Advanced Statistics: Pairs Trading QID QLD Scalper
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 | 0.025 | ||||
| SD | 0.242 | ||||
| Sharpe ratio (Glass type estimate) | 0.104 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.103 | ||||
| df | 86.000 | ||||
| t | 0.281 | ||||
| p | 0.390 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.624 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.832 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.625 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.831 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.187 | ||||
| Upside Potential Ratio | 1.572 | ||||
| Upside part of mean | 0.211 | ||||
| Downside part of mean | -0.186 | ||||
| Upside SD | 0.199 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.116 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.242 | ||||
| Covariance | 0.004 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 0.087 | ||||
| a (intercept, estimate of alpha) | 0.015 | ||||
| Mean Square Error | 0.059 | ||||
| DF error | 85.000 | ||||
| t(b) | 0.734 | ||||
| p(b) | 0.232 | ||||
| t(a) | 0.166 | ||||
| p(a) | 0.434 | ||||
| Lowerbound of 95% confidence interval for beta | -0.148 | ||||
| Upperbound of 95% confidence interval for beta | 0.322 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.166 | ||||
| Upperbound of 95% confidence interval for alpha | 0.196 | ||||
| Treynor index (mean / b) | 0.290 | ||||
| Jensen alpha (a) | 0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.233 | ||||
| Sharpe ratio (Glass type estimate) | -0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.009 | ||||
| df | 86.000 | ||||
| t | -0.025 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.737 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.719 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.737 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.719 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.015 | ||||
| Upside Potential Ratio | 1.326 | ||||
| Upside part of mean | 0.193 | ||||
| Downside part of mean | -0.196 | ||||
| Upside SD | 0.179 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.091 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 0.233 | ||||
| Covariance | 0.005 | ||||
| r | 0.088 | ||||
| b (slope, estimate of beta) | 0.090 | ||||
| a (intercept, estimate of alpha) | -0.010 | ||||
| Mean Square Error | 0.054 | ||||
| DF error | 85.000 | ||||
| t(b) | 0.811 | ||||
| p(b) | 0.210 | ||||
| t(a) | -0.119 | ||||
| p(a) | 0.547 | ||||
| Lowerbound of 95% confidence interval for beta | -0.131 | ||||
| Upperbound of 95% confidence interval for beta | 0.312 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.184 | ||||
| Upperbound of 95% confidence interval for alpha | 0.163 | ||||
| Treynor index (mean / b) | -0.024 | ||||
| Jensen alpha (a) | -0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.105 | ||||
| Expected Shortfall on VaR | 0.129 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 87.000 | ||||
| Minimum | 0.789 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.322 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.072 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 17.000 | ||||
| Percentage of outliers low | 0.195 | ||||
| Mean of outliers low | 0.937 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.195 | ||||
| Mean of outliers high | 1.093 | ||||
| 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) | -0.302 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.089 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.223 | ||||
| Maximum | 0.343 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.223 | ||||
| Mean of quarter 4 | 0.343 | ||||
| Inter Quartile Range | 0.217 | ||||
| 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) | 0.049 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.125 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.125 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.331 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.196 | ||||
| SD | 0.637 | ||||
| Sharpe ratio (Glass type estimate) | 0.307 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.307 | ||||
| df | 1913.000 | ||||
| t | 0.831 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.418 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.033 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.418 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.032 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.483 | ||||
| Upside Potential Ratio | 3.937 | ||||
| Upside part of mean | 1.593 | ||||
| Downside part of mean | -1.398 | ||||
| Upside SD | 0.491 | ||||
| Downside SD | 0.405 | ||||
| N nonnegative terms | 192.000 | ||||
| N negative terms | 1722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1914.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | 0.196 | ||||
| SD of predictor | 0.526 | ||||
| SD of criterion | 0.637 | ||||
| Covariance | 0.044 | ||||
| r | 0.131 | ||||
| b (slope, estimate of beta) | 0.159 | ||||
| a (intercept, estimate of alpha) | 0.159 | ||||
| Mean Square Error | 0.398 | ||||
| DF error | 1912.000 | ||||
| t(b) | 5.800 | ||||
| p(b) | 0.434 | ||||
| t(a) | 0.683 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | 0.105 | ||||
| Upperbound of 95% confidence interval for beta | 0.213 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 0.618 | ||||
| Treynor index (mean / b) | 1.229 | ||||
| Jensen alpha (a) | 0.159 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.629 | ||||
| Sharpe ratio (Glass type estimate) | -0.004 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.004 | ||||
| df | 1913.000 | ||||
| t | -0.011 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.729 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.721 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.729 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.721 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.006 | ||||
| Upside Potential Ratio | 3.348 | ||||
| Upside part of mean | 1.488 | ||||
| Downside part of mean | -1.490 | ||||
| Upside SD | 0.444 | ||||
| Downside SD | 0.444 | ||||
| N nonnegative terms | 192.000 | ||||
| N negative terms | 1722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1914.000 | ||||
| Mean of predictor | 0.091 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.522 | ||||
| SD of criterion | 0.629 | ||||
| Covariance | 0.043 | ||||
| r | 0.132 | ||||
| b (slope, estimate of beta) | 0.158 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.388 | ||||
| DF error | 1912.000 | ||||
| t(b) | 5.805 | ||||
| p(b) | 0.434 | ||||
| t(a) | -0.073 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.105 | ||||
| Upperbound of 95% confidence interval for beta | 0.212 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.469 | ||||
| Upperbound of 95% confidence interval for alpha | 0.435 | ||||
| Treynor index (mean / b) | -0.016 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.062 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1914.000 | ||||
| Minimum | 0.677 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.478 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 186.000 | ||||
| Percentage of outliers low | 0.097 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 204.000 | ||||
| Percentage of outliers high | 0.107 | ||||
| Mean of outliers high | 1.057 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.197 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| 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 | 12.000 | ||||
| Minimum | 0.044 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.165 | ||||
| Quartile 3 | 0.281 | ||||
| Maximum | 0.348 | ||||
| Mean of quarter 1 | 0.054 | ||||
| Mean of quarter 2 | 0.109 | ||||
| Mean of quarter 3 | 0.224 | ||||
| Mean of quarter 4 | 0.334 | ||||
| Inter Quartile Range | 0.206 | ||||
| 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) | -37.523 | ||||
| VaR(95%) (moments method) | 0.344 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.876 | ||||
| VaR(95%) (regression method) | 0.374 | ||||
| Expected Shortfall (regression method) | 0.374 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.049 | ||||
| Compounded annual return (geometric extrapolation) | 0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.122 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.127 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.552 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.571 | ||||
| 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 | 0.719 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.578 | ||||
| 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) | -8773737564198935.000 | ||||
| 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) | -1214289979808922389229402729742336.000 | ||||
| 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 | ||||