**Low coupon bonds are more volatile because the face value received at the maturity date as a lump sum is a big chunk of the total bond’s value. Interest payments along the way are not as significant. This means changes in interest rates will have a greater impact on the sum of the present value of the bond’s cash flows.**

Still confused? Keep reading.

If you’re tired of everyone telling you a lower coupon bond is more volatile because it is more sensitive to interest rate changes, but not *why *is that—this is for you.

I spent 3 days scanning the ends of the earth in search of the truth (books, blogs, forums). The answer is simple, but you need to understand how bonds work, and the intricacies of the time value of money.

Ready? Let’s dive in:

**Table of Contents**

## What are Low Coupon Bonds

**A bond** **is a fixed income debt security where a borrower pays a lender their principal plus interest on a loan.** The borrower is generally a government or corporation that wants to raise money.

Bonds are a type of fixed-income investment that complement stocks and other more aggressive investments in a portfolio.

**A low-coupon bond pays a low coupon (interest) rate.** The coupon rate is the fixed interest that the issuer pays the bondholder along the way until the bond’s maturity date, at which point the issuer pays back the face value of the loan to the bondholder.

Here are 6 key concepts you must understand about bonds:

**Face value**: Also called principal, or par value, it is the notional amount used to compute interest payments. It is repaid at maturity to the investor. It is a static value determined at the time of issuance, unlike market value.**Price**: The current market price of a bond is the present value of all its cash flows, agreed upon by buyers and sellers in the open market. It is a percentage of the bond’s original principal value.**Coupon**: The amount of annual interest paid by the issuer to the bondholder. It is a fixed dollar amount based on the par value, not a varying percentage like the yield.**Yield**: The expected yield-to-maturity (YTM) is how much the money invested will earn if the investor holds the bond until maturity. In other words, it is the coupon the investor receives*relative*to the price he paid for the bond. The higher the bond price, the lower the bond yield. It incorporates the credit risk (likelihood of default) and the interest rate risk (sensitivity to interest rate fluctuations). It’s the Internal Rate of Return of the investment—the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond.**Maturity**: This is when the bond expires. It’s a*linear*measure of the years until the repayment of the principal happens. It doesn’t change with interest rates, unlike the duration.**Duration**: The duration measures the sensitivity of bond prices to changes in interest rates. The higher the duration of a bond, the more sensitive it is to an interest rate change and, therefore, the more volatile.*Don’t confuse this with the bond’s maturity.*This is a key concept we’ll expand on further down below.

For example, a bond with a $1,000 *face value* and an interest rate of 5% has a *coupon *of $50, paid every year.

A thousand dollars is the *market price* of the bond when it is first issued. Additionally, the coupon rate is also equal to the YTM at that moment. Over time however, both will change along with market conditions and investors’ sentiment.

If the bond price rises to $1,250 (trading **at a premium**), the effective yield drops to 50/1,250=4%.

The price can also fall and trade **at a discount**. An $800 price would imply a 50/800=6.25% yield. This means buyers demand a return (yield) *higher *than what the bond pays (coupon *rate*).

*When do buyers demand higher returns?*

When newly issued bonds pay more than the already existing bonds.

This is why **bond prices have an inverse relationship with interest rates.** Rising interest rates make bond prices fall, while declining interest rates make bond prices rise.

It is very common for low-coupon bonds to trade at a discount from the par value, especially zero-coupon bonds:

### Zero Coupon Bonds

**A zero coupon bond does not pay interest. The only cash payment the investor receives is the face value of the bond on the maturity date.**

Thus, it will take the entire length of the bond for the investor to recoup their full original investment.

Now, you may be wondering:

A creditworthy company or government with a low risk of failing to meet their debt obligations generally pays lower interest on their bonds for the lower risk of default.

With that in mind, how are low-coupon bonds riskier if AAA-rated entities issue them?

You’re mixing up two different concepts:

- Risk of default (or
**credit risk**)—which is low for bonds from these entities. They’re unlikely to miss the promised timely payments to you as an investor. - The
**volatility**(risk) of the*price*of the bond—which is high. Why?

Let’s see:

## Understanding Bond Volatility

**Bond duration tells you how much a bond’s price changes if overall market interest rates move.**

Although *duration *is expressed in terms of years, it’s not the same thing as a bond’s *maturity *date.

It measures **interest rate risk**, while a bond’s *maturity *is the amount of time until the repayment of the principal is due. The greater the duration, the greater the interest rate risk (or reward) of bond prices.

Duration is the time the investor will have to wait to recoup her original investment, or the weighted average time to receive all the bond’s cash flows.

Now, what determines bond duration?

The 2 key factors are the **time to maturity** and the bond’s **coupon rate**:

### #1) Time to Maturity

As we’ve seen, bond duration is expressed in terms of years, but it’s not the same as maturity. That said, the maturity date of a bond is one of the *key* components in calculating duration.

Let’s see why:

When **interest rates rise**, the **price **of an *existing ***bond decreases** because a *new *bond will have a higher coupon rate, making it more attractive to investors.

Lower bond prices result in higher yields.

This happens because less demand will push the price down until it reaches an *equilibrium *price—when the yield-to-maturity of *existing* bonds is in line with the coupon rates being paid by *new *bonds.

