Bond Calculator: Why the Price Moves and the Coupon Does Not

The confusing part of bonds is that several numbers all get called the yield and they are rarely equal. A calculator sorts that out quickly, but only if you know which figure you are typing into which box.

Why the price moves when the coupon does not

Your bond pays $50 a year, fixed, and returns $1,000 at maturity. If new bonds of the same quality start paying $60, nobody will give you $1,000 for a bond paying $50. They will pay whatever makes your $50 stream add up to a 6% return.

The maths is two present values added together. The ten $50 coupons discounted at 6% are worth $368. The $1,000 at the end is worth $558. Total $926, so the price falls about $74. Run it the other way at a 4% yield and you get $406 of coupons plus $675 of principal, which is $1,081.

Longer bonds move further

Same 5% coupon, same rise to a 6% yield, but only three years left instead of ten: the price is $973, a fall of 2.7%. The ten-year fell 7.4%. That difference is duration, and it explains why a bond fund holding long maturities lost more than a short-dated one during the same rate move.

Coupon rate, current yield and yield to maturity

Three numbers, three meanings. The coupon rate is 5%, set at issue and printed on the bond forever. The current yield is the coupon divided by what you actually paid: $50 on a $926 purchase is 5.4%. The yield to maturity is 6%, because on top of the coupons you also collect the $74 climb back to $1,000 by maturity.

YTM is the one to compare against anything else, since it is the only figure that accounts for both income and the pull to par. The habit of checking which yield you are looking at is the same discipline as knowing the difference between APR and APY on a savings product.

Filling in the calculator

Face value is almost always $1,000 for US corporate and Treasury bonds, and £100 nominal for UK gilts. Coupon rate appears in the bond's name: a listing reading 5.000% due 2036 tells you both the coupon and the maturity. Years to maturity comes from that date, or enter the maturity date directly if the calculator asks for one. Market yield is quoted on the broker's screen next to the price; enter the yield and the calculator returns the price, or enter the price and it returns the yield.

Semiannual matters, a little

Most US bonds and UK gilts pay twice a year, so that 5% coupon arrives as $25 every six months. Priced properly on a semiannual basis at a 6% yield, our ten-year bond is $925.61 rather than the $926.39 you get treating it as annual. Under a dollar here, but the gap widens as the distance between coupon and yield grows, so set the frequency correctly.

Common questions

Why did my bond fund lose money when interest rates rose? Because the fund holds bonds whose fixed coupons became less attractive, so their market prices fell, exactly as in the $1,000 to $926 example. Nothing defaulted. If the fund holds to maturity the money comes back, but the daily valuation drops in the meantime.

Does par value matter if I hold to maturity? It is what you get back, so yes. Buy at $926 and hold to maturity and you receive $1,000 plus every coupon along the way. Buy at $1,081 and you still only get $1,000 back, so you take an $81 loss at maturity; the above-market coupons are what paid you for it along the way.

Is yield to maturity guaranteed? Only if you hold to maturity, the issuer pays, and you reinvest the coupons at the same rate. That last assumption is the one that usually breaks. If rates fall, your coupons get reinvested at less than 6% and your realised return comes in below the quoted YTM.

How does a bond compare with a savings account? A bond locks a rate for years and its price fluctuates if you sell early. A deposit account keeps its balance but the rate can be cut at any time. The comparison between locking in and staying liquid is the same one behind savings accounts, CDs and money market funds.