Advanced Statistics: Penny Stock Shorter
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 | 0.372 | ||||
| SD | 0.850 | ||||
| Sharpe ratio (Glass type estimate) | 0.438 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.427 | ||||
| df | 29.000 | ||||
| t | 0.692 | ||||
| p | 0.247 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.810 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.679 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.818 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.671 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.196 | ||||
| Upside Potential Ratio | 2.346 | ||||
| Upside part of mean | 0.730 | ||||
| Downside part of mean | -0.358 | ||||
| Upside SD | 0.783 | ||||
| Downside SD | 0.311 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.641 | ||||
| Mean of criterion | 0.372 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.850 | ||||
| Covariance | 0.002 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | 0.363 | ||||
| Mean Square Error | 0.748 | ||||
| DF error | 28.000 | ||||
| t(b) | 0.029 | ||||
| p(b) | 0.489 | ||||
| t(a) | 0.577 | ||||
| p(a) | 0.284 | ||||
| Lowerbound of 95% confidence interval for beta | -0.984 | ||||
| Upperbound of 95% confidence interval for beta | 1.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.927 | ||||
| Upperbound of 95% confidence interval for alpha | 1.654 | ||||
| Treynor index (mean / b) | 26.379 | ||||
| Jensen alpha (a) | 0.363 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.126 | ||||
| SD | 0.666 | ||||
| Sharpe ratio (Glass type estimate) | 0.190 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.185 | ||||
| df | 29.000 | ||||
| t | 0.300 | ||||
| p | 0.383 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.052 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.429 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.056 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.425 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.319 | ||||
| Upside Potential Ratio | 1.386 | ||||
| Upside part of mean | 0.550 | ||||
| Downside part of mean | -0.423 | ||||
| Upside SD | 0.523 | ||||
| Downside SD | 0.396 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | 0.126 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.666 | ||||
| Covariance | 0.007 | ||||
| r | 0.037 | ||||
| b (slope, estimate of beta) | 0.083 | ||||
| a (intercept, estimate of alpha) | 0.079 | ||||
| Mean Square Error | 0.459 | ||||
| DF error | 28.000 | ||||
| t(b) | 0.196 | ||||
| p(b) | 0.423 | ||||
| t(a) | 0.160 | ||||
| p(a) | 0.437 | ||||
| Lowerbound of 95% confidence interval for beta | -0.782 | ||||
| Upperbound of 95% confidence interval for beta | 0.947 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.931 | ||||
| Upperbound of 95% confidence interval for alpha | 1.089 | ||||
| Treynor index (mean / b) | 1.530 | ||||
| Jensen alpha (a) | 0.079 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.264 | ||||
| Expected Shortfall on VaR | 0.319 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.148 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 30.000 | ||||
| Minimum | 0.561 | ||||
| Quartile 1 | 0.986 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 2.216 | ||||
| Mean of quarter 1 | 0.897 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 1.224 | ||||
| Inter Quartile Range | 0.034 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.100 | ||||
| Mean of outliers low | 0.769 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 1.341 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.092 | ||||
| VaR(95%) (moments method) | 0.099 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.055 | ||||
| VaR(95%) (regression method) | 0.109 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.036 | ||||
| Median | 0.046 | ||||
| Quartile 3 | 0.105 | ||||
| Maximum | 0.543 | ||||
| Mean of quarter 1 | 0.023 | ||||
| Mean of quarter 2 | 0.046 | ||||
| Mean of quarter 3 | 0.105 | ||||
| Mean of quarter 4 | 0.543 | ||||
| Inter Quartile Range | 0.069 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.543 | ||||
| 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) | 0.212 | ||||
| Compounded annual return (geometric extrapolation) | 0.186 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.342 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.342 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.583 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.241 | ||||
| SD | 0.493 | ||||
| Sharpe ratio (Glass type estimate) | 0.489 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.489 | ||||
| df | 667.000 | ||||
| t | 0.781 | ||||
| p | 0.217 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.738 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.717 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.739 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.717 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.797 | ||||
| Upside Potential Ratio | 5.062 | ||||
| Upside part of mean | 1.532 | ||||
| Downside part of mean | -1.291 | ||||
| Upside SD | 0.389 | ||||
| Downside SD | 0.303 | ||||
| N nonnegative terms | 290.000 | ||||
| N negative terms | 378.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 668.000 | ||||
| Mean of predictor | 0.697 | ||||
| Mean of criterion | 0.241 | ||||
| SD of predictor | 0.366 | ||||
| SD of criterion | 0.493 | ||||
| Covariance | -0.010 | ||||
| r | -0.054 | ||||
| b (slope, estimate of beta) | -0.072 | ||||
| a (intercept, estimate of alpha) | 0.291 | ||||
| Mean Square Error | 0.242 | ||||
| DF error | 666.000 | ||||
| t(b) | -1.386 | ||||
| p(b) | 0.917 | ||||
| t(a) | 0.939 | ||||
| p(a) | 0.174 | ||||
| Lowerbound of 95% confidence interval for beta | -0.174 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.318 | ||||
| Upperbound of 95% confidence interval for alpha | 0.901 | ||||
| Treynor index (mean / b) | -3.343 | ||||
| Jensen alpha (a) | 0.291 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.123 | ||||
| SD | 0.484 | ||||
