Impact of interest rate risk on the Spanish banking sector 5level.^1 The formation of portfolios has a twofold advantage. First, it is an efficient way
of condensing substantial amounts of information. Second, it helps to smooth out the
noise in the data due to shocks to individual stocks. On the contrary, portfolios can
mask the dissimilarities among banks withineach portfolio. In this case, the mentioned
advantages seem to outweigh this inconvenience, according to the number of papers
based on bank stock portfolios (see, e.g., [5,6,17]). Monthly value-weighted portfolio
returns have been obtained using year-end market capitalisation as the weight factor
for each individual bank stock.
5 Empirical results
Table 2 contains the descriptive statistics of bank stock portfolio returns. They suggest
that the data series are skewed and leptokurtic relative to the normal distribution. In
addition, there is evidence of nonlinear dependence, possibly due to autoregressive
heteroskedasticity. Overall, these diagnostics indicate that a GARCH-type process
is appropriate for studying the IRR of bank stocks. Table 3 reports the parameters
of the GARCH models estimated using the three alternative interest rate proxies.^2
The coefficient on the market return,λi, is highly significant, positive and less than
unity in all cases. Further, its absolute value increases as the portfolio size increases,
indicating that market risk is directly related to bank size. This is a relevant and
unambiguous result, because it is not affected by the weight of banks in the market
index since they have been explicitly excluded from the market portfolio. The fact
thatλi<1 suggests that bank stock portfolios have less market risk than the overall
stock market.
Ta b le 2 .Descriptive statistics of bank portfolio stock returnsMean Variance Skewness Kurtosis JB Q(12) Q(24) Q^2 (12) Q^2 (24)L 0.016 0.006 − 0. 44 ∗∗∗ 5.15∗∗∗ 35.41∗∗∗ 9.63 12.55 49.59∗∗∗ 61.6∗∗∗
M 0.011 0.002 − 0. 002 5.34∗∗∗ 35.82∗∗∗ 9.89 19.51 95.92∗∗∗109.5∗∗∗
S 0.013 0.001 2.20∗∗∗13.42∗∗∗ 833.6∗∗∗ 29.28∗∗∗35.63∗ 25.93∗∗ 28.35JB is the Jarque-Bera test statistic which tests the null hypothesis of normality of returns. Q(n)
is the Ljung-Box statistic at a lag ofn, which tests the presence of serial correlation. As usual
∗∗∗,∗∗and∗denote significance at the 1%, 5% and 10% levels, respectively.
(^1) The composition of bank portfolios is fixed for the whole sample period. Alternatively, we
have also considered an annual restructuring of the portfolios according to their volume of
total assets, and the results obtained in that case were very similar to those reported in this
paper.
(^2) The final model to be estimated for portfolio S does not include the conditional variance of
interest rates since its inclusion would generate serious problems in the estimation of the
model due to the small variability of the returns on that portfolio.