Advanced Statistics: Stock Trend Trader
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 | 0.238 | ||||
| SD | 0.428 | ||||
| Sharpe ratio (Glass type estimate) | 0.556 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.543 | ||||
| df | 33.000 | ||||
| t | 0.935 | ||||
| p | 0.178 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.620 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.724 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.629 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.715 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.987 | ||||
| Upside Potential Ratio | 2.843 | ||||
| Upside part of mean | 0.685 | ||||
| Downside part of mean | -0.447 | ||||
| Upside SD | 0.353 | ||||
| Downside SD | 0.241 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | 0.238 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.428 | ||||
| Covariance | 0.061 | ||||
| r | 0.473 | ||||
| b (slope, estimate of beta) | 0.676 | ||||
| a (intercept, estimate of alpha) | -0.142 | ||||
| Mean Square Error | 0.147 | ||||
| DF error | 32.000 | ||||
| t(b) | 3.037 | ||||
| p(b) | 0.002 | ||||
| t(a) | -0.547 | ||||
| p(a) | 0.706 | ||||
| Lowerbound of 95% confidence interval for beta | 0.223 | ||||
| Upperbound of 95% confidence interval for beta | 1.129 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.671 | ||||
| Upperbound of 95% confidence interval for alpha | 0.387 | ||||
| Treynor index (mean / b) | 0.352 | ||||
| Jensen alpha (a) | -0.142 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.151 | ||||
| SD | 0.415 | ||||
| Sharpe ratio (Glass type estimate) | 0.364 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.356 | ||||
| df | 33.000 | ||||
| t | 0.613 | ||||
| p | 0.272 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.806 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.529 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.812 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.523 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.575 | ||||
| Upside Potential Ratio | 2.394 | ||||
| Upside part of mean | 0.629 | ||||
| Downside part of mean | -0.478 | ||||
| Upside SD | 0.316 | ||||
| Downside SD | 0.263 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.509 | ||||
| Mean of criterion | 0.151 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.415 | ||||
| Covariance | 0.059 | ||||
| r | 0.504 | ||||
| b (slope, estimate of beta) | 0.742 | ||||
| a (intercept, estimate of alpha) | -0.226 | ||||
| Mean Square Error | 0.132 | ||||
| DF error | 32.000 | ||||
| t(b) | 3.301 | ||||
| p(b) | 0.001 | ||||
| t(a) | -0.926 | ||||
| p(a) | 0.819 | ||||
| Lowerbound of 95% confidence interval for beta | 0.284 | ||||
| Upperbound of 95% confidence interval for beta | 1.200 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.724 | ||||
| Upperbound of 95% confidence interval for alpha | 0.271 | ||||
| Treynor index (mean / b) | 0.204 | ||||
| Jensen alpha (a) | -0.226 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.168 | ||||
| Expected Shortfall on VaR | 0.208 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.080 | ||||
| Expected Shortfall on VaR | 0.152 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.765 | ||||
| Quartile 1 | 0.939 | ||||
| Median | 1.021 | ||||
| Quartile 3 | 1.089 | ||||
| Maximum | 1.362 | ||||
| Mean of quarter 1 | 0.883 | ||||
| Mean of quarter 2 | 0.985 | ||||
| Mean of quarter 3 | 1.048 | ||||
| Mean of quarter 4 | 1.177 | ||||
| Inter Quartile Range | 0.150 | ||||
| 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 | 0.029 | ||||
| Mean of outliers high | 1.362 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.190 | ||||
| VaR(95%) (moments method) | 0.123 | ||||
| Expected Shortfall (moments method) | 0.152 | ||||
| Extreme Value Index (regression method) | 0.137 | ||||
| VaR(95%) (regression method) | 0.147 | ||||
| Expected Shortfall (regression method) | 0.214 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.054 | ||||
| Median | 0.093 | ||||
| Quartile 3 | 0.199 | ||||
| Maximum | 0.318 | ||||
| Mean of quarter 1 | 0.042 | ||||
| Mean of quarter 2 | 0.060 | ||||
| Mean of quarter 3 | 0.126 | ||||
| Mean of quarter 4 | 0.271 | ||||
| Inter Quartile Range | 0.146 | ||||
| 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) | 0.260 | ||||
| Compounded annual return (geometric extrapolation) | 0.215 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.677 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.795 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.035 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.326 | ||||
| SD | 0.557 | ||||
| Sharpe ratio (Glass type estimate) | 0.585 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.584 | ||||
| df | 753.000 | ||||
| t | 0.992 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.571 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.740 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.572 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.740 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.905 | ||||
| Upside Potential Ratio | 7.413 | ||||
| Upside part of mean | 2.671 | ||||
| Downside part of mean | -2.345 | ||||
| Upside SD | 0.425 | ||||
| Downside SD | 0.360 | ||||
| N nonnegative terms | 383.000 | ||||
| N negative terms | 371.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 754.000 | ||||
| Mean of predictor | 0.588 | ||||
| Mean of criterion | 0.326 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 0.557 | ||||
| Covariance | 0.060 | ||||
| r | 0.337 | ||||
| b (slope, estimate of beta) | 0.589 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.276 | ||||
| DF error | 752.000 | ||||
| t(b) | 9.811 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.065 | ||||
| p(a) | 0.526 | ||||
| Lowerbound of 95% confidence interval for beta | 0.471 | ||||
| Upperbound of 95% confidence interval for beta | 0.706 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.632 | ||||
| Upperbound of 95% confidence interval for alpha | 0.591 | ||||
| Treynor index (mean / b) | 0.554 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.173 | ||||
| SD | 0.551 | ||||
| Sharpe ratio (Glass type estimate) | 0.315 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.315 | ||||
| df | 753.000 | ||||
| t | 0.534 | ||||
| p | 0.297 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.841 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.470 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.841 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.470 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.455 | ||||
| Upside Potential Ratio | 6.792 | ||||