While both a 1-year and a 10-year bond will fall in value, the 1-year bond won’t fall as much. Why? Because within one year, the investor will receive the principal back.

At that point in time, he can reinvest into a new bond with a higher rate of interest. For the 10-year bond though? It’s **locked in** at the lower rate of interest until it matures or is sold.

This is why **the longer the maturity, the higher the duration, and the greater the interest rate risk**.

The shorter-maturity bond has a lower duration and less risk.

But **volatility (risk) goes both ways**, not just *down*.

When interest rates fall, long-term bonds **rise more** in price for the same reasons. When the 1-year bond expires, the investor can only buy bonds with a lower return.

The long-term bond has a *higher* interest rate that’s locked in for the next 20 years. Thus, its market value will increase further than the 1-year bond.

In conclusion, shorter maturities repay investors’ capital faster, which means less **exposure **to market conditions. As the money is returned, it can be reinvested earlier, for better or for worse.

### #2) Coupon Rate

Now, how does the coupon rate affect bond prices?

If you have two identical bonds except for their coupon rates, **the bond with the higher coupon rate will pay back its original costs** faster due to higher cash flows in the form of interest payments.

Thus, the higher the coupon rate, the lower the duration, and the lower the interest rate risk.

**For a zero-coupon bond, the time to maturity is equal to the duration.** Why? Because the only cash flow the investor receives is the principal repayment at *maturity*. And *duration *is the average time it takes to get his money back.

**When the bond has a coupon,** however,** the duration will always be lower than the maturity date.** The larger the coupon, the shorter the duration becomes.

Given that duration measures interest rate risk, this means:

**Bonds with low coupon rates are more sensitive to changes in interest rates than similar maturity bonds with high coupon rates.**

Here’s a further breakdown of why:

#### Why Are Low Coupon Bonds More Volatile Than High Coupon Bonds

Again, as we’ve seen:

- When interest rates
*rise*, the value of a bond*decreases* - When interest rates
*fall*, the value of a bond*increases*.

Low-coupon bonds have a lower current yield, so they’re more sensitive to changes in interest rates than high-coupon bonds. Why?

Because when the bond has a lower coupon, **its value is more dependent on the principal the investor receives at maturity.** In other words, it takes longer for a bondholder to get back its capital when the coupon rate is low.

The value of any asset is the sum of the present value of its future cash flows, right? Bonds are no different.

The cash flows a bond generates are the **interest payments** over time and the **face value** upon maturity.

Now, the price sensitivity of a bond to a given change in interest rates depends on the timing of these cash flows.

Interest rates affect the present value of a cash flow received in the *near *future less dramatically because it is discounted over a shorter period.

A cash flow in the *distant *future however, is more affected.

Given the same discount rate, the further down in time a cash flow is, the smaller its present value is. The interest rate used to discount it to the present has a greater impact.

*What does this mean?*

The par value is the most sensitive cash flow to interest rate fluctuations because it is the furthest down the line.

At the same time, the lower the coupon of a bond, the more likely it was sold at a discount and the investor has to wait until maturity to make money. This means:

**The value of a low-coupon bond is strongly dependent on its maturity value.**

Get it? Because this maturity value is the furthest down in time, it’s more sensitive (volatile) when it is discounted to the present using the current market interest rates.

For a high-coupon bond, however?

It has higher cash flows in the beginning in the form of interest payments—which **reduces its dependency on the maturity value**.

The interest you receive along the way is a more *significant *component of the total value of the bond. The par value will still fluctuate a lot with interest rate changes. However, the interest received over time makes it so the total sum that makes up the price of the bond *today *isn’t as affected.

**This is why a lower coupon bond’s duration is higher than that of a higher coupon bond.**

Another way to think about this:

Bonds with a higher coupon payment allow investors to **recoup **their initial investment costs *sooner*, reducing their exposure to interest rate risk.

## The Bottom Line (FAQs)

### Are lower coupon bonds more risky?

Yes and no. The companies or governments that issue them usually have lower default risk, so they offer lower returns as well. However, they’re more volatile. Meaning their price fluctuates more in percentage. This happens because the single most significant component of a low-coupon bond’s price is the final principal payment. Since it’s further in the future, interest rate changes have a bigger impact when you discount it to the present. With a high-coupon bond, the interest payments mitigate this volatility because they play a more significant role in the value of the bond, and are not as impacted when discounted to the present.

### Why are zero coupon bonds the most volatile?

Because you will only receive the full amount of your investment in a single lump sum cash flow when the bond matures. Thus, it is subject to interest rate fluctuations that affect its present value. There are no interest payments along the way to reduce the average time it takes you to recover the present value of the investment. This is why a zero-coupon bond trades at a deep discount and its duration is equal to its maturity.

### Why do low coupon bonds have higher duration?

All else equal bond price volatility is greater for bonds with longer maturities and lower coupons. Bonds with higher coupon rates—because they pay higher cash flows upfront—are less sensitive to interest rate changes than otherwise identical bonds with lower coupon rates—because most of the capital received is the lump sum at the end, which is more impacted when discounting back to the present.

Have any further questions? Feedback? Leave them in the comments below and I’ll get back to you as soon as possible.