Discount bond

What Is a Discount Bond?

A discount bond is a type of fixed-income instrument that trades for less than its face value, or par value. This occurs when a bond's coupon rate is lower than the prevailing market interest rates, making the bond's regular interest payments less attractive compared to newer bonds being issued. Consequently, investors demand a lower price to achieve a comparable yield to maturity. The concept of a discount bond falls under the broader category of fixed-income securities, which are debt instruments that provide a stream of predictable payments.

History and Origin

Bonds, as a form of debt, have a history stretching back to antiquity, predating equity markets. The first sovereign bond, for instance, was issued in 1693 by the Bank of England to fund conflict with France. The pricing of bonds, including whether they trade at a discount, premium, or par, has always been inherently tied to prevailing interest rates. The relationship between bond prices and interest rates has been a continuous area of study within financial economics. For example, in the mid-20th century, the U.S. government kept bond yields artificially low through the inflationary period of World War II until 1951. Once these restrictions were lifted, the bond market began to reflect the new inflationary environment, with long-term U.S. bond yields climbing significantly by 1981. The Federal Reserve's actions, particularly concerning interest rate policies, significantly influence the bond market and, by extension, whether bonds trade at a discount.¹⁸,¹⁷,

Key Takeaways

• A discount bond trades below its face value.
• It typically arises when a bond's coupon rate is lower than current market interest rates.
• The investor's return on a discount bond includes both the coupon payments (if any) and the capital gain realized at maturity when the bond pays its full face value.
• The price of a discount bond will gradually increase towards its face value as it approaches its maturity date.¹⁶

Formula and Calculation

The price of a discount bond is determined by calculating the present value of its future cash flows, which consist of its periodic coupon payments and its face value paid at maturity. The formula for the price of a bond is:

Where:

• (P) = Price of the bond
• (C) = Annual coupon payment
• (F) = Face value (par value) of the bond
• (r) = Market discount rate or yield to maturity
• (n) = Number of years to maturity

In the case of a discount bond, the market discount rate ((r)) is higher than the bond's coupon rate ((C/F)), resulting in a present value ((P)) that is less than the face value ((F)).

Interpreting the Discount Bond

When a bond trades at a discount, it signals that its stated coupon rate is less attractive than the returns available on comparable investments in the current market. The deeper the discount, the greater the difference between the bond's coupon rate and the prevailing market rates, or the longer the time until maturity. For investors, a discount bond offers the potential for capital appreciation in addition to any coupon payments. The investor effectively "buys low" and receives the full face value at maturity. Understanding the relationship between a bond's price and its yield to maturity is crucial for interpreting discount bonds, as the yield to maturity accounts for both the coupon payments and the capital gain from the discount.

Hypothetical Example

Consider a company, "Tech Innovations Inc.," which issued a 5-year bond with a face value of $1,000 and an annual coupon rate of 3% five years ago. This means it pays $30 in interest annually. Today, newly issued bonds with a similar credit rating are offering a 5% yield due to a general rise in interest rates.

An investor wants to purchase this Tech Innovations bond. Since the 3% coupon rate is lower than the current 5% market rate, the bond will trade at a discount. Let's calculate its approximate price if there are 5 years remaining until maturity:

• Coupon Payment (C): $30 (3% of $1,000)
• Face Value (F): $1,000
• Market Discount Rate (r): 5% or 0.05
• Years to Maturity (n): 5

Using the bond pricing formula:

For year 1: $\frac{$30}{(1.05)^1} = $28.57$
For year 2: $\frac{$30}{(1.05)^2} = $27.21$
For year 3: $\frac{$30}{(1.05)^3} = $25.92$
For year 4: $\frac{$30}{(1.05)^4} = $24.69$
For year 5 (coupon + face value): $\frac{$30 + $1,000}{(1.05)^{5} = \frac{$1,030}{(1.05)}5} = $807.03$

Adding these present values:
(P = $28.57 + $27.21 + $25.92 + $24.69 + $807.03 = $913.42)

Therefore, the bond would trade at approximately $913.42, a discount from its $1,000 face value. This discount bond provides the new investor with a higher overall return, aligning with the current market's 5% yield.

