Coupon Stripping

  

Burlesque Bonds! That’s the ticket.

Er...maybe not. Okay, okay...so when a coupon is "stripped," it's removed from the principal of a bond. In this sense, think of a bond as having two components:

1) Interest that it pays in the form of a semi-annual coupon

2) Principal

When the coupon is stripped off of the bond, it's sold separately to investors who are simply buying a stream into the future of interest payments only. They’re not worried about collecting the principal, so in practice, investors will simply do a discounted cash flow model of an interest payment of, say, $6,000 a year for 20 years. This would be a total set of interest payments of $120,000, for which investors will obviously pay less than $120,000 today to discount back for the time value of money, and the risk that the issuer of that bond goes belly up and one day decides it can no longer pay its coupons.

Maybe that number is half of the $120,000, or ⅔, or ¾, or something, but it’s some meaningful discount to the eventual total payout of $120,000, and the calculation of the math looks something like this:

To be all Wall Street-y, the way you would calculate the value here would be to make 20 columns, each representing one year forward of coupon payments, and then discount back by 1 plus the risk-free rate, i.e. what the Fed pays for an analogous time period, plus some premium added in for risk.

For example, if one-year Fed paper pays 2% to discount back the coupons for next year, you might add 100 basis points to the risk-free rate, to then divide that $6,000 payment by 1.03 to the first power.

Skipping forward 5 years, you might note that Federal paper is paying 4% for its 5-year term paper, and because it’s further into the future, you might need 250 basis points added onto the risk-free rate to account for the much higher degree of risk that the company issuing those bonds goes bye-bye.

So in this case, you would discount those 5-year out bonds by that $6,000 payment, then divide by 1 plus the risk-free rate of 4%, plus the risk premium you’ve added on of 2.5%, to come up with a total base of 6.5%, making the calculation 1.065 to the fifth power in the denominator…which then makes the present, risk-adjusted value of $6,000 paid 5 years from now to equal to about $4,590.

So if you keep doing this math for 20 years, you will come up with a fairly sophisticated answer as to how much those stripped coupon payments are worth cumulatively over the next 20 years.

Okay...then what happened to the principal off of which those coupons were stripped?

Well, the principal amount is actually much easier to come by. If it was $100,000, and was yielding 6% for 20 years, then that $100,000 of principal will need to be paid back after 20 years. So calculating the present value of that 20-year-from-now $100k payment is way easier than calculating the myriad coupon payments along the way. In fact, it is only one calculation, and we might note that Federal paper coming due in 20 years is yielding 4.25%...and we’re going to add quite a lot of risk for a bond 20 years forward, because bad things happen to good companies all the time, and we remember that, 20 years previous, Yahoo was the most highly valued company on the planet, and Amazon was worth less than Sears.

So we’re going to add 3.5%, or 350 basis points of risk premium to that 4.25% risk-free rate, to come up with a total discount rate of 7.75%. Now we’re going to calculate what that $100,000 is worth today when it’s paid out 20 years from now by dividing it by the quantity 1 + .0775 to the 20th power.

All that math then says that, twenty years from now, that $100,000 will be about $22,472.

So why would a company strip off coupon payments and principal in the first place? Simply put: because investors were willing to buy that bifurcated, stripped security. Some investors want small payments all the time, and don’t care about a final, large lump-sum payment. Other investors think lovers of zero coupon-style bonds don’t need any cash today, and instead are happy taking one lump payment with a relatively high return delivered waaaaaay at the very end of a couple of decades of interest-loving compoundage.

So yeah…that’s coupon stripping. And as far as stripping goes, this is, uh…about as G-rated as it gets.

Related or Semi-related Video

Finance: What is Coupon Stripping?3 Views

00:00

finance a la shmoop what is coupon stripping? burlesque bonds that's the [Burlesque bond dancer on stage]

00:08

ticket or maybe not okay okay when a coupon is

00:12

stripped it is removed from the principle of a bond so in this sense

00:18

think of a bond as having two components there's the interest that it pays in the

00:23

form of a semi-annual coupon and then there's well the principle when the

00:28

coupon is stripped off of the bond it is sold separately to investors who are [Bond sold to investor]

