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Summary
I've been meaning to write something about total-return considerations as they relate to the fixed-income market. The recent spike in yields, and the trade "unwinding" danger it poses, create a timely backdrop for doing so.
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Several weeks now, I began discussing the technical breakdown I thought in progress at the longer end of the yield curve. What was at an incipient stage then, no longer is. And there are plenty of fundamental reasons to justify the recent technical damage. But that is not the subject at hand.
There is some critical bond-market math not well understood by many investors, and it becomes increasingly important at times like the current one, when yields rise sharply over a relatively short period of time. What I have in mind is the measurement of a bond's total return, defined as the change in price netted against the income that is earned or accrued on the instrument.
The topic is particularly important now because of the large amount of highly leveraged trades that are residing in the Treasury market. Under certain conditions, there's a danger that at least some portion of these might have to be unwound quickly, thereby risking disorderly conditions and an increase in yields that feeds on itself.
Here's a simple example as a starting point. Let's say someone buys a fixed-rate instrument with a 4.50% coupon that matures in one year. Further, it has the standard face value of $1,000, for which the buyer pays "par" (100% of the face value, which also is the amount that will be received at maturity). My example creates a cost basis of $1,000.00. Conventional bonds pay interest semiannually, but for simplicity, we will assume that our bond has one interest payment, at maturity. We know that given these characteristics, our total return will be 4.50%, broken out as follows:
At Purchase At Maturity
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Cost $1,000.00
Proceeds -- $1,000.00
Income -- 45.00
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Total $1,000.00 $1,045.00
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Total return = $1,045.00/$1,000.00 = 4.50%, broken down
as follows: principal return of 0.00%, plus income return
of 4.50% ($45/$1,000) = 4.50%.
Most examples from the real-world bond market are not as simple, but they are not difficult, either, and they do more or less follow the same accounting conventions.
What I want specifically to illustrate here is how total return is adversely affected by a rise in open-market interest rates, or in my following example, how it can be very adversely affected by a rapid rise in rates over a short period of time. To do so, I will use the specific data attendant to the 10-year Treasury note that was auctioned in the Treasury's February refunding operation.
That instrument had a 4.50% coupon, and the price (cost) established in the auction was $996.81 (yield of 4.54%). In this case, the average price represented a small discount from the final maturity value of $1,000.00 per note, which means holders to maturity are guaranteed a modest capital gain ($3.19 per $1,000 note.) The issue matures on 2/15/2016.
As of late-session trading yesterday, this issue had risen to an open-market yield of 4.85%, a "mere" 31 basis points above its issue price yield of 4.54%, which corresponded to the price of $996.81. But this is the phenomenon I am attempting to illustrate. Although 31 basis points seems innocuous enough to many people, it is far from it for investors concerned about total return, and in today's world, that is a lot of investors. For instance, many institutional money managers mark to market every day, and investors who are leveraging their portfolios -- hedge funds, for instance -- have no choice, since the value of their holdings is being used as collateral against the money borrowed to carry their leveraged investment positions.
Before running through the math on the above, here are a few relevant items:
(1) Most coupon-bearing debt obligations pay interest semiannually, with each six-month interest payment equal to one-half the annual rate. For instance, in the case of a 4.50% coupon rate that pays semiannually, each coupon payment would be $22.50, half the $45.00 full year amount (assuming an obligation with a face value of $1,000.00).
(2) As of yesterday's close, only 43 days had elapsed since original investors paid for and took title to the 10-year Treasury issue auctioned in February.
(3) Treasury securities operate on a 360-day year for accrual purposes (versus a 365-day basis for many corporate obligations). Thus, each day, the holder of a Treasury coupon issue earns 1/360th of the annual coupon rate. Using a 4.50% coupon ($45 per year), this equals $0.125 per day per $1,000.00 note.
(4) Finally, because of how bond-market math works, price volatility increases as you go farther out on the yield curve. For instance, from par, a 30 basis-point increase in yield on a 10-year obligation with a 4.50% coupon produces a price decline of about $23.60 or 2.36%. The same 30 basis-point increase in yield on a 30-year bond with a 4.50% coupon produces a price decline of roughly $47.40 or 4.74%, more than double the price decline of the 10-year maturity.
(NOTE: Open-market bond prices fall when yields rise, and prices rise when yields fall. Thus, a large drop in yields can create a substantial increase in price. However and for reasons that are evident, this missive is looking at the negative side of the ledger.)
Using yesterday's late-session value, here is the total-return result for the Treasury 4.500s of 2/15/2016 between 2/15 and yesterday:
3/30/06 2/15/06 Return
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Orig. Cost $996.81 --
Princ. Value $972.55 -- -2.43%
Income Accrual 5.38 0.00 0.54%
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Total $977.93 $996.81 -1.89%
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Of course, were leverage employed in the above, the effective loss would be greater than shown. In turn, this could become an important consideration were rates to continue to rise the way they did this week, since it very well could trigger margin calls and possible forced liquidations to cover them.
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