What Is Duration (Horizon) Risk?

An investment with a short hold time can be less risky than the same investment with a longer hold time. This is mainly due to more factors and unknowns that can be introduced within a longer time frame.

Does duration work the same? It may sound as though duration is synonymous with investment holding time. But there is more to it, specifically when speaking about bonds.

Bonds and Interest Rates

Before we get into duration, let’s refresh on some bond basics. A bond pays out a coupon at regular intervals. The last payment (or terminal cash flow) is the return of the investment (i.e., principal). A zero-coupon bond is different since it has only one cash flow, the terminal cash flow.

The terminal cash flow also marks the time-to-maturity of the bond. A 5-year bond pays its last cash flow in five years, which is also its time-to-maturity.

A bond’s price is inversely related to interest rates. As interest rates rise, the bond price will fall and vice versa. This concept is captured in duration.

Duration Risk Defined

There are several aspects to duration. One is that duration tells an investor how long it will take a bond to pay out all of its cash flows. A 3-year bond will take three years to pay out all of its cash flows.

There are two main types of duration calculations:

• Original duration (also called Macaulay duration) — expressed in years. It represents the weighted average time to cash flow receipt.
  
  
• Modified duration — expressed in units. This is the most common duration calculation method. It shows the sensitivity of a bond’s price to changes in yields. In this case, duration tells you how a bond’s price will react to a 1% change in interest rates.

Let’s look at a couple of examples. A 5-year bond portfolio will lose 5% of its value for every 1% increase in interest rates. When interest rates are declining, a longer duration is preferred. When interest rates are rising, a shorter duration is preferred.

Another example is a bond with a duration of 3. This means for every 1% increase in yields, the bond’s price will fall by 3%.

Additionally, the larger the coupon payment, the lower the bond's duration. A high coupon means you are getting your investment returned to you sooner. Therefore, your asset is less sensitive to duration since it has a short time frame of exposure to the market.

Higher duration means a bond’s price is more sensitive to rate changes. We can sum it up like this:

Lower coupon = higher duration

Higher coupon = lower duration

Duration risk happens when an investor buys a bond and then rates increase, reducing the bond’s value. As an example, if an investor buys a 3-year bond that pays 1.5% and rates go up in the second year, their bond will lose value. Additionally, there will be less demand for the bond.

Investors can mitigate duration risk by choosing bonds with lower duration, which means those with durations of a few months or just a few years. Investors choosing bonds with a low duration are choosing to decrease their time of exposure in the market.

Duration is a linear estimate for a bond's price change based on yield changes. If plotted on a graph with bond prices on the y-axis and yields (i.e., interest rates) on the x-axis, duration forms a 45-degree line (blue) that slopes from the top left to bottom right. 

There is a one-to-one relation between bond prices and yields. But in practice, things are different (i.e., red line).

Convexity

Unlike duration, the actual price-yield line is curved (i.e., convexed). This is the red line in the above image. It has a similar slope to the duration line. The duration line is actually tangent to the price-yield line. Because the price-yield line is curved, depending on where you are on the line, bond prices can change faster than rates and vice versa. 

In the image, you can see in the upper left that bond prices change faster than interest rates on the price-yield line. Also depicted in the graph, unlike duration, there isn’t a linear relationship in the price-yield line.

Because convexity is not fixed, the price-yield curve varies across different bonds. You can think of duration as the textbook definition, whereas the convexity of the price-yield line is reality.

Duration risk is certainly a concern for bondholders, especially investors considering bonds with a longer/higher duration.