Advanced Statistics: Futures Trader Daily
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 | 0.211 | ||||
| SD | 0.352 | ||||
| Sharpe ratio (Glass type estimate) | 0.599 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.595 | ||||
| df | 96.000 | ||||
| t | 1.704 | ||||
| p | 0.046 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.097 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.292 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.100 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.289 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.203 | ||||
| Upside Potential Ratio | 2.994 | ||||
| Upside part of mean | 0.526 | ||||
| Downside part of mean | -0.314 | ||||
| Upside SD | 0.310 | ||||
| Downside SD | 0.176 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 97.000 | ||||
| Mean of predictor | 0.204 | ||||
| Mean of criterion | 0.211 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.352 | ||||
| Covariance | -0.005 | ||||
| r | -0.057 | ||||
| b (slope, estimate of beta) | -0.083 | ||||
| a (intercept, estimate of alpha) | 0.228 | ||||
| Mean Square Error | 0.125 | ||||
| DF error | 95.000 | ||||
| t(b) | -0.557 | ||||
| p(b) | 0.711 | ||||
| t(a) | 1.782 | ||||
| p(a) | 0.039 | ||||
| Lowerbound of 95% confidence interval for beta | -0.380 | ||||
| Upperbound of 95% confidence interval for beta | 0.213 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.026 | ||||
| Upperbound of 95% confidence interval for alpha | 0.483 | ||||
| Treynor index (mean / b) | -2.536 | ||||
| Jensen alpha (a) | 0.228 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.153 | ||||
| SD | 0.332 | ||||
| Sharpe ratio (Glass type estimate) | 0.460 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.456 | ||||
| df | 96.000 | ||||
| t | 1.308 | ||||
| p | 0.097 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.234 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.151 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.236 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.149 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.812 | ||||
| Upside Potential Ratio | 2.568 | ||||
| Upside part of mean | 0.483 | ||||
| Downside part of mean | -0.330 | ||||
| Upside SD | 0.275 | ||||
| Downside SD | 0.188 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 97.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | 0.153 | ||||
| SD of predictor | 0.213 | ||||
| SD of criterion | 0.332 | ||||
| Covariance | -0.004 | ||||
| r | -0.061 | ||||
| b (slope, estimate of beta) | -0.095 | ||||
| a (intercept, estimate of alpha) | 0.170 | ||||
| Mean Square Error | 0.111 | ||||
| DF error | 95.000 | ||||
| t(b) | -0.595 | ||||
| p(b) | 0.723 | ||||
| t(a) | 1.407 | ||||
| p(a) | 0.081 | ||||
| Lowerbound of 95% confidence interval for beta | -0.412 | ||||
| Upperbound of 95% confidence interval for beta | 0.222 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.070 | ||||
| Upperbound of 95% confidence interval for alpha | 0.409 | ||||
| Treynor index (mean / b) | -1.611 | ||||
| Jensen alpha (a) | 0.170 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.135 | ||||
| Expected Shortfall on VaR | 0.168 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.113 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 97.000 | ||||
| Minimum | 0.779 | ||||
| Quartile 1 | 0.960 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.064 | ||||
| Maximum | 1.455 | ||||
| Mean of quarter 1 | 0.918 | ||||
| Mean of quarter 2 | 0.987 | ||||
| Mean of quarter 3 | 1.030 | ||||
| Mean of quarter 4 | 1.155 | ||||
| Inter Quartile Range | 0.104 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.010 | ||||
| Mean of outliers low | 0.779 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.284 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.336 | ||||
| VaR(95%) (moments method) | 0.092 | ||||
| Expected Shortfall (moments method) | 0.155 | ||||
| Extreme Value Index (regression method) | 0.455 | ||||
| VaR(95%) (regression method) | 0.075 | ||||
| Expected Shortfall (regression method) | 0.131 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.033 | ||||
| Quartile 1 | 0.070 | ||||
| Median | 0.219 | ||||
| Quartile 3 | 0.327 | ||||
| Maximum | 0.458 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | 0.155 | ||||
| Mean of quarter 3 | 0.287 | ||||
| Mean of quarter 4 | 0.412 | ||||
| Inter Quartile Range | 0.257 | ||||
| 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) | 0.483 | ||||
| Compounded annual return (geometric extrapolation) | 0.217 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.475 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.527 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.291 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.233 | ||||
| SD | 0.413 | ||||
| Sharpe ratio (Glass type estimate) | 0.564 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.564 | ||||
| df | 2125.000 | ||||