00:34

simply buying a stream of cash flows into the future of interest payments

00:38

only they're not worried about collecting the principal so in practice

00:42

investors will simply do a discounted cash flow model of an interest payment

00:46

of I'll say six grand a year for 20 years which would be a total set of

00:51

interest payments of $120,000 for which investors will obviously pay less than

00:56

that amount today to discount back for the time value of money and the risk

01:01

that the issuer of that bond goes belly-up and one day decides it can no

01:05

longer pay its coupons so maybe that number is half of the hundred twenty [120k halved]

01:10

grand or two-thirds or three-fourths or something like that but it's some

01:14

meaningful discount to the eventual total payout of 120 thousand dollars and

01:18

the calculation of the math when it looks something like this to be all Wall

01:22

Streety and all the way you would calculate the value here would be to

01:26

make twenty columns each representing one year forward of coupon payments and [Columns appear for cash flow calculation]

01:31

then discounting back by one plus the risk-free rate ie what the Fed pays for

01:36

an analogous time period plus some premium added in for risk alright for

01:41

example if one year fed paper pays two percent to discount back the coupons for

01:46

next year well you might add a hundred basis points to the risk-free rate to

01:51

then divide that $6,000 payment by 1.03 to the first power

01:55

cause this bond issuer is not risk free all right skipping forward five years

02:00

well you might note that federal paper at that point is paying four percent for

02:04

its five-year term and because it's further into the future well you might [Power of 5 highlighted in calculation]

02:08

need to discount 250 basis points added on to that risk-free rate to account for

02:13

much higher degree of risk that while the company issuing those bonds goes

02:16

bye-bye so in this case you would discount those five year out bonds by

02:20

that six thousand dollar payment then divide by one plus the risk-free rate of

02:25

4% then you'd add in the risk premium you've added on top that's two and a

02:29

half percent to come up with a total base of six and a half percent making

02:33

the calculation 1.065 to the fifth power in the denominator which

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then makes the present risk adjusted value of six grand paid five years from [Calculation answer appears]

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now to equal about forty five hundred ninety bucks so if you keep doing this

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math for twenty years that's about how long it will take to do this problem you

02:51

will come up with a fairly sophisticated answer as to how much those stripped

02:55

coupon payments are worth cumulatively over the next twenty years so then what

03:01

happened to the principal off of which those coupons were you know stripped

03:05

well the principal amount is actually much easier to calculate if it was a [Man discussing principal amounts of stripped coupons]

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hundred grand while that was yielding six percent for twenty years well then

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that hundred thousand dollars of principal will need to be paid back

03:15

after 20 years once so calculating the present value of that 20 years from now

03:20

hundred grand payment is way easier than calculating the myriad coupon payments

03:25

we just did along the way in fact it's just this one calculation and we might [Man pressing calculator buttons]

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note that federal paper coming due in 20 years is yielding four and a quarter

03:33

percent and we're gonna add quite a lot of risk for a bond 20 years forward

03:39

because well, bad things happen to good companies all the time and we remember

03:42

that about two decades ago Yahoo was the most highly valued company on the planet [Yahoo logo appears]

03:47

and Amazon was worth a fraction of what Sears was worth so yeah bad things so

03:53

we're gonna add three and a half percent or three hundred fifty basis points of

03:57

risk premium each year to that four and a quarter percent risk-free rate to come

04:01

up with a total discount rate of 7 and 3/4 percent okay almost done hang with

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me so now we're gonna calculate what that hundred grand is worth today when

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it's paid out 20 years from now by dividing it by the quantity one plus [New calculation appears]

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0.0775 to the 20th power and all that math then says that the hundred

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grand 20 years from now is only worth about 22 grand and change so why would a

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company strip off coupon payments and principal

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in the first place answer simply put because investors were willing to buy

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that bifurcated stripped security well some investors want small payments all [Investor being paid small payments]

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the time and they don't care about a final large lump sum payment other

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investors think lovers of zero coupon style bonds don't need any cash today [Man in bed with coupon]

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and instead are having taking one lump payment with a relatively high return

04:48

delivered away at the very end of a couple of decades of interest loving

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compoundage-- like you could buy one of those hundred grand thingies 20 years

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from now for only 22 grand today so yeah that's coupon stripping and as far as [Man discussing coupon stripping]

05:00

real stripping goes well this is about as g-rated as it gets people here what [Woman with coupon for head pole-dancing]

05:05

do you think we're running here at shmoop..

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