Advanced Statistics: MicroBear/ Short Positions Only
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.041 | ||||
| SD | 0.136 | ||||
| Sharpe ratio (Glass type estimate) | 0.299 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.295 | ||||
| df | 61.000 | ||||
| t | 0.679 | ||||
| p | 0.250 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.566 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.161 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.569 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.159 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.553 | ||||
| Upside Potential Ratio | 2.003 | ||||
| Upside part of mean | 0.147 | ||||
| Downside part of mean | -0.107 | ||||
| Upside SD | 0.114 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | 0.041 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.136 | ||||
| Covariance | -0.000 | ||||
| r | -0.010 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | 0.042 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 60.000 | ||||
| t(b) | -0.076 | ||||
| p(b) | 0.530 | ||||
| t(a) | 0.663 | ||||
| p(a) | 0.255 | ||||
| Lowerbound of 95% confidence interval for beta | -0.141 | ||||
| Upperbound of 95% confidence interval for beta | 0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.085 | ||||
| Upperbound of 95% confidence interval for alpha | 0.169 | ||||
| Treynor index (mean / b) | -7.919 | ||||
| Jensen alpha (a) | 0.042 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.032 | ||||
| SD | 0.132 | ||||
| Sharpe ratio (Glass type estimate) | 0.241 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.238 | ||||
| df | 61.000 | ||||
| t | 0.547 | ||||
| p | 0.293 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.624 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.103 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.626 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.101 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.417 | ||||
| Upside Potential Ratio | 1.852 | ||||
| Upside part of mean | 0.141 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.076 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.132 | ||||
| Covariance | 0.000 | ||||
| r | 0.001 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | 0.032 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 60.000 | ||||
| t(b) | 0.007 | ||||
| p(b) | 0.497 | ||||
| t(a) | 0.516 | ||||
| p(a) | 0.304 | ||||
| Lowerbound of 95% confidence interval for beta | -0.140 | ||||
| Upperbound of 95% confidence interval for beta | 0.141 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | 0.154 | ||||
| Treynor index (mean / b) | 68.862 | ||||
| Jensen alpha (a) | 0.032 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.058 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 62.000 | ||||
| Minimum | 0.902 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.178 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.050 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.113 | ||||
| Mean of outliers low | 0.945 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.145 | ||||
| Mean of outliers high | 1.075 | ||||
| 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) | -0.105 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.047 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.069 | ||||
| Quartile 3 | 0.129 | ||||
| Maximum | 0.190 | ||||
| Mean of quarter 1 | 0.047 | ||||
| Mean of quarter 2 | 0.069 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.190 | ||||
| Inter Quartile Range | 0.071 | ||||
| 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) | 0.093 | ||||
| Compounded annual return (geometric extrapolation) | 0.079 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.414 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.414 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.078 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.035 | ||||
| SD | 0.095 | ||||
| Sharpe ratio (Glass type estimate) | 0.373 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.373 | ||||
| df | 1370.000 | ||||
| t | 0.853 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.484 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.230 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.484 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.230 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.539 | ||||
| Upside Potential Ratio | 3.940 | ||||
| Upside part of mean | 0.258 | ||||
| Downside part of mean | -0.222 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.065 | ||||
| N nonnegative terms | 146.000 | ||||
| N negative terms | 1225.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1371.000 | ||||
| Mean of predictor | 0.324 | ||||
| Mean of criterion | 0.035 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.095 | ||||
| Covariance | -0.001 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | 0.039 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 1369.000 | ||||
| t(b) | -1.191 | ||||
| p(b) | 0.520 | ||||
| t(a) | 0.939 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.042 | ||||
| Upperbound of 95% confidence interval for alpha | 0.120 | ||||
| Treynor index (mean / b) | -3.122 | ||||
| Jensen alpha (a) | 0.039 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.031 | ||||
| SD | 0.095 | ||||
| Sharpe ratio (Glass type estimate) | 0.325 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.325 | ||||
| df | 1370.000 | ||||
| t | 0.743 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.532 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.182 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.532 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.182 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.462 | ||||
| Upside Potential Ratio | 3.832 | ||||
| Upside part of mean | 0.255 | ||||
| Downside part of mean | -0.225 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 146.000 | ||||
| N negative terms | 1225.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1371.000 | ||||
| Mean of predictor | 0.287 | ||||
| Mean of criterion | 0.031 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.095 | ||||
| Covariance | -0.001 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | 0.034 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 1369.000 | ||||
| t(b) | -1.201 | ||||
| p(b) | 0.521 | ||||
| t(a) | 0.821 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | 0.115 | ||||
| Treynor index (mean / b) | -2.704 | ||||
| Jensen alpha (a) | 0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| 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 | 1371.000 | ||||
| Minimum | 0.934 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.058 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 95.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 146.000 | ||||
| Percentage of outliers high | 0.106 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.074 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.307 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.040 | ||||
| Maximum | 0.196 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.104 | ||||
| Inter Quartile Range | 0.029 | ||||
| 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 | 0.133 | ||||
| Mean of outliers high | 0.144 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.757 | ||||
| VaR(95%) (moments method) | 0.111 | ||||
| Expected Shortfall (moments method) | 0.125 | ||||
| Extreme Value Index (regression method) | 0.383 | ||||
| VaR(95%) (regression method) | 0.148 | ||||
| Expected Shortfall (regression method) | 0.279 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.092 | ||||
| Compounded annual return (geometric extrapolation) | 0.078 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.395 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.746 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.539 | ||||
| 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 | 1.074 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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 | 0.951 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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) | -8737854861574600.000 | ||||
| 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) | 417230414482901876409249424211968.000 | ||||
| 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 | ||||