Tell the coupon rate apart from the yield, and explain why the two differ once a bond is trading.
A bond's coupon rate and its yield are two different measures, so the same bond can show two different figures. The coupon rate is worked out on the bond's face value. The yield is worked out on the price you paid, and that price changes over the bond's life.
Hui Min ran into this over lunch. A colleague told her he had bought a bond "yielding almost 4.5%". That evening she looked the bond up and found its coupon was 4%. She assumed he had got the number wrong, but he was quoting the yield, and both figures describe the same bond.
You met the coupon in Lesson 1.1, "A bond is a loan with a fixed timetable". The coupon is the rate the borrower pays on face value. It is set on the issue date and written into the bond's terms, and it stays the same until maturity. Face value is the amount repaid at maturity, and the coupon is calculated on it. A 4% coupon on S$1,000 face value pays S$40 a year until maturity (an example figure). That cash goes to whoever holds the bond when each payment is made.
The price works separately from the coupon. Many bonds can be bought and sold between investors before they mature, and the price moves when they trade. Bond prices are quoted per 100 of face value. A price of 90 means you pay S$900 for S$1,000 of face value. A price of 110 means you pay S$1,100 for the same S$1,000.
So the coupon cash is certain, but what you pay to receive it depends on when you buy. Your return depends on what you pay, so the coupon rate and the yield differ.
Current yield is the yearly coupon divided by the price paid. It tells you how much coupon you get each year for every dollar you put in today. You can use the coupon as a rate or as cash per 100 of face value. Either way, divide it by the price paid per 100 of face value.
The 4% coupon works out like this at three prices:
At a price of 100: 4 / 100 = 4%, the same as the coupon. At a price of 90: 4 / 90 = about 4.44%. At a price of 110: 4 / 110 = about 3.64%.
Hui Min's colleague paid 90. His current yield is about 4.44%, which is the "almost 4.5%" he quoted at lunch.
Because the coupon is fixed, a lower price always gives a higher current yield and a higher price always gives a lower one. Module 2 covers this inverse relationship in full and uses it to explain why bond prices fall when interest rates rise.
Current yield leaves out part of the return: the gain or loss between the price you paid and face value at maturity. If you hold the bond to maturity, you are repaid the full face value whatever price you paid. Buying below face value is buying at a discount. Buying above face value is buying at a premium. A discount adds to your return and a premium reduces it.
Say the colleague's bond matures in three years. He paid 90 and will be repaid 100. That is a gain of S$100 per S$1,000 face value at maturity, on top of S$40 in coupons each year. If all goes to plan, he earns more than the 4.44% current yield suggests. Someone who paid 110 would be repaid 100 and take a loss of S$100 per S$1,000 face value. For that buyer, the current yield overstates the return.
Yield to maturity combines the coupons and the gain or loss at maturity into one yearly rate. Lesson 2.2, "Yield to maturity in plain words", takes you through it.
Yield to maturity is still a calculated figure. Fees, tax and what you do with the coupons all change what actually reaches your account. No yield figure takes off your own fees.
Buying through a broker or bank can involve commissions, platform charges, or a spread between the buying and selling price. Fees take the largest share on small holdings. A S$25 fee on a S$1,000 purchase takes 2.5% of your money on day one, and on a 3% bond that is most of a year's coupon.
Tax on interest income for individuals in Singapore depends on the type of investment. Don't assume how a bond or other instrument is taxed. Check the current rules for that specific instrument on the IRAS website.
What you do with each coupon also affects your return. A coupon left in a low-interest savings account adds less over the years than one reinvested at a better rate, and the gap grows large over a long holding. The compounding tables in How money works, lesson 2.4, "Build a compounding table in a spreadsheet", show how big that difference gets.
When someone quotes you a yield, first ask which one it is: coupon rate, current yield or yield to maturity. Coupon rate is cash per year on face value. Current yield is cash per year on price paid. Neither gives you the full return. Next, allow for fees, tax and how you will reinvest the coupons, because none of those figures include them.
The quickest way to make this stick is to run the numbers on one bond at three prices and watch the current yield move. Use a bond with a different coupon from the one above so you work it out fresh. Keep your answers, because you will reuse them in module 2.
Use made-up figures. Work out the current yield on a 3% coupon bond bought at 95, at 100 and at 105, then describe the pattern in one sentence.
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