# What is a Duration?

Duration measures how the prices of bonds or other fixed-income investments may be affected by changes in interest rates.

## 🤔 Understanding duration

Duration is useful for investors because it helps you understand the interest rate risk of your investment. It measures both the sensitivity to interest rate changes and the length of time it takes for you to recoup the bond's current price, taking into account all future coupon payments and value at maturity. Two factors generally affect the duration: The time to maturity (length of time before the bond ends) and the coupon rate (yield you receive). In general, the longer it takes you to recoup the bond's price, the more sensitive your investment is to changing interest rates. A good rule of thumb is that the longer the time to maturity, the higher the duration — the more sensitive the bond’s value is to interest rate changes.

Let's take a look at fictitious bonds issued by the fictitious Al's Corporation and Bob's Corporation. For this example, let’s say they have a similar price but a different duration. So, how will a change in the interest rate affect them? The current price for both bonds is $100, but it will take you three years to make back the cost of Al's bonds (that’s the duration), while it will take you five years with Bob's. Typically, with every 1% change in interest rates (up or down), the price will also change around 1% in the opposite direction, for each year of duration. So, if interest rates go up 1%, Al's bond price will drop about 3% (1% x 3 years) to $97, and Bob's will lose around 5% (1% x 5 years) to $95. Bob's bond is more sensitive to interest rate changes because of the longer duration.

## Takeaway

Duration is like a pressure gauge helping you measure sensitivity to changes...

Just as a pressure gauge tells you something about how the fluid or gas inside a tank may respond to external conditions, duration helps you understand how sensitive your investment is to interest rate fluctuations.

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## What is the duration of a portfolio?

A bond portfolio is simply a basket of fixed income securities that are grouped to increase diversification. It’s very similar to a stock portfolio. You may also see the terms portfolio and fund used interchangeably, so don’t let that confuse you.

The duration of a bond portfolio helps an investor understand its sensitivity to interest rate changes, as a whole. The duration of a portfolio and duration of an individual bond are generally used for the same reasons –- Understanding the sensitivity to interest rate changes and knowing how long it will take to recoup the price of the investment.

It also helps you compare different bond funds to see which might be better suited for your goals. As an example, perhaps you expect interest rates to rise soon. In this case, you may want to choose a fund with a lower duration and less interest rate risk.

## How does duration differ from maturity?

Duration and maturity are sometimes confused because they can both be measured in units of time.

But here’s the difference:

Maturity measures how long before a bond matures. If there is a 30-year bond that was issued ten years ago, it has a maturity of 20 years. It's is a linear measurement of time.

Duration, on the other hand, measures a bond's sensitivity to interest rate changes as well as the time it would take to recoup the current price of the bond. The duration can change as interest rates change (whereas maturity would not change in this circumstance). So a bond's duration today could be three years, but if interest rates change tomorrow, the bond's duration will also change.

## How does duration differ from convexity?

Duration measures the sensitivity to interest rates in a linear (straight line) way. It can be an excellent way to estimate that relationship — but the relationship between bond price and bond yield is curved.

Convexity measures that curvature. Professional investors typically use convexity as a risk management tool. It helps them better manage a portfolio’s exposure to interest rate changes.

## How does duration work?

Duration helps you know the effects of interest rates on your investment from two different angles. You understand it in terms of sensitivity and in time. Both aspects are valuable when you want to understand your interest rate risk. As a rule of thumb, if a bond has a higher duration, then the price will drop or rise more when interest rates change.

There are numerous factors that can heavily impact the duration.

- Time to maturity: This is the amount of time before a bond or other debt instrument matures or ends. In general, a bond maturing sooner, say one or two years, would allow you to recoup the cost of the bond relatively quickly. That means it has a short duration and less interest rate risk.
- Coupon rate: This is the interest rate paid to you by the company that issued the bond. Usually, the higher the coupon rate, the faster you will be able to recoup the price of the bond. That means you will have a lower duration and less exposure to interest rate risk.

## What is the Macauley duration?

Macaulay duration helps investors find the present value of a bond’s future coupon payments and value at maturity. In other words, how long does it take you to recoup the price of the bond? It does this by taking the weighted average term to maturity of the cash flow of the bonds.

