R19 BB#3 Simonsson - Cash Flow Matching

When funding liability, why do you need to take the par value of the liability and divided it by the coupon rate of the government bonds to find a par value to buy? I may be overthinking it - is there a simpler explanation on this? Fixed income section is killing me…

You don’t divide it by the coupon rate; you divide it by one plus the coupon rate (1 + rc).

“Why?” you ask?

Answer me this: what’s the last payment you receive on a coupon-paying bond?

ya I meant 1+coupon. sorry I was not clear.

So to retire a liability, you need to buy a bond. To determine how much bond to buy, you divide the par value of the liability by (1+coupon rate of the government bond you are matching your liabilities with). That gives you the par value of the government bond you need to buy.

I think I sort of get it. Fixed income section is still better than derivatives to me.

You didn’t answer my question; once you answer it correctly, you’ll get it completely, not merely sort of.

What’s the last payment you receive on a coupon-paying bond?

haha ok. The last payment you receive are coupon and principal.


So . . . coupon plus principal must equal the amount required to pay off the liability:

principal + coupon = liability
par + \left(coupon\ rate \times\ par\right) = liability
par\left(1 + coupon\ rate\right) = liability
par = \frac{liability}{1 + coupon\ rate}

EUREKA! THANK YOU!! This is going into my notes! So simple but CFAI never breaks it down for candidates to absorb contents easily. Thank you so much!!

My pleasure.

Back in 2016 I wrote an article on cash flow matching, detailing the process step-by-step: http://www.financialexamhelp123.com/cash-flow-matching/

(Full disclosure: as of 4/25/16, there is a charge to read the articles on my website. You can get an idea of the quality of the articles by looking at the free samples here: http://www.financialexamhelp123.com/sample-articles/.)