Advanced Statistics: SwingOrchestra
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 | -0.165 | ||||
| SD | 0.135 | ||||
| Sharpe ratio (Glass type estimate) | -1.219 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.188 | ||||
| df | 30.000 | ||||
| t | -1.959 | ||||
| p | 0.970 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.467 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.048 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.444 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.068 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.167 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.165 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.141 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.633 | ||||
| Mean of criterion | -0.165 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.135 | ||||
| Covariance | 0.002 | ||||
| r | 0.058 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | -0.183 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 29.000 | ||||
| t(b) | 0.313 | ||||
| p(b) | 0.378 | ||||
| t(a) | -1.775 | ||||
| p(a) | 0.957 | ||||
| Lowerbound of 95% confidence interval for beta | -0.158 | ||||
| Upperbound of 95% confidence interval for beta | 0.215 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.394 | ||||
| Upperbound of 95% confidence interval for alpha | 0.028 | ||||
| Treynor index (mean / b) | -5.776 | ||||
| Jensen alpha (a) | -0.183 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.176 | ||||
| SD | 0.147 | ||||
| Sharpe ratio (Glass type estimate) | -1.192 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.162 | ||||
| df | 30.000 | ||||
| t | -1.915 | ||||
| p | 0.967 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.438 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.073 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.416 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.093 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.144 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.176 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.583 | ||||
| Mean of criterion | -0.176 | ||||
| SD of predictor | 0.254 | ||||
| SD of criterion | 0.147 | ||||
| Covariance | 0.002 | ||||
| r | 0.054 | ||||
| b (slope, estimate of beta) | 0.031 | ||||
| a (intercept, estimate of alpha) | -0.194 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 29.000 | ||||
| t(b) | 0.290 | ||||
| p(b) | 0.387 | ||||
| t(a) | -1.726 | ||||
| p(a) | 0.953 | ||||
| Lowerbound of 95% confidence interval for beta | -0.189 | ||||
| Upperbound of 95% confidence interval for beta | 0.251 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.423 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -5.638 | ||||
| Jensen alpha (a) | -0.194 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.081 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.835 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.961 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.844 | ||||
| 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) | -3.992 | ||||
| VaR(95%) (regression method) | 0.341 | ||||
| Expected Shortfall (regression method) | 0.366 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.288 | ||||
| Quartile 1 | 0.288 | ||||
| Median | 0.288 | ||||
| Quartile 3 | 0.288 | ||||
| Maximum | 0.288 | ||||
| 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) | -0.112 | ||||
| Compounded annual return (geometric extrapolation) | -0.123 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.428 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.268 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.168 | ||||
| SD | 0.097 | ||||
| Sharpe ratio (Glass type estimate) | -1.729 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.727 | ||||
| df | 690.000 | ||||
| t | -2.808 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.939 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.518 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.937 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.517 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.936 | ||||
| Upside Potential Ratio | 0.747 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.233 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.087 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 682.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 691.000 | ||||
| Mean of predictor | 0.689 | ||||
| Mean of criterion | -0.168 | ||||
| SD of predictor | 0.382 | ||||
| SD of criterion | 0.097 | ||||
| Covariance | -0.001 | ||||
| r | -0.025 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.164 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 689.000 | ||||
| t(b) | -0.664 | ||||
| p(b) | 0.747 | ||||
| t(a) | -2.716 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.282 | ||||
| Upperbound of 95% confidence interval for alpha | -0.045 | ||||
| Treynor index (mean / b) | 26.140 | ||||
| Jensen alpha (a) | -0.164 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.173 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -1.750 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.748 | ||||
| df | 690.000 | ||||
| t | -2.842 | ||||
| p | 0.998 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.960 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.539 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.958 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.538 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.941 | ||||
| Upside Potential Ratio | 0.716 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.237 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 682.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 691.000 | ||||
| Mean of predictor | 0.615 | ||||
| Mean of criterion | -0.173 | ||||
| SD of predictor | 0.380 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | -0.001 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.169 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 689.000 | ||||
| t(b) | -0.682 | ||||
| p(b) | 0.752 | ||||
| t(a) | -2.759 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.289 | ||||
| Upperbound of 95% confidence interval for alpha | -0.049 | ||||
| Treynor index (mean / b) | 25.574 | ||||
| Jensen alpha (a) | -0.169 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 691.000 | ||||
| Minimum | 0.928 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.057 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 22.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.019 | ||||
| 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) | 0.012 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.082 | ||||
| Median | 0.152 | ||||
| Quartile 3 | 0.223 | ||||
| Maximum | 0.293 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.293 | ||||
| Inter Quartile Range | 0.140 | ||||
| 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) | -0.109 | ||||
| Compounded annual return (geometric extrapolation) | -0.121 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.413 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.413 | ||||
| Compounded annual return / Expected Shortfall lognormal | -9.187 | ||||
| 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 | 1.059 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.503 | ||||
| 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 | 0.930 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.507 | ||||
| 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) | -8743447148058312.000 | ||||
| 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) | -133475622202688350834341615501312.000 | ||||
| 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 | ||||