# The relationship between coupon rates and bond prices

### The Relationship Between Bonds and Interest Rates- Wells Fargo Funds When new bonds are issued, they typically carry coupon rates at or close to the prevailing market interest rate. Interest rates and bond prices have an inverse. Jan 8, The yield represents the effective interest rate on the bond, determined by the relationship between the coupon rate and the current price. When a bond is issued, it pays a fixed rate of interest called a coupon rate until it matures. This rate is related to the current prevailing interest rates and the.

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. 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. Now, let's say the opposite happens. Let's say that interest rates go down.

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

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.

### Coupon Rate - Learn How Coupon Rate Affects Bond Pricing

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.

## What Is the Relationship Between Bond Price Volatility and the Coupon Rate?

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. You just have to look at the final payment. There is no coupon. So if I were to draw a payout diagram, it would just look like this. This is one year. This is two years. Now let's say on day one, interest rates for a company like company A, this is company A's bonds, so this is starting off, so day one, day one. The way to think about it is let's P in this I'm going to do a little bit of math now, but hopefully it won't be too bad. Let's say P is the price that someone is willing to pay for a bond. Let me just be very clear here. If you do the math here, you get P times 1. The relationship between bond price volatility and the coupon rate is an inverse one — the higher the coupon rate, the less volatile the bond price is to interest rate change, and vise versa.

Bond investors rely on coupon payments as one of the sources to recover their bond investments. Bonds with higher coupon rates pay higher coupon payments, allowing investors to be paid back their initial investment costs sooner in terms of time value of money, and thus subjecting bond prices to interest rate change to a lesser degree. Tips Generally speaking, bonds which feature a higher coupon rate are less sensitive to price fluctuations.

## Coupon Rate

Coupon Rate and Bond Duration Coupon rate is linked to bond duration, a concept used to directly measure bond price volatility. Bond duration is the average time it takes to receive all periodic cash flows as measured in their present values; that is, equivalently the number of years to recover a bond investment as if in a single payment.

• The Relationship Between Bonds and Interest Rates
• Bond price relations
• Relationship between bond prices and interest rates

To calculate bond duration, the number of years to receive each cash payment is totaled and weighted by the percentage of each cash payment's present value over the sum of the present values of all cash payments, which is the investment cost. The concept of bond duration attempts at illustrating two equivalent scenarios in terms of how long a bond investment can be recovered: The higher the coupon rate and cash payments, the faster the bond investment is recovered and thus the shorter the bond duration is.

Bond Price Volatility and Bond Duration Bond duration makes it possible to compare price volatility of bonds of different coupon rates and maturity terms on a single basis. The longer the bond duration, the more volatile the bond price is to changing interest rates. Bond duration is also a direct measure of how much a bond's price will change for an interest rate change of basis points 1 percent.