Advanced Statistics: TraderXStocks-Options-ETF
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 | 0.632 | ||||
| SD | 1.322 | ||||
| Sharpe ratio (Glass type estimate) | 0.478 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.471 | ||||
| df | 51.000 | ||||
| t | 0.995 | ||||
| p | 0.162 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.470 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.422 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.475 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.256 | ||||
| Upside Potential Ratio | 2.783 | ||||
| Upside part of mean | 1.400 | ||||
| Downside part of mean | -0.768 | ||||
| Upside SD | 1.222 | ||||
| Downside SD | 0.503 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.421 | ||||
| Mean of criterion | 0.632 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 1.322 | ||||
| Covariance | -0.004 | ||||
| r | -0.013 | ||||
| b (slope, estimate of beta) | -0.068 | ||||
| a (intercept, estimate of alpha) | 0.661 | ||||
| Mean Square Error | 1.782 | ||||
| DF error | 50.000 | ||||
| t(b) | -0.088 | ||||
| p(b) | 0.535 | ||||
| t(a) | 0.918 | ||||
| p(a) | 0.181 | ||||
| Lowerbound of 95% confidence interval for beta | -1.622 | ||||
| Upperbound of 95% confidence interval for beta | 1.485 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.784 | ||||
| Upperbound of 95% confidence interval for alpha | 2.105 | ||||
| Treynor index (mean / b) | -9.228 | ||||
| Jensen alpha (a) | 0.661 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 1.177 | ||||
| Sharpe ratio (Glass type estimate) | -0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.015 | ||||
| df | 51.000 | ||||
| t | -0.031 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.957 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.927 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.956 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.927 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.020 | ||||
| Upside Potential Ratio | 1.131 | ||||
| Upside part of mean | 1.010 | ||||
| Downside part of mean | -1.028 | ||||
| Upside SD | 0.749 | ||||
| Downside SD | 0.893 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.385 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 1.177 | ||||
| Covariance | -0.026 | ||||
| r | -0.094 | ||||
| b (slope, estimate of beta) | -0.469 | ||||
| a (intercept, estimate of alpha) | 0.163 | ||||
| Mean Square Error | 1.401 | ||||
| DF error | 50.000 | ||||
| t(b) | -0.666 | ||||
| p(b) | 0.746 | ||||
| t(a) | 0.259 | ||||
| p(a) | 0.398 | ||||
| Lowerbound of 95% confidence interval for beta | -1.881 | ||||
| Upperbound of 95% confidence interval for beta | 0.944 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.102 | ||||
| Upperbound of 95% confidence interval for alpha | 1.428 | ||||
| Treynor index (mean / b) | 0.038 | ||||
| Jensen alpha (a) | 0.163 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.429 | ||||
| Expected Shortfall on VaR | 0.501 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.160 | ||||
| Expected Shortfall on VaR | 0.322 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.182 | ||||
| Quartile 1 | 0.908 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.095 | ||||
| Maximum | 2.775 | ||||
| Mean of quarter 1 | 0.793 | ||||
| Mean of quarter 2 | 0.959 | ||||
| Mean of quarter 3 | 1.034 | ||||
| Mean of quarter 4 | 1.439 | ||||
| Inter Quartile Range | 0.187 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.019 | ||||
| Mean of outliers low | 0.182 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.058 | ||||
| Mean of outliers high | 2.274 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.662 | ||||
| VaR(95%) (moments method) | 0.239 | ||||
| Expected Shortfall (moments method) | 0.677 | ||||
| Extreme Value Index (regression method) | 0.768 | ||||
| VaR(95%) (regression method) | 0.157 | ||||
| Expected Shortfall (regression method) | 0.446 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.085 | ||||
| Median | 0.449 | ||||
| Quartile 3 | 0.796 | ||||
| Maximum | 0.818 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.109 | ||||
| Mean of quarter 3 | 0.789 | ||||
| Mean of quarter 4 | 0.818 | ||||
| Inter Quartile Range | 0.711 | ||||
| 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) | 0.028 | ||||
| Compounded annual return (geometric extrapolation) | 0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.033 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.033 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.053 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.312 | ||||
| SD | 2.627 | ||||
| Sharpe ratio (Glass type estimate) | 0.499 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.499 | ||||
| df | 1152.000 | ||||
| t | 1.047 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.435 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.434 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.436 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.433 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.182 | ||||
| Upside Potential Ratio | 7.281 | ||||
| Upside part of mean | 4.377 | ||||
| Downside part of mean | -3.065 | ||||
| Upside SD | 2.558 | ||||
| Downside SD | 0.601 | ||||
| N nonnegative terms | 515.000 | ||||
| N negative terms | 638.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1153.000 | ||||
| Mean of predictor | 0.443 | ||||
| Mean of criterion | 1.312 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 2.627 | ||||
| Covariance | 0.095 | ||||
| r | 0.117 | ||||
| b (slope, estimate of beta) | 0.993 | ||||
| a (intercept, estimate of alpha) | 0.872 | ||||
| Mean Square Error | 6.815 | ||||
| DF error | 1151.000 | ||||
| t(b) | 3.994 | ||||
| p(b) | 0.426 | ||||
| t(a) | 0.698 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | 0.505 | ||||
| Upperbound of 95% confidence interval for beta | 1.481 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.580 | ||||
| Upperbound of 95% confidence interval for alpha | 3.323 | ||||
| Treynor index (mean / b) | 1.321 | ||||
| Jensen alpha (a) | 0.872 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 1.411 | ||||
| Sharpe ratio (Glass type estimate) | -0.013 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.013 | ||||
| df | 1152.000 | ||||
| t | -0.027 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.947 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.921 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.947 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.921 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.021 | ||||
| Upside Potential Ratio | 3.817 | ||||
