Impact of interest rate risk on the Spanish banking sector 3error term with zero mean and conditional variancehit, which is dependent on the
information set (^) t− 1 ,andVCIt− 1 the interest rate volatility in periodt−1. Moreover,
ωi,λi,θi,γi,α 0 ,α 1 ,βandδiare the parameters to be estimated. In particular,λi
describes the sensitivity of the return onith bank stock to general market fluctuations
and it can be seen as a measure of market risk. In turn,θireflects the sensitivity of
the return onith bank stock to movements in interest rates controlling for changes
in the market return. Hence, it is a measure ofith bank IRR. As usual, to preserve
the non-negativity requirement for the conditional varianceα 0 ,α 1 ,β≥0, whereas
α 1 +β<1 for stability to hold.
The GARCH-M approach is consistent with the patterns of leptokurtosis and
volatility clustering frequently observed in stock markets and allows for the consid-
eration of time-varying risk premia and an empirical assessment of the relationship
between risk and return. Some features of the model should be highlighted. First, it
incorporates the conditional variancehitas an additional explanatory variable in (1).
The specification of volatility in logarithmic form is based on [7]. Second, the typical
structure of GARCH processes has been extended in (2) by modelling the conditional
variance as a function of the conditional interest rate volatility lagged in one period. In
this respect, even though the effect of interest rate volatility on stock returns has been
considered in the literature to a lesser extent than the impact of interest rate changes,
the interest rate volatility is important enough to be taken intoaccount. As [5] points
out, this variable conveys critical information about the overall volatility of the finan-
cial markets and it influences the volatility of bank stock returns also at the micro
level.
There are also several critical aspects regarding the model estimation. The first
issue has to do with the possible multicolinearity between the series of market portfolio
return and interest rate changes, which could generate serious estimation problems.
Due to the significant negative correlation typically observed in the Spanish case
between these two variables, an orthogonalisation procedure has been used. Since the
central aim of this study is to analyse the banks’ IRR, the market portfolio return has
been orthogonalised as in [10] or [11]. Thus, the residuals from an auxiliary regression
of the market return series on a constant and the interest rate fluctuations series, by
construction uncorrelated with the interest rate changes, have replaced the original
market portfolio returns in (1).
A second issue concerns the choice of the interest rate proxy to be used. In this
sense, long-term interest rates are the proxy most employed in the literature, since
they are assumed to exert great influence on corporate decisions and overall economic
activity. Nevertheless, in order to enhance the robustness of the results, short-term
interest rates and the spread between long- and short-term rates have been used as
well. With regard to the short-term rates, an interbank rate has been chosen since the
money market has become a key reference for Spanish banks during recent years.
In turn, the interest rate spread is considered a good proxy for the slope of the yield
curve.