# Relationship between treasuries and interest rates

### Duration: Understanding the Relationship Between Bond Prices and Interest Rates - Fidelity

When it comes to how interest rates affect bond prices, there are three hear the term basis points—bps for short—in connection with bonds and interest rates. Dec 1, Interest rates are at their lowest levels in years. That's because the year Treasury note yield fell to percent on July 1, Investors. the purpose of this Investor Bulletin is to provide investors with a better understanding of the relationship among market interest rates, bond prices, and yield to.

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. FMRCo Of course, duration works both ways.

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

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. Relationship between price and yield in a hypothetical bond The impact of convexity is also more pronounced in long-duration bonds with small coupons—something known as "positive convexity," meaning it will act to reinforce or magnify the price volatility measure indicated by duration as discussed earlier.

Keep in mind that duration is just one consideration when assessing risks related to your fixed income portfolio.

Credit risk, inflation risk, liquidity risk, and call risk are other relevant variables that should be part of your overall analysis and research when choosing your investments. Viewing and using duration data on Fidelity. Take a test drive by signing up for Guest Access. Managing the duration of your portfolio Accessing the duration of an individual investment Plot the duration of your fixed income holdings using Fidelity's Guided Portfolio SummarySM GPS to see at a glance the weighted average duration of your fixed income holdings at Fidelity.

The duration of your fixed income investments is also plotted on a grid in comparison to the benchmark.

Use the Interest Rate Sensitivity Illustrator to calculate the impact of interest rate changes on the value of your bond and bond fund holdings. 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.

## Duration: Understanding the relationship between bond prices and interest rates

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.

## The Relationship Between Bonds and Interest Rates

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. Let's say that we're in a situation where interest rates, interest rates go down.

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

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.

**PART 2--BOND PRICES VS INTEREST RATES**

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.