# Relationship between price interest rate zero coupon bond

Find out what it means when a bond has a coupon rate of zero and how This means that, as interest rates go up or down, the market value of. Yield to maturity is a concept for fixed rate bonds and is the internal rate of d, of a zero-coupon bond which is the ratio of the price of the zero-coupon bond and. An easy way to grasp why bond prices move in the opposite direction as interest rates is to consider zero-coupon bonds, which don't pay.

What I want to do in this video is to give a not-too-math-y explanation of why bond prices move in the opposite direction as interest rates, so bond prices versus interest rates. To start off, I'll just start with a fairly simple bond, one that does pay a coupon, and we'll just talk a little bit about what you'd be willing to pay for that bond if interest rates moved up or down. Let's start with a bond from some company. Let me just write this down.

This could be company A. It doesn't just have to be from a company. It could be from a municipality or it could be from the U.

If we just draw the diagram for this, obviously I ran out of space on the actual bond certificate, but let's draw a diagram of the payments for this bond. Let me do it in a different color. Let me draw a little timeline right here.

This is two years in the future when the bond matures, so that is 24 months in the future. Halfway is 12 months, then this is 18 months, and this right here is six months.

Now, the day that this, let's say this is today that we're talking about the bond is issued, and you look at that and you say, you know what? Now, let's say that the moment after you buy that bond, just to make things a little bit Obviously, interest rates don't move this quickly, but let's say the moment after you buy that bond, or maybe to be a little bit more realistic, let's say the very next day, interest rates go up.

If interest rates go up, let me do this in a new color. Obviously for something less risky, you would expect less interest.

### Relationship between bond prices and interest rates (video) | Khan Academy

Interest rates have gone up. Now, let's say you need cash and you come to me and you say, "Hey, Sal, are you willing to buy "this certificate off of me? I'll actually do the math with a simpler bond than one that pays coupons right after this, but I just want to give the intuitive sense. Or you could just essentially say that the bond would be trading at a discount to par.

Bond would trade at a discount, at a discount to par.

## Bond Pricing

Now, let's say the opposite happens. Let's say that interest rates go down. Let's say that we're in a situation where interest rates, interest rates go down.

So how much could you sell this bond for? I'm not being precise with the math. I really just want to give you the gist of it. So now, I would pay more than par. Or, you would say that this bond is trading at a premium, a premium to par. So at least in the gut sense, when interest rates went up, people expect more from the bond. This bond isn't giving more, so the price will go down. Likewise, if interest rates go down, this bond is getting more than what people's expectations are, so people are willing to pay more for that bond.

Now let's actually do it with an actual, let's actually do the math to figure out the actual price that someone, a rational person would be willing to pay for a bond given what happens to interest rates.

And to do this, I'm going to do what's called a zero-coupon bond. I'm going to show you zero-coupon bond. Actually, the math is much simpler on this because you don't have to do it for all of the different coupons. Similarly, if you own a bond fund or bond exchange-traded fund ETFits net asset value will decline if interest rates rise. The degree to which values will fluctuate depends on several factors, including the maturity date and coupon rate on the bond or the bonds held by the fund or ETF.

Using a bond's duration to gauge interest rate risk While no one can predict the future direction of interest rates, examining the "duration" of each bond, bond fund, or bond ETF you own provides a good estimate of how sensitive your fixed income holdings are to a potential change in interest rates.

Investment professionals rely on duration because it rolls up several bond characteristics such as maturity date, coupon payments, etc. Duration is expressed in terms of years, but it is not the same thing as a bond's maturity date.

That said, the maturity date of a bond is one of the key components in figuring duration, as is the bond's coupon rate. In the case of a zero-coupon bond, the bond's remaining time to its maturity date is equal to its duration. When a coupon is added to the bond, however, the bond's duration number will always be less than the maturity date.

The larger the coupon, the shorter the duration number becomes. Generally, bonds with long maturities and low coupons have the longest durations. These bonds are more sensitive to a change in market interest rates and thus are more volatile in a changing rate environment.

Conversely, bonds with shorter maturity dates or higher coupons will have shorter durations.

### Bond Pricing - Formula, How to Calculate a Bond's Price

Bonds with shorter durations are less sensitive to changing rates and thus are less volatile in a changing rate environment. Why is this so? Because bonds with shorter maturities return investors' principal more quickly than long-term bonds do. Therefore, they carry less long-term risk because the principal is returned, and can be reinvested, earlier.

This hypothetical example is an approximation that ignores the impact of convexity; we assume the duration for the 6-month bonds and year bonds in this example to be 0.

Duration measures the percentage change in price with respect to a change in yield. FMRCo Of course, duration works both ways. If interest rates were to fall, the value of a bond with a longer duration would rise more than a bond with a shorter duration. Using a bond's convexity to gauge interest rate risk Keep in mind that while duration may provide a good estimate of the potential price impact of small and sudden changes in interest rates, it may be less effective for assessing the impact of large changes in rates.

This is because the relationship between bond prices and bond yields is not linear but convex—it follows the line "Yield 2" in the diagram below. This differential between the linear duration measure and the actual price change is a measure of convexity—shown in the diagram as the space between the blue line Yield 1 and the red line Yield 2.