# What drives the relationship between bond prices and yields

### Relationship Between Bond Price & Yield to Maturity - Budgeting Money

The yield to maturity of a bond reflects a bond's total return, including both interest payments and the increase or decrease in the value of the bond at maturity. Dec 15, But why does the relationship work this way? So, why would an investor purchase Bond A with a yield of 4 percent when he or she could buy. When new bonds are issued, they typically carry coupon rates at or close to the Interest rates and bond prices have an inverse relationship; so when one goes.

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. 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.

### The Relationship Between Bonds and Interest Rates- Wells Fargo Funds

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.

• Relationship Between Bond Price & Yield to Maturity
• Relationship between bond prices and interest rates
• Bond Basics: The Relationship Between Yield and Price

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.

## The Relationship Between Bonds and Interest Rates

Credit risk refers to the possibility that the company or government entity that issued a bond will default and be unable to pay back investors' principal or make interest payments.

Bonds issued by the U. However, Treasury bonds as well as other types of fixed income investments are sensitive to interest rate risk, which refers to the possibility that a rise in interest rates will cause the value of the bonds to decline. Bond prices and interest rates move in opposite directions, so when interest rates fall, the value of fixed income investments rises, and when interest rates go up, bond prices fall in value. If rates rise and you sell your bond prior to its maturity date the date on which your investment principal is scheduled to be returned to youyou could end up receiving less than what you paid for your bond.

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. 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.