You will be able to say what yield to maturity measures and when it is a fair guide to your return.
Hui Min is comparing two made-up bonds from similar borrowers, both maturing in two years. One has a 5% coupon and costs 104. The other has a 2% coupon and costs 96. The first one looks better: 5% is a lot more than 2%. Her bank's bond page, though, lists a yield of about 2.91% for the first and about 4.12% for the second. That yield is the number she should be comparing, and this lesson explains what it means.
In lesson 2.1, Price and yield move in opposite directions, you started from a market yield and worked out a price. Yield to maturity runs that calculation backwards. It is the single yearly rate that, used to discount every future payment, makes them add up to exactly today's price.
Take a made-up three-year bond with a 3% annual coupon, priced at 95. It will pay 3, 3 and then 103. Ask which discount rate turns those three payments into a present value of 95. The answer is about 4.83%. Discount the payments at 4.83% and they sum to 95. Use any other rate and they do not.
That 4.83% folds everything into one figure: the coupons, and the gain of 5 you collect when the bond repays 100 after you paid 95. Compare it with the current yield from lesson 1.2, Coupon, current yield and what you actually earn. That is 3 divided by 95, about 3.16%, and it misses the gain completely.
Back to Hui Min's pair. The 5% bond at 104 loses 4 at maturity, which drags its yield to maturity down to about 2.91%. The 2% bond at 96 gains 4, which lifts it to about 4.12%. On a like-for-like basis the low-coupon bond pays more, and the coupon on its own would have sent her the wrong way.
Yield to maturity is a projection. It comes true only if three things happen.
First, you hold the bond until it matures. If you sell early, your return depends on the price on the day you sell, which depends on market yields at the time. That could be higher or lower than the yield you started with.
Second, the issuer pays every coupon and the full face value on time. If it misses a payment, the number means nothing. This is why a bond from a weak borrower can show a high yield to maturity: the market has pushed its price down because it doubts the payments will arrive.
Third, the coupons you receive are reinvested at the same rate. The maths treats each coupon as if it keeps earning the yield to maturity until the end. In real life you might put the coupons into a savings account at a much lower rate, or spend them. On a short bond with small coupons the effect is minor. On a long bond with large coupons it can move your actual return a fair way from the quoted yield.
So treat yield to maturity as the return the bond offers if everything goes to plan, not as a guarantee of what you will earn.
Even with those assumptions, yield to maturity is the right number for comparing bonds, as long as you compare like with like. Two bonds of similar credit quality and similar remaining term can be ranked on it fairly. It puts a high-coupon bond bought at a premium and a low-coupon bond bought at a discount on the same footing, as Hui Min's example showed.
What it cannot do is compare very different risks. A 6% yield to maturity on a small company's bond and a 3% yield on an SGS bond are not two prices for the same thing. The 3 points between them are payment for credit risk, which module 6 covers. Nor does it compare very different terms well, because a two-year and a fifteen-year bond expose you to different amounts of price risk.
You never need to find yield to maturity by trial and error. Spreadsheets do it for you.
The RATE function takes the number of periods, the payment per period, the present value and the future value, the same arguments you used with PV in How money works. For the three-year bond above, enter =RATE(3, 3, -95, 100). The price goes in as a negative number because you pay it out, and the coupons and face value are positive because you receive them. The answer is about 4.83%.
For a bond that pays coupons twice a year, use the number of half-years and the half-yearly coupon, then multiply the answer by two to get the yearly figure. If you know the exact settlement and maturity dates, the YIELD function in Excel and Google Sheets handles odd dates and accrued interest, but RATE is enough for a clean example.
Check your answer by plugging the yield back into PV. If =PV(4.83%, 3, -3, -100) gives about 95, the two agree. Your turn comes next, with a bond that has a different coupon and term from the one here.
Use RATE in a spreadsheet to find the yield to maturity of a made-up 4-year bond priced at 97 with a 2.5% annual coupon.
Junxiong-WFG Organisation is an authorised representative of AIA Financial Advisers Private Limited (Reg. No. 201715016G).