Advanced Statistics: Marathon 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 | 0.085 | ||||
| SD | 0.142 | ||||
| Sharpe ratio (Glass type estimate) | 0.600 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.591 | ||||
| df | 47.000 | ||||
| t | 1.201 | ||||
| p | 0.118 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.390 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.396 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.578 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.112 | ||||
| Upside Potential Ratio | 4.126 | ||||
| Upside part of mean | 0.166 | ||||
| Downside part of mean | -0.081 | ||||
| Upside SD | 0.136 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.427 | ||||
| Mean of criterion | 0.085 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.142 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.086 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 46.000 | ||||
| t(b) | -0.017 | ||||
| p(b) | 0.507 | ||||
| t(a) | 1.079 | ||||
| p(a) | 0.143 | ||||
| Lowerbound of 95% confidence interval for beta | -0.163 | ||||
| Upperbound of 95% confidence interval for beta | 0.160 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.074 | ||||
| Upperbound of 95% confidence interval for alpha | 0.245 | ||||
| Treynor index (mean / b) | -61.552 | ||||
| Jensen alpha (a) | 0.086 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.075 | ||||
| SD | 0.133 | ||||
| Sharpe ratio (Glass type estimate) | 0.566 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.557 | ||||
| df | 47.000 | ||||
| t | 1.132 | ||||
| p | 0.132 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.424 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.550 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.430 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.543 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.852 | ||||
| Upside Potential Ratio | 3.857 | ||||
| Upside part of mean | 0.157 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.127 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.388 | ||||
| Mean of criterion | 0.075 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.133 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | 0.073 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 46.000 | ||||
| t(b) | 0.091 | ||||
| p(b) | 0.464 | ||||
| t(a) | 0.980 | ||||
| p(a) | 0.166 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.222 | ||||
| Treynor index (mean / b) | 10.352 | ||||
| Jensen alpha (a) | 0.073 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.962 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.191 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.058 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.188 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 1.077 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -149.163 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.858 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.037 | ||||
| Median | 0.042 | ||||
| Quartile 3 | 0.049 | ||||
| Maximum | 0.055 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.055 | ||||
| Inter Quartile Range | 0.012 | ||||
| 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) | 0.153 | ||||
| Compounded annual return (geometric extrapolation) | 0.127 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.300 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.300 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.803 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.124 | ||||
| SD | 0.329 | ||||
| Sharpe ratio (Glass type estimate) | 0.377 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.377 | ||||
| df | 1059.000 | ||||
| t | 0.759 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.597 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.352 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.598 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.352 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.675 | ||||
| Upside Potential Ratio | 2.649 | ||||
| Upside part of mean | 0.488 | ||||
| Downside part of mean | -0.364 | ||||
| Upside SD | 0.273 | ||||
| Downside SD | 0.184 | ||||
| N nonnegative terms | 130.000 | ||||
| N negative terms | 930.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1060.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | 0.124 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.329 | ||||
| Covariance | 0.026 | ||||
| r | 0.248 | ||||
| b (slope, estimate of beta) | 0.257 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.102 | ||||
| DF error | 1058.000 | ||||
| t(b) | 8.340 | ||||
| p(b) | 0.376 | ||||
| t(a) | 0.082 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.318 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 0.326 | ||||
| Treynor index (mean / b) | 0.483 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.074 | ||||
| SD | 0.315 | ||||
| Sharpe ratio (Glass type estimate) | 0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.235 | ||||
| df | 1059.000 | ||||
| t | 0.473 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.739 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.210 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.739 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.210 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.340 | ||||
| Upside Potential Ratio | 2.108 | ||||
| Upside part of mean | 0.459 | ||||
| Downside part of mean | -0.385 | ||||
| Upside SD | 0.227 | ||||
| Downside SD | 0.218 | ||||
| N nonnegative terms | 130.000 | ||||
| N negative terms | 930.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1060.000 | ||||
| Mean of predictor | 0.381 | ||||
| Mean of criterion | 0.074 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.315 | ||||
| Covariance | 0.025 | ||||
| r | 0.249 | ||||
| b (slope, estimate of beta) | 0.244 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 1058.000 | ||||
| t(b) | 8.362 | ||||
| p(b) | 0.376 | ||||
| t(a) | -0.126 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | 0.187 | ||||
| Upperbound of 95% confidence interval for beta | 0.302 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.317 | ||||
| Upperbound of 95% confidence interval for alpha | 0.279 | ||||
| Treynor index (mean / b) | 0.303 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1060.000 | ||||
| Minimum | 0.667 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.513 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 118.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 133.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.310 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.490 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.053 | ||||
| Maximum | 0.333 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.038 | ||||
| Mean of quarter 4 | 0.153 | ||||
| Inter Quartile Range | 0.051 | ||||
| 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 | 0.077 | ||||
| Mean of outliers high | 0.333 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.802 | ||||
| VaR(95%) (moments method) | 0.168 | ||||
| Expected Shortfall (moments method) | 0.833 | ||||
| Extreme Value Index (regression method) | 2.626 | ||||
| VaR(95%) (regression method) | 0.248 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.151 | ||||
| Compounded annual return (geometric extrapolation) | 0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.376 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.819 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.212 | ||||
| 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 | 0.825 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.460 | ||||
| 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 | 0.716 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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) | -8760160495522892.000 | ||||
| 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) | -211491938530123287535983181955072.000 | ||||
| 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 | ||||