Advanced Statistics: Interlink 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 | 0.099 | ||||
| SD | 0.259 | ||||
| Sharpe ratio (Glass type estimate) | 0.380 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.379 | ||||
| df | 212.000 | ||||
| t | 1.601 | ||||
| p | 0.055 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.087 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.088 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.845 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.776 | ||||
| Upside Potential Ratio | 1.780 | ||||
| Upside part of mean | 0.226 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.227 | ||||
| Downside SD | 0.127 | ||||
| N nonnegative terms | 33.000 | ||||
| N negative terms | 180.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 213.000 | ||||
| Mean of predictor | 0.064 | ||||
| Mean of criterion | 0.099 | ||||
| SD of predictor | 0.166 | ||||
| SD of criterion | 0.259 | ||||
| Covariance | 0.002 | ||||
| r | 0.042 | ||||
| b (slope, estimate of beta) | 0.066 | ||||
| a (intercept, estimate of alpha) | 0.094 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 211.000 | ||||
| t(b) | 0.610 | ||||
| p(b) | 0.271 | ||||
| t(a) | 1.522 | ||||
| p(a) | 0.065 | ||||
| Lowerbound of 95% confidence interval for beta | -0.146 | ||||
| Upperbound of 95% confidence interval for beta | 0.278 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.028 | ||||
| Upperbound of 95% confidence interval for alpha | 0.217 | ||||
| Treynor index (mean / b) | 1.501 | ||||
| Jensen alpha (a) | 0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.067 | ||||
| SD | 0.250 | ||||
| Sharpe ratio (Glass type estimate) | 0.266 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.265 | ||||
| df | 212.000 | ||||
| t | 1.122 | ||||
| p | 0.132 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.200 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.732 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.200 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.731 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.439 | ||||
| Upside Potential Ratio | 1.344 | ||||
| Upside part of mean | 0.204 | ||||
| Downside part of mean | -0.137 | ||||
| Upside SD | 0.199 | ||||
| Downside SD | 0.152 | ||||
| N nonnegative terms | 33.000 | ||||
| N negative terms | 180.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 213.000 | ||||
| Mean of predictor | 0.049 | ||||
| Mean of criterion | 0.067 | ||||
| SD of predictor | 0.170 | ||||
| SD of criterion | 0.250 | ||||
| Covariance | 0.003 | ||||
| r | 0.062 | ||||
| b (slope, estimate of beta) | 0.091 | ||||
| a (intercept, estimate of alpha) | 0.062 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 211.000 | ||||
| t(b) | 0.905 | ||||
| p(b) | 0.183 | ||||
| t(a) | 1.042 | ||||
| p(a) | 0.149 | ||||
| Lowerbound of 95% confidence interval for beta | -0.107 | ||||
| Upperbound of 95% confidence interval for beta | 0.290 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.055 | ||||
| Upperbound of 95% confidence interval for alpha | 0.179 | ||||
| Treynor index (mean / b) | 0.729 | ||||
| Jensen alpha (a) | 0.062 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.107 | ||||
| Expected Shortfall on VaR | 0.133 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.072 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 213.000 | ||||
| Minimum | 0.598 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.452 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.078 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 27.000 | ||||
| Percentage of outliers low | 0.127 | ||||
| Mean of outliers low | 0.941 | ||||
| Number of outliers high | 38.000 | ||||
| Percentage of outliers high | 0.178 | ||||
| Mean of outliers high | 1.109 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -23.040 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.201 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.065 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.060 | ||||
| Quartile 1 | 0.089 | ||||
| Median | 0.166 | ||||
| Quartile 3 | 0.258 | ||||
| Maximum | 0.402 | ||||
| Mean of quarter 1 | 0.070 | ||||
| Mean of quarter 2 | 0.115 | ||||
| Mean of quarter 3 | 0.217 | ||||
| Mean of quarter 4 | 0.337 | ||||
| Inter Quartile Range | 0.170 | ||||
| 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) | 0.345 | ||||
| Compounded annual return (geometric extrapolation) | 0.117 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.291 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.346 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.878 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.218 | ||||
| SD | 0.559 | ||||
| Sharpe ratio (Glass type estimate) | 0.390 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.390 | ||||
| df | 4670.000 | ||||
| t | 1.645 | ||||
