What is the pull-to-par effect and how does it work for premium and discount bonds?
I know that bonds converge toward par value as they approach maturity, but I'm struggling to visualize how this works for both premium and discount bonds. Can someone explain the mechanics and show why it happens?
The pull-to-par effect describes how a bond's price converges toward its par (face) value as maturity approaches, regardless of whether it currently trades at a premium or discount.
Why It Happens:
A bond's price is the present value of its remaining cash flows. As time passes (holding yields constant), fewer coupon payments remain, and the par value repayment at maturity gets closer. The premium or discount shrinks because there are fewer future coupons to create the price difference.
Premium Bond Example — Langford Energy 8% (fictional):
Par = $1,000, Coupon = 8%, YTM = 6%, originally 10 years to maturity.
| Years to Maturity | Price |
|---|---|
| 10 | $1,147.20 |
| 7 | $1,112.10 |
| 5 | $1,084.25 |
| 3 | $1,053.46 |
| 1 | $1,018.87 |
| 0 | $1,000.00 |
The $147.20 premium erodes steadily over 10 years.
Discount Bond Example — Langford Energy 4% (fictional):
Par = $1,000, Coupon = 4%, YTM = 6%, 10 years to maturity.
| Years to Maturity | Price |
|---|---|
| 10 | $852.80 |
| 7 | $887.90 |
| 5 | $915.75 |
| 3 | $946.54 |
| 1 | $981.13 |
| 0 | $1,000.00 |
Accounting Implications:
- Premium bonds: the pull-to-par creates an amortization of premium — a capital loss that offsets the above-market coupon income
- Discount bonds: the pull-to-par creates an accretion of discount — a capital gain that supplements the below-market coupon income
Exam Tip: The CFA exam tests whether you understand that a bond's return equals its YTM only if yields remain unchanged. The pull-to-par is a component of return — for discount bonds, it adds to total return; for premium bonds, it subtracts.
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