Advanced Statistics: Grandma's
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.166 | ||||
| Sharpe ratio (Glass type estimate) | 0.107 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.105 | ||||
| df | 77.000 | ||||
| t | 0.272 | ||||
| p | 0.393 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.663 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.875 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.663 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.874 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.161 | ||||
| Upside Potential Ratio | 1.940 | ||||
| Upside part of mean | 0.214 | ||||
| Downside part of mean | -0.196 | ||||
| Upside SD | 0.123 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.198 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.166 | ||||
| Covariance | 0.028 | ||||
| r | 0.563 | ||||
| b (slope, estimate of beta) | 0.316 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 76.000 | ||||
| t(b) | 5.938 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.809 | ||||
| p(a) | 0.789 | ||||
| Lowerbound of 95% confidence interval for beta | 0.210 | ||||
| Upperbound of 95% confidence interval for beta | 0.422 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 0.065 | ||||
| Treynor index (mean / b) | 0.056 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.004 | ||||
| SD | 0.165 | ||||
| Sharpe ratio (Glass type estimate) | 0.026 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.025 | ||||
| df | 77.000 | ||||
| t | 0.065 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.743 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.794 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.743 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.794 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.037 | ||||
| Upside Potential Ratio | 1.797 | ||||
| Upside part of mean | 0.206 | ||||
| Downside part of mean | -0.201 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.114 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.153 | ||||
| Mean of criterion | 0.004 | ||||
| SD of predictor | 0.292 | ||||
| SD of criterion | 0.165 | ||||
| Covariance | 0.028 | ||||
| r | 0.573 | ||||
| b (slope, estimate of beta) | 0.323 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 76.000 | ||||
| t(b) | 6.092 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.840 | ||||
| p(a) | 0.798 | ||||
| Lowerbound of 95% confidence interval for beta | 0.217 | ||||
| Upperbound of 95% confidence interval for beta | 0.429 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.153 | ||||
| Upperbound of 95% confidence interval for alpha | 0.062 | ||||
| Treynor index (mean / b) | 0.013 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.075 | ||||
| Expected Shortfall on VaR | 0.093 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.878 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 1.158 | ||||
| Mean of quarter 1 | 0.949 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.063 | ||||
| Inter Quartile Range | 0.047 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.890 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.136 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.080 | ||||
| VaR(95%) (moments method) | 0.049 | ||||
| Expected Shortfall (moments method) | 0.070 | ||||
| Extreme Value Index (regression method) | 0.053 | ||||
| VaR(95%) (regression method) | 0.047 | ||||
| Expected Shortfall (regression method) | 0.065 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.055 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.097 | ||||
| Maximum | 0.287 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.062 | ||||
| Mean of quarter 3 | 0.092 | ||||
| Mean of quarter 4 | 0.192 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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 | 0.287 | ||||
| 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) | 0.057 | ||||
| Compounded annual return (geometric extrapolation) | 0.049 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.172 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.257 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.531 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.032 | ||||
| SD | 0.268 | ||||
| Sharpe ratio (Glass type estimate) | 0.120 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.120 | ||||
| df | 1707.000 | ||||
| t | 0.307 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.647 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.888 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.647 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.888 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.166 | ||||
| Upside Potential Ratio | 5.928 | ||||
| Upside part of mean | 1.154 | ||||
| Downside part of mean | -1.121 | ||||
| Upside SD | 0.185 | ||||
| Downside SD | 0.195 | ||||
| N nonnegative terms | 849.000 | ||||
| N negative terms | 859.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1708.000 | ||||
| Mean of predictor | 0.352 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.542 | ||||
| SD of criterion | 0.268 | ||||
| Covariance | 0.090 | ||||
| r | 0.619 | ||||
| b (slope, estimate of beta) | 0.306 | ||||
| a (intercept, estimate of alpha) | -0.075 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 1706.000 | ||||
| t(b) | 32.542 | ||||
| p(b) | 0.191 | ||||
| t(a) | -0.913 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.288 | ||||
| Upperbound of 95% confidence interval for beta | 0.325 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.238 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | 0.105 | ||||
| Jensen alpha (a) | -0.075 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.270 | ||||
| Sharpe ratio (Glass type estimate) | -0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.015 | ||||
| df | 1707.000 | ||||
| t | -0.038 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.783 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.753 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.783 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.753 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.020 | ||||
| Upside Potential Ratio | 5.627 | ||||
| Upside part of mean | 1.137 | ||||
| Downside part of mean | -1.141 | ||||
| Upside SD | 0.180 | ||||
| Downside SD | 0.202 | ||||
| N nonnegative terms | 849.000 | ||||
