Advanced Statistics: Emerald Bay
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 | 0.105 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | 0.564 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.555 | ||||
| df | 45.000 | ||||
| t | 1.105 | ||||
| p | 0.138 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.447 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.569 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.453 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.562 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.970 | ||||
| Upside Potential Ratio | 3.473 | ||||
| Upside part of mean | 0.185 | ||||
| Downside part of mean | -0.080 | ||||
| Upside SD | 0.179 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.446 | ||||
| Mean of criterion | 0.105 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | 0.001 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | 0.099 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 44.000 | ||||
| t(b) | 0.103 | ||||
| p(b) | 0.459 | ||||
| t(a) | 0.901 | ||||
| p(a) | 0.186 | ||||
| Lowerbound of 95% confidence interval for beta | -0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.257 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.123 | ||||
| Upperbound of 95% confidence interval for alpha | 0.321 | ||||
| Treynor index (mean / b) | 8.364 | ||||
| Jensen alpha (a) | 0.099 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.089 | ||||
| SD | 0.169 | ||||
| Sharpe ratio (Glass type estimate) | 0.530 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.521 | ||||
| df | 45.000 | ||||
| t | 1.037 | ||||
| p | 0.153 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.480 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.534 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.486 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.528 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.627 | ||||
| Upside Potential Ratio | 3.106 | ||||
| Upside part of mean | 0.171 | ||||
| Downside part of mean | -0.081 | ||||
| Upside SD | 0.160 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.413 | ||||
| Mean of criterion | 0.089 | ||||
| SD of predictor | 0.217 | ||||
| SD of criterion | 0.169 | ||||
| Covariance | 0.001 | ||||
| r | 0.025 | ||||
| b (slope, estimate of beta) | 0.019 | ||||
| a (intercept, estimate of alpha) | 0.081 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 44.000 | ||||
| t(b) | 0.165 | ||||
| p(b) | 0.435 | ||||
| t(a) | 0.817 | ||||
| p(a) | 0.209 | ||||
| Lowerbound of 95% confidence interval for beta | -0.217 | ||||
| Upperbound of 95% confidence interval for beta | 0.256 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.282 | ||||
| Treynor index (mean / b) | 4.623 | ||||
| Jensen alpha (a) | 0.081 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.302 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.062 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.109 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.174 | ||||
| Mean of outliers high | 1.092 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -98.007 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.395 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | 0.044 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.027 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.072 | ||||
| Maximum | 0.110 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.110 | ||||
| Inter Quartile Range | 0.044 | ||||
| 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) | 0.174 | ||||
| Compounded annual return (geometric extrapolation) | 0.143 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.300 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.300 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.609 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.098 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | 0.701 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.701 | ||||
| df | 1010.000 | ||||
| t | 1.378 | ||||
| p | 0.478 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.297 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.700 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.297 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.699 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.323 | ||||
| Upside Potential Ratio | 4.572 | ||||
| Upside part of mean | 0.338 | ||||
| Downside part of mean | -0.240 | ||||
| Upside SD | 0.118 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 122.000 | ||||
| N negative terms | 889.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1011.000 | ||||
| Mean of predictor | 0.489 | ||||
| Mean of criterion | 0.098 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | 0.099 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 1009.000 | ||||
| t(b) | -0.215 | ||||
| p(b) | 0.504 | ||||
| t(a) | 1.391 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -0.029 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.041 | ||||
| Upperbound of 95% confidence interval for alpha | 0.239 | ||||
| Treynor index (mean / b) | -34.452 | ||||
| Jensen alpha (a) | 0.099 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.088 | ||||
| SD | 0.136 | ||||
| Sharpe ratio (Glass type estimate) | 0.650 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.650 | ||||
| df | 1010.000 | ||||
| t | 1.278 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.348 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.648 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.348 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.648 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.169 | ||||
| Upside Potential Ratio | 4.381 | ||||
| Upside part of mean | 0.332 | ||||
| Downside part of mean | -0.243 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.076 | ||||
| N nonnegative terms | 122.000 | ||||
| N negative terms | 889.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1011.000 | ||||
| Mean of predictor | 0.431 | ||||
| Mean of criterion | 0.088 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.136 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | 0.090 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 1009.000 | ||||
| t(b) | -0.216 | ||||
| p(b) | 0.504 | ||||
| t(a) | 1.290 | ||||
| p(a) | 0.474 | ||||
| Lowerbound of 95% confidence interval for beta | -0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | 0.226 | ||||
| Treynor index (mean / b) | -33.071 | ||||
| Jensen alpha (a) | 0.090 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1011.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.163 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 65.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 122.000 | ||||
| Percentage of outliers high | 0.121 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.043 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.114 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.055 | ||||
| Maximum | 0.131 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.042 | ||||
| Mean of quarter 4 | 0.111 | ||||
| Inter Quartile Range | 0.050 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.131 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2131.999 | ||||
| VaR(95%) (moments method) | 0.114 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -5.589 | ||||
| VaR(95%) (regression method) | 0.270 | ||||
| Expected Shortfall (regression method) | 0.270 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.173 | ||||
| Compounded annual return (geometric extrapolation) | 0.142 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.078 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.280 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.409 | ||||
| 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 | 0.987 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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 | 0.873 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.478 | ||||
| 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) | -8743826221580244.000 | ||||
| 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) | 210201511297741480098583336189952.000 | ||||
| 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 | ||||