Advanced Statistics: MGM Intraday
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 | 0.151 | ||||
| SD | 0.318 | ||||
| Sharpe ratio (Glass type estimate) | 0.473 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.463 | ||||
| df | 38.000 | ||||
| t | 0.852 | ||||
| p | 0.200 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.623 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.562 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.629 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.555 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.800 | ||||
| Upside Potential Ratio | 2.444 | ||||
| Upside part of mean | 0.460 | ||||
| Downside part of mean | -0.309 | ||||
| Upside SD | 0.256 | ||||
| Downside SD | 0.188 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.476 | ||||
| Mean of criterion | 0.151 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.318 | ||||
| Covariance | 0.030 | ||||
| r | 0.361 | ||||
| b (slope, estimate of beta) | 0.446 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 37.000 | ||||
| t(b) | 2.353 | ||||
| p(b) | 0.012 | ||||
| t(a) | -0.326 | ||||
| p(a) | 0.627 | ||||
| Lowerbound of 95% confidence interval for beta | 0.062 | ||||
| Upperbound of 95% confidence interval for beta | 0.830 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.446 | ||||
| Upperbound of 95% confidence interval for alpha | 0.323 | ||||
| Treynor index (mean / b) | 0.337 | ||||
| Jensen alpha (a) | -0.062 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.101 | ||||
| SD | 0.313 | ||||
| Sharpe ratio (Glass type estimate) | 0.324 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.317 | ||||
| df | 38.000 | ||||
| t | 0.583 | ||||
| p | 0.282 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.768 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.411 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.772 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.407 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.485 | ||||
| Upside Potential Ratio | 2.058 | ||||
| Upside part of mean | 0.430 | ||||
| Downside part of mean | -0.329 | ||||
| Upside SD | 0.230 | ||||
| Downside SD | 0.209 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | 0.101 | ||||
| SD of predictor | 0.239 | ||||
| SD of criterion | 0.313 | ||||
| Covariance | 0.026 | ||||
| r | 0.344 | ||||
| b (slope, estimate of beta) | 0.451 | ||||
| a (intercept, estimate of alpha) | -0.096 | ||||
| Mean Square Error | 0.089 | ||||
| DF error | 37.000 | ||||
| t(b) | 2.231 | ||||
| p(b) | 0.016 | ||||
| t(a) | -0.510 | ||||
| p(a) | 0.693 | ||||
| Lowerbound of 95% confidence interval for beta | 0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.861 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.475 | ||||
| Upperbound of 95% confidence interval for alpha | 0.284 | ||||
| Treynor index (mean / b) | 0.225 | ||||
| Jensen alpha (a) | -0.096 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.131 | ||||
| Expected Shortfall on VaR | 0.163 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.113 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.739 | ||||
| Quartile 1 | 0.963 | ||||
| Median | 1.006 | ||||
| Quartile 3 | 1.071 | ||||
| Maximum | 1.346 | ||||
| Mean of quarter 1 | 0.920 | ||||
| Mean of quarter 2 | 0.987 | ||||
| Mean of quarter 3 | 1.044 | ||||
| Mean of quarter 4 | 1.116 | ||||
| Inter Quartile Range | 0.108 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.739 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.346 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.513 | ||||
| VaR(95%) (moments method) | 0.092 | ||||
| Expected Shortfall (moments method) | 0.195 | ||||
| Extreme Value Index (regression method) | 1.087 | ||||
| VaR(95%) (regression method) | 0.086 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.050 | ||||
| Median | 0.099 | ||||
| Quartile 3 | 0.144 | ||||
| Maximum | 0.295 | ||||
| Mean of quarter 1 | 0.022 | ||||
| Mean of quarter 2 | 0.093 | ||||
| Mean of quarter 3 | 0.105 | ||||
| Mean of quarter 4 | 0.226 | ||||
| Inter Quartile Range | 0.095 | ||||
| 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 | 0.295 | ||||
| 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) | 0.186 | ||||
| Compounded annual return (geometric extrapolation) | 0.157 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.531 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.692 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.962 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.235 | ||||
| SD | 0.438 | ||||
| Sharpe ratio (Glass type estimate) | 0.536 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.536 | ||||
| df | 854.000 | ||||
| t | 0.969 | ||||
| p | 0.167 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.549 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.621 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.550 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.621 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.763 | ||||
| Upside Potential Ratio | 7.105 | ||||
| Upside part of mean | 2.184 | ||||
| Downside part of mean | -1.950 | ||||
| Upside SD | 0.312 | ||||
| Downside SD | 0.307 | ||||
| N nonnegative terms | 422.000 | ||||
| N negative terms | 433.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 855.000 | ||||
| Mean of predictor | 0.496 | ||||
| Mean of criterion | 0.235 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.438 | ||||
| Covariance | 0.079 | ||||
| r | 0.570 | ||||
| b (slope, estimate of beta) | 0.789 | ||||
| a (intercept, estimate of alpha) | -0.156 | ||||
| Mean Square Error | 0.129 | ||||
| DF error | 853.000 | ||||
| t(b) | 20.264 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.780 | ||||
| p(a) | 0.782 | ||||
| Lowerbound of 95% confidence interval for beta | 0.712 | ||||
| Upperbound of 95% confidence interval for beta | 0.865 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.549 | ||||
| Upperbound of 95% confidence interval for alpha | 0.237 | ||||
| Treynor index (mean / b) | 0.298 | ||||
| Jensen alpha (a) | -0.156 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.137 | ||||
| SD | 0.446 | ||||
| Sharpe ratio (Glass type estimate) | 0.306 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.306 | ||||
| df | 854.000 | ||||
| t | 0.553 | ||||
| p | 0.290 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.779 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.779 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.391 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.415 | ||||
| Upside Potential Ratio | 6.489 | ||||
| Upside part of mean | 2.138 | ||||
| Downside part of mean | -2.001 | ||||
| Upside SD | 0.301 | ||||