Practical Applications

Discount bonds are common in various financial contexts, especially within the broader bond market and portfolio management.

• Secondary Market Trading: When existing bonds are traded on the secondary market, their prices fluctuate based on prevailing interest rates. If interest rates rise after a bond is issued, its price will fall below par, making it a discount bond. Conversely, if interest rates fall, the bond may trade at a premium.
• Zero-Coupon Bonds: All zero-coupon bonds are inherently discount bonds. These bonds do not pay periodic interest; instead, they are sold at a deep discount to their face value and mature at par, with the investor's return being the difference between the purchase price and the face value.¹⁵
• Interest Rate Expectations: The presence of many discount bonds in the market can signal a period of rising interest rates, as investors demand higher yields for their capital. This is closely related to the concept of the yield curve. For instance, an inverted yield curve, where short-term rates are higher than long-term rates, has historically preceded U.S. recessions.¹⁴,¹³,¹²,¹¹ This phenomenon reflects market expectations about future interest rate movements and economic conditions.
• Regulatory Framework: The pricing and trading of bonds, including discount bonds, are subject to regulatory oversight. The U.S. Securities and Exchange Commission (SEC) plays a significant role in establishing rules and regulations for the bond markets to ensure transparency and fair practices. For example, the SEC has worked to improve price transparency in the corporate bond market through systems like TRACE (Trade Reporting and Compliance Engine).¹⁰,⁹,⁸,⁷,⁶

Limitations and Criticisms

While discount bonds offer opportunities for capital appreciation, they also come with certain considerations and potential drawbacks:

• Interest Rate Risk: The price of a discount bond is inversely related to interest rate movements. If market interest rates continue to rise after an investor purchases a discount bond, the bond's price will fall further, leading to a potential capital loss if sold before maturity. Bonds with longer duration are generally more sensitive to interest rate changes.⁵,⁴
• Reinvestment Risk: For coupon-paying discount bonds, the lower coupon payments mean less cash flow available for reinvestment, especially in an environment of rising interest rates. This can impact the overall return of a fixed-income portfolio.
• Liquidity: Some discount bonds, especially those issued by smaller entities or with unusual features, might have lower liquidity in the secondary market. This could make it challenging to sell the bond quickly at a fair price before its maturity.
• Credit Risk: As with any bond, a discount bond carries credit risk, which is the risk that the issuer may default on its payments. A bond trading at a significant discount might sometimes signal higher perceived credit risk by the market, rather than just higher market interest rates. Investors must assess the issuer's financial health carefully.

Discount Bond vs. Premium Bond

The primary difference between a discount bond and a premium bond lies in their trading price relative to their face value and the underlying reason for that price.

While a discount bond offers a capital gain at maturity, a premium bond will result in a capital loss at maturity because the investor paid more than the face value. Both types of bonds will converge to their face value as they approach maturity, a phenomenon known as "pull to par."³

FAQs

Why would an investor buy a discount bond?

An investor buys a discount bond to earn a yield higher than the bond's stated coupon rate, due to the built-in capital appreciation. When the bond matures, the investor receives the full par value, which is higher than the purchase price, in addition to any coupon payments received. This capital gain contributes to the overall return on investment.

Are zero-coupon bonds always discount bonds?

Yes, zero-coupon bonds are always discount bonds. They do not pay periodic interest; instead, they are sold at a price significantly below their face value and mature at their full par value. The investor's entire return comes from the difference between the discounted purchase price and the face value received at maturity.²

How does a change in interest rates affect a discount bond?

If market interest rates rise, the price of an existing discount bond will fall further, increasing its discount. Conversely, if market interest rates fall, the price of a discount bond will increase, reducing its discount and potentially causing it to trade at par or even a premium if rates drop significantly below its coupon. This inverse relationship between bond prices and interest rates is a fundamental concept in bond valuation.

What is "pull to par" for a discount bond?

"Pull to par" refers to the tendency of a bond's price to gradually move towards its face value as it approaches its maturity date. For a discount bond, this means its price will incrementally increase over time, assuming market interest rates remain constant, until it reaches its par value at maturity. This effect accelerates as the bond gets closer to maturity.¹