Advanced Statistics: mftstocks
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 | 0.072 | ||||
| SD | 0.144 | ||||
| Sharpe ratio (Glass type estimate) | 0.497 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.493 | ||||
| df | 88.000 | ||||
| t | 1.353 | ||||
| p | 0.090 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.228 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.219 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.231 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.216 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.951 | ||||
| Upside Potential Ratio | 2.646 | ||||
| Upside part of mean | 0.199 | ||||
| Downside part of mean | -0.128 | ||||
| Upside SD | 0.124 | ||||
| Downside SD | 0.075 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 44.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.222 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.209 | ||||
| SD of criterion | 0.144 | ||||
| Covariance | 0.007 | ||||
| r | 0.229 | ||||
| b (slope, estimate of beta) | 0.158 | ||||
| a (intercept, estimate of alpha) | 0.037 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 87.000 | ||||
| t(b) | 2.194 | ||||
| p(b) | 0.015 | ||||
| t(a) | 0.676 | ||||
| p(a) | 0.250 | ||||
| Lowerbound of 95% confidence interval for beta | 0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.301 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.145 | ||||
| Treynor index (mean / b) | 0.454 | ||||
| Jensen alpha (a) | 0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.061 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | 0.440 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.436 | ||||
| df | 88.000 | ||||
| t | 1.197 | ||||
| p | 0.117 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.284 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.161 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.287 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.158 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.791 | ||||
| Upside Potential Ratio | 2.468 | ||||
| Upside part of mean | 0.192 | ||||
| Downside part of mean | -0.130 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 44.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.199 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.199 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | 0.007 | ||||
| r | 0.234 | ||||
| b (slope, estimate of beta) | 0.164 | ||||
| a (intercept, estimate of alpha) | 0.029 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 87.000 | ||||
| t(b) | 2.249 | ||||
| p(b) | 0.014 | ||||
| t(a) | 0.551 | ||||
| p(a) | 0.291 | ||||
| Lowerbound of 95% confidence interval for beta | 0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.309 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.133 | ||||
| Treynor index (mean / b) | 0.374 | ||||
| Jensen alpha (a) | 0.029 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.075 | ||||
| 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 | 89.000 | ||||
| Minimum | 0.908 | ||||
| Quartile 1 | 0.988 | ||||
| Median | 1.004 | ||||
| Quartile 3 | 1.021 | ||||
| Maximum | 1.214 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.063 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.022 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.079 | ||||
| Mean of outliers high | 1.105 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.400 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | 0.064 | ||||
| Extreme Value Index (regression method) | 0.075 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.037 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.041 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.129 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.051 | ||||
| Mean of quarter 4 | 0.101 | ||||
| Inter Quartile Range | 0.039 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.126 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -8.569 | ||||
| VaR(95%) (moments method) | 0.102 | ||||
| Expected Shortfall (moments method) | 0.102 | ||||
| Extreme Value Index (regression method) | -2.499 | ||||
| VaR(95%) (regression method) | 0.157 | ||||
| Expected Shortfall (regression method) | 0.158 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.160 | ||||
| Compounded annual return (geometric extrapolation) | 0.111 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.862 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.104 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.482 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.072 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | 0.461 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.461 | ||||
| df | 1948.000 | ||||
| t | 1.259 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.257 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.180 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.257 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.180 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.792 | ||||
| Upside Potential Ratio | 7.188 | ||||
| Upside part of mean | 0.655 | ||||
| Downside part of mean | -0.582 | ||||
| Upside SD | 0.127 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 911.000 | ||||
| N negative terms | 1038.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1949.000 | ||||
| Mean of predictor | 0.241 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | 0.008 | ||||
| r | 0.195 | ||||
| b (slope, estimate of beta) | 0.113 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 1947.000 | ||||
| t(b) | 8.774 | ||||
| p(b) | 0.377 | ||||
| t(a) | 0.795 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | 0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.139 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.155 | ||||
| Treynor index (mean / b) | 0.636 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.060 | ||||
| SD | 0.153 | ||||
| Sharpe ratio (Glass type estimate) | 0.393 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.393 | ||||
| df | 1948.000 | ||||
| t | 1.073 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.325 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.112 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.326 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.112 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.650 | ||||
