Advanced Statistics: Dux II
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 | 0.008 | ||||
| SD | 0.072 | ||||
| Sharpe ratio (Glass type estimate) | 0.112 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.110 | ||||
| df | 54.000 | ||||
| t | 0.240 | ||||
| p | 0.406 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.804 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.027 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.805 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.026 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.254 | ||||
| Upside Potential Ratio | 2.411 | ||||
| Upside part of mean | 0.076 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.064 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.359 | ||||
| Mean of criterion | 0.008 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 0.072 | ||||
| Covariance | -0.001 | ||||
| r | -0.075 | ||||
| b (slope, estimate of beta) | -0.024 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 53.000 | ||||
| t(b) | -0.544 | ||||
| p(b) | 0.706 | ||||
| t(a) | 0.447 | ||||
| p(a) | 0.328 | ||||
| Lowerbound of 95% confidence interval for beta | -0.113 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.058 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | -0.333 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.006 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | 0.080 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.078 | ||||
| df | 54.000 | ||||
| t | 0.170 | ||||
| p | 0.433 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.836 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.995 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.837 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.994 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.175 | ||||
| Upside Potential Ratio | 2.325 | ||||
| Upside part of mean | 0.074 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | 0.006 | ||||
| SD of predictor | 0.208 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | -0.001 | ||||
| r | -0.070 | ||||
| b (slope, estimate of beta) | -0.024 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 53.000 | ||||
| t(b) | -0.512 | ||||
| p(b) | 0.695 | ||||
| t(a) | 0.369 | ||||
| p(a) | 0.357 | ||||
| Lowerbound of 95% confidence interval for beta | -0.116 | ||||
| Upperbound of 95% confidence interval for beta | 0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.086 | ||||
| Treynor index (mean / b) | -0.236 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.973 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.081 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.109 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.164 | ||||
| Mean of outliers high | 1.042 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.284 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| Extreme Value Index (regression method) | 0.014 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.017 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.055 | ||||
| Maximum | 0.091 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.091 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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) | 0.056 | ||||
| Compounded annual return (geometric extrapolation) | 0.051 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.561 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.561 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.263 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.007 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | 0.106 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.106 | ||||
| df | 1214.000 | ||||
| t | 0.229 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.804 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.016 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.804 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.168 | ||||
| Upside Potential Ratio | 6.176 | ||||
| Upside part of mean | 0.271 | ||||
| Downside part of mean | -0.264 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 323.000 | ||||
| N negative terms | 892.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1215.000 | ||||
| Mean of predictor | 0.399 | ||||
| Mean of criterion | 0.007 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1213.000 | ||||
| t(b) | -0.169 | ||||
| p(b) | 0.503 | ||||
| t(a) | 0.242 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.056 | ||||
| Upperbound of 95% confidence interval for alpha | 0.071 | ||||
| Treynor index (mean / b) | -6.445 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.005 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | 0.072 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.072 | ||||
| df | 1214.000 | ||||
| t | 0.154 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.838 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.982 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.838 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.982 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.113 | ||||
| Upside Potential Ratio | 6.103 | ||||
| Upside part of mean | 0.270 | ||||
| Downside part of mean | -0.265 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 323.000 | ||||
| N negative terms | 892.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1215.000 | ||||
| Mean of predictor | 0.355 | ||||
| Mean of criterion | 0.005 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.005 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 1213.000 | ||||
| t(b) | -0.157 | ||||
| p(b) | 0.503 | ||||
| t(a) | 0.166 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.058 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -4.680 | ||||
| Jensen alpha (a) | 0.005 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1215.000 | ||||
| Minimum | 0.973 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.031 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 228.000 | ||||
| Percentage of outliers low | 0.188 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 224.000 | ||||
| Percentage of outliers high | 0.184 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.069 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.051 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.006 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 26.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.005 | ||||
| Quartile 3 | 0.019 | ||||
| Maximum | 0.119 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.012 | ||||
| Mean of quarter 4 | 0.058 | ||||
| Inter Quartile Range | 0.017 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.115 | ||||
| Mean of outliers high | 0.091 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.021 | ||||
| VaR(95%) (moments method) | 0.054 | ||||
| Expected Shortfall (moments method) | 0.058 | ||||
| Extreme Value Index (regression method) | -0.120 | ||||
| VaR(95%) (regression method) | 0.085 | ||||
| Expected Shortfall (regression method) | 0.117 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.055 | ||||
| Compounded annual return (geometric extrapolation) | 0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.421 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.860 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.719 | ||||
| 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 | 0.965 | ||||
| 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 | 0.850 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.478 | ||||
| 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) | -8746618817090316.000 | ||||
| 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) | 420311660878672370413188702797824.000 | ||||
| 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 | ||||