Advanced Statistics: W R stopped 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 | -0.042 | ||||
| SD | 0.100 | ||||
| Sharpe ratio (Glass type estimate) | -0.416 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.411 | ||||
| df | 77.000 | ||||
| t | -1.059 | ||||
| p | 0.854 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.186 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.357 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.183 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.360 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.613 | ||||
| Upside Potential Ratio | 0.751 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.074 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.236 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.100 | ||||
| Covariance | 0.002 | ||||
| r | 0.048 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 76.000 | ||||
| t(b) | 0.415 | ||||
| p(b) | 0.340 | ||||
| t(a) | -1.115 | ||||
| p(a) | 0.866 | ||||
| Lowerbound of 95% confidence interval for beta | -0.054 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.125 | ||||
| Upperbound of 95% confidence interval for alpha | 0.035 | ||||
| Treynor index (mean / b) | -2.948 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.468 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.463 | ||||
| df | 77.000 | ||||
| t | -1.193 | ||||
| p | 0.882 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.239 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.306 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.235 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.309 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.650 | ||||
| Upside Potential Ratio | 0.677 | ||||
| Upside part of mean | 0.048 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.071 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.181 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.002 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.016 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 76.000 | ||||
| t(b) | 0.439 | ||||
| p(b) | 0.331 | ||||
| t(a) | -1.242 | ||||
| p(a) | 0.891 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.086 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.128 | ||||
| Upperbound of 95% confidence interval for alpha | 0.030 | ||||
| Treynor index (mean / b) | -2.977 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.870 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.149 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -52.245 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.078 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.074 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.049 | ||||
| Quartile 1 | 0.098 | ||||
| Median | 0.147 | ||||
| Quartile 3 | 0.196 | ||||
| Maximum | 0.245 | ||||
| Mean of quarter 1 | 0.049 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.245 | ||||
| Inter Quartile Range | 0.098 | ||||
| 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) | -0.009 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.009 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.038 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.053 | ||||
| SD | 0.448 | ||||
| Sharpe ratio (Glass type estimate) | 0.117 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.117 | ||||
| df | 1720.000 | ||||
| t | 0.301 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.647 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.882 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.647 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.882 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.180 | ||||
| Upside Potential Ratio | 2.575 | ||||
| Upside part of mean | 0.752 | ||||
| Downside part of mean | -0.699 | ||||
| Upside SD | 0.340 | ||||
| Downside SD | 0.292 | ||||
| N nonnegative terms | 128.000 | ||||
| N negative terms | 1593.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1721.000 | ||||
| Mean of predictor | 0.359 | ||||
| Mean of criterion | 0.053 | ||||
| SD of predictor | 0.563 | ||||
| SD of criterion | 0.448 | ||||
| Covariance | 0.049 | ||||
| r | 0.193 | ||||
| b (slope, estimate of beta) | 0.154 | ||||
| a (intercept, estimate of alpha) | -0.002 | ||||
| Mean Square Error | 0.193 | ||||
| DF error | 1719.000 | ||||
| t(b) | 8.168 | ||||
| p(b) | 0.378 | ||||
| t(a) | -0.015 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.117 | ||||
| Upperbound of 95% confidence interval for beta | 0.191 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.339 | ||||
| Upperbound of 95% confidence interval for alpha | 0.334 | ||||
| Treynor index (mean / b) | 0.342 | ||||
| Jensen alpha (a) | -0.002 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.445 | ||||
| Sharpe ratio (Glass type estimate) | -0.104 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.104 | ||||
| df | 1720.000 | ||||
| t | -0.267 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.869 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.661 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.869 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.661 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.145 | ||||
| Upside Potential Ratio | 2.194 | ||||
| Upside part of mean | 0.701 | ||||
| Downside part of mean | -0.747 | ||||
| Upside SD | 0.309 | ||||
| Downside SD | 0.319 | ||||
| N nonnegative terms | 128.000 | ||||
| N negative terms | 1593.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1721.000 | ||||
| Mean of predictor | 0.203 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.557 | ||||
| SD of criterion | 0.445 | ||||
| Covariance | 0.047 | ||||
| r | 0.189 | ||||
| b (slope, estimate of beta) | 0.151 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.191 | ||||
| DF error | 1719.000 | ||||
| t(b) | 7.989 | ||||
| p(b) | 0.380 | ||||
| t(a) | -0.452 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.114 | ||||
| Upperbound of 95% confidence interval for beta | 0.188 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.411 | ||||
| Upperbound of 95% confidence interval for alpha | 0.257 | ||||
| Treynor index (mean / b) | -0.306 | ||||
| Jensen alpha (a) | -0.077 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1721.000 | ||||
| Minimum | 0.791 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.289 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 157.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 161.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.525 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.355 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.043 | ||||
| Quartile 3 | 0.193 | ||||
| Maximum | 0.350 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.043 | ||||
| Mean of quarter 3 | 0.193 | ||||
| Mean of quarter 4 | 0.350 | ||||
| Inter Quartile Range | 0.191 | ||||
| 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) | -0.007 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.007 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.042 | ||||
| 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 | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.476 | ||||
| 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 | 0.927 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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) | -8736747765592621.000 | ||||
| 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) | 1103189274577958247848756331413504.000 | ||||
| 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 | ||||