What follows is a transcript of the video recording.
Let’s Try a Practice Question
Which of the following yield is the highest for a bond trading at a discount?
A. Current Yield
D. Nominal Yield
What Is the Difference Between a Yield-to-Call and Yield to Maturity?
We have a bond here, it’s trading at a discount. Which one of these yields do you think are going to be the highest? We’ve got a little bit of a split in responses with yield-to-call, yield-to maturity. The correct answer here is “B,” yield-to-call. When a bond is trading at a discount, the yield-to-call (YTC) is going to be the highest. YTC is higher than YTM (yield to maturity) because the investor receives the discount back at an accelerated rate. This one gets a little tricky. You might be thinking, what even is yield-to-call, yield to maturity. What does that even mean? How do we even calculate that?
The Bond Yield Triangle
I made up a little slide here that I think is going to be a good reference, a good resource in order visualize how these different types of yields work. On this next slide here, we’ve got the teeter-totter and you may have seen this before. It’s the bond yield triangle.
For purposes of this exam, you won’t have to calculate yield-to-maturity or yield-to-call. It’s actually more important to understand here, fundamentally, what’s going on. I like to use this representation, this little slide here to picture exactly what’s going on. Sometimes on this exam, you may just want to memorize these types of things. You may or may not need to use yield-to- call or yield-to-maturity outside of the exam. It’s best to take this bond triangle here and have it back pocket. What I mean by that is, when I was taking this exam for the bond yield triangle, I would, on a piece of scratch paper, draw out the triangle as I left it here, I put discount on the left, I put premium on the right here and I would order it in the way that it appears here.
The way to remember it is, on the right-hand side, for premium, nominal yields, NY is always going to be at the top. NY obviously, for everybody here, if you don’t know, “NY” stands for “New York.” If you’re a New Yorker, anything that’s labeled “NY” is “New York” and everything in New York trades at a premium, everything is priced at a premium. Everything that exists is at a premium. If you want to eat, if you want to go to the club, if you want to take an Uber, everything is going to be a premium. Premium at the top, NY followed by CY then yield-to- maturity than yield-to -call.
On the flip side, you have the discount there and another trick to remember this one is YMC not A. It’s like the song YMCA, right. It’s fun to stay at the YMCA. For me, it’s fun to stay at the bond yield triangle, the teeter-totter and the way that I remember that, is YMC not A.
We have the yield-to-call, the yield-to-maturity, the current yield, and then the nominal yield there. On the right-hand side here, I have a little example for everybody to help us understand intuitively what’s going on here. Let’s say that we buy an 8% bond for $900. We have an 8% bond, we buy it for $900. It has a 10 year to maturity and is callable in five years. A lot of stuff going on here for this bond, but don’t be surprised if you get a question like this on SIE. Fortunately, we’ll be able to go through it piece by piece.
What Is the Nominal Yield for this Bond?
So, for everybody here, if you want to type in the questions pin here, what is the nominal yield for this bond? Nominal yield? Hey, and I have a question for Tom, actually, Tom, what’s another way to say nominal yield? What is another term? Coupon. I don’t know why they have two different names for it, but it’s the same as the coupon.
You might have to be able to use that term interchangeably, nominal yield, coupon yield, coupon, but effectively, this is just a coupon. So, for this example here, the coupon is going to be 80 bucks, the annual interest here. When are interest payments made on a bond? When are interest payments made on the bond? Interest payments are made semi-annually. The coupons will be paid semi-annually on bonds. This 80 is the annual interest but we divide this by par to get the nominal yield, which is 8%. So, that’s the nominal yield 8%, it’s a coupon payment and we get paid those coupons semi-annually.
What Is the Current Yield on this bond?
Current yield’s formula is going to be, the annual interest divided by the current market price. So, our annual interest here was 80, the current market price is 900. Therefore, our interest, current yield is going to be 8.9%. Nominal yield, current yield 8.9%. Now we have the yield to maturity and the yield to call. Yield to maturity and yield to call, you don’t have to calculate these, but the most important thing to remember about these is the following. The differences between yield to maturity and yield to call.
What Happens When a Bond Matures?
Yield to maturity is effectively saying, how much money will we get? What is the rate of return? What is the rate of return? What is the yield if we hold this bond until maturity? So, if we hold this bond to maturity, if we hold this bond to maturity, what’s going to happen? Can anybody tell me here, what happens when a bond matures? What do you get on that maturity date? Two important things. We will get the final coupon.
Upon maturity, we will get a final coupon and we get the par value back. What yield-to-maturity is saying, well, look, we paid, we paid 900 bucks for this bond. We paid 900 bucks for this bond, but we’re going to get a 1,000 back at maturity. So, if you think about this, if this is a 10-year bond, we’re going to get the difference of par less what we paid for it, which is going to be a 100. And, over the 10 years that we hold this bond, we’re going to be getting hypothetically, $10 of extra interest per year. That’s on top of the 80 that we are getting annually. So, you can think of it like this, we’ve had discount on this bond, we’re getting $100 at the end upon maturity, we’re going to be getting therefore, $100, we divide that by 10 year which is the maturity of this bond. Ten extra dollars per year, you add the annual interest, which is, the coupon here is 80. So we’re getting 90 bucks and 90. If we want to calculate the yield on that, we’re going to put 90, we’re going to divide that by 900, which is what we paid for it and that’s a 10% yield there. So, you can see how the bond triangle is coming together.
What Is the Current Yield?
The nominal yield, the coupon, was the lowest, because this is a discount bond. Then we have the current yield at 8.9%, yield to maturity is going to be 10%. And the yield to call is going to take that one step further by saying, look, if a bond has a callable date. For instance, this bond, in my example has a five-year callable date. Come year five, it’s going to be able to be called. If this bond is called in five years, what’s the return going to look like? And we can see here from a high level, I’m not going to go into the math here just for sake of time, but we can see that it’s the same concept as the yield-to-maturity. Instead of maturing in 10 years, it’s going to mature in five years. You’re going to get the par value, you’re going to get that annual interest. And you’re going to take that one hundred bucks that you’re getting and distribute it in the five years that you hold it and not the 10 years. So, the return there is going to be a little bit higher than the yield-to-maturity.
That’s how, that’s how intuitively these different yields work hand in hand. You don’t have to know the calculations but know that this is how it works at a fundamental level. Cool. Bond Yield. Best case scenario for these types of questions, draw down this triangle and write out, write the yields here, YMC not A for discount, New York at a premium, always for a premium. And then current yield, yield-to-maturity, yield-to-call.