Advanced Statistics: FiveStar Stocks
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 | 0.400 | ||||
| SD | 0.374 | ||||
| Sharpe ratio (Glass type estimate) | 1.067 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.048 | ||||
| df | 41.000 | ||||
| t | 1.997 | ||||
| p | 0.026 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.012 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.134 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.024 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.119 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.700 | ||||
| Upside Potential Ratio | 4.112 | ||||
| Upside part of mean | 0.608 | ||||
| Downside part of mean | -0.209 | ||||
| Upside SD | 0.358 | ||||
| Downside SD | 0.148 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 14.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | 0.400 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 0.374 | ||||
| Covariance | 0.039 | ||||
| r | 0.404 | ||||
| b (slope, estimate of beta) | 0.590 | ||||
| a (intercept, estimate of alpha) | 0.099 | ||||
| Mean Square Error | 0.120 | ||||
| DF error | 40.000 | ||||
| t(b) | 2.795 | ||||
| p(b) | 0.004 | ||||
| t(a) | 0.461 | ||||
| p(a) | 0.324 | ||||
| Lowerbound of 95% confidence interval for beta | 0.163 | ||||
| Upperbound of 95% confidence interval for beta | 1.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.334 | ||||
| Upperbound of 95% confidence interval for alpha | 0.532 | ||||
| Treynor index (mean / b) | 0.677 | ||||
| Jensen alpha (a) | 0.099 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.334 | ||||
| SD | 0.337 | ||||
| Sharpe ratio (Glass type estimate) | 0.992 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.974 | ||||
| df | 41.000 | ||||
| t | 1.856 | ||||
| p | 0.035 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.083 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.056 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.095 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.043 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.099 | ||||
| Upside Potential Ratio | 3.483 | ||||
| Upside part of mean | 0.554 | ||||
| Downside part of mean | -0.220 | ||||
| Upside SD | 0.307 | ||||
| Downside SD | 0.159 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 14.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | 0.334 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.337 | ||||
| Covariance | 0.038 | ||||
| r | 0.456 | ||||
| b (slope, estimate of beta) | 0.623 | ||||
| a (intercept, estimate of alpha) | 0.043 | ||||
| Mean Square Error | 0.092 | ||||
| DF error | 40.000 | ||||
| t(b) | 3.243 | ||||
| p(b) | 0.001 | ||||
| t(a) | 0.230 | ||||
| p(a) | 0.410 | ||||
| Lowerbound of 95% confidence interval for beta | 0.235 | ||||
| Upperbound of 95% confidence interval for beta | 1.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.332 | ||||
| Upperbound of 95% confidence interval for alpha | 0.417 | ||||
| Treynor index (mean / b) | 0.536 | ||||
| Jensen alpha (a) | 0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.124 | ||||
| Expected Shortfall on VaR | 0.158 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.818 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.025 | ||||
| Quartile 3 | 1.071 | ||||
| Maximum | 1.486 | ||||
| Mean of quarter 1 | 0.939 | ||||
| Mean of quarter 2 | 1.008 | ||||
| Mean of quarter 3 | 1.045 | ||||
| Mean of quarter 4 | 1.155 | ||||
| Inter Quartile Range | 0.076 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.048 | ||||
| Mean of outliers low | 0.837 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.048 | ||||
| Mean of outliers high | 1.414 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.813 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.027 | ||||
| Extreme Value Index (regression method) | 0.224 | ||||
| VaR(95%) (regression method) | 0.058 | ||||
| Expected Shortfall (regression method) | 0.108 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.141 | ||||
| Maximum | 0.189 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.069 | ||||
| Mean of quarter 3 | 0.101 | ||||
| Mean of quarter 4 | 0.185 | ||||
| Inter Quartile Range | 0.108 | ||||
| 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) | 0.787 | ||||
| Compounded annual return (geometric extrapolation) | 0.459 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.435 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.479 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.907 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.458 | ||||
| SD | 0.587 | ||||
| Sharpe ratio (Glass type estimate) | 0.781 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.780 | ||||
| df | 931.000 | ||||
| t | 1.473 | ||||
| p | 0.071 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.259 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.820 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.260 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.820 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.344 | ||||
| Upside Potential Ratio | 7.004 | ||||
| Upside part of mean | 2.388 | ||||
| Downside part of mean | -1.930 | ||||
| Upside SD | 0.478 | ||||
| Downside SD | 0.341 | ||||
| N nonnegative terms | 489.000 | ||||
| N negative terms | 443.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 932.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | 0.458 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 0.587 | ||||
| Covariance | 0.048 | ||||
| r | 0.257 | ||||
| b (slope, estimate of beta) | 0.473 | ||||
| a (intercept, estimate of alpha) | 0.201 | ||||
| Mean Square Error | 0.322 | ||||
| DF error | 930.000 | ||||
| t(b) | 8.111 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.664 | ||||
| p(a) | 0.254 | ||||
| Lowerbound of 95% confidence interval for beta | 0.359 | ||||
| Upperbound of 95% confidence interval for beta | 0.587 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.393 | ||||
| Upperbound of 95% confidence interval for alpha | 0.795 | ||||
| Treynor index (mean / b) | 0.969 | ||||
| Jensen alpha (a) | 0.201 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.295 | ||||
| SD | 0.566 | ||||
| Sharpe ratio (Glass type estimate) | 0.521 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.521 | ||||
| df | 931.000 | ||||
| t | 0.983 | ||||
| p | 0.163 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.518 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.561 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.519 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.560 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.785 | ||||
| Upside Potential Ratio | 6.093 | ||||
| Upside part of mean | 2.291 | ||||