| Upside part of mean | 2.588 | ||||
| Downside part of mean | -2.414 | ||||
| Upside SD | 0.398 | ||||
| Downside SD | 0.381 | ||||
| N nonnegative terms | 383.000 | ||||
| N negative terms | 371.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 754.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | 0.173 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 0.551 | ||||
| Covariance | 0.064 | ||||
| r | 0.356 | ||||
| b (slope, estimate of beta) | 0.607 | ||||
| a (intercept, estimate of alpha) | -0.152 | ||||
| Mean Square Error | 0.265 | ||||
| DF error | 752.000 | ||||
| t(b) | 10.463 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.498 | ||||
| p(a) | 0.691 | ||||
| Lowerbound of 95% confidence interval for beta | 0.493 | ||||
| Upperbound of 95% confidence interval for beta | 0.721 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.751 | ||||
| Upperbound of 95% confidence interval for alpha | 0.447 | ||||
| Treynor index (mean / b) | 0.286 | ||||
| Jensen alpha (a) | -0.152 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 754.000 | ||||
| Minimum | 0.776 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.312 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 46.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.926 | ||||
| Number of outliers high | 44.000 | ||||
| Percentage of outliers high | 0.058 | ||||
| Mean of outliers high | 1.084 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.508 | ||||
| VaR(95%) (moments method) | 0.031 | ||||
| Expected Shortfall (moments method) | 0.072 | ||||
| Extreme Value Index (regression method) | 0.313 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.049 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 16.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.039 | ||||
| Quartile 3 | 0.118 | ||||
| Maximum | 0.403 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.091 | ||||
| Mean of quarter 4 | 0.288 | ||||
| Inter Quartile Range | 0.100 | ||||
| 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 | 0.188 | ||||
| Mean of outliers high | 0.343 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -23.591 | ||||
| VaR(95%) (moments method) | 0.254 | ||||
| Expected Shortfall (moments method) | 0.254 | ||||
| Extreme Value Index (regression method) | -1.738 | ||||
| VaR(95%) (regression method) | 0.441 | ||||
| Expected Shortfall (regression method) | 0.456 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.302 | ||||
| Compounded annual return (geometric extrapolation) | 0.243 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.602 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.844 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.620 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.114 | ||||
| SD | 0.419 | ||||
| Sharpe ratio (Glass type estimate) | 0.271 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.270 | ||||
| df | 130.000 | ||||
| t | 0.192 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.501 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.043 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.502 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.042 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.366 | ||||
| Upside Potential Ratio | 7.780 | ||||
| Upside part of mean | 2.411 | ||||
| Downside part of mean | -2.298 | ||||
| Upside SD | 0.279 | ||||
| Downside SD | 0.310 | ||||
| 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 | 1.358 | ||||
| Mean of criterion | 0.114 | ||||
| SD of predictor | 0.473 | ||||
| SD of criterion | 0.419 | ||||
| Covariance | 0.106 | ||||
| r | 0.532 | ||||
| b (slope, estimate of beta) | 0.471 | ||||
| a (intercept, estimate of alpha) | -0.526 | ||||
| Mean Square Error | 0.127 | ||||
| DF error | 129.000 | ||||
| t(b) | 7.145 | ||||
| p(b) | 0.178 | ||||
| t(a) | -1.029 | ||||
| p(a) | 0.557 | ||||
| Lowerbound of 95% confidence interval for beta | 0.341 | ||||
| Upperbound of 95% confidence interval for beta | 0.602 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.538 | ||||
| Upperbound of 95% confidence interval for alpha | 0.485 | ||||
| Treynor index (mean / b) | 0.241 | ||||
| Jensen alpha (a) | -0.526 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.424 | ||||
| Sharpe ratio (Glass type estimate) | 0.059 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.059 | ||||
| df | 130.000 | ||||
| t | 0.042 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.713 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.831 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.713 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.830 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.078 | ||||
| Upside Potential Ratio | 7.358 | ||||
| Upside part of mean | 2.373 | ||||
| Downside part of mean | -2.348 | ||||
| Upside SD | 0.273 | ||||
| Downside SD | 0.323 | ||||
| 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 | 1.242 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.477 | ||||
| SD of criterion | 0.424 | ||||
| Covariance | 0.109 | ||||
| r | 0.539 | ||||
| b (slope, estimate of beta) | 0.480 | ||||
| a (intercept, estimate of alpha) | -0.571 | ||||
| Mean Square Error | 0.129 | ||||
| DF error | 129.000 | ||||
| t(b) | 7.274 | ||||
| p(b) | 0.174 | ||||
| t(a) | -1.111 | ||||
| p(a) | 0.562 | ||||
| Lowerbound of 95% confidence interval for beta | 0.349 | ||||
| Upperbound of 95% confidence interval for beta | 0.610 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.588 | ||||
| Upperbound of 95% confidence interval for alpha | 0.446 | ||||
| Treynor index (mean / b) | 0.052 | ||||
| Jensen alpha (a) | -0.571 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.872 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.016 | ||||
| Maximum | 1.075 | ||||
| Mean of quarter 1 | 0.971 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.916 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.064 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.105 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | 0.038 | ||||
| Extreme Value Index (regression method) | 0.487 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.114 | ||||
| Maximum | 0.327 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.023 | ||||
| Mean of quarter 3 | 0.043 | ||||
| Mean of quarter 4 | 0.327 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.327 | ||||
| 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) | 0.070 | ||||
| Compounded annual return (geometric extrapolation) | 0.071 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.219 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.219 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.361 | ||||