Advanced Statistics: SolidSwingTrader
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 | -0.002 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.037 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.036 | ||||
| df | 60.000 | ||||
| t | -0.082 | ||||
| p | 0.533 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.906 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.833 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.905 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.833 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.058 | ||||
| Upside Potential Ratio | 1.767 | ||||
| Upside part of mean | 0.059 | ||||
| Downside part of mean | -0.061 | ||||
| Upside SD | 0.041 | ||||
| Downside SD | 0.034 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.301 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.220 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.001 | ||||
| r | 0.071 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.544 | ||||
| p(b) | 0.294 | ||||
| t(a) | -0.278 | ||||
| p(a) | 0.609 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.058 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -0.114 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.003 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.063 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.062 | ||||
| df | 60.000 | ||||
| t | -0.141 | ||||
| p | 0.556 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.932 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.807 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.931 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.808 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.097 | ||||
| Upside Potential Ratio | 1.713 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.062 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.034 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.275 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.206 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.001 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.632 | ||||
| p(b) | 0.265 | ||||
| t(a) | -0.360 | ||||
| p(a) | 0.640 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.088 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.060 | ||||
| Upperbound of 95% confidence interval for alpha | 0.041 | ||||
| Treynor index (mean / b) | -0.157 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.953 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.041 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.115 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.230 | ||||
| Mean of outliers high | 1.025 | ||||
| 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) | -0.169 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.031 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.027 | ||||
| Quartile 3 | 0.047 | ||||
| Maximum | 0.074 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.037 | ||||
| Mean of quarter 4 | 0.074 | ||||
| Inter Quartile Range | 0.031 | ||||
| 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) | 0.045 | ||||
| Compounded annual return (geometric extrapolation) | 0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.560 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.560 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.332 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.050 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.050 | ||||
| df | 1337.000 | ||||
| t | -0.112 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.917 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.818 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.917 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.818 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.073 | ||||
| Upside Potential Ratio | 4.892 | ||||
| Upside part of mean | 0.159 | ||||
| Downside part of mean | -0.161 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 247.000 | ||||
| N negative terms | 1091.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1338.000 | ||||
| Mean of predictor | 0.326 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.001 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 1336.000 | ||||
| t(b) | 1.949 | ||||
| p(b) | 0.473 | ||||
| t(a) | -0.262 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -0.244 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.003 | ||||
| SD | 0.048 | ||||
| Sharpe ratio (Glass type estimate) | -0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.073 | ||||
| df | 1337.000 | ||||
| t | -0.166 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.941 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.794 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.941 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.794 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.107 | ||||
| Upside Potential Ratio | 4.838 | ||||
| Upside part of mean | 0.158 | ||||
| Downside part of mean | -0.161 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 247.000 | ||||
| N negative terms | 1091.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1338.000 | ||||
| Mean of predictor | 0.291 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.048 | ||||
| Covariance | 0.001 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 1336.000 | ||||
| t(b) | 1.943 | ||||
| p(b) | 0.473 | ||||
| t(a) | -0.298 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.035 | ||||
| Treynor index (mean / b) | -0.364 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1338.000 | ||||
| Minimum | 0.968 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.024 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 210.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 257.000 | ||||
| Percentage of outliers high | 0.192 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.274 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.140 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 24.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.020 | ||||
| Maximum | 0.083 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.043 | ||||
| Inter Quartile Range | 0.019 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.071 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.297 | ||||
| VaR(95%) (moments method) | 0.049 | ||||
| Expected Shortfall (moments method) | 0.077 | ||||
| Extreme Value Index (regression method) | 0.877 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.229 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.045 | ||||
| Compounded annual return (geometric extrapolation) | 0.041 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.500 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.954 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.835 | ||||
| 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 | 1.123 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.506 | ||||
| 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 | 0.993 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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) | -8736517925093865.000 | ||||
| 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) | -94592098029103881424019530973184.000 | ||||
| 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 | ||||