| Downside SD | 0.329 | ||||
| N nonnegative terms | 422.000 | ||||
| N negative terms | 433.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 855.000 | ||||
| Mean of predictor | 0.444 | ||||
| Mean of criterion | 0.137 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.446 | ||||
| Covariance | 0.085 | ||||
| r | 0.591 | ||||
| b (slope, estimate of beta) | 0.819 | ||||
| a (intercept, estimate of alpha) | -0.227 | ||||
| Mean Square Error | 0.130 | ||||
| DF error | 853.000 | ||||
| t(b) | 21.381 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.133 | ||||
| p(a) | 0.871 | ||||
| Lowerbound of 95% confidence interval for beta | 0.744 | ||||
| Upperbound of 95% confidence interval for beta | 0.894 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.620 | ||||
| Upperbound of 95% confidence interval for alpha | 0.166 | ||||
| Treynor index (mean / b) | 0.167 | ||||
| Jensen alpha (a) | -0.227 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 855.000 | ||||
| Minimum | 0.713 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.009 | ||||
| Maximum | 1.158 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.017 | ||||
| Number outliers low | 56.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 63.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.059 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.476 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.056 | ||||
| Extreme Value Index (regression method) | 0.166 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.037 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 26.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.060 | ||||
| Maximum | 0.398 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.181 | ||||
| Inter Quartile Range | 0.053 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.115 | ||||
| Mean of outliers high | 0.302 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.139 | ||||
| VaR(95%) (moments method) | 0.169 | ||||
| Expected Shortfall (moments method) | 0.259 | ||||
| Extreme Value Index (regression method) | 0.354 | ||||
| VaR(95%) (regression method) | 0.246 | ||||
| Expected Shortfall (regression method) | 0.473 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.246 | ||||
| Compounded annual return (geometric extrapolation) | 0.198 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.497 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.091 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.618 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.376 | ||||
| SD | 0.694 | ||||
| Sharpe ratio (Glass type estimate) | 0.542 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.538 | ||||
| df | 130.000 | ||||
| t | 0.383 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.232 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.234 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.311 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.808 | ||||
| Upside Potential Ratio | 9.400 | ||||
| Upside part of mean | 4.371 | ||||
| Downside part of mean | -3.995 | ||||
| Upside SD | 0.512 | ||||
| Downside SD | 0.465 | ||||
| N nonnegative terms | 62.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.975 | ||||
| Mean of criterion | 0.376 | ||||
| SD of predictor | 0.489 | ||||
| SD of criterion | 0.694 | ||||
| Covariance | 0.168 | ||||
| r | 0.494 | ||||
| b (slope, estimate of beta) | 0.701 | ||||
| a (intercept, estimate of alpha) | -0.308 | ||||
| Mean Square Error | 0.367 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.457 | ||||
| p(b) | 0.199 | ||||
| t(a) | -0.357 | ||||
| p(a) | 0.520 | ||||
| Lowerbound of 95% confidence interval for beta | 0.487 | ||||
| Upperbound of 95% confidence interval for beta | 0.916 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.016 | ||||
| Upperbound of 95% confidence interval for alpha | 1.399 | ||||
| Treynor index (mean / b) | 0.536 | ||||
| Jensen alpha (a) | -0.308 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.138 | ||||
| SD | 0.691 | ||||
| Sharpe ratio (Glass type estimate) | 0.200 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.199 | ||||
| df | 130.000 | ||||
| t | 0.141 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.573 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.971 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.573 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.971 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.287 | ||||
| Upside Potential Ratio | 8.813 | ||||
| Upside part of mean | 4.246 | ||||
| Downside part of mean | -4.108 | ||||
| Upside SD | 0.492 | ||||
| Downside SD | 0.482 | ||||
| N nonnegative terms | 62.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.855 | ||||
| Mean of criterion | 0.138 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 0.691 | ||||
| Covariance | 0.170 | ||||
| r | 0.506 | ||||
| b (slope, estimate of beta) | 0.717 | ||||
| a (intercept, estimate of alpha) | -0.475 | ||||
| Mean Square Error | 0.359 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.655 | ||||
| p(b) | 0.192 | ||||
| t(a) | -0.558 | ||||
| p(a) | 0.531 | ||||
| Lowerbound of 95% confidence interval for beta | 0.504 | ||||
| Upperbound of 95% confidence interval for beta | 0.930 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.160 | ||||
| Upperbound of 95% confidence interval for alpha | 1.210 | ||||
| Treynor index (mean / b) | 0.193 | ||||
| Jensen alpha (a) | -0.475 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.883 | ||||
| Quartile 1 | 0.978 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.027 | ||||
| Maximum | 1.158 | ||||
| Mean of quarter 1 | 0.949 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.055 | ||||
| Inter Quartile Range | 0.049 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.883 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.122 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.552 | ||||
| VaR(95%) (moments method) | 0.051 | ||||
| Expected Shortfall (moments method) | 0.058 | ||||
| Extreme Value Index (regression method) | -0.490 | ||||
| VaR(95%) (regression method) | 0.053 | ||||
| Expected Shortfall (regression method) | 0.061 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.058 | ||||
| Quartile 3 | 0.164 | ||||
| Maximum | 0.270 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.058 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.270 | ||||
| Inter Quartile Range | 0.132 | ||||
| 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) | 0.191 | ||||
| Compounded annual return (geometric extrapolation) | 0.200 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.739 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.739 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.386 | ||||