The Hill tail index estimator) α^k for the left and right tails
| Asset | Mean/median | Left-tail exponent | Right-tail exponent | ||||
|---|---|---|---|---|---|---|---|
| α^2.5% | α^5% | α^10% | α^2.5% | α^5% | α^10% | ||
| rX | Mean | 3.55 | 3.60 | 3.50 | 2.79 | 3.18 | 3.37 |
| Median | 3.56 | 3.63 | 3.35 | 2.79 | 3.09 | 3.21 | |
| rZ | Mean | 3.57 | 3.62 | 3.51 | 2.79 | 3.19 | 3.39 |
| Median | 3.60 | 3.63 | 3.39 | 2.78 | 3.13 | 3.25 | |
| Asset | Mean/median | Left-tail exponent | Right-tail exponent | ||||
|---|---|---|---|---|---|---|---|
| α^2.5% | α^5% | α^10% | α^2.5% | α^5% | α^10% | ||
| Mean | 3.55 | 3.60 | 3.50 | 2.79 | 3.18 | 3.37 | |
| Median | 3.56 | 3.63 | 3.35 | 2.79 | 3.09 | 3.21 | |
| Mean | 3.57 | 3.62 | 3.51 | 2.79 | 3.19 | 3.39 | |
| Median | 3.60 | 3.63 | 3.39 | 2.78 | 3.13 | 3.25 | |
Notes:
The table reports the estimates of the mean and the median of the Hill tail index estimators) α^k for k ∈ {2.5, 5, 10} per cent of the smallest (left-tail) and largest (right-tail) returns of the two markets; computations are based on 1,000 time series, each containing 5,000 observations
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