Advanced Statistics: 4 Point Stop in the S&P
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 | 0.022 | ||||
| SD | 0.772 | ||||
| Sharpe ratio (Glass type estimate) | 0.029 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.028 | ||||
| df | 37.000 | ||||
| t | 0.051 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.073 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.130 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.073 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.130 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.039 | ||||
| Upside Potential Ratio | 0.673 | ||||
| Upside part of mean | 0.380 | ||||
| Downside part of mean | -0.358 | ||||
| Upside SD | 0.512 | ||||
| Downside SD | 0.564 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.029 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.772 | ||||
| Covariance | 0.095 | ||||
| r | 0.471 | ||||
| b (slope, estimate of beta) | 1.389 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.477 | ||||
| DF error | 36.000 | ||||
| t(b) | 3.205 | ||||
| p(b) | 0.001 | ||||
| t(a) | -0.045 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | 0.510 | ||||
| Upperbound of 95% confidence interval for beta | 2.268 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.805 | ||||
| Upperbound of 95% confidence interval for alpha | 0.770 | ||||
| Treynor index (mean / b) | 0.016 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.680 | ||||
| SD | 7.014 | ||||
| Sharpe ratio (Glass type estimate) | -0.525 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.514 | ||||
| df | 37.000 | ||||
| t | -0.934 | ||||
| p | 0.822 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.629 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.587 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.622 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.594 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.526 | ||||
| Upside Potential Ratio | 0.041 | ||||
| Upside part of mean | 0.290 | ||||
| Downside part of mean | -3.970 | ||||
| Upside SD | 0.383 | ||||
| Downside SD | 6.992 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | -0.009 | ||||
| Mean of criterion | -3.680 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 7.014 | ||||
| Covariance | 1.448 | ||||
| r | 0.724 | ||||
| b (slope, estimate of beta) | 17.802 | ||||
| a (intercept, estimate of alpha) | -3.524 | ||||
| Mean Square Error | 24.068 | ||||
| DF error | 36.000 | ||||
| t(b) | 6.295 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.278 | ||||
| p(a) | 0.895 | ||||
| Lowerbound of 95% confidence interval for beta | 12.067 | ||||
| Upperbound of 95% confidence interval for beta | 23.538 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.116 | ||||
| Upperbound of 95% confidence interval for alpha | 2.067 | ||||
| Treynor index (mean / b) | -0.207 | ||||
| Jensen alpha (a) | -3.524 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.974 | ||||
| Expected Shortfall on VaR | 0.986 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.100 | ||||
| Expected Shortfall on VaR | 0.223 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.836 | ||||
| Mean of quarter 1 | 0.900 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.121 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.000 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.605 | ||||
| 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) | -0.316 | ||||
| Compounded annual return (geometric extrapolation) | -0.974 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.974 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.987 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.292 | ||||
| SD | 0.939 | ||||
| Sharpe ratio (Glass type estimate) | -0.311 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.311 | ||||
| df | 1110.000 | ||||
| t | -0.559 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.402 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.780 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.402 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.780 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.355 | ||||
| Upside Potential Ratio | 1.378 | ||||
| Upside part of mean | 1.134 | ||||
| Downside part of mean | -1.427 | ||||
| Upside SD | 0.452 | ||||
| Downside SD | 0.823 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 1062.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1111.000 | ||||
| Mean of predictor | 0.092 | ||||
| Mean of criterion | -0.292 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.939 | ||||
| Covariance | 0.043 | ||||
| r | 0.145 | ||||
| b (slope, estimate of beta) | 0.435 | ||||
| a (intercept, estimate of alpha) | -0.332 | ||||
| Mean Square Error | 0.864 | ||||
| DF error | 1109.000 | ||||
| t(b) | 4.882 | ||||
| p(b) | 0.408 | ||||
| t(a) | -0.642 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | 0.260 | ||||
| Upperbound of 95% confidence interval for beta | 0.610 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.348 | ||||
| Upperbound of 95% confidence interval for alpha | 0.683 | ||||
| Treynor index (mean / b) | -0.672 | ||||
| Jensen alpha (a) | -0.332 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.609 | ||||
| SD | 5.885 | ||||
| Sharpe ratio (Glass type estimate) | -0.613 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.613 | ||||
| df | 1110.000 | ||||
| t | -1.102 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.704 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.478 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.704 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.478 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.615 | ||||
| Upside Potential Ratio | 0.178 | ||||
| Upside part of mean | 1.046 | ||||
| Downside part of mean | -4.655 | ||||
| Upside SD | 0.404 | ||||
| Downside SD | 5.872 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 1062.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1111.000 | ||||
| Mean of predictor | 0.043 | ||||
| Mean of criterion | -3.609 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 5.885 | ||||
| Covariance | 0.146 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 1.487 | ||||
| a (intercept, estimate of alpha) | -3.673 | ||||
| Mean Square Error | 34.447 | ||||
| DF error | 1109.000 | ||||
| t(b) | 2.647 | ||||
| p(b) | 0.450 | ||||
| t(a) | -1.125 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | 0.385 | ||||
| Upperbound of 95% confidence interval for beta | 2.590 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.081 | ||||
| Upperbound of 95% confidence interval for alpha | 2.735 | ||||
| Treynor index (mean / b) | -2.427 | ||||
| Jensen alpha (a) | -3.673 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.413 | ||||
| Expected Shortfall on VaR | 0.482 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1111.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.364 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 30.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.851 | ||||
| Number of outliers high | 49.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.075 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.281 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.804 | ||||
| VaR(95%) (regression method) | -0.016 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.171 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.036 | ||||
| Mean of quarter 3 | 0.049 | ||||
| Mean of quarter 4 | 0.593 | ||||
| Inter Quartile Range | 0.150 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.182 | ||||
| Mean of outliers high | 0.743 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.570 | ||||
| VaR(95%) (moments method) | 0.653 | ||||
| Expected Shortfall (moments method) | 0.687 | ||||
| Extreme Value Index (regression method) | 0.392 | ||||
| VaR(95%) (regression method) | 1.040 | ||||
| Expected Shortfall (regression method) | 2.071 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.310 | ||||
| Compounded annual return (geometric extrapolation) | -0.972 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.972 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.639 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.015 | ||||
| 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 | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.699 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.280 | ||||
| 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) | -7936535306446244.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -7901674975671223.000 | ||||
| df | 171.000 | ||||
| t | -5611977934314593.000 | ||||
| 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) | -8739115425704417.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7064234525638030.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.660 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.279 | ||||
| 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 | 170.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -5550293726397719.000 | ||||
| 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) | 86917921720792643871721075507200.000 | ||||
| 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 | 172.000 | ||||
| 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 | ||||
