Bond Revolution in Singapore – Lesson 6 : Yields, Coupons And Carry

Yields are a tough business. Thank God for Excel and Bloomberg.

There I said it.

Do not ask me to compute yields off paper or even a calculator. Because I cannot.

So what makes me qualified to talk about yields ?

Because I know the right questions to ask.

Yield is Not Coupon. The yield of the bond would be what its coupon would be if it were issued at the moment. Does that make sense ?


The income return on an investment. This refers to the interest or dividends received from a security and is usually expressed annually as a percentageSource : Investopedia

There are dozens of yield definitions on Bloomberg, all for different purposes. Yield to call or put, annualised yields, monthly yield, discounted yield, yield to worst, true yield, simple yield and so on.

I usually take a fleeting interest in the yield when making an investment decision. When someone else computes it for me, I will confirm the convention they used. You really cannot blame the sales guy if they give you the annualized yield when the bond pays semi annual coupons as it annualized number would be higher and they would not be caught lying anyway.

The industry standard practice is to use Yield To Maturity which is the yield you get assuming you reinvested all the coupons of the bond you get at the same yield you bought the bond at all the way till it matures. No prizes for guessing that bonds with higher coupons will have more difficulties in delivering their promised yields as they have much higher reinvestment risks.

For callable and puttable bonds, the yield to use is Yield to Worst which assumes the bond would be called or put if the strike price is higher (puttable) or lower (callable) than the current market price.

The beauty of a yield is that it does not mean anything unless you have something to compare it against. Now that is the difficulty most retail investors face.

To be told that they can buy a perpetual bond at 6.5% versus annual dividends of 4% sounds like riches until you compare it with something else. But that is a lesson for another chapter.


Bond market traders do not usually care much about the coupon, preferring to trade the market on yields. Coupons, are however, important to the fund manager.

Besides presenting reinvestment risks, coupons are an important part of the cash-flow management process for investors.

Say a pensioner invests his savings in a fixed income instrument, he would have to consider the income stream for his cash-flow needs over the duration of the investment.

That is not to say we write off all zero coupon instruments such as treasury bills because the interest would be realized the minute the bill is sold. And it follows the same for bonds as well.

Which Do We Use ?

The yield is the more important in making the initial investment decision, followed by the coupon consideration for the suitability of the cash-flow projections.

That is not too confusing, is it ?

Prices, Duration and Convexity

Big words time.

I like to throw the high sounding word convexity around my non-bond friends so they would think I am do sophisticated work in derivatives, as I like to tell people. Any other bond person would hardly be impressed, I can imagine, as I would not be as well if someone else tells me the same thing.

Convexity is a lovely concept of the relationship between the bond price, its coupon and its yield. Coupon affects the price which then correlates to its yield in decreasing magnitude. The higher the price, the faster it will creep towards parity i.e. the face value of the bond which is, almost always, 100. Similarly, the lower the price, the faster the accretion rate towards parity.

And the rate is different. So do not complain that your 110 paper loses more money for 1% than your 70 cts paper gains for the same 1%.

Here is a picture of what it looks like.

Duration is the average maturity of the bond which is also a consideration for investors especially for fund managers who have targets for their portfolio. It is simply the average lifespan it takes to recover the cost price of the bond.

Thus bonds with higher coupons have shorter durations than bonds with lower coupons for the same maturity date.

The industry practice is to use modified duration  which is an extension of Macaulay duration and gives the price change of the bond per unit change in interest rate. The definition definitely sounds much easier than the term. 


Why buy a high coupon bond with shorter duration at a higher price against a lower coupon bond with longer duration at the same yield for a lower price ?

Answer : I won’t because of CONVEXITY. Unless the coupon is really important to me. I hope it makes sense so far.

There is also another reason I do not like high premium bonds and that is a credit issue which I will expound on in another lesson. The gist is that premiums you pay for the bond is not recoverable in the case of a default or during a call exercise etc.

Do note convexity and duration applies to all bonds, including zero coupons, floating rate notes, convertibles and any instrument that has yield and maturity. From that, the price can be understood.

Rules of Thumb

  1. Price goes up with lower yields and vice versa.
  2. Price goes down more quickly when the coupon is higher than when the coupon is lower for the same yield change.
  3. Duration is lower when coupon is higher but it also means you are paying a higher price for the same yield.
  4. High coupons imply a higher reinvestment risk and a chance that the yield to maturity may not be the eventual one you get.

Let’s finish off with the concept of carry, for the sake of completeness.

Carry is a term used to refer to the return of the bond after deducting its cost of borrowing. That is assuming you bought the bond on a loan which is increasingly common. Of course most of retail investors manage their assets as a portfolio and the carry would be calculated for the portfolio as a whole. Carry cost would be the cost of the borrowing.

I will finish off by unveiling the formula to calculate yield to maturity from the bond price and urge readers not to be stumped and attempt this at home. Excel can do a quick job for you as with other on line tools.


C = coupon
R = yield
F = Face value of the bond i.e. parity or 100 upon redemption

Work backwards to arrive at yield.

Until the next lesson, lets just focus on the basic expectation of yield  and that it is not perfect.