coupon, yield, the inverse price-rate relationship
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Start studyingYes, a bond’s price falls when market interest rates rise because the bond’s fixed coupon payments become less attractive compared to newer bonds paying higher rates. The price adjusts so that a buyer who purchases the bond today earns a yield roughly equal to the current market rate.
A bond’s price is simply the present value of all its future cash flows—the coupon payments and the final face value. When market rates rise, the discount rate used to calculate that present value also rises. A higher discount rate reduces the present value of every future payment, so the bond’s price must drop. The size of the drop depends on how far into the future those payments lie. A payment due in one year is barely affected by a rate change; a payment due in thirty years is heavily affected.
Suppose you buy a newly issued ten-year bond with a face value of $1,000 and a 5% coupon. It pays $50 each year and returns $1,000 at maturity. Now imagine that one day later, market rates jump to 6% for a similar ten-year bond. Your bond still pays only $50 per year. A new $1,000 bond would pay $60 per year. To make your bond competitive, its price must fall so that a buyer’s total return—the $50 coupons plus the gain or loss at maturity—equals 6%. That price is roughly $926. If you sell at that price, you lose $74. If you hold to maturity, you collect all $50 payments and the full $1,000, so your actual yield ends up being 5%, not the 6% the market now offers. You have not lost money in cash, but you have missed the opportunity to earn a higher rate.
Many people think a bond’s price falls because the issuer is in trouble. That is credit risk, a separate issue. The price drop described here happens even for a perfectly safe government bond if market rates rise. The two risks are independent. A bond can lose market value due to rising rates while the issuer remains fully solvent. Conversely, a bond can default while rates are stable. Confusing the two is why some investors panic when their bond fund’s net asset value drops during a period of rising rates, even though the underlying issuers are fine.
The inverse relationship between bond prices and interest rates assumes the bond’s coupon and maturity are fixed and that the bond is held in a secondary market. It does not apply to floating-rate bonds whose coupons reset periodically with market rates; those bonds experience very little price change when rates move. It also does not apply to bonds held to maturity by an investor who never sells; for that investor, the price fluctuations are irrelevant except as an opportunity cost. Finally, the relationship is weaker for very short-term bonds because the discounting effect is tiny over a few months.
Cram Bonds are the safe boring thing, right. You buy one, you cannot lose money.
Rep That belief has cost a lot of people a lot of sleep. A bond is a loan, and loans can be resold for less than you paid.
Cram Resold. I thought I just hold it and collect interest.
Rep You can. A bond has a face value, say one thousand, and a coupon, say five percent. The issuer pays you fifty a year, then returns the thousand at maturity.
Cram So where does losing money come in.
Rep Only if you sell early. Suppose new bonds start paying seven percent. Nobody wants your five percent bond at full price anymore.
Cram So they offer me less than a thousand for it.
Rep Exactly. The price drops until your fixed fifty a year works out to roughly seven percent for the buyer. That is the inverse relationship.
Cram Rates go up, prices go down. Rates go down, prices go up.
Rep Right. The coupon is frozen the day it is issued. Price is the only thing left that can move.
Cram So the loss is not real unless I sell.
Rep If the issuer keeps paying and you hold to maturity, you get your thousand back regardless of what happened in between.
Cram Then why does anyone care about the price swings.
Rep Because funds sell constantly, and because the longer the bond, the harder it swings. A thirty year bond moves far more than a two year one.
Cram So bonds are safe from surprises, not safe from prices.
Rep Well put. Two risks, not one. The issuer might not pay, and rates might move. Holding to maturity removes the second, never the first.