Amortized cut off yield

What Is Amortized Cut-Off Yield?

Amortized cut-off yield refers to the specific yield determined in a Treasury bills auction that serves as the highest accepted yield for successful competitive bids, and it implicitly incorporates the concept of the discount on these instruments being "amortized" over their short lifespan. This term falls under the broader category of Fixed-income securities and is particularly relevant in government debt markets. When governments, such as the U.S. Treasury, issue short-term debt like Treasury bills, they do so through an auction process where investors bid on a yield basis. The amortized cut-off yield signifies the rate at which the bills are effectively awarded, and since T-bills are sold at a discount to their face value, the "amortized" aspect refers to the accounting treatment where this discount is recognized as income over the instrument's life until maturity.

History and Origin

The practice of auctioning U.S. Treasury bills dates back to their introduction in 1929¹⁵. These regular auctions were established to help finance government operations, particularly during the Great Depression. Initially, bids were often made on a price basis, but a significant modification in 1983 shifted the process to receive bids on a yield basis, commonly known as the bank discount basis for bills¹⁴.

The concept of a "cut-off yield" emerged as a critical element of these auctions. It represents the highest yield that the Treasury accepts for competitive bids, effectively determining the rate for all successful bidders in a uniform-price auction format¹², ¹³. The U.S. Treasury implemented a single-price auction format, where all successful bidders receive the same yield as the highest accepted bid, starting in 1992 for certain securities and extending to all auction offerings by October 1998¹¹. This evolution aimed to promote competitive bidding and reduce borrowing costs for the government¹⁰. The "amortized" aspect is not a separate historical event but rather a descriptive term derived from the accounting principle of recognizing the discount on these instruments as interest income over time, mirroring the gradual increase in value from the purchase price to the face value at maturity.

Key Takeaways

• The amortized cut-off yield is the highest yield accepted by the issuer in an auction for discount instruments like Treasury bills.
• It serves as the uniform yield at which all successful competitive and non-competitive bids are awarded the securities.
• The "amortized" component highlights that the discount embedded in the instrument, derived from this yield, is recognized as income over its holding period until maturity.
• This yield is crucial for determining the effective cost of borrowing for the issuing government and the return for investors.
• Amortized cut-off yield is primarily associated with short-term, zero-coupon financial instruments sold at a discount.

Formula and Calculation

While "amortized cut-off yield" itself is a result of an auction process rather than a direct calculation, the cut-off yield determined in the auction is fundamentally a discount rate. For a Treasury bill, the purchase price is determined based on the yield. The yield can then be converted into a price. The discount yield formula, which is closely related to how Treasury bills are quoted, is:

[
\text{Discount Yield} = \frac{\text{Face Value} - \text{Purchase Price}}{\text{Face Value}} \times \frac{360}{\text{Days to Maturity}}
]

Where:

• Face Value: The par value of the security, typically $1,000 for Treasury bills.
• Purchase Price: The price at which the investor acquires the security, which is at a discount to face value.
• Days to Maturity: The number of days remaining until the security matures.

Conversely, to find the purchase price given a specific discount yield (like the cut-off yield):

[
\text{Purchase Price} = \text{Face Value} \times \left(1 - \frac{\text{Discount Yield} \times \text{Days to Maturity}}{360}\right)
]

This formula uses a 360-day year convention for simplification, common in money markets⁹. The "amortized" aspect refers to the accounting treatment where the difference between the purchase price and the face value (the discount) is recognized as interest income over the life of the bill until it reaches its full value at maturity. This process is akin to the amortization schedule for bond discounts in accounting.

Interpreting the Amortized Cut-Off Yield

The amortized cut-off yield is a crucial indicator in the market for short-term government debt. For investors, it represents the effective annualized return they will earn if they hold the Treasury bill until its maturity. A lower amortized cut-off yield implies a higher price paid for the T-bill, reflecting stronger demand or lower prevailing interest rates in the market. Conversely, a higher cut-off yield suggests weaker demand or higher market interest rates.

For the issuing government, the amortized cut-off yield indicates the cost of borrowing short-term funds. The Treasury aims to achieve the lowest possible borrowing costs, and the auction mechanism, including the determination of this yield, plays a vital role in this objective. The uniformity of the yield in single-price auctions means that all successful bidders, whether through competitive bid or non-competitive bid, receive the same return.

Hypothetical Example

Suppose the U.S. Treasury announces an auction for 26-week (182-day) Treasury bills with a face value of $1,000. During the auction, various investors submit competitive bids, specifying the yield at which they are willing to purchase the bills. Individual investors might submit non-competitive bids, agreeing to accept the yield determined by the auction.

At the conclusion of the auction, the Treasury accepts bids starting from the lowest yield up to the point where the entire announced amount of bills is sold. Let's say the final accepted yield, which clears the issue, is 5.25%. This 5.25% is the amortized cut-off yield for this particular auction.

