Can someone explain the short-term pattern between time and bond prices

Question

One of the factors that affect bond prices is time. There is a long term pattern and a short term pattern in this. According to my lecture notes they are:

Long-term pattern

• The price of discount or premium bond (greater or below the FV) will move towards par value over time.

Short term pattern:

• Between coupon payments, the prices of all bonds rise at a rate equal to the yield-to- maturity as the remaining cash flows of the bond become closer.
• After the payment, the price drops by the amount of the coupon.

Here is a diagram for short term:

can someone please explain why? Why does the price of the bond or prices of all bonds rise when the bond becomes closer to the next coupon payment? Why the drop? Can someone please explain the zig-ziggy pattern?

Thanks

Answer 1

There are two ways of quoting prices for bonds: clean and dirty.

The "clean" price for a bond is what you typically see quoted from brokers, and does not take the accrued part of a coupon into account. It is a much smoother curve and only changes when underlying market conditions (interest rates, risk of default) change.

What you are seeing is the change in "dirty" price. The dirty price is the clean price plus the interest that has accrued since the last coupon. It represents what you actually pay for the bond, since you must compensate the bond seller for whatever interest has accrued.

However, when the next coupon is paid, you get the entire coupon. So in the end you still pay the "clean" price because you get back whatever accrued interest you paid to the seller.

The diagram is a bit misleading because it should not be grounded at zero. If you pay X for a bond that pays a coupon of C on the coupon date, as time goes on the payment ("dirty" price) will rise towards X+C, then drop back down to X (all else being equal). But again, the "additional" part of the payment is returned back to you when the coupon is paid since you get to keep it all.

Answer 2

Bonds make coupon payments, which are paid to whoever holds the bond at the time of payment.

Suppose a bond pays annually. If you bought the bond the day after one payment and held it until the day before the next payment, you’d miss out on both payments.

You’re ok with missing the first coupon payment because you bought the bond late.

But the second payment represents an accrual of a year’s ‘interest’. So your buyer is effectively paying you the accrued interest on top of the ‘intrinsic’ price of the bond itself, then getting it back the next day via the coupon payment.

Since the ‘interest’ is deemed to accrue linearly, there is a linear progression in the price (at least that portion attributable to the coupon) until the coupon is paid. Once it has been paid, the accruals start again from zero. This gives you the zig-zag pattern.