| N negative terms | 859.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1708.000 | ||||
| Mean of predictor | 0.206 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.540 | ||||
| SD of criterion | 0.270 | ||||
| Covariance | 0.090 | ||||
| r | 0.619 | ||||
| b (slope, estimate of beta) | 0.310 | ||||
| a (intercept, estimate of alpha) | -0.068 | ||||
| Mean Square Error | 0.045 | ||||
| DF error | 1706.000 | ||||
| t(b) | 32.529 | ||||
| p(b) | 0.191 | ||||
| t(a) | -0.815 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.291 | ||||
| Upperbound of 95% confidence interval for beta | 0.328 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.231 | ||||
| Upperbound of 95% confidence interval for alpha | 0.095 | ||||
| Treynor index (mean / b) | -0.013 | ||||
| Jensen alpha (a) | -0.068 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1708.000 | ||||
| Minimum | 0.847 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.116 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 90.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 103.000 | ||||
| Percentage of outliers high | 0.060 | ||||
| Mean of outliers high | 1.038 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.683 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | 0.477 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.103 | ||||
| Maximum | 0.337 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.055 | ||||
| Mean of quarter 4 | 0.239 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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 | 0.118 | ||||
| Mean of outliers high | 0.324 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.783 | ||||
| VaR(95%) (moments method) | 0.230 | ||||
| Expected Shortfall (moments method) | 0.254 | ||||
| Extreme Value Index (regression method) | -1.042 | ||||
| VaR(95%) (regression method) | 0.281 | ||||
| Expected Shortfall (regression method) | 0.300 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.046 | ||||
| Compounded annual return (geometric extrapolation) | 0.041 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.171 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.203 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.267 | ||||
| SD | 0.477 | ||||
| Sharpe ratio (Glass type estimate) | 0.560 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.557 | ||||
| df | 130.000 | ||||
| t | 0.396 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.214 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.332 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.216 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.329 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.725 | ||||
| Upside Potential Ratio | 6.616 | ||||
| Upside part of mean | 2.439 | ||||
| Downside part of mean | -2.172 | ||||
| Upside SD | 0.300 | ||||
| Downside SD | 0.369 | ||||
| N nonnegative terms | 78.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.114 | ||||
| Mean of criterion | 0.267 | ||||
| SD of predictor | 0.705 | ||||
| SD of criterion | 0.477 | ||||
| Covariance | 0.129 | ||||
| r | 0.383 | ||||
| b (slope, estimate of beta) | 0.259 | ||||
| a (intercept, estimate of alpha) | -0.281 | ||||
| Mean Square Error | 0.196 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.708 | ||||
| p(b) | 0.262 | ||||
| t(a) | -0.441 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | 0.150 | ||||
| Upperbound of 95% confidence interval for beta | 0.368 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.540 | ||||
| Upperbound of 95% confidence interval for alpha | 0.978 | ||||
| Treynor index (mean / b) | 1.030 | ||||
| Jensen alpha (a) | -0.281 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.150 | ||||
| SD | 0.490 | ||||
| Sharpe ratio (Glass type estimate) | 0.307 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.305 | ||||
| df | 130.000 | ||||
| t | 0.217 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.466 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.078 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.467 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.077 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.385 | ||||
| Upside Potential Ratio | 6.131 | ||||
| Upside part of mean | 2.395 | ||||
| Downside part of mean | -2.245 | ||||
| Upside SD | 0.292 | ||||
| Downside SD | 0.391 | ||||
| N nonnegative terms | 78.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.846 | ||||
| Mean of criterion | 0.150 | ||||
| SD of predictor | 0.737 | ||||
| SD of criterion | 0.490 | ||||
| Covariance | 0.143 | ||||
| r | 0.397 | ||||
| b (slope, estimate of beta) | 0.264 | ||||
| a (intercept, estimate of alpha) | -0.336 | ||||
| Mean Square Error | 0.203 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.911 | ||||
| p(b) | 0.254 | ||||
| t(a) | -0.521 | ||||
| p(a) | 0.529 | ||||
| Lowerbound of 95% confidence interval for beta | 0.157 | ||||
| Upperbound of 95% confidence interval for beta | 0.370 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.614 | ||||
| Upperbound of 95% confidence interval for alpha | 0.941 | ||||
| Treynor index (mean / b) | 0.570 | ||||
| Jensen alpha (a) | -0.336 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.847 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.926 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.071 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.446 | ||||
| VaR(95%) (moments method) | 0.027 | ||||
| Expected Shortfall (moments method) | 0.057 | ||||
| Extreme Value Index (regression method) | 0.222 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.047 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.027 | ||||
| Quartile 3 | 0.079 | ||||
| Maximum | 0.311 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.193 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.311 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.844 | ||||
| VaR(95%) (moments method) | 0.217 | ||||
| Expected Shortfall (moments method) | 0.225 | ||||
| Extreme Value Index (regression method) | 0.219 | ||||
| VaR(95%) (regression method) | 0.324 | ||||
| Expected Shortfall (regression method) | 0.532 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.204 | ||||
| Compounded annual return (geometric extrapolation) | 0.214 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.689 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.109 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.581 | ||||