In the equation above: t= the respective time period C= periodic coupon payment (usually semiannual) y= periodic yield n= total number of periods (example: 3 year maturity, semiannual payments = 6 periods) M = maturity value Current bond price = the present value of cash flows

If you like Greek, then you loved that! But it basically boils down to:

Macaulay Duration = the present value of a bond’s cash flows, weighted by the time to receive them and divided by its current market value.

Macaulay duration example calculation

Let’s look at a bond with a $100 face value paying a 6% coupon and maturing in 2 years. The interest rate is 4% (compounding semi-annually), the coupon payment is paid twice per year, and the principal is paid on the final payment. Since the bond matures in 2 years and pays a semi-annual coupon, there will be four periods. To get started, you need to calculate what the cash flows will look like during the next 2 years:

Period 1: $3 Period 2: $3 Period 3: $3 Period 4: $103

Now we need to apply a discount factor for each period. You calculate this as 1 / (1 + r)n where r is the interest rate, and n is the period. The interest rate is compounding semi-annually so 4% / 2 = 2%. Now you can calculate the discount factors.

Period 1: 1 / (1+.02)^1 = .9804 Period 2: 1 / (1+.02)^2 = .9612 Period 3: 1 / (1+.02)^3 = .9423 Period 4: 1 / (1+.02)^4 = .9238

To find the present value of the bond’s cash flows, you multiply the period number by that period’s cash flow and then by its discount factor. Present value = period x period cash flow x period discount factor

Period 1: 1 x $3 x .9804 = $2.94 Period 2: 2 x $3 x .9612 = $5.77 Period 3: 3 x $3 x .9423 = $8.48 Period 4: 4 x $103 x .9238 = $380.62

This gives you $397.81 as the numerator in the Macaulay Duration.

Next, you calculate the current bond price by adding up the present value of the cash flows for each period. This calculation gives you the denominator.

Period 1: $3 / (1+.02)^1 = $2.94 Period 2: $3 / (1+.02)^2 = $2.88 Period 3: $3 / (1+.02)^3 = $2.83 Period 4: $103 / (1+.02)^4 = $95.16

This gives you a total of $103.81 for the denominator.

Macaulay Duration = $397.81 / $103.81 = 3.83 years.

Remember that everything is being paid and compounded semi-annually. In this example, we calculated for four periods. So when you divide the Macaulay duration by two, you’ll get 1.91 years. The duration is less than the time to maturity of 2 years. When a bond pays a coupon, the duration will be shorter than the time to maturity.

## What is a modified duration?

Modified duration measures the change in the value of a security based on changes in interest rates. A general rule is that with every 1% change in interest rates (up or down), the price will also change around 1% in the opposite direction, for each year of duration. For example, if a bond has a value of $100, a duration of 4 years, and rates rise 1%, then the price would decrease by 4% to $96 (1% x 4 years).

Modified duration example calculation

Modified duration builds on Macaulay duration, which is the present value of a bond's future coupon payments and value at maturity. You use a modified duration to understand how a 1% change in interest rates will affect the bond price.

In this equation: YTM = yield to maturity n = number of coupon periods per year

For example, a bond has a Macaulay Duration of 2.5 years, a current yield of 5%, and coupons are paid once per year. How would a 1% rise in interest rates affect this bond? The calculation would look something like:

2.5 / (1.05/1) = 2.38%

This means that if interest rates rise 1%, then the bond’s price will drop approximately 2.38%.

## What are duration strategies?

There are two types of duration strategies an investor typically follows – long duration and short duration. If you use a long-duration approach, you are likely buying bonds with a long time to maturity, giving you higher exposure to interest rate risks. You might use this strategy when interest rates are moving lower — like during a recession.

You could use a short-duration strategy if you believe interest rates will rise in the short term. With a short-duration approach, you might buy bonds with a short time to maturity and a shorter duration. Each strategy depends on your view of the interest rate environment.

You can never reliably predict if interest rates will rise or fall. Carefully consider your investment objectives. All investments carry risk.

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