| Upside Potential Ratio | 6.978 | ||||
| Upside part of mean | 0.647 | ||||
| Downside part of mean | -0.587 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 911.000 | ||||
| N negative terms | 1038.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1949.000 | ||||
| Mean of predictor | 0.205 | ||||
| Mean of criterion | 0.060 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.153 | ||||
| Covariance | 0.008 | ||||
| r | 0.196 | ||||
| b (slope, estimate of beta) | 0.112 | ||||
| a (intercept, estimate of alpha) | 0.037 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1947.000 | ||||
| t(b) | 8.836 | ||||
| p(b) | 0.376 | ||||
| t(a) | 0.674 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | 0.087 | ||||
| Upperbound of 95% confidence interval for beta | 0.137 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.145 | ||||
| Treynor index (mean / b) | 0.536 | ||||
| Jensen alpha (a) | 0.037 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.019 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1949.000 | ||||
| Minimum | 0.904 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.173 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 113.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 155.000 | ||||
| Percentage of outliers high | 0.080 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.414 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.014 | ||||
| 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 | 56.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.148 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.089 | ||||
| Inter Quartile Range | 0.032 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.107 | ||||
| Mean of outliers high | 0.132 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.490 | ||||
| VaR(95%) (moments method) | 0.088 | ||||
| Expected Shortfall (moments method) | 0.102 | ||||
| Extreme Value Index (regression method) | -0.877 | ||||
| VaR(95%) (regression method) | 0.090 | ||||
| Expected Shortfall (regression method) | 0.098 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.157 | ||||
| Compounded annual return (geometric extrapolation) | 0.110 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.741 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.236 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.755 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.029 | ||||
| SD | 0.170 | ||||
| Sharpe ratio (Glass type estimate) | 0.168 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.167 | ||||
| df | 130.000 | ||||
| t | 0.119 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.604 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.939 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.605 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.939 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.256 | ||||
| Upside Potential Ratio | 8.650 | ||||
| Upside part of mean | 0.964 | ||||
| Downside part of mean | -0.936 | ||||
| Upside SD | 0.128 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 60.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.058 | ||||
| Mean of criterion | 0.029 | ||||
| SD of predictor | 0.389 | ||||
| SD of criterion | 0.170 | ||||
| Covariance | 0.024 | ||||
| r | 0.355 | ||||
| b (slope, estimate of beta) | 0.155 | ||||
| a (intercept, estimate of alpha) | -0.136 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.310 | ||||
| p(b) | 0.279 | ||||
| t(a) | -0.591 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | 0.084 | ||||
| Upperbound of 95% confidence interval for beta | 0.227 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.589 | ||||
| Upperbound of 95% confidence interval for alpha | 0.318 | ||||
| Treynor index (mean / b) | 0.184 | ||||
| Jensen alpha (a) | -0.136 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.170 | ||||
| Sharpe ratio (Glass type estimate) | 0.084 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.083 | ||||
| df | 130.000 | ||||
| t | 0.059 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.688 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.855 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.689 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.855 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.126 | ||||
| Upside Potential Ratio | 8.495 | ||||
| Upside part of mean | 0.956 | ||||
| Downside part of mean | -0.942 | ||||
| Upside SD | 0.126 | ||||
| Downside SD | 0.113 | ||||
| N nonnegative terms | 60.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.980 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.390 | ||||
| SD of criterion | 0.170 | ||||
| Covariance | 0.023 | ||||
| r | 0.351 | ||||
| b (slope, estimate of beta) | 0.153 | ||||
| a (intercept, estimate of alpha) | -0.136 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.261 | ||||
| p(b) | 0.281 | ||||
| t(a) | -0.593 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | 0.082 | ||||
| Upperbound of 95% confidence interval for beta | 0.224 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.588 | ||||
| Upperbound of 95% confidence interval for alpha | 0.317 | ||||
| Treynor index (mean / b) | 0.093 | ||||
| Jensen alpha (a) | -0.136 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.967 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.042 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.226 | ||||
| VaR(95%) (moments method) | 0.012 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| Extreme Value Index (regression method) | -0.126 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.024 | ||||
| Maximum | 0.142 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.070 | ||||
| Inter Quartile Range | 0.018 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.142 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.415 | ||||
| VaR(95%) (moments method) | 0.072 | ||||
| Expected Shortfall (moments method) | 0.148 | ||||
| Extreme Value Index (regression method) | 2.483 | ||||
| VaR(95%) (regression method) | 0.148 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.059 | ||||
| Compounded annual return (geometric extrapolation) | 0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.423 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.858 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.806 | ||||