| Sharpe ratio (Glass type estimate) | 0.254 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.254 | ||||
| df | 667.000 | ||||
| t | 0.406 | ||||
| p | 0.342 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.973 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.482 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.974 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.481 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.376 | ||||
| Upside Potential Ratio | 4.476 | ||||
| Upside part of mean | 1.464 | ||||
| Downside part of mean | -1.341 | ||||
| Upside SD | 0.357 | ||||
| Downside SD | 0.327 | ||||
| N nonnegative terms | 290.000 | ||||
| N negative terms | 378.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 668.000 | ||||
| Mean of predictor | 0.628 | ||||
| Mean of criterion | 0.123 | ||||
| SD of predictor | 0.369 | ||||
| SD of criterion | 0.484 | ||||
| Covariance | -0.009 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.068 | ||||
| a (intercept, estimate of alpha) | 0.166 | ||||
| Mean Square Error | 0.234 | ||||
| DF error | 666.000 | ||||
| t(b) | -1.348 | ||||
| p(b) | 0.911 | ||||
| t(a) | 0.545 | ||||
| p(a) | 0.293 | ||||
| Lowerbound of 95% confidence interval for beta | -0.168 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.432 | ||||
| Upperbound of 95% confidence interval for alpha | 0.764 | ||||
| Treynor index (mean / b) | -1.798 | ||||
| Jensen alpha (a) | 0.166 | ||||
| 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 | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 668.000 | ||||
| Minimum | 0.746 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.307 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 61.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 60.000 | ||||
| Percentage of outliers high | 0.090 | ||||
| Mean of outliers high | 1.053 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.115 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 24.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.028 | ||||
| Maximum | 0.628 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.018 | ||||
| Mean of quarter 4 | 0.167 | ||||
| Inter Quartile Range | 0.026 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.282 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.883 | ||||
| VaR(95%) (moments method) | 0.167 | ||||
| Expected Shortfall (moments method) | 1.461 | ||||
| Extreme Value Index (regression method) | 1.660 | ||||
| VaR(95%) (regression method) | 0.199 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.208 | ||||
| Compounded annual return (geometric extrapolation) | 0.182 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.290 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.091 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.065 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.101 | ||||
| SD | 0.151 | ||||
| Sharpe ratio (Glass type estimate) | 0.672 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.668 | ||||
| df | 130.000 | ||||
| t | 0.475 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.102 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.444 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.105 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.441 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.416 | ||||
| Upside Potential Ratio | 7.100 | ||||
| Upside part of mean | 0.211 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.147 | ||||
| Downside SD | 0.030 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 127.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.473 | ||||
| Mean of criterion | 0.101 | ||||
| SD of predictor | 0.563 | ||||
| SD of criterion | 0.151 | ||||
| Covariance | 0.002 | ||||
| r | 0.019 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.094 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.216 | ||||
| p(b) | 0.488 | ||||
| t(a) | 0.433 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.335 | ||||
| Upperbound of 95% confidence interval for alpha | 0.523 | ||||
| Treynor index (mean / b) | 19.884 | ||||
| Jensen alpha (a) | 0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.091 | ||||
| SD | 0.144 | ||||
| Sharpe ratio (Glass type estimate) | 0.631 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.627 | ||||
| df | 130.000 | ||||
| t | 0.446 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.143 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.403 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.145 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.400 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.033 | ||||
| Upside Potential Ratio | 6.701 | ||||
| Upside part of mean | 0.201 | ||||
| Downside part of mean | -0.110 | ||||
| Upside SD | 0.140 | ||||
| Downside SD | 0.030 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 127.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.312 | ||||
| Mean of criterion | 0.091 | ||||
| SD of predictor | 0.564 | ||||
| SD of criterion | 0.144 | ||||
| Covariance | 0.002 | ||||
| r | 0.020 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.084 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.226 | ||||
| p(b) | 0.487 | ||||
| t(a) | 0.408 | ||||
| p(a) | 0.477 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.324 | ||||
| Upperbound of 95% confidence interval for alpha | 0.492 | ||||
| Treynor index (mean / b) | 17.883 | ||||
| Jensen alpha (a) | 0.084 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.981 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.051 | ||||
| VaR(95%) (moments method) | -0.047 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.185 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.032 | ||||
| Maximum | 0.032 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| 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) | 0.139 | ||||
| Compounded annual return (geometric extrapolation) | 0.144 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.530 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.098 | ||||