Advanced Statistics: SPY trading
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 | -0.039 | ||||
| SD | 0.049 | ||||
| Sharpe ratio (Glass type estimate) | -0.802 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.783 | ||||
| df | 32.000 | ||||
| t | -1.329 | ||||
| p | 0.903 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.994 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.402 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.980 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.415 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.206 | ||||
| Upside Potential Ratio | 0.967 | ||||
| Upside part of mean | 0.031 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.587 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.049 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.002 | ||||
| p(b) | 0.499 | ||||
| t(a) | -1.130 | ||||
| p(a) | 0.866 | ||||
| Lowerbound of 95% confidence interval for beta | -0.060 | ||||
| Upperbound of 95% confidence interval for beta | 0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.109 | ||||
| Upperbound of 95% confidence interval for alpha | 0.031 | ||||
| Treynor index (mean / b) | -786.634 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.833 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.814 | ||||
| df | 32.000 | ||||
| t | -1.382 | ||||
| p | 0.912 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.026 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.372 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.012 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.385 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.227 | ||||
| Upside Potential Ratio | 0.934 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.036 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.019 | ||||
| p(b) | 0.492 | ||||
| t(a) | -1.183 | ||||
| p(a) | 0.877 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.110 | ||||
| Upperbound of 95% confidence interval for alpha | 0.029 | ||||
| Treynor index (mean / b) | -64.741 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.967 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.053 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.121 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.061 | ||||
| Mean of outliers high | 1.047 | ||||
| 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) | -0.835 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.030 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.025 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.039 | ||||
| Quartile 3 | 0.046 | ||||
| Maximum | 0.053 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.053 | ||||
| Inter Quartile Range | 0.014 | ||||
| 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) | 0.004 | ||||
| Compounded annual return (geometric extrapolation) | 0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.078 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.078 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.131 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -0.635 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.634 | ||||
| df | 735.000 | ||||
| t | -1.065 | ||||
| p | 0.856 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.805 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.535 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.804 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.535 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.916 | ||||
| Upside Potential Ratio | 2.118 | ||||
| Upside part of mean | 0.088 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 713.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 736.000 | ||||
| Mean of predictor | 0.619 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | -0.001 | ||||
| r | -0.028 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 734.000 | ||||
| t(b) | -0.767 | ||||
| p(b) | 0.778 | ||||
| t(a) | -0.972 | ||||
| p(a) | 0.834 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | 7.628 | ||||
| Jensen alpha (a) | -0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -0.665 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.664 | ||||
| df | 735.000 | ||||
| t | -1.115 | ||||
| p | 0.867 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.835 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.505 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.834 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.506 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.945 | ||||
| Upside Potential Ratio | 2.066 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 713.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 736.000 | ||||
| Mean of predictor | 0.560 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | -0.001 | ||||
| r | -0.028 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 734.000 | ||||
| t(b) | -0.752 | ||||
| p(b) | 0.774 | ||||
| t(a) | -1.033 | ||||
| p(a) | 0.849 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.108 | ||||
| Upperbound of 95% confidence interval for alpha | 0.034 | ||||
| Treynor index (mean / b) | 8.216 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 736.000 | ||||
| Minimum | 0.962 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.032 | ||||
| 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 | 27.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 23.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.553 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.322 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.097 | ||||
| Quartile 1 | 0.097 | ||||
| Median | 0.097 | ||||
| Quartile 3 | 0.097 | ||||
| Maximum | 0.097 | ||||
| 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) | 0.004 | ||||
| Compounded annual return (geometric extrapolation) | 0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.041 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.515 | ||||
| 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 | 0.515 | ||||
| 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 | 0.867 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.514 | ||||
| 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) | -8751984838043295.000 | ||||
| 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) | 154679908317921700426673498882048.000 | ||||
| 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 | ||||