Advanced Statistics: Highway Star
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 | -0.005 | ||||
| SD | 0.059 | ||||
| Sharpe ratio (Glass type estimate) | -0.085 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 40.000 | ||||
| t | -0.157 | ||||
| p | 0.562 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.145 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.976 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.144 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.977 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.332 | ||||
| Upside Potential Ratio | 2.513 | ||||
| Upside part of mean | 0.038 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | -0.005 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.059 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.004 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 39.000 | ||||
| t(b) | -0.029 | ||||
| p(b) | 0.512 | ||||
| t(a) | -0.121 | ||||
| p(a) | 0.548 | ||||
| Lowerbound of 95% confidence interval for beta | -0.075 | ||||
| Upperbound of 95% confidence interval for beta | 0.072 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.070 | ||||
| Treynor index (mean / b) | 4.702 | ||||
| Jensen alpha (a) | -0.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.117 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.115 | ||||
| df | 40.000 | ||||
| t | -0.216 | ||||
| p | 0.585 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.177 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.945 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.175 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.946 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.436 | ||||
| Upside Potential Ratio | 2.405 | ||||
| Upside part of mean | 0.036 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 39.000 | ||||
| t(b) | 0.010 | ||||
| p(b) | 0.496 | ||||
| t(a) | -0.192 | ||||
| p(a) | 0.576 | ||||
| Lowerbound of 95% confidence interval for beta | -0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.075 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.064 | ||||
| Treynor index (mean / b) | -17.416 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.986 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.106 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.098 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.195 | ||||
| Mean of outliers high | 1.018 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.010 | ||||
| Maximum | 0.014 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.014 | ||||
| Inter Quartile Range | 0.007 | ||||
| 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) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.038 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.821 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.821 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.147 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.006 | ||||
| SD | 0.034 | ||||
| Sharpe ratio (Glass type estimate) | -0.179 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.178 | ||||
| df | 896.000 | ||||
| t | -0.331 | ||||
| p | 0.629 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.238 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.881 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.238 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.881 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.351 | ||||
| Upside Potential Ratio | 4.494 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 836.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 897.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | -0.006 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.034 | ||||
| Covariance | 0.000 | ||||
| r | 0.036 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 895.000 | ||||
| t(b) | 1.078 | ||||
| p(b) | 0.141 | ||||
| t(a) | -0.430 | ||||
| p(a) | 0.666 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | 0.028 | ||||
| Treynor index (mean / b) | -1.702 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.007 | ||||
| SD | 0.034 | ||||
| Sharpe ratio (Glass type estimate) | -0.196 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.196 | ||||
| df | 896.000 | ||||
| t | -0.363 | ||||
| p | 0.642 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.256 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.863 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.255 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.863 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.382 | ||||
| Upside Potential Ratio | 4.446 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 836.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 897.000 | ||||
| Mean of predictor | 0.462 | ||||
| Mean of criterion | -0.007 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.034 | ||||
| Covariance | 0.000 | ||||
| r | 0.037 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 895.000 | ||||
| t(b) | 1.096 | ||||
| p(b) | 0.137 | ||||
| t(a) | -0.454 | ||||
| p(a) | 0.675 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | 0.028 | ||||
| Treynor index (mean / b) | -1.827 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 897.000 | ||||
| Minimum | 0.982 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.024 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 64.000 | ||||
| Percentage of outliers low | 0.071 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 68.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.418 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.456 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.003 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.011 | ||||
| Maximum | 0.027 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.008 | ||||
| Mean of quarter 4 | 0.024 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 0.027 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -17.848 | ||||
| VaR(95%) (moments method) | 0.020 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| Extreme Value Index (regression method) | -1.773 | ||||
| VaR(95%) (regression method) | 0.033 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.038 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.407 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.574 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.835 | ||||
| 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 | 1.054 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.516 | ||||
| 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 | 0.919 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.519 | ||||
| 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) | -8747197417096735.000 | ||||
| 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) | 651625479862981106179049902833664.000 | ||||
| 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 | ||||