| Upside part of mean | 3.335 | ||||
| Downside part of mean | -3.353 | ||||
| Upside SD | 1.108 | ||||
| Downside SD | 0.874 | ||||
| N nonnegative terms | 515.000 | ||||
| N negative terms | 638.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1153.000 | ||||
| Mean of predictor | 0.395 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 1.411 | ||||
| Covariance | 0.080 | ||||
| r | 0.182 | ||||
| b (slope, estimate of beta) | 0.823 | ||||
| a (intercept, estimate of alpha) | -0.343 | ||||
| Mean Square Error | 1.928 | ||||
| DF error | 1151.000 | ||||
| t(b) | 6.279 | ||||
| p(b) | 0.385 | ||||
| t(a) | -0.516 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.566 | ||||
| Upperbound of 95% confidence interval for beta | 1.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.645 | ||||
| Upperbound of 95% confidence interval for alpha | 0.960 | ||||
| Treynor index (mean / b) | -0.022 | ||||
| Jensen alpha (a) | -0.343 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.134 | ||||
| Expected Shortfall on VaR | 0.164 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1153.000 | ||||
| Minimum | 0.241 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 5.812 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.063 | ||||
| Inter Quartile Range | 0.024 | ||||
| Number outliers low | 73.000 | ||||
| Percentage of outliers low | 0.063 | ||||
| Mean of outliers low | 0.904 | ||||
| Number of outliers high | 68.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.184 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.407 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.075 | ||||
| Extreme Value Index (regression method) | 0.240 | ||||
| VaR(95%) (regression method) | 0.040 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.060 | ||||
| Quartile 3 | 0.107 | ||||
| Maximum | 0.937 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.043 | ||||
| Mean of quarter 3 | 0.076 | ||||
| Mean of quarter 4 | 0.439 | ||||
| Inter Quartile Range | 0.086 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.873 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.585 | ||||
| VaR(95%) (moments method) | 0.433 | ||||
| Expected Shortfall (moments method) | 1.221 | ||||
| Extreme Value Index (regression method) | 0.053 | ||||
| VaR(95%) (regression method) | 0.514 | ||||
| Expected Shortfall (regression method) | 0.784 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.028 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.060 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.160 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.368 | ||||
| SD | 0.319 | ||||
| Sharpe ratio (Glass type estimate) | -1.152 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.146 | ||||
| df | 130.000 | ||||
| t | -0.815 | ||||
| p | 0.536 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.925 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.625 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.921 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.630 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.387 | ||||
| Upside Potential Ratio | 1.941 | ||||
| Upside part of mean | 0.515 | ||||
| Downside part of mean | -0.883 | ||||
| Upside SD | 0.177 | ||||
| Downside SD | 0.265 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 102.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.277 | ||||
| Mean of criterion | -0.368 | ||||
| SD of predictor | 0.408 | ||||
| SD of criterion | 0.319 | ||||
| Covariance | 0.002 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.384 | ||||
| Mean Square Error | 0.103 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.184 | ||||
| p(b) | 0.490 | ||||
| t(a) | -0.832 | ||||
| p(a) | 0.546 | ||||
| Lowerbound of 95% confidence interval for beta | -0.124 | ||||
| Upperbound of 95% confidence interval for beta | 0.149 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.298 | ||||
| Upperbound of 95% confidence interval for alpha | 0.529 | ||||
| Treynor index (mean / b) | -28.955 | ||||
| Jensen alpha (a) | -0.384 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.421 | ||||
| SD | 0.329 | ||||
| Sharpe ratio (Glass type estimate) | -1.278 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.270 | ||||
| df | 130.000 | ||||
| t | -0.903 | ||||
| p | 0.539 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.501 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.046 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.506 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.494 | ||||
| Upside Potential Ratio | 1.775 | ||||
| Upside part of mean | 0.500 | ||||
| Downside part of mean | -0.921 | ||||
| Upside SD | 0.170 | ||||
| Downside SD | 0.282 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 102.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.191 | ||||
| Mean of criterion | -0.421 | ||||
| SD of predictor | 0.409 | ||||
| SD of criterion | 0.329 | ||||
| Covariance | 0.001 | ||||
| r | 0.010 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.431 | ||||
| Mean Square Error | 0.109 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.113 | ||||
| p(b) | 0.494 | ||||
| t(a) | -0.906 | ||||
| p(a) | 0.551 | ||||
| Lowerbound of 95% confidence interval for beta | -0.132 | ||||
| Upperbound of 95% confidence interval for beta | 0.148 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.371 | ||||
| Upperbound of 95% confidence interval for alpha | 0.510 | ||||
| Treynor index (mean / b) | -52.516 | ||||
| Jensen alpha (a) | -0.431 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.854 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.099 | ||||
| Mean of quarter 1 | 0.987 | ||||
| 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 | 31.000 | ||||
| Percentage of outliers low | 0.237 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 29.000 | ||||
| Percentage of outliers high | 0.221 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.640 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.651 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.133 | ||||
| Quartile 1 | 0.156 | ||||
| Median | 0.178 | ||||
| Quartile 3 | 0.201 | ||||
| Maximum | 0.223 | ||||
| Mean of quarter 1 | 0.133 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.223 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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) | -0.344 | ||||
| Compounded annual return (geometric extrapolation) | -0.314 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.408 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.408 | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.367 | ||||