Discount yield: Meaning, Criticisms & Real-World Uses

What Is Discount Yield?

Discount yield is a method of calculating the return on a debt instrument that is sold at a discount to its face value and pays no explicit interest until its maturity. This calculation, commonly applied in fixed income markets, expresses the investor's return as a percentage of the face value, rather than the purchase price. It is most frequently used for Treasury bills, commercial paper, and short-term municipal notes. The discount yield represents the annualized percentage return an investor would earn if they bought the security at a discount and held it until it matures, receiving the full face value. The term is central to understanding the pricing of short-term, zero-coupon instruments.

History and Origin

The concept of a discount basis for short-term government debt instruments, particularly Treasury bills, emerged as a practical method for issuing and trading these securities. Unlike longer-term bonds that pay periodic interest rate coupons, Treasury bills were designed to be simple, issued at a price lower than their face value, with the difference constituting the investor's return. In the United States, bidding in Treasury bill auctions transitioned to a bank discount yield basis, rather than a price basis, to align with existing market pricing conventions. This change was a significant development in the U.S. financial system, establishing a standardized way for market participants to evaluate these short-term instruments.⁵ This streamlined the auction process and made it easier for investors to compare returns on different bills.

Key Takeaways

Discount yield calculates the return on a short-term debt instrument sold at a discount, such as Treasury bills.
It expresses the return as a percentage of the face value, not the purchase price.
The calculation typically assumes a 360-day year, which simplifies computations but affects comparability.
Discount yield does not account for compounding interest.
It is a key measure for evaluating the return on money market instruments.

Formula and Calculation

The formula for calculating the discount yield is:

\text{Discount Yield} = \left( \frac{\text{Face Value} - \text{Purchase Price}}{\text{Face Value}} \right) \times \left( \frac{360}{\text{Days to Maturity}} \right)

Where:

Face Value: The par value of the security, which is the amount repaid at maturity.
Purchase Price: The price at which the investor buys the security.
360: The assumed number of days in a year for this calculation (conventionally used in money markets).
Days to Maturity: The number of days remaining until the security matures.

For example, if an investor purchases a $10,000 Treasury bill for $9,850 that matures in 90 days, the calculation would be:

\text{Discount Yield} = \left( \frac{\$10,000 - \$9,850}{\$10,000} \right) \times \left( \frac{360}{90} \right)

\text{Discount Yield} = \left( \frac{\$150}{\$10,000} \right) \times 4

\text{Discount Yield} = 0.015 \times 4 = 0.06 \text{ or } 6\%

This formula shows how the difference between the purchase price and face value, known as the discount, is annualized over a 360-day year.⁴

Interpreting the Discount Yield

The discount yield provides a straightforward measure of return for short-term, zero-coupon bond-like instruments. A higher discount yield implies a greater return for the investor on a particular security. For instance, a 5% discount yield on a Treasury bill means that for every $100 of face value, the investor effectively earns a 5% annualized return based on the discount.

Investors use this yield to compare various short-term debt instruments. Since these securities are often considered proxies for the risk-free rate, their discount yields are closely watched as indicators of short-term market expectations and liquidity conditions. Changes in discount yields can reflect shifts in monetary policy or broader market sentiment regarding short-term interest rates. When evaluating these figures, it is crucial to remember the underlying conventions, particularly the 360-day year assumption.

Hypothetical Example

Consider an investor, Sarah, who is looking to invest in a short-term U.S. government security. She finds a 180-day Treasury bill with a face value of $5,000 being offered at a purchase price of $4,925. To determine the discount yield:

Calculate the discount:
Discount = Face Value - Purchase Price
Discount = $5,000 - $4,925 = $75
Calculate the discount yield:
Discount Yield = (Discount / Face Value) × (360 / Days to Maturity)
Discount Yield = ($75 / $5,000) × (360 / 180)
Discount Yield = 0.015 × 2
Discount Yield = 0.03 or 3%

So, the discount yield for Sarah's Treasury bill is 3%. This means if she holds the bill until maturity, her annualized return on a discount basis would be 3%. This simple calculation helps her quickly assess the potential return from this investment analysis.

Practical Applications

Discount yield is widely used in the bond market, particularly for pricing and quoting Treasury bills and other money market instruments. These short-term securities are auctioned regularly by governments to manage their financing needs. The discount yield determined in the primary market auctions then influences trading in the secondary market.

For instance, the U.S. Department of the Treasury issues various maturities of Treasury bills, and their yields are tracked by financial institutions and investors. The Federal Reserve also publishes selected interest rates, including those for Treasury bills, in its H.15 statistical release, which is a key data source for market participants. Th³is data is crucial for assessing market liquidity and for informing investment decisions involving short-term government debt.

Limitations and Criticisms

While straightforward, discount yield has notable limitations, primarily stemming from its calculation methodology. One major criticism is the use of a 360-day year instead of a 365-day year. This convention, common in money markets, can lead to a slightly misrepresented annualized yield when comparing it to other investments that use a 365-day basis, such as corporate bonds or notes. This discrepancy makes direct comparisons challenging and can lead to misunderstandings if not properly adjusted.

F²urthermore, the discount yield does not account for the concept of compounding interest, as it is a simple interest calculation based on the face value rather than the actual purchase price. This means it may understate the true annualized return, especially for instruments with longer maturities within the "short-term" category. For comprehensive investment analysis, particularly when evaluating complex market dynamics or the impact of monetary policy, a simple discount yield may not capture the full picture. Broader market forces, such as changes in term premiums and short-rate expectations, can significantly affect bond yields, and these are not directly reflected in the basic discount yield calculation.

#¹# Discount Yield vs. Bond Equivalent Yield

The distinction between discount yield and bond equivalent yield (BEY) is crucial for comparing investment returns accurately. Discount yield, as discussed, is based on the face value of the security and uses a 360-day year. It expresses the return as a discount from the face value.

In contrast, the bond equivalent yield is an annualized yield that makes the return on a discount bond more comparable to the yield on a coupon-bearing bond. BEY uses the actual purchase price in its calculation, not the face value, and it typically assumes a 365-day year. This provides a more accurate representation of the investment's return and allows for a more direct comparison with other debt instruments. For example, a 90-day Treasury bill with a 4% discount yield would have a slightly higher bond equivalent yield due to the different base and day count convention, as the BEY reflects the yield relative to the price paid, not the face value.

FAQs

What types of securities commonly use discount yield?

Discount yield is primarily used for short-term, zero-coupon securities like Treasury bills, commercial paper, and some municipal notes. These instruments are sold at a discount and mature at their face value, with the difference representing the investor's interest.

Why does discount yield use a 360-day year?

The use of a 360-day year is a long-standing convention in money markets, simplifying calculations for short-term instruments. While convenient, it makes the discount yield less directly comparable to yields that are annualized using a 365-day year.

Is discount yield a true annualized return?

No, the discount yield is not a true annualized return in the same way that yield to maturity or bond equivalent yield are for other securities. It is a simple interest calculation based on the security's face value and does not account for compounding interest or the actual 365 days in a calendar year, which can lead to slight differences when comparing various investments.

How does discount yield relate to the concept of interest?

For discount securities, the "interest" an investor earns is the difference between the purchase price and the higher face value received at maturity. The discount yield expresses this implicit interest as an annualized percentage of the face value.

Can discount yield be negative?

The discount yield cannot be negative. If the purchase price were higher than the face value, implying a negative return, the instrument would not be sold on a discount basis. In practice, short-term debt instruments like Treasury bills are always issued at a discount (or occasionally at par) to ensure a positive yield for investors.