Advanced Statistics: The Sweet Spot
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 | 0.234 | ||||
| SD | 0.825 | ||||
| Sharpe ratio (Glass type estimate) | 0.284 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.278 | ||||
| df | 38.000 | ||||
| t | 0.512 | ||||
| p | 0.306 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.807 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.371 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.811 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.367 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.816 | ||||
| Upside Potential Ratio | 1.978 | ||||
| Upside part of mean | 0.567 | ||||
| Downside part of mean | -0.333 | ||||
| Upside SD | 0.765 | ||||
| Downside SD | 0.287 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.529 | ||||
| Mean of criterion | 0.234 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.825 | ||||
| Covariance | -0.001 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | 0.241 | ||||
| Mean Square Error | 0.698 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.028 | ||||
| p(b) | 0.511 | ||||
| t(a) | 0.455 | ||||
| p(a) | 0.326 | ||||
| Lowerbound of 95% confidence interval for beta | -0.997 | ||||
| Upperbound of 95% confidence interval for beta | 0.970 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.833 | ||||
| Upperbound of 95% confidence interval for alpha | 1.315 | ||||
| Treynor index (mean / b) | -17.265 | ||||
| Jensen alpha (a) | 0.241 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.019 | ||||
| SD | 0.608 | ||||
| Sharpe ratio (Glass type estimate) | 0.032 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.031 | ||||
| df | 38.000 | ||||
| t | 0.057 | ||||
| p | 0.477 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.056 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.119 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.056 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.118 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.056 | ||||
| Upside Potential Ratio | 1.182 | ||||
| Upside part of mean | 0.403 | ||||
| Downside part of mean | -0.384 | ||||
| Upside SD | 0.494 | ||||
| Downside SD | 0.341 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.482 | ||||
| Mean of criterion | 0.019 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.608 | ||||
| Covariance | -0.002 | ||||
| r | -0.010 | ||||
| b (slope, estimate of beta) | -0.023 | ||||
| a (intercept, estimate of alpha) | 0.030 | ||||
| Mean Square Error | 0.379 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.061 | ||||
| p(b) | 0.524 | ||||
| t(a) | 0.078 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | -0.798 | ||||
| Upperbound of 95% confidence interval for beta | 0.751 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.756 | ||||
| Upperbound of 95% confidence interval for alpha | 0.817 | ||||
| Treynor index (mean / b) | -0.830 | ||||
| Jensen alpha (a) | 0.030 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.250 | ||||
| Expected Shortfall on VaR | 0.301 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.183 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.639 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.353 | ||||
| Mean of quarter 1 | 0.904 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.187 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.154 | ||||
| Mean of outliers low | 0.840 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.179 | ||||
| Mean of outliers high | 1.267 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -250.838 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.639 | ||||
| VaR(95%) (regression method) | 0.149 | ||||
| Expected Shortfall (regression method) | 0.222 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.631 | ||||
| Quartile 1 | 0.631 | ||||
| Median | 0.631 | ||||
| Quartile 3 | 0.631 | ||||
| Maximum | 0.631 | ||||
| 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 | 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) | 0.070 | ||||
| Compounded annual return (geometric extrapolation) | 0.065 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.103 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.217 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.211 | ||||
| SD | 0.799 | ||||
| Sharpe ratio (Glass type estimate) | 0.264 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.264 | ||||
| df | 867.000 | ||||
| t | 0.481 | ||||
| p | 0.315 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.813 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.341 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.813 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.341 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.994 | ||||
| Upside Potential Ratio | 4.671 | ||||
| Upside part of mean | 0.992 | ||||
| Downside part of mean | -0.780 | ||||
| Upside SD | 0.770 | ||||
| Downside SD | 0.212 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 800.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 868.000 | ||||
| Mean of predictor | 0.557 | ||||
| Mean of criterion | 0.211 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.799 | ||||
| Covariance | -0.007 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | 0.248 | ||||
| Mean Square Error | 0.639 | ||||
| DF error | 866.000 | ||||
| t(b) | -0.781 | ||||
| p(b) | 0.782 | ||||
| t(a) | 0.561 | ||||
| p(a) | 0.287 | ||||
| Lowerbound of 95% confidence interval for beta | -0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.100 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.619 | ||||
| Upperbound of 95% confidence interval for alpha | 1.115 | ||||
| Treynor index (mean / b) | -3.192 | ||||
| Jensen alpha (a) | 0.248 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.554 | ||||
| Sharpe ratio (Glass type estimate) | 0.032 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.032 | ||||
| df | 867.000 | ||||
| t | 0.059 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.044 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.109 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.044 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.109 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.081 | ||||
| Upside Potential Ratio | 3.691 | ||||
| Upside part of mean | 0.822 | ||||
| Downside part of mean | -0.804 | ||||
| Upside SD | 0.507 | ||||
| Downside SD | 0.223 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 800.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 868.000 | ||||
| Mean of predictor | 0.504 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.554 | ||||
| Covariance | -0.006 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.061 | ||||
| a (intercept, estimate of alpha) | 0.049 | ||||
| Mean Square Error | 0.307 | ||||
| DF error | 866.000 | ||||
| t(b) | -1.042 | ||||
| p(b) | 0.851 | ||||
| t(a) | 0.159 | ||||
| p(a) | 0.437 | ||||
| Lowerbound of 95% confidence interval for beta | -0.176 | ||||
| Upperbound of 95% confidence interval for beta | 0.054 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.552 | ||||
| Upperbound of 95% confidence interval for alpha | 0.649 | ||||
| Treynor index (mean / b) | -0.296 | ||||
| Jensen alpha (a) | 0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 868.000 | ||||
| Minimum | 0.843 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.353 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 85.000 | ||||
| Percentage of outliers low | 0.098 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 69.000 | ||||
| Percentage of outliers high | 0.079 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.805 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.006 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.029 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.046 | ||||
| Quartile 3 | 0.148 | ||||
| Maximum | 0.663 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.020 | ||||
| Mean of quarter 3 | 0.071 | ||||
| Mean of quarter 4 | 0.418 | ||||
| Inter Quartile Range | 0.141 | ||||
| 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 | 0.663 | ||||
| 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) | 0.069 | ||||
| Compounded annual return (geometric extrapolation) | 0.064 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.097 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.153 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.940 | ||||
| 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 | 0.988 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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 | 0.868 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.489 | ||||
| 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) | -8747075452533064.000 | ||||
| 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) | 102212280215832638426222419771392.000 | ||||
| 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 | ||||