# Relationship between ytm and duration

### Duration vs. Maturity and Why the Difference Matters

I've been talking to a lot of investors about how to prepare a portfolio for rising rates lately, and the same buzzwords keep popping up in these. The terms “duration” and “maturity” differ in the world of finance from See the diagram below to understand the relationship between the If you plug in all the numbers and calculate the YTM when n=20 (10 years later). An interesting property of Macaulay duration is revealed by letting N, the number of periods to maturity, get large and approach infinity. In equation , the.

Average of Time Payments are Received Duration can be thought of as the weighted average of when the bondholder receives payment.

## What’s the Difference Between Duration and Maturity?

Check that the way the weights react is consistent with the relationships on the previous slide. 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 also change the coupon rate and see the effect on the 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?

**Investopedia Video: The Basics Of Bond Duration**

However, it is customary to first calculate what is called Maucaulay Duration, and then use this to calculate Modified Duration. Using Duration Specifically, the steps in using duration are: The Macaulay Duration is: These are weights and sum to 1. Duration cannot exceed the number of periods to maturity of the bond.

### az-links.info: Learn Finance Fast - Duration

An example of this would be a movie with perhaps a duration of two hours or a roller coaster with a duration of one and a half minutes. A year Treasury Bond, as the name implies, matures or pays back its face value 30 years from its initial date.

Investors are not obligated to hold the bond for the entire period as they have the option of being sold within the secondary market. Individual investors or portfolio managers can buy or sell bond holdings to adjust the average maturity of the portfolio. Why would they want to do that? Generally speaking, the further out the maturity, the wider the potential price swings of the market value of the bond.

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

That is a very important concept to bond investors, but it is a general concept as compared to an attempt at better detailing the relationship when we cover duration. Keep in mind bond investors recognize two types of return, the first is the interest payment income which may be paid quarterly, semi-annually or even annually. If investing in a fixed-income mutual fund, interest payments are in the form of mutual fund dividends and may be paid monthly.

Those payment cycles will play a role when duration is covered. The second type of return is from price changes of the bond itself why maturity matters.

Bonds are often quoted with two yields. This refers to the annual interest payable as a percent of the original face or par value. This quote takes into account the amount of years left until the bond matures and the impact the market and secondary trading of the original bond has had on the investors final total return. The formula for YTM takes several things into account: Original Face or Par Value F 3. Price bond was purchased P 4.

The Yield to Maturity is 7. Other than a few reasons that would cause a bond to end its existence prior to maturity, the life span of a bond tells an investor how long the bond may be exposed to risk — the primary one being the erosion of its value purchasing power when inflation is present higher bond price, and a lower return than the coupon rate as in example 2 on YTM.

Complexity increases in the details of various ways duration is calculated. We will quickly outline the calculations but then then circle back and focus on the broader concept and why investors look at duration in conjunction with maturity.

Macaulay duration, modified duration and effective duration are three types of duration calculations. Investors will more than likely run across effective duration numbers.