Advanced Statistics: StingRay Long/Short Equity Trading System
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 | 0.164 | ||||
| SD | 0.522 | ||||
| Sharpe ratio (Glass type estimate) | 0.314 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.311 | ||||
| df | 67.000 | ||||
| t | 0.748 | ||||
| p | 0.228 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.512 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.138 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.514 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.136 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.474 | ||||
| Upside Potential Ratio | 1.768 | ||||
| Upside part of mean | 0.612 | ||||
| Downside part of mean | -0.448 | ||||
| Upside SD | 0.388 | ||||
| Downside SD | 0.346 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.314 | ||||
| Mean of criterion | 0.164 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.522 | ||||
| Covariance | 0.082 | ||||
| r | 0.666 | ||||
| b (slope, estimate of beta) | 1.470 | ||||
| a (intercept, estimate of alpha) | -0.298 | ||||
| Mean Square Error | 0.154 | ||||
| DF error | 66.000 | ||||
| t(b) | 7.252 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.685 | ||||
| p(a) | 0.952 | ||||
| Lowerbound of 95% confidence interval for beta | 1.065 | ||||
| Upperbound of 95% confidence interval for beta | 1.875 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.650 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | 0.112 | ||||
| Jensen alpha (a) | -0.298 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.019 | ||||
| SD | 0.559 | ||||
| Sharpe ratio (Glass type estimate) | 0.034 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.034 | ||||
| df | 67.000 | ||||
| t | 0.082 | ||||
| p | 0.468 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.789 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.858 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.789 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.857 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.043 | ||||
| Upside Potential Ratio | 1.236 | ||||
| Upside part of mean | 0.548 | ||||
| Downside part of mean | -0.529 | ||||
| Upside SD | 0.335 | ||||
| Downside SD | 0.443 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.283 | ||||
| Mean of criterion | 0.019 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.559 | ||||
| Covariance | 0.080 | ||||
| r | 0.628 | ||||
| b (slope, estimate of beta) | 1.546 | ||||
| a (intercept, estimate of alpha) | -0.419 | ||||
| Mean Square Error | 0.192 | ||||
| DF error | 66.000 | ||||
| t(b) | 6.557 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.136 | ||||
| p(a) | 0.982 | ||||
| Lowerbound of 95% confidence interval for beta | 1.075 | ||||
| Upperbound of 95% confidence interval for beta | 2.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.810 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | 0.012 | ||||
| Jensen alpha (a) | -0.419 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.232 | ||||
| Expected Shortfall on VaR | 0.281 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.173 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.465 | ||||
| Quartile 1 | 0.982 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.053 | ||||
| Maximum | 1.496 | ||||
| Mean of quarter 1 | 0.860 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.026 | ||||
| Mean of quarter 4 | 1.185 | ||||
| Inter Quartile Range | 0.071 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.088 | ||||
| Mean of outliers low | 0.699 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 1.299 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.461 | ||||
| VaR(95%) (moments method) | 0.087 | ||||
| Expected Shortfall (moments method) | 0.203 | ||||
| Extreme Value Index (regression method) | 0.370 | ||||
| VaR(95%) (regression method) | 0.132 | ||||
| Expected Shortfall (regression method) | 0.282 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.075 | ||||
| Quartile 3 | 0.246 | ||||
| Maximum | 0.686 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.045 | ||||
| Mean of quarter 3 | 0.080 | ||||
| Mean of quarter 4 | 0.549 | ||||
| Inter Quartile Range | 0.232 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.686 | ||||
| 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) | 0.076 | ||||
| Compounded annual return (geometric extrapolation) | 0.065 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.095 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.119 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.232 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.133 | ||||
| SD | 0.434 | ||||
| Sharpe ratio (Glass type estimate) | 0.307 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.306 | ||||
| df | 1487.000 | ||||
| t | 0.731 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.516 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.129 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.516 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.129 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.404 | ||||
| Upside Potential Ratio | 5.456 | ||||
| Upside part of mean | 1.800 | ||||
| Downside part of mean | -1.667 | ||||
| Upside SD | 0.282 | ||||
| Downside SD | 0.330 | ||||
| N nonnegative terms | 702.000 | ||||
| N negative terms | 786.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1488.000 | ||||
| Mean of predictor | 0.329 | ||||
| Mean of criterion | 0.133 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.434 | ||||
| Covariance | 0.062 | ||||
| r | 0.527 | ||||
| b (slope, estimate of beta) | 0.845 | ||||
| a (intercept, estimate of alpha) | -0.145 | ||||
| Mean Square Error | 0.136 | ||||
| DF error | 1486.000 | ||||
| t(b) | 23.885 | ||||
| p(b) | 0.237 | ||||
| t(a) | -0.934 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | 0.775 | ||||
| Upperbound of 95% confidence interval for beta | 0.914 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.450 | ||||
| Upperbound of 95% confidence interval for alpha | 0.160 | ||||
| Treynor index (mean / b) | 0.158 | ||||
| Jensen alpha (a) | -0.145 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.031 | ||||
| SD | 0.465 | ||||
| Sharpe ratio (Glass type estimate) | 0.066 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.066 | ||||
| df | 1487.000 | ||||
| t | 0.157 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.757 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.888 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.757 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.888 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.081 | ||||
