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 | 32566.087 | ||||
| SD | 75208.244 | ||||
| Sharpe ratio (Glass type estimate) | 0.433 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.428 | ||||
| df | 63.000 | ||||
| t | 1.000 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.421 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.283 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.424 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 73092.738 | ||||
| Upside Potential Ratio | 73093.348 | ||||
| Upside part of mean | 32566.359 | ||||
| Downside part of mean | -0.272 | ||||
| Upside SD | 75208.243 | ||||
| Downside SD | 0.446 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.322 | ||||
| Mean of criterion | 32566.087 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 75208.244 | ||||
| Covariance | 2881.626 | ||||
| r | 0.134 | ||||
| b (slope, estimate of beta) | 35036.543 | ||||
| a (intercept, estimate of alpha) | 21270.260 | ||||
| Mean Square Error | 5644919631.717 | ||||
| DF error | 62.000 | ||||
| t(b) | 1.062 | ||||
| p(b) | 0.146 | ||||
| t(a) | 0.621 | ||||
| p(a) | 0.268 | ||||
| Lowerbound of 95% confidence interval for beta | -30942.659 | ||||
| Upperbound of 95% confidence interval for beta | 101015.745 | ||||
| Lowerbound of 95% confidence interval for alpha | -47153.610 | ||||
| Upperbound of 95% confidence interval for alpha | 89694.131 | ||||
| Treynor index (mean / b) | 0.929 | ||||
| Jensen alpha (a) | 21270.260 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 7.631 | ||||
| Sharpe ratio (Glass type estimate) | -0.006 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.006 | ||||
| df | 63.000 | ||||
| t | -0.013 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.854 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.843 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.854 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.843 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.008 | ||||
| Upside Potential Ratio | 0.441 | ||||
| Upside part of mean | 2.413 | ||||
| Downside part of mean | -2.457 | ||||
| Upside SD | 5.234 | ||||
| Downside SD | 5.471 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 7.631 | ||||
| Covariance | 0.480 | ||||
| r | 0.224 | ||||
| b (slope, estimate of beta) | 6.058 | ||||
| a (intercept, estimate of alpha) | -1.730 | ||||
| Mean Square Error | 56.220 | ||||
| DF error | 62.000 | ||||
| t(b) | 1.806 | ||||
| p(b) | 0.038 | ||||
| t(a) | -0.512 | ||||
| p(a) | 0.695 | ||||
| Lowerbound of 95% confidence interval for beta | -0.648 | ||||
| Upperbound of 95% confidence interval for beta | 12.763 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.483 | ||||
| Upperbound of 95% confidence interval for alpha | 5.023 | ||||
| Treynor index (mean / b) | -0.007 | ||||
| Jensen alpha (a) | -1.730 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.973 | ||||
| Expected Shortfall on VaR | 0.987 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.077 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 173687.000 | ||||
| Mean of quarter 1 | 0.924 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 10856.453 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.389 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 86844.627 | ||||
| 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) | 0.816 | ||||
| VaR(95%) (regression method) | -0.025 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.221 | ||||
| Quartile 1 | 0.416 | ||||
| Median | 0.611 | ||||
| Quartile 3 | 0.805 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.221 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.389 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 429628.991 | ||||
| SD | 346383.759 | ||||
| Sharpe ratio (Glass type estimate) | 1.240 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.240 | ||||
| df | 1411.000 | ||||
| t | 2.879 | ||||
| p | 0.451 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.395 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.086 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.394 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.085 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 302282.386 | ||||
| Upside Potential Ratio | 302284.245 | ||||
| Upside part of mean | 429631.633 | ||||
| Downside part of mean | -2.642 | ||||
| Upside SD | 347276.898 | ||||
| Downside SD | 1.421 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 1375.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1412.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | 429628.991 | ||||
| SD of predictor | 0.536 | ||||
| SD of criterion | 346383.759 | ||||
| Covariance | 43259.725 | ||||
| r | 0.233 | ||||
| b (slope, estimate of beta) | 150539.572 | ||||
| a (intercept, estimate of alpha) | 366165.143 | ||||
| Mean Square Error | 113549883010.118 | ||||
| DF error | 1410.000 | ||||
| t(b) | 8.996 | ||||
| p(b) | 0.384 | ||||
| t(a) | 2.520 | ||||
| p(a) | 0.467 | ||||
| Lowerbound of 95% confidence interval for beta | 117712.330 | ||||
| Upperbound of 95% confidence interval for beta | 183366.814 | ||||
| Lowerbound of 95% confidence interval for alpha | 81089.518 | ||||
| Upperbound of 95% confidence interval for alpha | 651240.768 | ||||
| Treynor index (mean / b) | 2.854 | ||||
| Jensen alpha (a) | 366165.143 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 22.526 | ||||
| Sharpe ratio (Glass type estimate) | -0.002 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.002 | ||||
| df | 1411.000 | ||||
| t | -0.005 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.842 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.846 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.842 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.003 | ||||
| Upside Potential Ratio | 1.365 | ||||
| Upside part of mean | 21.576 | ||||
| Downside part of mean | -21.620 | ||||
| Upside SD | 16.037 | ||||
| Downside SD | 15.807 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 1375.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1412.000 | ||||
| Mean of predictor | 0.280 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.532 | ||||
| SD of criterion | 22.526 | ||||
| Covariance | 4.208 | ||||
| r | 0.351 | ||||
| b (slope, estimate of beta) | 14.888 | ||||
| a (intercept, estimate of alpha) | -4.209 | ||||
| Mean Square Error | 445.087 | ||||
| DF error | 1410.000 | ||||
| t(b) | 14.093 | ||||
| p(b) | 0.324 | ||||
| t(a) | -0.463 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 12.816 | ||||
| Upperbound of 95% confidence interval for beta | 16.961 | ||||
| Lowerbound of 95% confidence interval for alpha | -22.045 | ||||
| Upperbound of 95% confidence interval for alpha | 13.627 | ||||
| Treynor index (mean / b) | -0.003 | ||||
| Jensen alpha (a) | -4.209 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.899 | ||||
| Expected Shortfall on VaR | 0.937 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.078 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1412.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 354460.438 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 6560.262 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 31.000 | ||||
| Percentage of outliers low | 0.022 | ||||
| Mean of outliers low | 0.548 | ||||
| Number of outliers high | 37.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 62579.901 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.461 | ||||
| VaR(95%) (moments method) | -0.019 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -6.137 | ||||
| VaR(95%) (regression method) | -96.925 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| 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 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) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.014 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.465 | ||||
| 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 | 0.904 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.465 | ||||
| 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) | -8736400493094917.000 | ||||
| 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) | 83063533390280968295221678833664.000 | ||||
| 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 | ||||