Advanced Statistics: Trading Trends and Turns
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 | 0.198 | ||||
| SD | 0.319 | ||||
| Sharpe ratio (Glass type estimate) | 0.620 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.605 | ||||
| df | 31.000 | ||||
| t | 1.013 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.595 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.826 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.604 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.815 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.109 | ||||
| Upside Potential Ratio | 3.088 | ||||
| Upside part of mean | 0.550 | ||||
| Downside part of mean | -0.353 | ||||
| Upside SD | 0.264 | ||||
| Downside SD | 0.178 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.608 | ||||
| Mean of criterion | 0.198 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.319 | ||||
| Covariance | 0.054 | ||||
| r | 0.617 | ||||
| b (slope, estimate of beta) | 0.716 | ||||
| a (intercept, estimate of alpha) | -0.238 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 30.000 | ||||
| t(b) | 4.289 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.277 | ||||
| p(a) | 0.894 | ||||
| Lowerbound of 95% confidence interval for beta | 0.375 | ||||
| Upperbound of 95% confidence interval for beta | 1.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.618 | ||||
| Upperbound of 95% confidence interval for alpha | 0.142 | ||||
| Treynor index (mean / b) | 0.276 | ||||
| Jensen alpha (a) | -0.238 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.148 | ||||
| SD | 0.311 | ||||
| Sharpe ratio (Glass type estimate) | 0.476 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.464 | ||||
| df | 31.000 | ||||
| t | 0.777 | ||||
| p | 0.221 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.734 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.678 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.741 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.670 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.788 | ||||
| Upside Potential Ratio | 2.747 | ||||
| Upside part of mean | 0.517 | ||||
| Downside part of mean | -0.368 | ||||
| Upside SD | 0.246 | ||||
| Downside SD | 0.188 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.559 | ||||
| Mean of criterion | 0.148 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 0.311 | ||||
| Covariance | 0.051 | ||||
| r | 0.636 | ||||
| b (slope, estimate of beta) | 0.772 | ||||
| a (intercept, estimate of alpha) | -0.284 | ||||
| Mean Square Error | 0.060 | ||||
| DF error | 30.000 | ||||
| t(b) | 4.513 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.597 | ||||
| p(a) | 0.940 | ||||
| Lowerbound of 95% confidence interval for beta | 0.423 | ||||
| Upperbound of 95% confidence interval for beta | 1.122 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.646 | ||||
| Upperbound of 95% confidence interval for alpha | 0.079 | ||||
| Treynor index (mean / b) | 0.192 | ||||
| Jensen alpha (a) | -0.284 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.127 | ||||
| Expected Shortfall on VaR | 0.158 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.118 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.852 | ||||
| Quartile 1 | 0.955 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.093 | ||||
| Maximum | 1.200 | ||||
| Mean of quarter 1 | 0.910 | ||||
| Mean of quarter 2 | 0.980 | ||||
| Mean of quarter 3 | 1.047 | ||||
| Mean of quarter 4 | 1.144 | ||||
| Inter Quartile Range | 0.137 | ||||
| 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) | -0.538 | ||||
| VaR(95%) (moments method) | 0.096 | ||||
| Expected Shortfall (moments method) | 0.110 | ||||
| Extreme Value Index (regression method) | -0.514 | ||||
| VaR(95%) (regression method) | 0.110 | ||||
| Expected Shortfall (regression method) | 0.126 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.072 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.208 | ||||
| Maximum | 0.240 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | 0.084 | ||||
| Mean of quarter 3 | 0.190 | ||||
| Mean of quarter 4 | 0.227 | ||||
| Inter Quartile Range | 0.136 | ||||
| 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) | 0.251 | ||||
| Compounded annual return (geometric extrapolation) | 0.212 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.884 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.934 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.338 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.522 | ||||
| Sharpe ratio (Glass type estimate) | -0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.035 | ||||
| df | 712.000 | ||||
| t | -0.057 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.223 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.154 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.223 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.154 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.039 | ||||
| Upside Potential Ratio | 4.310 | ||||
| Upside part of mean | 2.002 | ||||
| Downside part of mean | -2.020 | ||||
| Upside SD | 0.237 | ||||
| Downside SD | 0.465 | ||||
| N nonnegative terms | 375.000 | ||||
| N negative terms | 338.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 713.000 | ||||
| Mean of predictor | 0.664 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.522 | ||||
| Covariance | 0.073 | ||||
| r | 0.377 | ||||
| b (slope, estimate of beta) | 0.532 | ||||
| a (intercept, estimate of alpha) | -0.371 | ||||
| Mean Square Error | 0.234 | ||||
| DF error | 711.000 | ||||
| t(b) | 10.866 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.259 | ||||
| p(a) | 0.896 | ||||
| Lowerbound of 95% confidence interval for beta | 0.436 | ||||
| Upperbound of 95% confidence interval for beta | 0.628 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.950 | ||||
| Upperbound of 95% confidence interval for alpha | 0.208 | ||||
| Treynor index (mean / b) | -0.034 | ||||
| Jensen alpha (a) | -0.371 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.227 | ||||
| SD | 0.732 | ||||
| Sharpe ratio (Glass type estimate) | -0.310 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.310 | ||||
| df | 712.000 | ||||
| t | -0.511 | ||||
| p | 0.695 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.498 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.878 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.498 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.879 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.327 | ||||
| Upside Potential Ratio | 2.845 | ||||
| Upside part of mean | 1.975 | ||||
| Downside part of mean | -2.201 | ||||
| Upside SD | 0.232 | ||||
| Downside SD | 0.694 | ||||
| N nonnegative terms | 375.000 | ||||
