Advanced Statistics: Psicotrade
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 | -0.042 | ||||
| SD | 0.005 | ||||
| Sharpe ratio (Glass type estimate) | -7.797 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.698 | ||||
| df | 59.000 | ||||
| t | -17.435 | ||||
| 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) | -9.340 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.055 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.304 | ||||
| Upside Potential Ratio | 0.131 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | -0.011 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.189 | ||||
| SD of criterion | 0.005 | ||||
| Covariance | 0.000 | ||||
| r | 0.086 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.659 | ||||
| p(b) | 0.256 | ||||
| t(a) | -17.337 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | -17.077 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.005 | ||||
| Sharpe ratio (Glass type estimate) | -7.831 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.731 | ||||
| df | 59.000 | ||||
| t | -17.511 | ||||
| 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) | -9.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.084 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.305 | ||||
| Upside Potential Ratio | 0.130 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | -0.029 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.193 | ||||
| SD of criterion | 0.005 | ||||
| Covariance | 0.000 | ||||
| r | 0.086 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.659 | ||||
| p(b) | 0.256 | ||||
| t(a) | -17.381 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.005 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | -17.507 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.012 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.006 | ||||
| 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) | 0.002 | ||||
| Compounded annual return (geometric extrapolation) | 0.002 | ||||
| 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 | 0.360 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.005 | ||||
| Sharpe ratio (Glass type estimate) | -7.823 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.819 | ||||
| df | 1735.000 | ||||
| t | -17.573 | ||||
| p | 0.741 | ||||
| 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) | -8.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.909 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -17.553 | ||||
| Upside Potential Ratio | 0.988 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 1735.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1736.000 | ||||
| Mean of predictor | 0.042 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.005 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 1734.000 | ||||
| t(b) | -0.331 | ||||
| p(b) | 0.504 | ||||
| t(a) | -17.565 | ||||
| p(a) | 0.694 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | 266.376 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.005 | ||||
| Sharpe ratio (Glass type estimate) | -7.871 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.868 | ||||
| df | 1735.000 | ||||
| t | -17.683 | ||||
| p | 0.742 | ||||
| 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) | -8.779 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -6.957 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -17.559 | ||||
| Upside Potential Ratio | 0.982 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 1735.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1736.000 | ||||
| Mean of predictor | 0.005 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.005 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 1734.000 | ||||
| t(b) | -0.324 | ||||
| p(b) | 0.504 | ||||
| t(a) | -17.678 | ||||
| p(a) | 0.695 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | 274.130 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| 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 | 1736.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.012 | ||||
| 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 | 9.000 | ||||
| Percentage of outliers low | 0.005 | ||||
| Mean of outliers low | 1.000 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.006 | ||||
| Mean of outliers high | 1.001 | ||||
| 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 | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.000 | ||||
| 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 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) | 0.002 | ||||
| Compounded annual return (geometric extrapolation) | 0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | 238.889 | ||||
| Compounded annual return / average of 25% largest draw downs | 238.889 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.327 | ||||
| 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 | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.695 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.272 | ||||
| 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) | -7936535306446244.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -7901674975671223.000 | ||||
| df | 171.000 | ||||
| t | -5611977934314593.000 | ||||
| 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) | -8739115425704417.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7064234525638030.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.657 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.272 | ||||
| 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 | 170.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -5548360382961750.000 | ||||
| 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) | 76800479683881990739501116293120.000 | ||||
| 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 | 172.000 | ||||
| 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 | ||||