| Downside part of mean | -1.996 | ||||
| Upside SD | 0.424 | ||||
| Downside SD | 0.376 | ||||
| N nonnegative terms | 489.000 | ||||
| N negative terms | 443.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 932.000 | ||||
| Mean of predictor | 0.493 | ||||
| Mean of criterion | 0.295 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.566 | ||||
| Covariance | 0.048 | ||||
| r | 0.262 | ||||
| b (slope, estimate of beta) | 0.461 | ||||
| a (intercept, estimate of alpha) | 0.068 | ||||
| Mean Square Error | 0.299 | ||||
| DF error | 930.000 | ||||
| t(b) | 8.277 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.234 | ||||
| p(a) | 0.407 | ||||
| Lowerbound of 95% confidence interval for beta | 0.352 | ||||
| Upperbound of 95% confidence interval for beta | 0.570 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.503 | ||||
| Upperbound of 95% confidence interval for alpha | 0.640 | ||||
| Treynor index (mean / b) | 0.641 | ||||
| Jensen alpha (a) | 0.068 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 932.000 | ||||
| Minimum | 0.673 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.493 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.017 | ||||
| Number outliers low | 50.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.935 | ||||
| Number of outliers high | 45.000 | ||||
| Percentage of outliers high | 0.048 | ||||
| Mean of outliers high | 1.090 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.511 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.058 | ||||
| Extreme Value Index (regression method) | 0.386 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.045 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.034 | ||||
| Maximum | 0.416 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.126 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.145 | ||||
| Mean of outliers high | 0.183 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.189 | ||||
| VaR(95%) (moments method) | 0.107 | ||||
| Expected Shortfall (moments method) | 0.172 | ||||
| Extreme Value Index (regression method) | 0.227 | ||||
| VaR(95%) (regression method) | 0.126 | ||||
| Expected Shortfall (regression method) | 0.213 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.659 | ||||
| Compounded annual return (geometric extrapolation) | 0.404 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.971 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.193 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.896 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.057 | ||||
| SD | 0.796 | ||||
| Sharpe ratio (Glass type estimate) | -0.071 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.071 | ||||
| df | 130.000 | ||||
| t | -0.050 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.843 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.701 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.843 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.701 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.119 | ||||
| Upside Potential Ratio | 6.804 | ||||
| Upside part of mean | 3.229 | ||||
| Downside part of mean | -3.285 | ||||
| Upside SD | 0.635 | ||||
| Downside SD | 0.475 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 67.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.092 | ||||
| Mean of criterion | -0.057 | ||||
| SD of predictor | 0.417 | ||||
| SD of criterion | 0.796 | ||||
| Covariance | 0.068 | ||||
| r | 0.205 | ||||
| b (slope, estimate of beta) | 0.391 | ||||
| a (intercept, estimate of alpha) | -0.484 | ||||
| Mean Square Error | 0.612 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.375 | ||||
| p(b) | 0.371 | ||||
| t(a) | -0.432 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | 0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.717 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.701 | ||||
| Upperbound of 95% confidence interval for alpha | 1.734 | ||||
| Treynor index (mean / b) | -0.145 | ||||
| Jensen alpha (a) | -0.484 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.351 | ||||
| SD | 0.762 | ||||
| Sharpe ratio (Glass type estimate) | -0.461 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.458 | ||||
| df | 130.000 | ||||
| t | -0.326 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.232 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.312 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.231 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.314 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.674 | ||||
| Upside Potential Ratio | 5.878 | ||||
| Upside part of mean | 3.061 | ||||
| Downside part of mean | -3.412 | ||||
| Upside SD | 0.552 | ||||
| Downside SD | 0.521 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 67.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.003 | ||||
| Mean of criterion | -0.351 | ||||
| SD of predictor | 0.417 | ||||
| SD of criterion | 0.762 | ||||
| Covariance | 0.066 | ||||
| r | 0.209 | ||||
| b (slope, estimate of beta) | 0.382 | ||||
| a (intercept, estimate of alpha) | -0.734 | ||||
| Mean Square Error | 0.559 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.429 | ||||
| p(b) | 0.368 | ||||
| t(a) | -0.686 | ||||
| p(a) | 0.538 | ||||
| Lowerbound of 95% confidence interval for beta | 0.071 | ||||
| Upperbound of 95% confidence interval for beta | 0.692 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.849 | ||||
| Upperbound of 95% confidence interval for alpha | 1.381 | ||||
| Treynor index (mean / b) | -0.920 | ||||
| Jensen alpha (a) | -0.734 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.748 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.403 | ||||
| Mean of quarter 1 | 0.959 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.035 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.837 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.184 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.447 | ||||
| VaR(95%) (moments method) | 0.046 | ||||
| Expected Shortfall (moments method) | 0.087 | ||||
| Extreme Value Index (regression method) | 0.394 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.070 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.067 | ||||
| Quartile 3 | 0.212 | ||||
| Maximum | 0.298 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | 0.067 | ||||
| Mean of quarter 3 | 0.212 | ||||
| Mean of quarter 4 | 0.298 | ||||
| Inter Quartile Range | 0.185 | ||||
| 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) | -0.285 | ||||
| Compounded annual return (geometric extrapolation) | -0.264 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.887 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.887 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.825 | ||||