3 Discussion
3.1 A positive interest rate shock
When the rate on loans is set monopolistically interest rates on bonds have a strong impact on the
rate on loans, in contrast with the perfectly competitive case.18 Our results show that contempo-
raneous interest rate shocks are the only that are smoothed.19 On the contrary shocks to expected
future rates need not be smoothed, and can produce a more than proportional increase of the rate
on loans. This kind of shocks can be smoothed only if the demand for loans is highly sensitive to
the rate on bonds. We can conclude that interest rate shocks are normally smoothed only when the
shock is expected to be transitory. If the shock is expected to affect permanently future interest
rates, the impact on the rate on loans may even be stronger than on the rate on bonds. Default
costs have no influence on the contemporaneous rate coefficient, but affect the coefficient of the
expected rate on bonds. The forward looking part becomes less important only when default costs
are very large.
An interest rate shock reduces the quantity of loans issued and increases more than propor-
tionally the size of the portfolio of bonds. The main force behind the result is the market power
of the bank. The sensitivity of the demand for loans on the rate on bonds is important in this
context. When its value is high relative to the coefficient of the own rate, the strength of the result
is proportionally reduced. When the competition from the bond market is strong, the impact of
the rate on bonds on the issuance of loans is reduced, because the market power of the bank is
proportionally reduced. In the case of a perfectly competitive market for loans, and assuming that
the rate on loans is perfectly correlated with the rate on bonds, the result is never overturned, but
it becomes far less significant.
Another important observation is that the impact of the shock on the two assets is not symmet-
ric, because the size of the portfolio is affected too. Not surprisingly, the effect is much stronger
on the bond component of the portfolio, because the negative impact on the issuance of loans is
necessarily more limited. We can conclude that the amount of bonds in the portfolio is necessarily
much more volatile than the quantity of loans. The reason is that the bond market does not take
default costs into account in the way banks do, because, assuming that risk is correctly priced in
an efficient market, expected default costs reduce proportionally the expected return in a linear
way, so that net returns are not affected. The case of the bank is different because it deals with
uncertainty, and the impact of default costs on its profits must be non-linear. It can finally be
observed that under our assumptions a higher rate of growth of output increases the rate on loans,
reducing the smoothing, even disregarding any effect of income on the demand for loans.20
In the former section we began to discuss the effect of the correlation between interest rates
and default costs. We have seen that because of this correlation the bank tends to issue more
loans. The assumption that higher rates on bonds increase default costs on loans can be justified
considering that large firms need both loans and bonds, and higher market interest rate reduce
the cash flow and increase the risk of default on both categories of assets. We did not formally
introduce a default cost on bonds, because we did not specify whether the bonds that the bank
buys were risk-free or high yield risky bonds. In the second case, assuming that default costs are a
linear function of the quantity purchased, these costs would proportionally shrink the net returns
of bonds. Even in this case the pattern of our results would not change, only the relevance of the
different effects would be different.
The results of our model show that the correlation between the interest rate on bonds and
the default costs tends to offset the direct effect of the interest rates on bonds. The correlation
is positive because higher interest rates reduce the free cash-flow of the borrowers, so that the
risk of default becomes proportionally higher. We have not made any assumption regarding this
correlation, but it is likely to be much larger when interest rates are high. The increase of the
interest rate implies in fact a reduction of the free cash flow that is proportional to the initial level
of the rate. So we can expect the effect of an interest rate shock on the composition of the portfolio
18Our results for a perfectly competitive framework confirm the finding of Cosimano [4].
19As it can easily be realised form Equation (46). The own coefficient b is in fact always larger than the cross
coefficient d of the demand for loans.
20The derivative of rL with respect to γY is in fact normally positive.
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