| N negative terms | 338.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 713.000 | ||||
| Mean of predictor | 0.594 | ||||
| Mean of criterion | -0.227 | ||||
| SD of predictor | 0.376 | ||||
| SD of criterion | 0.732 | ||||
| Covariance | 0.074 | ||||
| r | 0.270 | ||||
| b (slope, estimate of beta) | 0.526 | ||||
| a (intercept, estimate of alpha) | -0.539 | ||||
| Mean Square Error | 0.497 | ||||
| DF error | 711.000 | ||||
| t(b) | 7.489 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.255 | ||||
| p(a) | 0.895 | ||||
| Lowerbound of 95% confidence interval for beta | 0.388 | ||||
| Upperbound of 95% confidence interval for beta | 0.664 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.382 | ||||
| Upperbound of 95% confidence interval for alpha | 0.304 | ||||
| Treynor index (mean / b) | -0.431 | ||||
| Jensen alpha (a) | -0.539 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.072 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 713.000 | ||||
| Minimum | 0.343 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.131 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 24.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.917 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.018 | ||||
| Mean of outliers high | 1.062 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.427 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.050 | ||||
| Extreme Value Index (regression method) | 0.216 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.012 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.110 | ||||
| Maximum | 0.661 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.254 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 0.405 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.236 | ||||
| VaR(95%) (moments method) | 0.267 | ||||
| Expected Shortfall (moments method) | 0.421 | ||||
| Extreme Value Index (regression method) | 0.469 | ||||
| VaR(95%) (regression method) | 0.264 | ||||
| Expected Shortfall (regression method) | 0.506 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.144 | ||||
| Compounded annual return (geometric extrapolation) | -0.167 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.253 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.658 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.862 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.918 | ||||
| SD | 1.006 | ||||
| Sharpe ratio (Glass type estimate) | -0.912 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.907 | ||||
| df | 130.000 | ||||
| t | -0.645 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.685 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.863 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.681 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.867 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.953 | ||||
| Upside Potential Ratio | 2.321 | ||||
| Upside part of mean | 2.235 | ||||
| Downside part of mean | -3.152 | ||||
| Upside SD | 0.284 | ||||
| Downside SD | 0.963 | ||||
| N nonnegative terms | 76.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.001 | ||||
| Mean of criterion | -0.918 | ||||
| SD of predictor | 0.486 | ||||
| SD of criterion | 1.006 | ||||
| Covariance | 0.101 | ||||
| r | 0.207 | ||||
| b (slope, estimate of beta) | 0.429 | ||||
| a (intercept, estimate of alpha) | -1.347 | ||||
| Mean Square Error | 0.976 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.405 | ||||
| p(b) | 0.369 | ||||
| t(a) | -0.957 | ||||
| p(a) | 0.553 | ||||
| Lowerbound of 95% confidence interval for beta | 0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.782 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.134 | ||||
| Upperbound of 95% confidence interval for alpha | 1.439 | ||||
| Treynor index (mean / b) | -2.139 | ||||
| Jensen alpha (a) | -1.347 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.814 | ||||
| SD | 1.561 | ||||
| Sharpe ratio (Glass type estimate) | -1.162 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.156 | ||||
| df | 130.000 | ||||
| t | -0.822 | ||||
| p | 0.536 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.936 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.615 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.931 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.620 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.182 | ||||
| Upside Potential Ratio | 1.431 | ||||
| Upside part of mean | 2.196 | ||||
| Downside part of mean | -4.010 | ||||
| Upside SD | 0.274 | ||||
| Downside SD | 1.535 | ||||
| N nonnegative terms | 76.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.883 | ||||
| Mean of criterion | -1.814 | ||||
| SD of predictor | 0.484 | ||||
| SD of criterion | 1.561 | ||||
| Covariance | 0.094 | ||||
| r | 0.125 | ||||
| b (slope, estimate of beta) | 0.403 | ||||
| a (intercept, estimate of alpha) | -2.170 | ||||
| Mean Square Error | 2.417 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.429 | ||||
| p(b) | 0.421 | ||||
| t(a) | -0.981 | ||||
| p(a) | 0.555 | ||||
| Lowerbound of 95% confidence interval for beta | -0.155 | ||||
| Upperbound of 95% confidence interval for beta | 0.961 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.548 | ||||
| Upperbound of 95% confidence interval for alpha | 2.208 | ||||
| Treynor index (mean / b) | -4.503 | ||||
| Jensen alpha (a) | -2.170 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.153 | ||||
| Expected Shortfall on VaR | 0.186 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.343 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.131 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.858 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.100 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.759 | ||||
| VaR(95%) (moments method) | 0.037 | ||||
| Expected Shortfall (moments method) | 0.163 | ||||
| Extreme Value Index (regression method) | 0.142 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.038 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.661 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.057 | ||||
| Mean of quarter 4 | 0.322 | ||||
| Inter Quartile Range | 0.063 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.447 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.155 | ||||
| VaR(95%) (moments method) | 0.231 | ||||
| Expected Shortfall (moments method) | 0.232 | ||||
| Extreme Value Index (regression method) | 0.398 | ||||
| VaR(95%) (regression method) | 0.740 | ||||
| Expected Shortfall (regression method) | 1.641 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -1.175 | ||||
| Compounded annual return (geometric extrapolation) | -0.830 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.255 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.575 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.472 | ||||