Fixed Income: Coupon Rate vs YTM

CFA Level I Fixed Income
#1

Hi Guys,

Can someone please show me a simple and easy to understand distinction between a coupon rate and YTM and exactly why is it important to know anything about a coupon rate when the focus on YTM is making so much good sense to me. I will appreciate an easy to understand example.

Kind Regards,

Thapelo

#2

Think of a simple bond as having two components. Your coupon payments, and then your face-value payment at maturity. In order to calculate your IRR (ie, your YTM), do you agree that we need to know the amount of coupon payments and their frequency? That is why the coupon rate is important.

Imagine a zero-coupon bond. A bond that pays no coupon, just the face-value at maturity. What is the YTM? Well, if you tried to go from just the coupon rate to the YTM, you are going to have a bad time.

The coupon rate is just a type of cash-flow. The face-value payment at maturity is also another type of cash-flow. To calculate our yield if we held the bond to maturity, we need to discount both cash-flows appropriately.

Hope that helps distinguish the two.

#3

Hi ThapeloZA,

consider a bond with a 10% coupon rate (paid year at year end), 2 year left until maturity, a par value of $1000 and currently trading at $500.

The coupon rate of this bond is 10%. It determines the interest payment you will receive at the end of each year. In the example you will receive $100 (which is 10% of par value) at the end of each year. The YTM is different, because it also considers any gains/losses you will make on your principal. It considers ALL cash flows you receive and pay from investing in the bond. If you buy this bond at the beginning of the first year you pay $500 immediately. At the end of year 1 you receive $100 interest. At the end of year 2 you receive $100 interest and the par value of the bond, which is $1000 (so $1100 total at the end of year 2). Your yield of maturity in this case would be 58,7%, which is way more than the coupon rate (10%) of the bond. This can also be the other way around: Suppose the bond is currently trading at $2000. Your YTM for the investment would then become -23.3%, which is considerably less than the coupon rate.

Why is it important to know the coupon rate? There are several reasons

  • maybe you want to use the interim cash flows to finance something. the coupon rate tells you how much money you will receive at each interest payment date
  • the coupon rate is one of the main factors that determines interest rate sensitivity of a bonds value. A bond with a higher coupon rate has less interest rate risk than a bond with a lower coupon rate (see the section on duration in fixed income)
#4

Hi There, - thanks for the response above

But how did you get the 58.7% and -23.3% - sorry I am a bit lost there???

#5

Hi Huntling,

Thanks for arleting me get to grips with the IRRs to get the full picture - appreciate it :slight_smile:

T

#6

You just take the cash flows and calculate the IRR (this is the discount rate at which the net present value of the stream of cash flows would be zero).

So in the first case:

  • start of year 1: outflow of $500 (initial investment outlay)
  • end of year 1: inflow of $100 (interest payment)
  • end of year 2: inflow of $1100 ($100 interest payment and $1000 par value of bond)
  • The NPV of these cash flows (at the beginning of year 1) becomes zero for a discount rate of roughly 58.7% (use the cash flow function of your calculator, if you have the Texas Instruments BA II Plus calculator)

Similarly for the second case:

  • start of year 1: outflow of $2000 (initial investment outlay)
  • end of year 1: inflow of $100 (interest payment)
  • end of year 2: inflow of $1100 ($100 interest payment and $1000 par value of bond)
  • The NPV of these cash flows (at the beginning of year 1) becomes zero for a discount rate of roughly -23.3% (use the cash flow function of your calculator, if you have the Texas Instruments BA II Plus calculator)
#7

Thanks so much Nukular,

Now it makes perfect sense :slight_smile:

T