329 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.604 | ||||
| Inter Quartile Range | 0.295 | ||||
| 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) | 0.110 | ||||
| Compounded annual return (geometric extrapolation) | 0.083 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.137 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.137 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.312 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.678 | ||||
| SD | 2.532 | ||||
| Sharpe ratio (Glass type estimate) | 0.663 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.662 | ||||
| df | 2067.000 | ||||
| t | 1.862 | ||||
| p | 0.031 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.035 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.361 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.035 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.360 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.170 | ||||
| Upside Potential Ratio | 4.405 | ||||
| Upside part of mean | 3.406 | ||||
| Downside part of mean | -1.728 | ||||
| Upside SD | 2.412 | ||||
| Downside SD | 0.773 | ||||
| N nonnegative terms | 83.000 | ||||
| N negative terms | 1985.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2068.000 | ||||
| Mean of predictor | 0.212 | ||||
| Mean of criterion | 1.678 | ||||
| SD of predictor | 0.521 | ||||
| SD of criterion | 2.532 | ||||
| Covariance | -0.192 | ||||
| r | -0.145 | ||||
| b (slope, estimate of beta) | -0.707 | ||||
| a (intercept, estimate of alpha) | 1.828 | ||||
| Mean Square Error | 6.277 | ||||
| DF error | 2066.000 | ||||
| t(b) | -6.683 | ||||
| p(b) | 1.000 | ||||
| t(a) | 2.049 | ||||
| p(a) | 0.020 | ||||
| Lowerbound of 95% confidence interval for beta | -0.915 | ||||
| Upperbound of 95% confidence interval for beta | -0.500 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 3.577 | ||||
| Treynor index (mean / b) | -2.372 | ||||
| Jensen alpha (a) | 1.828 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.035 | ||||
| SD | 1.695 | ||||
| Sharpe ratio (Glass type estimate) | 0.021 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.021 | ||||
| df | 2067.000 | ||||
| t | 0.058 | ||||
| p | 0.477 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.677 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.718 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.677 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.718 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.030 | ||||
| Upside Potential Ratio | 1.927 | ||||
| Upside part of mean | 2.279 | ||||
| Downside part of mean | -2.244 | ||||
| Upside SD | 1.214 | ||||
| Downside SD | 1.183 | ||||
| N nonnegative terms | 83.000 | ||||
| N negative terms | 1985.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2068.000 | ||||
| Mean of predictor | 0.078 | ||||
| Mean of criterion | 0.035 | ||||
| SD of predictor | 0.518 | ||||
| SD of criterion | 1.695 | ||||
| Covariance | -0.161 | ||||
| r | -0.184 | ||||
| b (slope, estimate of beta) | -0.601 | ||||
| a (intercept, estimate of alpha) | 0.082 | ||||
| Mean Square Error | 2.778 | ||||
| DF error | 2066.000 | ||||
| t(b) | -8.490 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.138 | ||||
| p(a) | 0.445 | ||||
| Lowerbound of 95% confidence interval for beta | -0.739 | ||||
| Upperbound of 95% confidence interval for beta | -0.462 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.082 | ||||
| Upperbound of 95% confidence interval for alpha | 1.245 | ||||
| Treynor index (mean / b) | -0.058 | ||||
| Jensen alpha (a) | 0.082 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.158 | ||||
| Expected Shortfall on VaR | 0.194 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2068.000 | ||||
| Minimum | 0.187 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 5.724 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.052 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 85.000 | ||||
| Percentage of outliers low | 0.041 | ||||
| Mean of outliers low | 0.843 | ||||
| Number of outliers high | 83.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.324 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.789 | ||||
| VaR(95%) (moments method) | -0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.162 | ||||
| VaR(95%) (regression method) | -0.014 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.036 | ||||
| Quartile 1 | 0.101 | ||||
| Median | 0.222 | ||||
| Quartile 3 | 0.361 | ||||
| Maximum | 0.888 | ||||
| Mean of quarter 1 | 0.049 | ||||
| Mean of quarter 2 | 0.202 | ||||
| Mean of quarter 3 | 0.265 | ||||
| Mean of quarter 4 | 0.558 | ||||
| Inter Quartile Range | 0.260 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.888 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.321 | ||||
| VaR(95%) (moments method) | 0.681 | ||||
| Expected Shortfall (moments method) | 1.070 | ||||
| Extreme Value Index (regression method) | 3.779 | ||||
| VaR(95%) (regression method) | 1.614 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.110 | ||||
| Compounded annual return (geometric extrapolation) | 0.082 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.092 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.147 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.424 | ||||
| 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 | 0.627 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.535 | ||||
| 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 | 0.475 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.560 | ||||
| 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) | -8787658847464427.000 | ||||
| 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) | -128450711362811962067064824266752.000 | ||||
| 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 | ||||