Tail Dependence - ETH - Entrepreneurial Risks - ETH Zürich

28
+tail −tail
ν b γ n ν b γ n ν b γ n ν b γ n
k 100 100 100 100 229 229 229 229 100 100 100 100 229 229 229 229
Asset ε Asset ε Asset ε Asset ε Asset ε Asset ε Asset ε Asset ε
BMY 3.36 3.14 3.66 3.63 3.31 3.05 3.59 3.38 2.55 2.57 1.80* 1.76* 2.46* 2.46* 2.04* 1.97*
CVX 3.73 3.67 4.26 3.89 3.49* 3.54* 3.83 3.60 3.61 3.61 2.30* 2.27* 3.14 3.20 2.33* 2.29*
HPQ 3.42 3.02 3.94 3.42 2.88 2.65* 3.29 3.01 2.82 3.02 1.80* 1.70* 2.91 2.53* 2.35* 2.17*
KO 3.50 3.08 3.70 3.36 3.48 3.40 3.36 3.24 2.79 3.08 1.80* 1.75* 2.48* 2.59* 1.80* 1.79*
MMM 3.80 3.34 4.10 3.86 3.56* 3.22 3.69 3.54 2.89 3.34 2.23* 2.21* 2.48* 2.39* 2.04* 1.96*
PG 3.40 3.14 3.57 3.76 3.19 3.03 3.60 3.39 2.45* 3.14 1.57* 1.55* 2.40* 2.41* 1.69* 1.66*
SGP 3.37 3.11 3.78 3.72 3.36 2.97 3.88 3.45 2.69 3.11 1.70* 1.65* 2.40* 2.27* 1.84* 1.78*
TXN 3.51 3.52 3.99 3.99 3.03 3.10 3.34 3.34 2.67 3.52 1.77* 1.77* 2.73 2.68* 2.05* 2.03*
WAG 3.61 3.99* 3.92 4.22 3.33 3.40 3.81 3.58 2.42* 3.99* 1.46* 1.43* 2.44* 2.65* 1.93* 1.92*
S&P 500 3.23 − 3.71 − 3.09 − 3.56 − 3.16 − 3.37 − 3.13 − 3.04 −
Table 3.5: Comparison of tail index estimators ˆν (Hill’s estimator) and ˆ b γ n (estimator by Gabaix) for positive and negative tails of the S&P 500
index, 9 included assets, and the residues ε obtained by regressing each asset on the S&P 500 index, during the time intervals ranging from January
1991 to December 2000 with a 4% quantile of k = 100 values and from July 1985 to April 2008 with a 4% quantile of k = 229 values. Values with
∗ represent tail indexes, which can’t be considered equal to the respective S&P 500 index at the 95% condfidence level.