Advanced Statistics: The New Gamblers
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.492 | ||||
| SD | 0.900 | ||||
| Sharpe ratio (Glass type estimate) | -0.547 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.536 | ||||
| df | 39.000 | ||||
| t | -0.998 | ||||
| p | 0.838 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.624 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.537 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.616 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.544 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.729 | ||||
| Upside Potential Ratio | 0.634 | ||||
| Upside part of mean | 0.428 | ||||
| Downside part of mean | -0.920 | ||||
| Upside SD | 0.595 | ||||
| Downside SD | 0.675 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.531 | ||||
| Mean of criterion | -0.492 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.900 | ||||
| Covariance | -0.010 | ||||
| r | -0.036 | ||||
| b (slope, estimate of beta) | -0.106 | ||||
| a (intercept, estimate of alpha) | -0.436 | ||||
| Mean Square Error | 0.830 | ||||
| DF error | 38.000 | ||||
| t(b) | -0.223 | ||||
| p(b) | 0.588 | ||||
| t(a) | -0.779 | ||||
| p(a) | 0.780 | ||||
| Lowerbound of 95% confidence interval for beta | -1.067 | ||||
| Upperbound of 95% confidence interval for beta | 0.855 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.567 | ||||
| Upperbound of 95% confidence interval for alpha | 0.696 | ||||
| Treynor index (mean / b) | 4.647 | ||||
| Jensen alpha (a) | -0.436 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.498 | ||||
| SD | 5.669 | ||||
| Sharpe ratio (Glass type estimate) | -0.617 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.605 | ||||
| df | 39.000 | ||||
| t | -1.127 | ||||
| p | 0.867 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.695 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.469 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.687 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.477 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.617 | ||||
| Upside Potential Ratio | 0.056 | ||||
| Upside part of mean | 0.318 | ||||
| Downside part of mean | -3.816 | ||||
| Upside SD | 0.413 | ||||
| Downside SD | 5.673 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.477 | ||||
| Mean of criterion | -3.498 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 5.669 | ||||
| Covariance | 0.097 | ||||
| r | 0.059 | ||||
| b (slope, estimate of beta) | 1.177 | ||||
| a (intercept, estimate of alpha) | -4.059 | ||||
| Mean Square Error | 32.862 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.367 | ||||
| p(b) | 0.358 | ||||
| t(a) | -1.162 | ||||
| p(a) | 0.874 | ||||
| Lowerbound of 95% confidence interval for beta | -5.307 | ||||
| Upperbound of 95% confidence interval for beta | 7.660 | ||||
| Lowerbound of 95% confidence interval for alpha | -11.128 | ||||
| Upperbound of 95% confidence interval for alpha | 3.010 | ||||
| Treynor index (mean / b) | -2.973 | ||||
| Jensen alpha (a) | -4.059 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.949 | ||||
| Expected Shortfall on VaR | 0.971 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.242 | ||||
| Expected Shortfall on VaR | 0.486 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.944 | ||||
| Median | 0.995 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.062 | ||||
| Mean of quarter 1 | 0.730 | ||||
| Mean of quarter 2 | 0.978 | ||||
| Mean of quarter 3 | 0.998 | ||||
| Mean of quarter 4 | 1.145 | ||||
| Inter Quartile Range | 0.056 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.125 | ||||
| Mean of outliers low | 0.553 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.461 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.685 | ||||
| VaR(95%) (moments method) | 0.263 | ||||
| Expected Shortfall (moments method) | 0.925 | ||||
| Extreme Value Index (regression method) | 0.772 | ||||
| VaR(95%) (regression method) | 0.311 | ||||
| Expected Shortfall (regression method) | 1.476 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.300 | ||||
| Compounded annual return (geometric extrapolation) | -0.968 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.968 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.998 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.500 | ||||
| SD | 0.909 | ||||
| Sharpe ratio (Glass type estimate) | -0.551 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.550 | ||||
| df | 884.000 | ||||
| t | -1.012 | ||||
| p | 0.844 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.617 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.516 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.617 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.516 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.793 | ||||
| Upside Potential Ratio | 1.951 | ||||
| Upside part of mean | 1.230 | ||||
| Downside part of mean | -1.731 | ||||
| Upside SD | 0.654 | ||||
| Downside SD | 0.631 | ||||
| N nonnegative terms | 238.000 | ||||
| N negative terms | 647.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 885.000 | ||||
| Mean of predictor | 0.551 | ||||
| Mean of criterion | -0.500 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.909 | ||||
| Covariance | -0.015 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.149 | ||||
| a (intercept, estimate of alpha) | -0.418 | ||||
| Mean Square Error | 0.825 | ||||
| DF error | 883.000 | ||||
| t(b) | -1.559 | ||||
| p(b) | 0.940 | ||||
| t(a) | -0.842 | ||||
| p(a) | 0.800 | ||||
| Lowerbound of 95% confidence interval for beta | -0.336 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.394 | ||||
| Upperbound of 95% confidence interval for alpha | 0.557 | ||||
| Treynor index (mean / b) | 3.361 | ||||
| Jensen alpha (a) | -0.418 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.452 | ||||
