Advanced Statistics: Low Price Bet
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 | -0.137 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | -0.838 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.822 | ||||
| df | 39.000 | ||||
| t | -1.530 | ||||
| p | 0.933 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.922 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.256 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.911 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.267 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.939 | ||||
| Upside Potential Ratio | 0.427 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.199 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | -0.137 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | 0.009 | ||||
| r | 0.216 | ||||
| b (slope, estimate of beta) | 0.137 | ||||
| a (intercept, estimate of alpha) | -0.206 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 38.000 | ||||
| t(b) | 1.362 | ||||
| p(b) | 0.091 | ||||
| t(a) | -2.021 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.340 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.413 | ||||
| Upperbound of 95% confidence interval for alpha | 0.000 | ||||
| Treynor index (mean / b) | -1.001 | ||||
| Jensen alpha (a) | -0.206 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.151 | ||||
| SD | 0.171 | ||||
| Sharpe ratio (Glass type estimate) | -0.881 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.864 | ||||
| df | 39.000 | ||||
| t | -1.609 | ||||
| p | 0.942 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.967 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.215 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.955 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.226 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.958 | ||||
| Upside Potential Ratio | 0.374 | ||||
| Upside part of mean | 0.059 | ||||
| Downside part of mean | -0.210 | ||||
| Upside SD | 0.075 | ||||
| Downside SD | 0.158 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | -0.151 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.171 | ||||
| Covariance | 0.009 | ||||
| r | 0.223 | ||||
| b (slope, estimate of beta) | 0.156 | ||||
| a (intercept, estimate of alpha) | -0.224 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 38.000 | ||||
| t(b) | 1.409 | ||||
| p(b) | 0.083 | ||||
| t(a) | -2.110 | ||||
| p(a) | 0.979 | ||||
| Lowerbound of 95% confidence interval for beta | -0.068 | ||||
| Upperbound of 95% confidence interval for beta | 0.380 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.439 | ||||
| Upperbound of 95% confidence interval for alpha | -0.009 | ||||
| Treynor index (mean / b) | -0.968 | ||||
| Jensen alpha (a) | -0.224 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.090 | ||||
| Expected Shortfall on VaR | 0.108 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.110 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.121 | ||||
| Mean of quarter 1 | 0.947 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.150 | ||||
| Mean of outliers low | 0.912 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.150 | ||||
| Mean of outliers high | 1.036 | ||||
| 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) | -0.722 | ||||
| VaR(95%) (regression method) | 0.089 | ||||
| Expected Shortfall (regression method) | 0.115 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.357 | ||||
| Quartile 1 | 0.357 | ||||
| Median | 0.357 | ||||
| Quartile 3 | 0.357 | ||||
| Maximum | 0.357 | ||||
| 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) | -0.090 | ||||
| Compounded annual return (geometric extrapolation) | -0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.284 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.938 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.123 | ||||
| SD | 0.232 | ||||
| Sharpe ratio (Glass type estimate) | -0.531 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.530 | ||||
| df | 877.000 | ||||
| t | -0.972 | ||||
| p | 0.834 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.602 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.540 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.601 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.541 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.727 | ||||
| Upside Potential Ratio | 2.494 | ||||
| Upside part of mean | 0.423 | ||||
| Downside part of mean | -0.546 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.170 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 811.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 878.000 | ||||
| Mean of predictor | 0.544 | ||||
| Mean of criterion | -0.123 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.232 | ||||
| Covariance | -0.002 | ||||
| r | -0.021 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.115 | ||||
| Mean Square Error | 0.054 | ||||
| DF error | 876.000 | ||||
| t(b) | -0.630 | ||||
| p(b) | 0.736 | ||||
| t(a) | -0.898 | ||||
| p(a) | 0.815 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.365 | ||||
| Upperbound of 95% confidence interval for alpha | 0.136 | ||||
| Treynor index (mean / b) | 7.727 | ||||
| Jensen alpha (a) | -0.115 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.150 | ||||
| SD | 0.233 | ||||
| Sharpe ratio (Glass type estimate) | -0.644 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.644 | ||||
| df | 877.000 | ||||
| t | -1.179 | ||||
| p | 0.881 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.715 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.427 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.715 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.427 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.845 | ||||
| Upside Potential Ratio | 2.308 | ||||
| Upside part of mean | 0.411 | ||||
| Downside part of mean | -0.561 | ||||
| Upside SD | 0.151 | ||||
| Downside SD | 0.178 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 811.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 878.000 | ||||
| Mean of predictor | 0.495 | ||||
| Mean of criterion | -0.150 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.233 | ||||
| Covariance | -0.002 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.142 | ||||
| Mean Square Error | 0.055 | ||||
| DF error | 876.000 | ||||
| t(b) | -0.650 | ||||
| p(b) | 0.742 | ||||
| t(a) | -1.110 | ||||
| p(a) | 0.866 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.394 | ||||
| Upperbound of 95% confidence interval for alpha | 0.109 | ||||
| Treynor index (mean / b) | 9.168 | ||||
| Jensen alpha (a) | -0.142 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 878.000 | ||||
| Minimum | 0.855 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.146 | ||||
| Mean of quarter 1 | 0.992 | ||||
| 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 | 81.000 | ||||
| Percentage of outliers low | 0.092 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 70.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.020 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.138 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.254 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.021 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.019 | ||||
| Quartile 1 | 0.026 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.227 | ||||
| Maximum | 0.421 | ||||
| Mean of quarter 1 | 0.019 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.421 | ||||
| Inter Quartile Range | 0.201 | ||||
| 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) | -0.089 | ||||
| Compounded annual return (geometric extrapolation) | -0.101 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.239 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.239 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.379 | ||||
| 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 | 0.999 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.469 | ||||
| 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 | 0.887 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.472 | ||||
| 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) | -8740638855570024.000 | ||||
| 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) | -404574597625564883083454257823744.000 | ||||
| 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 | ||||