for loans due to an increase of the rate on bonds may offset the negative supply side effect due
to the fact that the rate represents the opportunity cost of direct lending. This seems to suggest
that banks may provide insurance, increasing the issuance of loans when borrowers are hit by a
shock, to firms that have access to the bond market, when it becomes difficult for these firms to get
financed in the market. On the contrary, when a negative shock hits small firms or other borrowers
that do not get access to the bond market, banks are likely to reduce the issuance of loans.
3.3 Net worth
This model does not allow a correct assessment of the importance of the own capital and of capital
requirements, for two reasons. In first instance the volatility of deposits induced by bank runs
might be relevant for the problem, but this problem could be solved introducing a stochastic error
in the demand for depots schedule. Second, and much more important, the stock market has not
been introduced in the analysis, and it is a relevant omission, because we are explicitly analysing
conditions under which the Modigliani-Miller theorem does not hold. The explicit introduction
of the stock market would be quite complex, since we should model agency problems in condition
of opaque information, and is far beyond the scope of this work. Nevertheless it can be useful to
study the importance of the level of initial capital, under the very restrictive assumptions described
earlier, of a strong equity rationing.
In this case, the relevance of net worth for the problem of the bank does not depend on the lag
structure adopted, because the result is exactly the same if adopt a different structure for the lags of
the feedback, as in the appendix. Net worth increases the portfolio of assets in a very asymmetric
way, because independently of the expected returns of different securities, banks use net worth
almost entirely to finance loans, and only a modest fraction is invested in bonds. The share of
bonds might become substantial only in the case when the exogenous rate of growth of deposits is
much larger than the discount factor. Under our assumptions, this happens when the nominal rate
of growth of income is much larger than the real interest rate on equity. The surprising result is the
irrelevance of the relative returns of different classes of assets. This result is due to our assumption
that the level of net worth remains constant in every period, independently of the dimension of the
portfolio, which is not very realistic. This implies that banks are allowed to distribute all profits
in every period and there are no legally binding capital requirements. Besides banks do not need a
buffer because there is no penalty if profits become negative during a period, for example because
of a negative shock that affects the average quality of credit increasing the default cost. In this
extreme situation net worth increases the size of the portfolio at no cost, so banks normally use
most of the net worth to finance loans because loans allow the portfolio to grow, while bonds do
not. As we would intuitively expect net worth in this case has no effect on the other liability,
deposits. A larger net worth allows a one-off proportional increase of the portfolio of assets, loans
in particular, without increasing the amount of deposits. Yet this result is not trivial, because since
a higher capitalisation allows the bank to lend more creating liquidity, it could be supposed that
deposits should be positively correlated with net worth. On the contrary, the model shows that a
higher net worth increases direct lending without creating liquidity.
The model can easily be extended to analyse the impact of the legal requirement of a minimum
ratio between capital and loans. If the net worth of the bank has to cover at least a fixed proportion
of the loans issued, since in our model the bank would never have an incentive to keep a higher
than necessary share of capital, we could assume that:
Lt + Ft + Rt = Dt + NWt, (51)
Rt = qDt , (52)
NWt = δLt. (53)
so that the budget constraint becomes the following:
(1 - δ)Lt =(1- q)Dt - Ft. (54)
It can be easily realised that in this case the results of the model would change in a simple way. The
term in net worth obviously disappears, and in the final result both intercept terms are multiplied
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