For an investor who successfully bid at or below this yield, or a non-competitive bidder, the purchase price for a $1,000 face value T-bill would be calculated as:

[
\text{Purchase Price} = $1,000 \times \left(1 - \frac{0.0525 \times 182}{360}\right)
]

[
\text{Purchase Price} = $1,000 \times (1 - 0.0265625)
]

[
\text{Purchase Price} = $1,000 \times 0.9734375
]

[
\text{Purchase Price} = $973.4375
]

So, an investor would pay $973.4375 for a $1,000 T-bill. The discount is $26.5625 ($1,000 - $973.4375). As the T-bill approaches its maturity date, its value incrementally increases from $973.4375 to $1,000. This gradual increase in value, representing the recognition of the discount as income, is the "amortized" aspect.

Practical Applications

The amortized cut-off yield has several practical applications in financial markets and public finance:

• Government Debt Management: For government treasuries, it's a direct measure of the cost of short-term borrowing. Treasury departments analyze these yields to gauge market demand and manage national debt effectively.
• Investor Returns: Investors, from large institutions like primary dealers to individual investors, use the amortized cut-off yield to understand the precise return they will receive on their Treasury bill investments. This is particularly relevant given that T-bills are sold in book-entry form and do not pay periodic interest⁸.
• Benchmarking: The cut-off yield on Treasury bills serves as a benchmark for other short-term debt instruments in the broader financial market. Short-term corporate debt or commercial paper yields often relate to or are quoted in reference to T-bill yields.
• Monetary Policy Influence: Central banks, such as the U.S. Federal Reserve, monitor Treasury bill auctions and their resulting yields closely as part of their assessment of market liquidity and short-term interest rates, which can influence monetary policy decisions.

Limitations and Criticisms

While the amortized cut-off yield provides a clear and standardized measure for Treasury bill auctions, it has certain limitations:

• Yield Convention: The discount yield calculation, often used for Treasury bills and underlying the auction's yield determination, typically employs a 360-day year convention⁷. This differs from the actual 365-day year used for many other fixed-income instruments, which can lead to slight discrepancies when comparing yields across different types of securities. This can sometimes make direct comparisons with bond equivalent yields or other annual yields challenging.
• Simple Interest Basis: The discount yield is based on simple interest, meaning it does not account for the potential for compounding, which is a consideration for longer-term investments or when reinvesting returns. For this reason, other yield measures like the bond equivalent yield are often used for comparison.
• Auction Dynamics: The final amortized cut-off yield is a result of competitive bidding in the auction. Factors such as market liquidity, the number and aggressiveness of bidders, and overall economic conditions can influence this yield, potentially leading to fluctuations that might not always reflect a pure fundamental value⁶. For instance, periods of high demand for safe-haven assets can drive yields lower, irrespective of other economic indicators.
• No Periodic Payments: Unlike amortizing bonds that make regular principal and interest payments, Treasury bills are zero-coupon instruments⁵. The "amortization" in this context refers to the accounting treatment of the discount, not to periodic cash flows received by the investor, which might be a point of confusion for those accustomed to other types of amortized debt.

Amortized Cut-Off Yield vs. Discount Yield

The terms "Amortized Cut-Off Yield" and "Discount Yield" are closely related but refer to different aspects.

The Discount Yield is a general calculation method used for short-term, zero-coupon instruments like Treasury bills, commercial paper, and municipal notes. It expresses the return as a percentage of the face value and uses a 360-day year convention⁴. It's a way to calculate the expected return if the bond is held to maturity.

The Amortized Cut-Off Yield, on the other hand, specifically refers to the result of an auction, particularly for Treasury bills. It is the highest accepted discount yield at which the issuer (e.g., the U.S. Treasury) sells the securities to satisfy the offering amount², ³. All successful bidders in a uniform-price auction receive the securities at this yield¹. The "amortized" part implicitly acknowledges that the discount implied by this yield (the difference between the purchase price and face value) is systematically recognized as interest income over the life of the bill until it reaches its full face value at maturity. While the cut-off yield is a discount yield, the "amortized cut-off yield" emphasizes its origin from an auction and the accounting treatment of the resulting discount.

FAQs

What does "amortized" mean in this context?

In the context of amortized cut-off yield for Treasury bills, "amortized" refers to the accounting process where the initial discount (the difference between the purchase price and the face value) is gradually recognized as interest income over the life of the security until it matures. T-bills do not pay periodic interest; instead, they are bought at a discount and mature at their full face value. The increase in value over time is the investor's return.

How does the cut-off yield affect my investment?

The cut-off yield is the effective return you will receive if you hold the Treasury bills until their maturity. If you submit a non-competitive bid, you are guaranteed to receive the bills at this yield. If you submit a competitive bid, your bid must be at or below the cut-off yield to be successful.

Is the amortized cut-off yield the same as the yield to maturity?

For Treasury bills, which are zero-coupon instruments, the discount yield and the bond equivalent yield are commonly used. The amortized cut-off yield from an auction is essentially the discount yield determined in the auction. While "yield to maturity" (YTM) is a broader concept applicable to all bonds, for a zero-coupon bond like a T-bill, the discount yield or bond equivalent yield can be considered its yield to maturity, adjusted for different conventions.