8 L. Ballester, R. Ferrer, and C. Gonz ́alez
Turning to the mean equation of the GARCH-M model, the parameterγihas
usually been interpreted as the compensation required to invest in risky assets by risk-
averse investors. Since volatility as measured in GARCH models is not a measure
of systematic risk, but total risk,γidoes not necessarily have to be positive because
increases of total risk do not always imply higher returns.^3 For our case, the estimated
values forγidiffer in sign across bank portfolios (positive for portfolios L and M and
negative for portfolio S). This heterogeneity among banks may be basically derived
from differences in product and client specialisation, interest rate hedging strategies,
etc. The absence of a conclusive result concerning this parameter is in line with the
lack of consensus found in prior research. In this sense, whereas [12] and [4] detected
a positive relationship between risk and return (γi>0), [5,9,13] suggested a negative
relationship (γi<0). In turn, [2] and [16] found an insignificantγi.
With regard to the conditional variance equation,α 1 andβare positive and signif-
icant in the majority of cases. In addition, the volatility persistence (α 1 +β)isalways
less than unity, consistent with the stationarity conditions of the model. This implies
that the traditional constant-variance capital asset pricing models are inappropriate
for describing the distribution of bank stock returns in the Spanish case.
The parameterδi, which measures the effect of interest rate volatility on bank
portfolio return volatility, is negative and significant for portfolios L and M.^4 A pos-
sible explanation suggested by [5] is that, in response to an increase in interest rate
volatility, L and M banks seek shelter from IRR and are able to reduce their exposure
within one month, e.g., by holding derivatives and/or reducing the duration gap of
their assets and liabilities. Hence, this generates a lower bank stock volatility in the
following period. Moreover, a direct relationship seems to exist between the absolute
value ofδi, the bank size and the term to maturity of interest rates. Thus, analogously
to the previous evidence with interest rate changes, interest rate volatility has a greater
negative effect on bank return volatility as the bank size increases. Further, interest
rate volatility has a larger impact when long-term rates are considered. In sum, it
can be concluded that the Spanish bank industry does show a significant interest rate
exposure, especially with respect to long-term interest rates.
In addition, the proposed GARCH model has been augmented with the purpose
of checking whether the introduction of the euro as the single currency within the
Monetary European Union from January 1, 1999 has significantly altered the de-
gree of IRR of Spanish banks.^5 Thus, the following extended model has been esti-
(^3) [13] indicates several reasons for the relationship between risk and return being negative.
In the framework of the financial sector, [5] also suggests an explanation to get a negative
trade-off coefficient between risk and return.
(^4) Recall that this parameter does not appear in the model for portfolio S.
(^5) Since the GARCH model estimation requires a considerable number of observations, a
dummy variable procedure has been employed instead of estimating the model for each
subperiod.