| SD | 5.641 | ||||
| Sharpe ratio (Glass type estimate) | -0.612 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.611 | ||||
| df | 884.000 | ||||
| t | -1.125 | ||||
| p | 0.869 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.679 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.455 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.678 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.455 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.614 | ||||
| Upside Potential Ratio | 0.194 | ||||
| Upside part of mean | 1.092 | ||||
| Downside part of mean | -4.544 | ||||
| Upside SD | 0.474 | ||||
| Downside SD | 5.622 | ||||
| N nonnegative terms | 238.000 | ||||
| N negative terms | 647.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 885.000 | ||||
| Mean of predictor | 0.499 | ||||
| Mean of criterion | -3.452 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 5.641 | ||||
| Covariance | 0.012 | ||||
| r | 0.007 | ||||
| b (slope, estimate of beta) | 0.116 | ||||
| a (intercept, estimate of alpha) | -3.510 | ||||
| Mean Square Error | 31.860 | ||||
| DF error | 883.000 | ||||
| t(b) | 0.198 | ||||
| p(b) | 0.421 | ||||
| t(a) | -1.138 | ||||
| p(a) | 0.872 | ||||
| Lowerbound of 95% confidence interval for beta | -1.036 | ||||
| Upperbound of 95% confidence interval for beta | 1.269 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.565 | ||||
| Upperbound of 95% confidence interval for alpha | 2.545 | ||||
| Treynor index (mean / b) | -29.656 | ||||
| Jensen alpha (a) | -3.510 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.444 | ||||
| Expected Shortfall on VaR | 0.515 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 885.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.094 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 147.000 | ||||
| Percentage of outliers low | 0.166 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 118.000 | ||||
| Percentage of outliers high | 0.133 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.091 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.641 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.010 | ||||
| Quartile 3 | 0.505 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.497 | ||||
| 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) | -0.296 | ||||
| Compounded annual return (geometric extrapolation) | -0.967 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.967 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.967 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.876 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.044 | ||||
| SD | 1.414 | ||||
| Sharpe ratio (Glass type estimate) | -1.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.437 | ||||
| df | 130.000 | ||||
| t | -1.022 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.220 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.335 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.340 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.445 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -2.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 1.414 | ||||
| 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 | 0.983 | ||||
| Mean of criterion | -2.044 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 1.414 | ||||
| Covariance | 0.024 | ||||
| r | 0.034 | ||||
| b (slope, estimate of beta) | 0.100 | ||||
| a (intercept, estimate of alpha) | -2.142 | ||||
| Mean Square Error | 2.013 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.391 | ||||
| p(b) | 0.478 | ||||
| t(a) | -1.059 | ||||
| p(a) | 0.559 | ||||
| Lowerbound of 95% confidence interval for beta | -0.404 | ||||
| Upperbound of 95% confidence interval for beta | 0.604 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.143 | ||||
| Upperbound of 95% confidence interval for alpha | 1.859 | ||||
| Treynor index (mean / b) | -20.495 | ||||
| Jensen alpha (a) | -2.142 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -20.671 | ||||
| SD | 14.586 | ||||
| Sharpe ratio (Glass type estimate) | -1.417 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.409 | ||||
| df | 130.000 | ||||
| t | -1.002 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.192 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.363 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.186 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.368 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.417 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -20.671 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 14.586 | ||||
| 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 | 0.863 | ||||
| Mean of criterion | -20.671 | ||||
| SD of predictor | 0.491 | ||||
| SD of criterion | 14.586 | ||||
| Covariance | 0.236 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.982 | ||||
| a (intercept, estimate of alpha) | -21.518 | ||||
| Mean Square Error | 214.152 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.375 | ||||
| p(b) | 0.479 | ||||
| t(a) | -1.034 | ||||
| p(a) | 0.558 | ||||
| Lowerbound of 95% confidence interval for beta | -4.194 | ||||
| Upperbound of 95% confidence interval for beta | 6.158 | ||||
| Lowerbound of 95% confidence interval for alpha | -62.707 | ||||
| Upperbound of 95% confidence interval for alpha | 19.671 | ||||
| Treynor index (mean / b) | -21.045 | ||||
| Jensen alpha (a) | -21.518 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.790 | ||||
| Expected Shortfall on VaR | 0.849 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.970 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.000 | ||||
| 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 | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -2.000 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.178 | ||||