| p | 0.050 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.075 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.854 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.075 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.854 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.655 | ||||
| Upside Potential Ratio | 3.299 | ||||
| Upside part of mean | 1.096 | ||||
| Downside part of mean | -0.879 | ||||
| Upside SD | 0.449 | ||||
| Downside SD | 0.332 | ||||
| N nonnegative terms | 543.000 | ||||
| N negative terms | 4128.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 4671.000 | ||||
| Mean of predictor | 0.107 | ||||
| Mean of criterion | 0.218 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.559 | ||||
| Covariance | -0.020 | ||||
| r | -0.107 | ||||
| b (slope, estimate of beta) | -0.176 | ||||
| a (intercept, estimate of alpha) | 0.237 | ||||
| Mean Square Error | 0.309 | ||||
| DF error | 4669.000 | ||||
| t(b) | -7.370 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.797 | ||||
| p(a) | 0.036 | ||||
| Lowerbound of 95% confidence interval for beta | -0.222 | ||||
| Upperbound of 95% confidence interval for beta | -0.129 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.022 | ||||
| Upperbound of 95% confidence interval for alpha | 0.495 | ||||
| Treynor index (mean / b) | -1.240 | ||||
| Jensen alpha (a) | 0.237 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.066 | ||||
| SD | 0.553 | ||||
| Sharpe ratio (Glass type estimate) | 0.119 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.119 | ||||
| df | 4670.000 | ||||
| t | 0.504 | ||||
| p | 0.307 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.345 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.584 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.345 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.584 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.166 | ||||
| Upside Potential Ratio | 2.553 | ||||
| Upside part of mean | 1.014 | ||||
| Downside part of mean | -0.948 | ||||
| Upside SD | 0.385 | ||||
| Downside SD | 0.397 | ||||
| N nonnegative terms | 543.000 | ||||
| N negative terms | 4128.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 4671.000 | ||||
| Mean of predictor | 0.049 | ||||
| Mean of criterion | 0.066 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.553 | ||||
| Covariance | -0.019 | ||||
| r | -0.099 | ||||
| b (slope, estimate of beta) | -0.161 | ||||
| a (intercept, estimate of alpha) | 0.074 | ||||
| Mean Square Error | 0.303 | ||||
| DF error | 4669.000 | ||||
| t(b) | -6.804 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.567 | ||||
| p(a) | 0.285 | ||||
| Lowerbound of 95% confidence interval for beta | -0.208 | ||||
| Upperbound of 95% confidence interval for beta | -0.115 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.182 | ||||
| Upperbound of 95% confidence interval for alpha | 0.330 | ||||
| Treynor index (mean / b) | -0.409 | ||||
| Jensen alpha (a) | 0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 4671.000 | ||||
| Minimum | 0.458 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.589 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 589.000 | ||||
| Percentage of outliers low | 0.126 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 572.000 | ||||
| Percentage of outliers high | 0.122 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.794 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.027 | ||||
| Extreme Value Index (regression method) | 0.533 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 49.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.054 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.631 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.089 | ||||
| Mean of quarter 4 | 0.301 | ||||
| Inter Quartile Range | 0.119 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.102 | ||||
| Mean of outliers high | 0.412 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.359 | ||||
| VaR(95%) (moments method) | 0.295 | ||||
| Expected Shortfall (moments method) | 0.350 | ||||
| Extreme Value Index (regression method) | -0.319 | ||||
| VaR(95%) (regression method) | 0.351 | ||||
| Expected Shortfall (regression method) | 0.426 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.343 | ||||
| Compounded annual return (geometric extrapolation) | 0.116 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.184 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.386 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.717 | ||||
| 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 | 0.119 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.133 | ||||
| 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 | 0.110 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.133 | ||||
| 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) | -8788282180294180.000 | ||||
| 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) | -25367972787455492271103803392000.000 | ||||
| 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 | ||||