In this
paper, from a viewpoint of the traditional business
schemes in banking and insurance, we consider the
effectiveness of the convergence of banking business
and insurance business. Specifically, regarding
banking business and insurance business as the
businesses which respectively make profits by pooling
and managing the risks in their loan portfolio and
policy portfolio, we consider the effectiveness of
combining the two portfolios or two businesses
compared to each portfolio. The effectiveness is
evaluated in terms of asymptotic default probability
when each portfolio size is large. According to this
criterion, the asymptotic default probability of an
integrated portfolio is smaller than that of each
portfolio under a certain condition.
The concept on
which the insurance business relies for pooling and
managing risk in its portfolio is a law of large
numbers in probability theory. In a large and
homogeneous pool of policies where the probability of
the occurrence of an accident is constant, the
frequency of accidents relative to the size of
policies is regarded as close to constant. Hence
so long as the rate of premium is set more than the
probability of the occurrence, the probability that
the collection of premiums received is bigger than the
loss paid goes to one as the portfolio size gets
large.
The
principle of the law of large numbers is in fact used
together with the diversification principle of risk in
the management of a loan portfolio in the traditional
banking. When the default probability of each
loan is constants and the default events are
independent, the default probability of a bank becomes
smaller as the portfolio seize gets larger, so long as
a default-adjusted spread of loan interest rate and
deposit interest rate is positive (Section 3). In this
sense, risk management in banking business is similar
to that in insurance business and the evaluation
criterion based on the asymptotic default probability
is reasonable.
This paper
only treats one-period model for simplicity of
arguments. A dynamic extension is left open for
complication of modeling. Our results state that under
a condition on default probability of loans, deposit
rate, loan rate, premium rate, accident rate, and
return rate for premiums, an integrated portfolio is
more effective in asymptotic default probability than
any of a bank portfolio and an insurance portfolio.
Consequently the convergence of banking and insurance
will be theoretically justified. In addition, the
condition can be used to find a strategic position for
a finanssurancce institution with loan rate, deposit
rate and insurance premium as control variables.
The content of the paper is as
follows.
Section 2 Principle of Traditional
Insurance Business:Law of Large Numbers,
Section 3 Effect of Pooling Credit Risk
and Insurance Risk on Portfolios,
Section 4 Effectiveness of a Finanssurance Portfolio:
General Case.
