Advanced Statistics: My Trading Robot YM
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 | -0.075 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -1.571 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.551 | ||||
| df | 60.000 | ||||
| t | -3.542 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.479 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.652 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.464 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.639 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.480 | ||||
| Upside Potential Ratio | 0.142 | ||||
| Upside part of mean | 0.007 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.002 | ||||
| r | 0.182 | ||||
| b (slope, estimate of beta) | 0.033 | ||||
| a (intercept, estimate of alpha) | -0.089 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.419 | ||||
| p(b) | 0.081 | ||||
| t(a) | -3.840 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.135 | ||||
| Upperbound of 95% confidence interval for alpha | -0.042 | ||||
| Treynor index (mean / b) | -2.254 | ||||
| Jensen alpha (a) | -0.089 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.076 | ||||
| SD | 0.049 | ||||
| Sharpe ratio (Glass type estimate) | -1.551 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.531 | ||||
| df | 60.000 | ||||
| t | -3.497 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.457 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.633 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.443 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.620 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.461 | ||||
| Upside Potential Ratio | 0.136 | ||||
| Upside part of mean | 0.007 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.363 | ||||
| Mean of criterion | -0.076 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.049 | ||||
| Covariance | 0.003 | ||||
| r | 0.213 | ||||
| b (slope, estimate of beta) | 0.042 | ||||
| a (intercept, estimate of alpha) | -0.091 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.678 | ||||
| p(b) | 0.049 | ||||
| t(a) | -3.922 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.138 | ||||
| Upperbound of 95% confidence interval for alpha | -0.045 | ||||
| Treynor index (mean / b) | -1.839 | ||||
| Jensen alpha (a) | -0.091 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.922 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.027 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.022 | ||||
| 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) | -0.465 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.154 | ||||
| Quartile 1 | 0.154 | ||||
| Median | 0.154 | ||||
| Quartile 3 | 0.154 | ||||
| Maximum | 0.154 | ||||
| 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) | -0.030 | ||||
| Compounded annual return (geometric extrapolation) | -0.032 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.206 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.908 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.211 | ||||
| Sharpe ratio (Glass type estimate) | -0.254 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.254 | ||||
| df | 1345.000 | ||||
| t | -0.576 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.119 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.611 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.119 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.611 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.362 | ||||
| Upside Potential Ratio | 2.372 | ||||
| Upside part of mean | 0.352 | ||||
| Downside part of mean | -0.406 | ||||
| Upside SD | 0.150 | ||||
| Downside SD | 0.148 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 1291.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1346.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.479 | ||||
| SD of criterion | 0.211 | ||||
| Covariance | -0.008 | ||||
| r | -0.076 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 1344.000 | ||||
| t(b) | -2.795 | ||||
| p(b) | 0.538 | ||||
| t(a) | -0.401 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.057 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.220 | ||||
| Upperbound of 95% confidence interval for alpha | 0.145 | ||||
| Treynor index (mean / b) | 1.600 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.076 | ||||
| SD | 0.211 | ||||
| Sharpe ratio (Glass type estimate) | -0.360 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.360 | ||||
| df | 1345.000 | ||||
| t | -0.815 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.225 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.505 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.224 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.505 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.493 | ||||
| Upside Potential Ratio | 2.212 | ||||
| Upside part of mean | 0.341 | ||||
| Downside part of mean | -0.417 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 1291.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1346.000 | ||||
| Mean of predictor | 0.378 | ||||
| Mean of criterion | -0.076 | ||||
| SD of predictor | 0.461 | ||||
| SD of criterion | 0.211 | ||||
| Covariance | -0.008 | ||||
| r | -0.079 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.044 | ||||
| DF error | 1344.000 | ||||
| t(b) | -2.898 | ||||
| p(b) | 0.539 | ||||
| t(a) | -0.670 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | -0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.245 | ||||
| Upperbound of 95% confidence interval for alpha | 0.120 | ||||
| Treynor index (mean / b) | 2.106 | ||||
| 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%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1346.000 | ||||
| Minimum | 0.881 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.129 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 52.000 | ||||
| Percentage of outliers low | 0.039 | ||||
| Mean of outliers low | 0.964 | ||||
| Number of outliers high | 55.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.637 | ||||
| VaR(95%) (moments method) | -0.003 | ||||
| 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 | 3.000 | ||||
| Minimum | 0.054 | ||||
| Quartile 1 | 0.072 | ||||
| Median | 0.090 | ||||
| Quartile 3 | 0.157 | ||||
| Maximum | 0.223 | ||||
| Mean of quarter 1 | 0.054 | ||||
| Mean of quarter 2 | 0.090 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.223 | ||||
| Inter Quartile Range | 0.085 | ||||
| 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) | -0.030 | ||||
| Compounded annual return (geometric extrapolation) | -0.031 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.141 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.141 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.173 | ||||
| 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 | 1.238 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.375 | ||||
| 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 | 1.165 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.376 | ||||
| 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) | -8641302674849681.000 | ||||
| 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) | 94126403996522830997438123212800.000 | ||||
| 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 | ||||