| Upside Potential Ratio | 4.662 | ||||
| Upside part of mean | 1.762 | ||||
| Downside part of mean | -1.732 | ||||
| Upside SD | 0.271 | ||||
| Downside SD | 0.378 | ||||
| N nonnegative terms | 702.000 | ||||
| N negative terms | 786.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1488.000 | ||||
| Mean of predictor | 0.293 | ||||
| Mean of criterion | 0.031 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.465 | ||||
| Covariance | 0.062 | ||||
| r | 0.503 | ||||
| b (slope, estimate of beta) | 0.879 | ||||
| a (intercept, estimate of alpha) | -0.227 | ||||
| Mean Square Error | 0.162 | ||||
| DF error | 1486.000 | ||||
| t(b) | 22.425 | ||||
| p(b) | 0.249 | ||||
| t(a) | -1.344 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | 0.802 | ||||
| Upperbound of 95% confidence interval for beta | 0.956 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.559 | ||||
| Upperbound of 95% confidence interval for alpha | 0.104 | ||||
| Treynor index (mean / b) | 0.035 | ||||
| Jensen alpha (a) | -0.227 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1488.000 | ||||
| Minimum | 0.551 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.236 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 147.000 | ||||
| Percentage of outliers low | 0.099 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 145.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 1.045 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.662 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.066 | ||||
| Extreme Value Index (regression method) | 0.411 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.051 | ||||
| Maximum | 0.738 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.186 | ||||
| Inter Quartile Range | 0.045 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 0.289 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.762 | ||||
| VaR(95%) (moments method) | 0.199 | ||||
| Expected Shortfall (moments method) | 0.878 | ||||
| Extreme Value Index (regression method) | 1.114 | ||||
| VaR(95%) (regression method) | 0.201 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.093 | ||||
| Compounded annual return (geometric extrapolation) | 0.077 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.105 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.417 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.349 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.341 | ||||
| SD | 0.579 | ||||
| Sharpe ratio (Glass type estimate) | -0.588 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.585 | ||||
| df | 130.000 | ||||
| t | -0.416 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.360 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.186 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.358 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.188 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.812 | ||||
| Upside Potential Ratio | 7.861 | ||||
| Upside part of mean | 3.297 | ||||
| Downside part of mean | -3.638 | ||||
| Upside SD | 0.396 | ||||
| Downside SD | 0.419 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.996 | ||||
| Mean of criterion | -0.341 | ||||
| SD of predictor | 0.455 | ||||
| SD of criterion | 0.579 | ||||
| Covariance | 0.201 | ||||
| r | 0.765 | ||||
| b (slope, estimate of beta) | 0.974 | ||||
| a (intercept, estimate of alpha) | -1.311 | ||||
| Mean Square Error | 0.140 | ||||
| DF error | 129.000 | ||||
| t(b) | 13.499 | ||||
| p(b) | 0.066 | ||||
| t(a) | -2.454 | ||||
| p(a) | 0.633 | ||||
| Lowerbound of 95% confidence interval for beta | 0.831 | ||||
| Upperbound of 95% confidence interval for beta | 1.117 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.367 | ||||
| Upperbound of 95% confidence interval for alpha | -0.254 | ||||
| Treynor index (mean / b) | -0.350 | ||||
| Jensen alpha (a) | -1.311 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.508 | ||||
| SD | 0.581 | ||||
| Sharpe ratio (Glass type estimate) | -0.874 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.869 | ||||
| df | 130.000 | ||||
| t | -0.618 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.646 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.901 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.643 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.905 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.170 | ||||
| Upside Potential Ratio | 7.416 | ||||
| Upside part of mean | 3.221 | ||||
| Downside part of mean | -3.729 | ||||
| Upside SD | 0.384 | ||||
| Downside SD | 0.434 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.891 | ||||
| Mean of criterion | -0.508 | ||||
| SD of predictor | 0.456 | ||||
| SD of criterion | 0.581 | ||||
| Covariance | 0.202 | ||||
| r | 0.763 | ||||
| b (slope, estimate of beta) | 0.973 | ||||
| a (intercept, estimate of alpha) | -1.375 | ||||
| Mean Square Error | 0.142 | ||||
| DF error | 129.000 | ||||
| t(b) | 13.410 | ||||
| p(b) | 0.067 | ||||
| t(a) | -2.559 | ||||
| p(a) | 0.639 | ||||
| Lowerbound of 95% confidence interval for beta | 0.829 | ||||
| Upperbound of 95% confidence interval for beta | 1.116 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.438 | ||||
| Upperbound of 95% confidence interval for alpha | -0.312 | ||||
| Treynor index (mean / b) | -0.522 | ||||
| Jensen alpha (a) | -1.375 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.879 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 0.998 | ||||
| Quartile 3 | 1.018 | ||||
| Maximum | 1.118 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.043 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.897 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.104 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.153 | ||||
| VaR(95%) (moments method) | 0.044 | ||||
| Expected Shortfall (moments method) | 0.056 | ||||
| Extreme Value Index (regression method) | 0.002 | ||||
| VaR(95%) (regression method) | 0.043 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.435 | ||||
| Quartile 1 | 0.435 | ||||
| Median | 0.435 | ||||
| Quartile 3 | 0.435 | ||||
| Maximum | 0.435 | ||||
| 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) | -0.414 | ||||
| Compounded annual return (geometric extrapolation) | -0.371 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.853 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.077 | ||||