Estimating the Cost of Liability Cashflow Mismatch

Summary

The document considers how to measure the cost of mismatched cashflows when a bond backs a liability. The bond and liability are described as having equal present value and duration, yet their payment schedules differ. The proposed method tracks the net cash balance through time: invest surplus cash at the stated investment rate, finance shortfalls at the borrowing rate, then discount the ending balance to estimate the mismatch cost or gain.

The answer reports a calculated cost for the questioner's example and frames the method as a way to quantify ongoing financing effects. It does not show the underlying cashflow schedule or formulas in the supplied text, so the calculation cannot be independently checked here. The approach also depends on the assumed reinvestment and borrowing rates and the chosen discount factor; it is not a general valuation treatment for all liability-driven investment portfolios.

Key ideas

• Cashflow mismatch can create financing costs even when a bond and liability have equal present value and duration.
• Track net cashflows over time to identify when surplus funds are invested and when shortfalls must be financed.
• Apply the different assumed investment and borrowing rates to those balances.
• Discount the final cash balance to estimate the net cost or gain under the stated assumptions.

Tags

# Charging for cashflow mismatch in Liability Driven investment


# Charging for cashflow mismatch in Liability Driven investment












I am doing a course on LDI and the following question came up:

We are given a liability schedule. The liability is backed by a bond paying fixed coupons. The bond and the liability have the same PV and duration, but there is a big degree of mismatch. I am asked to determine the cost of the cashflow mismatch and express it as a haircut to the bond yield. The Bond Yield is 5.06%. I am also asked to assume that I can reinvest excess cash at 5.06%, but any borrowing will be at a rate of 6%. I added the asset and liability cashflows below.

Don't know how to approach the question, any help is much appreciated!

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/80184

Im just making this up as I go along, but given the two rates you have specified, financing at 6% and investing at 5.06% I would simply evaluate your net cashflows on an on going basis at see what you end up with.

Your final cash balance multiplied by your final DF is the cost (or gain) of your strategy. If you had no mismatches your net cash balance would always be zero and there would be nothing to finance or invest. I get a cost of this as -0.679.

I would consider it trivial to reverse engineer my formulas below.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.