Advanced Statistics: Have Fun
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 | 0.032 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | 0.461 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.457 | ||||
| df | 74.000 | ||||
| t | 1.153 | ||||
| p | 0.126 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.328 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.247 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.331 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.244 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.181 | ||||
| Upside Potential Ratio | 3.155 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.053 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.135 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.217 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.005 | ||||
| r | -0.301 | ||||
| b (slope, estimate of beta) | -0.096 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 73.000 | ||||
| t(b) | -2.698 | ||||
| p(b) | 0.996 | ||||
| t(a) | 1.661 | ||||
| p(a) | 0.050 | ||||
| Lowerbound of 95% confidence interval for beta | -0.166 | ||||
| Upperbound of 95% confidence interval for beta | -0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.009 | ||||
| Upperbound of 95% confidence interval for alpha | 0.098 | ||||
| Treynor index (mean / b) | -0.333 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | 0.437 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.433 | ||||
| df | 74.000 | ||||
| t | 1.093 | ||||
| p | 0.139 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.351 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.223 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.354 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.220 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.081 | ||||
| Upside Potential Ratio | 3.043 | ||||
| Upside part of mean | 0.083 | ||||
| Downside part of mean | -0.053 | ||||
| Upside SD | 0.062 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.110 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | -0.004 | ||||
| r | -0.302 | ||||
| b (slope, estimate of beta) | -0.092 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 73.000 | ||||
| t(b) | -2.702 | ||||
| p(b) | 0.996 | ||||
| t(a) | 1.515 | ||||
| p(a) | 0.067 | ||||
| Lowerbound of 95% confidence interval for beta | -0.159 | ||||
| Upperbound of 95% confidence interval for beta | -0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.012 | ||||
| Upperbound of 95% confidence interval for alpha | 0.092 | ||||
| Treynor index (mean / b) | -0.321 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 75.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.087 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.093 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.227 | ||||
| Mean of outliers high | 1.035 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.982 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.318 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.026 | ||||
| Maximum | 0.054 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.054 | ||||
| Inter Quartile Range | 0.012 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.054 | ||||
| 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) | 0.093 | ||||
| Compounded annual return (geometric extrapolation) | 0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.418 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.418 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.067 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.048 | ||||
| SD | 0.195 | ||||
| Sharpe ratio (Glass type estimate) | 0.244 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.244 | ||||
| df | 1656.000 | ||||
| t | 0.613 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.536 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.023 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.536 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.023 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.363 | ||||
| Upside Potential Ratio | 3.570 | ||||
| Upside part of mean | 0.468 | ||||
| Downside part of mean | -0.420 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.131 | ||||
| N nonnegative terms | 190.000 | ||||
| N negative terms | 1467.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1657.000 | ||||
| Mean of predictor | 0.359 | ||||
| Mean of criterion | 0.048 | ||||
| SD of predictor | 0.584 | ||||
| SD of criterion | 0.195 | ||||
| Covariance | -0.039 | ||||
| r | -0.342 | ||||
| b (slope, estimate of beta) | -0.114 | ||||
| a (intercept, estimate of alpha) | 0.088 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 1655.000 | ||||
| t(b) | -14.782 | ||||
| p(b) | 0.713 | ||||
| t(a) | 1.212 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | -0.129 | ||||
| Upperbound of 95% confidence interval for beta | -0.099 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.055 | ||||
| Upperbound of 95% confidence interval for alpha | 0.231 | ||||
| Treynor index (mean / b) | -0.417 | ||||
| Jensen alpha (a) | 0.088 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.195 | ||||
| Sharpe ratio (Glass type estimate) | 0.146 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.146 | ||||
| df | 1656.000 | ||||
| t | 0.368 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.633 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.926 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.633 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.926 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.208 | ||||
| Upside Potential Ratio | 3.341 | ||||
| Upside part of mean | 0.458 | ||||
| Downside part of mean | -0.429 | ||||
| Upside SD | 0.139 | ||||
| Downside SD | 0.137 | ||||
| N nonnegative terms | 190.000 | ||||
| N negative terms | 1467.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1657.000 | ||||
| Mean of predictor | 0.194 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.571 | ||||
| SD of criterion | 0.195 | ||||
| Covariance | -0.038 | ||||
| r | -0.344 | ||||
| b (slope, estimate of beta) | -0.118 | ||||
| a (intercept, estimate of alpha) | 0.051 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 1655.000 | ||||
| t(b) | -14.913 | ||||
| p(b) | 0.715 | ||||
| t(a) | 0.705 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | -0.133 | ||||
| Upperbound of 95% confidence interval for beta | -0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.194 | ||||
| Treynor index (mean / b) | -0.243 | ||||
| Jensen alpha (a) | 0.051 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1657.000 | ||||
| Minimum | 0.839 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.153 | ||||
| Mean of quarter 1 | 0.994 | ||||
| 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 | 170.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 202.000 | ||||
| Percentage of outliers high | 0.122 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.236 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| 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 | 30.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.022 | ||||
| Quartile 3 | 0.041 | ||||
| Maximum | 0.171 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.083 | ||||
| Inter Quartile Range | 0.037 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 0.139 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.109 | ||||
| VaR(95%) (moments method) | 0.088 | ||||
| Expected Shortfall (moments method) | 0.124 | ||||
| Extreme Value Index (regression method) | 0.507 | ||||
| VaR(95%) (regression method) | 0.098 | ||||
| Expected Shortfall (regression method) | 0.197 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.092 | ||||
| Compounded annual return (geometric extrapolation) | 0.075 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.439 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.908 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.081 | ||||
| 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 | 1.889 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.743 | ||||
| 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 | 1.623 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.716 | ||||
| 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) | -8714084059217397.000 | ||||
| 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) | -284862882247547755809303666098176.000 | ||||
| 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 | ||||