Advanced Statistics: KC Legacy (closed)
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 | -0.110 | ||||
| SD | 0.187 | ||||
| Sharpe ratio (Glass type estimate) | -0.586 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.580 | ||||
| df | 77.000 | ||||
| t | -1.494 | ||||
| p | 0.930 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.359 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.190 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.355 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.194 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.637 | ||||
| Upside Potential Ratio | 0.279 | ||||
| Upside part of mean | 0.048 | ||||
| Downside part of mean | -0.158 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.172 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.235 | ||||
| Mean of criterion | -0.110 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.187 | ||||
| Covariance | 0.007 | ||||
| r | 0.130 | ||||
| b (slope, estimate of beta) | 0.081 | ||||
| a (intercept, estimate of alpha) | -0.129 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 76.000 | ||||
| t(b) | 1.147 | ||||
| p(b) | 0.128 | ||||
| t(a) | -1.715 | ||||
| p(a) | 0.955 | ||||
| Lowerbound of 95% confidence interval for beta | -0.060 | ||||
| Upperbound of 95% confidence interval for beta | 0.223 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.278 | ||||
| Upperbound of 95% confidence interval for alpha | 0.021 | ||||
| Treynor index (mean / b) | -1.345 | ||||
| Jensen alpha (a) | -0.129 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.131 | ||||
| SD | 0.218 | ||||
| Sharpe ratio (Glass type estimate) | -0.599 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.593 | ||||
| df | 77.000 | ||||
| t | -1.527 | ||||
| p | 0.935 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.371 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.178 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.367 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.181 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.628 | ||||
| Upside Potential Ratio | 0.216 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.176 | ||||
| Upside SD | 0.072 | ||||
| Downside SD | 0.208 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.191 | ||||
| Mean of criterion | -0.131 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.218 | ||||
| Covariance | 0.010 | ||||
| r | 0.163 | ||||
| b (slope, estimate of beta) | 0.125 | ||||
| a (intercept, estimate of alpha) | -0.155 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 76.000 | ||||
| t(b) | 1.437 | ||||
| p(b) | 0.077 | ||||
| t(a) | -1.784 | ||||
| p(a) | 0.961 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.298 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.327 | ||||
| Upperbound of 95% confidence interval for alpha | 0.018 | ||||
| Treynor index (mean / b) | -1.048 | ||||
| Jensen alpha (a) | -0.155 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.131 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.623 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.158 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.128 | ||||
| Mean of outliers low | 0.925 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.115 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.942 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.934 | ||||
| VaR(95%) (regression method) | 0.032 | ||||
| Expected Shortfall (regression method) | 1.126 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.431 | ||||
| Quartile 1 | 0.431 | ||||
| Median | 0.431 | ||||
| Quartile 3 | 0.431 | ||||
| Maximum | 0.431 | ||||
| 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) | -0.066 | ||||
| Compounded annual return (geometric extrapolation) | -0.083 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.193 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.633 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.351 | ||||
| Sharpe ratio (Glass type estimate) | -0.189 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.189 | ||||
| df | 1709.000 | ||||
| t | -0.484 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.957 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.578 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.957 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.578 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.260 | ||||
| Upside Potential Ratio | 1.947 | ||||
| Upside part of mean | 0.497 | ||||
| Downside part of mean | -0.563 | ||||
| Upside SD | 0.240 | ||||
| Downside SD | 0.255 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 1630.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1710.000 | ||||
| Mean of predictor | 0.351 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.540 | ||||
| SD of criterion | 0.351 | ||||
| Covariance | -0.012 | ||||
| r | -0.065 | ||||
| b (slope, estimate of beta) | -0.042 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.122 | ||||
| DF error | 1708.000 | ||||
| t(b) | -2.705 | ||||
| p(b) | 0.533 | ||||
| t(a) | -0.376 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.073 | ||||
| Upperbound of 95% confidence interval for beta | -0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.320 | ||||
| Upperbound of 95% confidence interval for alpha | 0.217 | ||||
| Treynor index (mean / b) | 1.566 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.130 | ||||
| SD | 0.363 | ||||
| Sharpe ratio (Glass type estimate) | -0.359 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.359 | ||||
| df | 1709.000 | ||||
| t | -0.918 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.127 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.408 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.127 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.408 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.458 | ||||
| Upside Potential Ratio | 1.649 | ||||
| Upside part of mean | 0.470 | ||||
| Downside part of mean | -0.601 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.285 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 1630.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1710.000 | ||||
| Mean of predictor | 0.206 | ||||
| Mean of criterion | -0.130 | ||||
| SD of predictor | 0.540 | ||||
| SD of criterion | 0.363 | ||||
| Covariance | -0.012 | ||||
| r | -0.061 | ||||
| b (slope, estimate of beta) | -0.041 | ||||
| a (intercept, estimate of alpha) | -0.122 | ||||
| Mean Square Error | 0.131 | ||||
| DF error | 1708.000 | ||||
| t(b) | -2.535 | ||||
| p(b) | 0.531 | ||||
| t(a) | -0.860 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | -0.073 | ||||
| Upperbound of 95% confidence interval for beta | -0.009 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.400 | ||||
| Upperbound of 95% confidence interval for alpha | 0.156 | ||||
| Treynor index (mean / b) | 3.171 | ||||
| Jensen alpha (a) | -0.122 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1710.000 | ||||
| Minimum | 0.651 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.172 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 134.000 | ||||
| Percentage of outliers low | 0.078 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 130.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.837 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.015 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.176 | ||||
| Median | 0.179 | ||||
| Quartile 3 | 0.215 | ||||
| Maximum | 0.500 | ||||
| Mean of quarter 1 | 0.091 | ||||
| Mean of quarter 2 | 0.179 | ||||
| Mean of quarter 3 | 0.215 | ||||
| Mean of quarter 4 | 0.500 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.007 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.500 | ||||
| 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) | -0.066 | ||||
| Compounded annual return (geometric extrapolation) | -0.083 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.166 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.166 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.814 | ||||
| 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 | 1.062 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.519 | ||||
| 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 | 0.925 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.523 | ||||
| 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) | -8747314663355103.000 | ||||
| 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) | -361108226098618857911266714845184.000 | ||||
| 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 | ||||