Cash flow matching is a process of
hedging in which a company or other entity matches its cash outflows (i.e., financial obligations) with its cash inflows over a given time horizon. It is a subset of
immunization
Immunization, or immunisation, is the process by which an individual's immune system becomes fortified against an infectious agent (known as the immunogen).
When this system is exposed to molecules that are foreign to the body, called ''non-s ...
strategies in
finance
Finance is the study and discipline of money, currency and capital assets. It is related to, but not synonymous with economics, the study of production, distribution, and consumption of money, assets, goods and services (the discipline of f ...
. Cash flow matching is of particular importance to
defined benefit pension plans
Defined benefit (DB) pension plan is a type of pension plan in which an employer/sponsor promises a specified pension payment, lump-sum, or combination thereof on retirement that depends on an employee's earnings history, tenure of service and ag ...
.
Solution with linear programming
It is possible to solve the simple cash flow matching problem using
linear programming
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is ...
.
Suppose that we have a choice of
bonds with which to receive cash flows over
time periods in order to cover liabilities
for each time period. The
th bond in time period
is assumed to have known cash flows
and initial price
. It possible to buy
bonds and to run a surplus
in a given time period, both of which must be non-negative, and leads to the set of constraints:
Our goal is to minimize the initial cost of purchasing bonds to meet the liabilities in each time period, given by
. Together, these requirements give rise to the associated linear programming problem:
where
and
, with entries:
In the instance when fixed income instruments (not necessarily bonds) are used to provide the dedicated cash flows, it is unlikely to be the case that fractional components are available for purchase. Therefore, a more realistic approach to cash flow matching is to employ
mixed-integer linear programming to select a discrete number of instruments with which to match liabilities.
See also
*
Cash flow hedging
*
Debt sculpting
*
Duration gap
*
Dedicated portfolio theory
*
Fannie Mae
The Federal National Mortgage Association (FNMA), commonly known as Fannie Mae, is a United States government-sponsored enterprise (GSE) and, since 1968, a publicly traded company. Founded in 1938 during the Great Depression as part of the N ...
*
Immunization (finance)
In finance, interest rate immunization is a portfolio management strategy designed to take advantage of the offsetting effects of interest rate risk and reinvestment risk.
In theory, immunization can be used to ensure that the value of a portfo ...
*
References
{{Financial_risk
Cash flow
Corporate finance
Derivatives (finance)
Financial risk management
Linear programming