A bond s coupon rate is equal to its yield to maturity if its purchase price is equal to its par value. The par value of a bond is its face value, or the stated value of the bond at the time of issuance, as determined by the issuing entity. Read more What is the difference between yield to maturity and the coupon rate? The par value of a bond does not dictate its market price , however. These factors include the bond s coupon rate, maturity date, prevailing interest rates and the availability of more lucrative bonds.

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- Coupon Rate
- Duration: Understanding the relationship between bond prices and interest rates
- When is a bond s coupon rate and yield to maturity the same?
- The Relationship Between Bonds and Interest Rates
- Whatâ€™s the Difference Between Premium Bonds and Discount Bonds?
- An Introduction to Duration
- Understanding Fixed-Income Risk and Return

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Duration is a measure of interest-rate risk. Or, stated differently, duration is a measure of how sensitive the price of a fixed-income instrument is to interest-rate changes. For a review of bond coupon rates and yields see these presentations: Duration can be thought of as the weighted average of when the bondholder receives payment. Check that the way the weights react is consistent with the relationships on the previous slide.

With the following app, you can set the maximum yield-to-maturity, and time to maturity, and see the resulting 3D duration surface. You can also change the coupon rate and see the effect on the duration surface. However, it is customary to first calculate what is called Maucaulay Duration, and then use this to calculate Modified Duration. The Macaulay Duration is:.

These are weights and sum to 1. Also note, we can calculate the duration of a bond portfolio as the weighted average of the duration of all of the individual the bonds in the portfolio. Calculate the Macaulay and Modified Durations for the following bonds. You can check your answers with the interactive app on the following slide. All bonds have annual payments in the interactive app. In terms of percent, we can say:.

An Introduction to Duration. Duration is Approximate Duration is a linear approximation of a nonlinear relationship. Duration is more accurate as the change in the interest rate becomes smaller. Duration can increase or decrease given an increase in the time to maturity but it usually increases. You can look at this relationship in the upcoming interactive 3D app. Average of Time Payments are Received Duration can be thought of as the weighted average of when the bondholder receives payment.

This will give you an intuitive understanding of how these variables affect duration. Interactive App With the following app, you can set the maximum yield-to-maturity, and time to maturity, and see the resulting 3D duration surface. You can move the 3D surface around, and zoom in and out, with your mouse. Can you see the case where duration is decreasing with an increased time to maturity?

Using Duration Specifically, the steps in using duration are: The Macaulay Duration is: Macaulay Duration From our definition above, we can make the following observations: Duration cannot exceed the number of periods to maturity of the bond. The Duration of a zero-coupon bond is the number of years until maturity. You can also use the following app to see duration decrease when maturity increases.

Modified Duration Calculation. In terms of percent, we can say: Also in Fixed Income and Other Debt 1. Exchange Traded Notes notifications. Yield to Maturity notifications. Convexity notifications notifications notifications. Duration notifications notifications notifications.

## Coupon Rate

Bonds can prove extremely helpful to anyone concerned about capital preservation and income generation. Bonds also may help partially offset the risk that comes with equity investing and often are recommended as part of a diversified portfolio. They can be used to accomplish a variety of investment objectives. These concepts are important to grasp whether you are investing in individual bonds or bond funds. The primary difference between these two ways of investing in bonds also is important to understand: When you invest in a bond fund, however, the value of your investment fluctuates daily â€” your principal is at risk.

Duration is a measure of interest-rate risk.

Coupon interest rates are determined as a percentage of the bond s par value, also known as face value , but differ from interest rates on other financial products because it is the dollar amount, not the percentage, that is fixed over time. Coupon rates are largely influenced by the national interest rates controlled by the government. Most bonds have fixed coupon rates, meaning that no matter what the national interest rate may be or how much the bond s market price fluctuates, the annual coupon payments remain stable. When new bonds are issued with higher interest rates, they are automatically more valuable to investors because they pay more interest per year compared to pre-existing bonds. The yield represents the effective interest rate on the bond, determined by the relationship between the coupon rate and the current price.

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

Beginning bond investors have a significant learning curve ahead of them that can be pretty daunting, but they can take heart in knowing that it s manageable when it s taken in steps. It s onward and upward after you master this. In short, "coupon" tells you what the bond paid when it was issued. But then the bond trades in the open market after it s issued. So now you have to fast-forward 10 years down the road.

### When is a bond s coupon rate and yield to maturity the same?

There are two fundamental ways that you can profit from owning bonds: Many people who invest in bonds because they want a steady stream of income are surprised to learn that bond prices can fluctuate, just as they do with any security traded in the secondary market. If you sell a bond before its maturity date, you may get more than its face value; you could also receive less if you must sell when bond prices are down. The closer the bond is to its maturity date, the closer to its face value the price is likely to be. Though the ups and downs of the bond market are not usually as dramatic as the movements of the stock market, they can still have a significant impact on your overall return. They move in opposite directions, much like a seesaw. The opposite is true as well: When bond prices rise, yields in general fall, and vice versa. However, other factors have an impact on all bonds.

### The Relationship Between Bonds and Interest Rates

When you buy a bond, either directly or through a mutual fund, you re lending money to the bond s issuer, who promises to pay you back the principal or par value when the loan is due on the bond s maturity date. In the meantime, the issuer also promises to pay you periodic interest payments to compensate you for the use of your money. The rate at which the issuer pays youâ€”the bond s stated interest rate or coupon rateâ€”is generally fixed at issuance. An inverse relationship 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 relationship; so when one goes up, the other goes down.

## Whatâ€™s the Difference Between Premium Bonds and Discount Bonds?

Posted on July 19, by Robin Russo. A bond will trade at a premium when it offers a coupon interest rate that is higher than the current prevailing interest rates being offered for new bonds. This is because investors want a higher yield and will pay for it. In a sense they are paying it forward to get the higher coupon payment. A bond will trade at a discount when it offers a coupon rate that is lower than prevailing interest rates. Since investors always want a higher yield, they will pay less for a bond with a coupon rate lower than the prevailing rates. So they are buying it at a discount to make up for the lower coupon rate. Said another way, if a bond that is trading on the market is currently priced higher than its original price its par value , it is called a premium bond.

### An Introduction to Duration

The bond price can be calculated using the present value approach. Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. Bond Price: Bond price is the present value of coupon payments and face value paid at maturity. The bond price can be summarized as the sum of the present value of the par value repaid at maturity and the present value of coupon payments. The present value of coupon payments is the present value of an annuity of coupon payments.

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### Understanding Fixed-Income Risk and Return

DuckDuckGo has been a profitable company since without storing or sharing any personal information on people using our search engine. As we like to say, what you search on Convexity can be kind of confusing. In particular it is confusing because it relates closely to duration. Here are the basic definitions of the two:. Duration The sensitivity of a bond s price to changes in interest rates the first derivative of the price with respect to rates. Convexity The sensitivity of a bond s duration to changes in interest rates the second derivative of the price with respect to rates. As User says, the farther out the payments on a bond, the more sensitive they will be to changes in interest rates and thus the higher the duration of a bond. One way to think about this is because each payment in a bond x years out is discounted at the rate of:. Since the interest rate is compounding over so many more time periods, any change in it affects the later payment much more. You can see that the blue line 5 year zero coupon looks a lot steeper than the red line at most normal interest rates. The blue 5 year bond is usually more sensitive to small changes in rates- at any given rate - than the red 2 year bond. In other words, it is a higher duration bond. Generally, the farther out the cash flows, the higher the duration.

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