# Why Symmetric Cash Flow Matching Reduces Liability Cost

Hi everyone,

P51 Fixed Income, can someone please explain why symmetric cash flow matching (uses short-term debt to fund liability prior to when it is due) results in a reduction in the cost of funding the liability? Thank you much!

Would think it increases the cost of funding the liability given debt is used.

Meanwhile, in the last paragraph of Exentions to Basic Cash Flow Matching, it says that combination matching (duration + CF match) disadvantage is the cost to fund the liability is greater given it is CF matched in the short-term

Would appreciate some help They’re assuming a normal yield curve.

Suppose that you have a liability due in 21 months. You cannot find a 21-month zero-coupon bond, but you can invest in a 24-month zero. So you buy the zero today, and in 21 months you borrow for 3 months to pay off the liability. The interest you earn on the zero is greater than the interest you pay on the 3-month loan, so you make some additional spread.

But why use any debt if the 24-month zero maturity is after the liability maturity?

Really appreciate everything S2000

Because you need cash at 21 months to pay the liability.

Suppose if the cashflow occurs before the liability, how in this situation the cost will be reduced? As the cashflow received will be invested at lower rates untill the liability date. I think the symmetric cash flow matching is applicable for cashflow occuring after the liability date? Isn’t it?

Or you could sell the asset on the open market before maturity, which should cost less.

How it will cost less? Can u please give a example?

Because you’re not paying interest.

I am still confused. If i have a liability due in 21 months and i have the option to invest in 18-month zero only. So i buy it now and after 18months i get the cash. So i can invest that cash for three months at risk free rate. Which asset you are talking about? and paying interest on what? If you comparing it with the other scenario of cashflow occuring after the liability date where we borrow and pay interest on it. In that case we have invested for 24month brother so we get high return due to longer period of investment. Here in 18months we get less so if you say we are not paying interest now then we got lower return too on the other hand due to short period of investment. So its a net off.

I’m not talking about a shorter asset duration. Just did a quick exercise, you are better off borrowing the money due, than selling the asset before its maturity to pay off the liability.

If the PV of the asset is the same as the PV of the liability, then you have to at least invest as long as the liability due, in a composite, that translates to one asset with higher duration (higher dollar duration would be even better) than the longest liability.

For example, if the spot curve is 5%, 7%, and 10% for years 1,2,3.

PV liability = PV asset = \$100

Duration of liability = 2

Duration of asset = 3

All zero bonds

If the yield curve does not change, then you borrow the FV of the liability after 2 years (\$114.5) at 5%, then when the asset matures after one year (at \$133.1), you pay off the borrowing FV (\$120.2), and net ~\$13 profit. Selling the asset instead gives you slightly less profit.

Read the bold sentenses. The example you gave is when cashflow occurs after the liability date. I am pretty clear with that as CFA text has explained it well and S2000 also gave wonderful explanation. I am talking about cashflow occuring before the liability date.

It’s the same concept, you would reinvest until it is due, then borrow the difference. If the durations are matched in a normal yield curve, then the asset needs to have a higher YTM than the liability, because of reinvestment risk. The cost of the liability (or surplus) depends on your reinvestment risk primarily, the duration mismatch if any, and the YTM of the asset/liability.

You should be looking at the cost in total, not of that specific cashflow. If the range of assets is wider than the range of liabilities, the cost of funding the liability can be reduced.

Another example as the above, but instead of a 3 year bond asset, you have 2 bonds 1 and 3 year each with a PV of \$50. The first becomes due, you reinvest, that’s 50*1.05^2 = \$55.2, borrow the difference of 114.5-55.2 = \$59.3 at 5%, pay off the borrowing and net the proceeds of the 3 year bond, you profit \$4.2.

The cost of the liability is reduced.