Advanced Statistics: Alphergence - DayTrade 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 | -0.030 | ||||
| SD | 0.024 | ||||
| Sharpe ratio (Glass type estimate) | -1.251 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.226 | ||||
| df | 37.000 | ||||
| t | -2.226 | ||||
| p | 0.984 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.381 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.106 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.362 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.089 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.006 | ||||
| Upside Potential Ratio | 0.979 | ||||
| Upside part of mean | 0.015 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.020 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.514 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.024 | ||||
| Covariance | -0.002 | ||||
| r | -0.284 | ||||
| b (slope, estimate of beta) | -0.027 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 36.000 | ||||
| t(b) | -1.776 | ||||
| p(b) | 0.958 | ||||
| t(a) | -1.044 | ||||
| p(a) | 0.848 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | 0.015 | ||||
| Treynor index (mean / b) | 1.099 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.023 | ||||
| Sharpe ratio (Glass type estimate) | -1.278 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.252 | ||||
| df | 37.000 | ||||
| t | -2.275 | ||||
| p | 0.986 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.409 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.131 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.390 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.114 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.019 | ||||
| Upside Potential Ratio | 0.962 | ||||
| Upside part of mean | 0.014 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.020 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.474 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.239 | ||||
| SD of criterion | 0.023 | ||||
| Covariance | -0.002 | ||||
| r | -0.293 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 36.000 | ||||
| t(b) | -1.840 | ||||
| p(b) | 0.963 | ||||
| t(a) | -1.106 | ||||
| p(a) | 0.862 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | 1.042 | ||||
| Jensen alpha (a) | -0.016 | ||||
| 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 | 0.016 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.988 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.037 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.105 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.012 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.012 | ||||
| Maximum | 0.012 | ||||
| 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) | 0.014 | ||||
| Compounded annual return (geometric extrapolation) | 0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.196 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.864 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -0.929 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.928 | ||||
| df | 834.000 | ||||
| t | -1.658 | ||||
| p | 0.951 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.027 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.170 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.027 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.171 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.413 | ||||
| Upside Potential Ratio | 2.490 | ||||
| Upside part of mean | 0.052 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.024 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 798.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 835.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | 0.000 | ||||
| r | 0.014 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 833.000 | ||||
| t(b) | 0.413 | ||||
| p(b) | 0.340 | ||||
| t(a) | -1.691 | ||||
| p(a) | 0.954 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.005 | ||||
| Treynor index (mean / b) | -22.177 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -0.946 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.946 | ||||
| df | 834.000 | ||||
| t | -1.690 | ||||
| p | 0.954 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.045 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.153 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.044 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.153 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.428 | ||||
| Upside Potential Ratio | 2.460 | ||||
| Upside part of mean | 0.052 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.024 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 798.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 835.000 | ||||
| Mean of predictor | 0.503 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | 0.000 | ||||
| r | 0.015 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 833.000 | ||||
| t(b) | 0.425 | ||||
| p(b) | 0.335 | ||||
| t(a) | -1.720 | ||||
| p(a) | 0.957 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | -21.996 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 835.000 | ||||
| Minimum | 0.979 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.026 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 24.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 39.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.522 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.459 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.004 | ||||
| Maximum | 0.073 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.004 | ||||
| Mean of quarter 4 | 0.073 | ||||
| Inter Quartile Range | 0.003 | ||||
| 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 | 0.073 | ||||
| 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) | 0.014 | ||||
| Compounded annual return (geometric extrapolation) | 0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.193 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.193 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.375 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.189 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.060 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.506 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8726292613203217.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -3710343178408995970165910110470144.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| 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 for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| 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 | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||