| t | 1.608 | ||||
| p | 0.054 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.124 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.253 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.124 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.252 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.959 | ||||
| Upside Potential Ratio | 6.477 | ||||
| Upside part of mean | 1.576 | ||||
| Downside part of mean | -1.343 | ||||
| Upside SD | 0.334 | ||||
| Downside SD | 0.243 | ||||
| N nonnegative terms | 932.000 | ||||
| N negative terms | 1194.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2126.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | 0.233 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.413 | ||||
| Covariance | 0.023 | ||||
| r | 0.183 | ||||
| b (slope, estimate of beta) | 0.254 | ||||
| a (intercept, estimate of alpha) | 0.176 | ||||
| Mean Square Error | 0.165 | ||||
| DF error | 2124.000 | ||||
| t(b) | 8.588 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.230 | ||||
| p(a) | 0.109 | ||||
| Lowerbound of 95% confidence interval for beta | 0.196 | ||||
| Upperbound of 95% confidence interval for beta | 0.312 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.456 | ||||
| Treynor index (mean / b) | 0.920 | ||||
| Jensen alpha (a) | 0.176 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.152 | ||||
| SD | 0.401 | ||||
| Sharpe ratio (Glass type estimate) | 0.379 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.379 | ||||
| df | 2125.000 | ||||
| t | 1.080 | ||||
| p | 0.140 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.309 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.067 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.309 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.067 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.562 | ||||
| Upside Potential Ratio | 5.649 | ||||
| Upside part of mean | 1.529 | ||||
| Downside part of mean | -1.377 | ||||
| Upside SD | 0.296 | ||||
| Downside SD | 0.271 | ||||
| N nonnegative terms | 932.000 | ||||
| N negative terms | 1194.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2126.000 | ||||
| Mean of predictor | 0.189 | ||||
| Mean of criterion | 0.152 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.401 | ||||
| Covariance | 0.022 | ||||
| r | 0.203 | ||||
| b (slope, estimate of beta) | 0.303 | ||||
| a (intercept, estimate of alpha) | 0.095 | ||||
| Mean Square Error | 0.154 | ||||
| DF error | 2124.000 | ||||
| t(b) | 9.540 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.687 | ||||
| p(a) | 0.246 | ||||
| Lowerbound of 95% confidence interval for beta | 0.241 | ||||
| Upperbound of 95% confidence interval for beta | 0.365 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.176 | ||||
| Upperbound of 95% confidence interval for alpha | 0.365 | ||||
| Treynor index (mean / b) | 0.502 | ||||
| Jensen alpha (a) | 0.095 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2126.000 | ||||
| Minimum | 0.637 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.576 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 86.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.952 | ||||
| Number of outliers high | 125.000 | ||||
| Percentage of outliers high | 0.059 | ||||
| Mean of outliers high | 1.051 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.441 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | 0.035 | ||||
| Extreme Value Index (regression method) | 0.327 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.026 | ||||
| Quartile 3 | 0.081 | ||||
| Maximum | 0.509 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.042 | ||||
| Mean of quarter 4 | 0.254 | ||||
| Inter Quartile Range | 0.072 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.156 | ||||
| Mean of outliers high | 0.330 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.203 | ||||
| VaR(95%) (moments method) | 0.213 | ||||
| Expected Shortfall (moments method) | 0.272 | ||||
| Extreme Value Index (regression method) | 0.200 | ||||
| VaR(95%) (regression method) | 0.254 | ||||
| Expected Shortfall (regression method) | 0.408 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.482 | ||||
| Compounded annual return (geometric extrapolation) | 0.217 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.425 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.853 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.401 | ||||
| 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 | 1.308 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.396 | ||||
| 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 | 1.227 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.398 | ||||
| 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) | -8643168021795610.000 | ||||
| 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) | -62955820941618075091017408708608.000 | ||||
| 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 | ||||