# Relationship between bond price and market yield

market interest rates, bond prices, and yield to maturity of treasury bonds, below, can help you visualize the relationship between market interest rates and. If you buy a $ bond at par value and a coupon rate of 10 percent you will receive interest payments of 10 percent each year until the bond matures. But what. To explain the relationship between bond prices and bond yields, let's The market value of a bond will fluctuate as interest rates rise and fall.

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.

## Bond prices, rates, and yields

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.

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

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.

## Relationship between bond prices and interest rates

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. So what is this number right here? Let's get a calculator out. Let's get the calculator out. If we have 1, divided by 1. Now, what happens if the interest rate goes up, let's say, the very next day?

And I'm not going to be very specific.

I'm going to assume it's always two years out. It's one day less, but that's not going to change the math dramatically. Let's say it's the very next second that interest rates were to go up. Let's say second one, so it doesn't affect our math in any dramatic way. Let's say interest rates go up. Inflation Inflationary conditions generally lead to a higher interest rate environment.

Therefore, inflation has the same effect as interest rates. When the inflation rate rises, the price of a bond tends to drop, because the bond may not be paying enough interest to stay ahead of inflation.

The longer a bond's maturity, the more chance there is that inflation will rise rapidly at some point and lower the bond's price. That's one reason bonds with a long maturity offer somewhat higher interest rates: They need to do so to attract buyers who otherwise would fear a rising inflation rate. That's one of the biggest risks incurred when agreeing to tie up your money for, say, 30 years.

Minimizing bond price confusion Bond pricing involves many factors, but determining the price of a bond can be even harder because of how bonds are traded. Because stocks are traded throughout the day, it's easier for investors to know at a glance what other investors are currently willing to pay for a share.

But with bonds, the situation is often not so straightforward. Prices on statements may not be what you paid The price you see on a statement for many fixed-income securities, especially those that are not actively traded, is a price that is derived by industry pricing providers, rather than the last-trade price as with stocks.

The derived price takes into account factors such as coupon rate, maturity, and credit rating. The price is also based on large trading blocks. But the price may not take into account every factor that can impact the actual price you would be offered if you actually attempted to sell the bond.

### Bond Prices, Rates, and Yields - Fidelity

Derived pricing is commonly used throughout the industry. Of the hundreds of thousands of bonds that are registered in the United States, less thanare generally available on any given day. These bonds will be quoted with an offered price, the price the dealer is asking the investor to pay. Treasury and corporate bonds are more frequently also listed with bid prices, the price investors would receive if they're selling the bond. Less liquid bonds, such as municipal bonds, are rarely quoted with a dealer's bid price.

If the bid price is not listed, you must receive a quote from a bond trader. Call a Fidelity representative at Yield Yield is the anticipated return on an investment, expressed as an annual percentage. There are several ways to calculate yield, but whichever way you calculate it, the relationship between price and yield remains constant: The higher the price you pay for a bond, the lower the yield, and vice versa.

Current yield is the simplest way to calculate yield: While current yield is easy to calculate, it is not as accurate a measure as yield to maturity. The yield to maturity in this example is around 9. Yield to maturity Yield to maturity is often the yield that investors inquire about when considering a bond.

Yield to maturity requires a complex calculation. It considers the following factors. Coupon rate—The higher a bond's coupon rate, or interest payment, the higher its yield. That's because each year the bond will pay a higher percentage of its face value as interest. Price—The higher a bond's price, the lower its yield. That's because an investor buying the bond has to pay more for the same return.

Years remaining until maturity—Yield to maturity factors in the compound interest you can earn on a bond if you reinvest your interest payments. Difference between face value and price—If you keep a bond to maturity, you receive the bond's face value.

The actual price you paid for the bond may be more or less than the face value of the bond. Yield to maturity factors in this difference. It is 5 years from maturity. The bond's current yield is 6. But the bond's yield to maturity in this case is higher. Yield to call Yield to call is the yield calculated to the next call date, instead of to maturity, using the same formula.