In my last blog, From Bond Proceeds to Rebates: The Lifecycle of a Construction Account, I discussed the life of a drawdown schedule, yield restrictions, and the potential need to rebate earnings to the Treasury. Since its release, several readers have asked how the arbitrage yield is determined. In this follow-up, I’ll dive into the math of bond statistics to answer that question.
As bond transactions are priced, clients are usually given a summary sheet filled with various statistics about the transaction. To begin, let’s break down the math of these statistics and explore why they are relevant.
What is the Arbitrage Yield of a Municipal Bond?
The arbitrage yield of a municipal bond is the maximum investment rate that tax-exempt bond proceeds are allowed to earn by the federal government without having to rebate.
Essentially, it represents the highest yield that can be earned on the investment of bond proceeds without violating federal arbitrage regulations, except in specific cases. Exceeding this yield may require the issuer to rebate excess earnings to the Treasury. This yield is crucial for ensuring compliance with tax laws and avoiding penalties.
Why does this Yield Constraint Exist?
The federal government, specifically the Treasury, does not want a municipal issuer to sell tax-exempt bonds and then invest the bond proceeds in securities that yield higher than the issuer’s borrowing rate.
The Treasury imposes this yield constraint to prevent municipal issuers from profiting by investing tax-exempt bond proceeds in higher-yielding securities. Without this restriction, municipalities could potentially issue tax-exempt bonds at a lower borrowing rate, invest the proceeds in higher-yielding taxable investments, and pocket the difference, a practice known as arbitrage. This would undermine the purpose of tax-exempt bonds, which are designed to support public projects, not generate profit for the issuer.
The arbitrage yield is the rate the Treasury interprets as the issuer’s borrowing rate. By enforcing this yield constraint, the Treasury ensures that municipalities cannot take unfair advantage of the tax-exempt status and keeps the focus on funding public goods rather than earning arbitrage profits. This system helps maintain the integrity of tax-exempt bonds while protecting federal revenues.
Why is the Arbitrage Yield Important?
When a bond financing is executed, the money the issuer receives from the sale of the bonds is usually deposited in an account which is designed to pay-out over time to meet the client’s future obligations (e.g., construction needs, future interest payments).
These accounts are subject to different rules depending on their classification, and the arbitrage yield plays a critical role in determining how much the issuer can earn on the funds within these accounts.
Depending on the use of the money, these accounts are classified as either:
- Restricted and Subject to Rebate: The arbitrage yield is the maximum the money in the fund is permitted to earn. However, if the accounts earn over the arbitrage yield, the issuer can rebate the excess earning back to the Treasury. These accounts are closely monitored to ensure that any over-earnings do not result in arbitrage violations.
- Restricted and Not Subject to Rebate: The maximum allowable earnings for the money in that fund is the arbitrage yield, and at no point can the account's earnings exceed this limit. Earnings on these funds must strictly remain at or below the arbitrage yield, with no option for rebate if excess earnings occur. The funds are effectively locked into compliance with the yield constraint, making it vital for issuers to monitor these accounts carefully to avoid non-compliance.
- Unrestricted: Any money deposited in an unrestricted account can earn the maximum available return in the current market. The arbitrage yield is irrelevant on this type of account.
Examples of unrestricted accounts are a tax-exempt current refunding escrow account or a tax-exempt funded construction account that meets any of the three spending exception rules.
Any account classified as restricted has a maximum return equal to the arbitrage yield.
Notes
- If two accounts are yield restricted (excluding any refunding escrow account) issuers can combine the investment returns from both accounts as long as the combined investment return remains below the arbitrage yield. This analysis is usually done by a rebate specialist.
- When executing a taxable advance refunding, the escrow investments are restricted to the refunded bonds arbitrage yield.
However, once the escrow for the taxable refunding bonds is fully depleted, those taxable bonds can be refunded by tax-exempt bonds at any time.
What the Refunding is Going On? Exploring Tax-Exempt Bond Refunding
How is the Arbitrage Yield Calculated?
The arbitrage yield is the rate at which the present value of the bond series’ cash flow (both principal and interest payments) equals the amount of money the borrower receives from the sale of the securities on the delivery date. This calculation ensures that the proceeds from the bond sale are properly accounted for.
The amount received from the sale of the securities is determined using the following formula:
+ Face amount of the bond series
- Combined original issue discount (OID)
+ Combined original issue premium (OIP)
- Bond insurance premium or surety cost (if applicable)
+ Accrued interest
= Money received
Applying the Yield-to-Call Rule
To calculate the bond series’ cash flow, each bond must be analyzed individually, with a focus on its likelihood of being called before maturity. This involves evaluating the bond’s potential callability, similar to how bonds are priced at the minimum of their price-to-maturity, price-to-first-call, or price-to-par-call.
For each bond, the cash flow is analyzed to determine whether it should extend to the bond’s maturity date or its call date. This is done by calculating the lowest yield, which helps establish the most likely scenario for the bond’s lifecycle. This approach is known as the "yield-to-call" rule, and it ensures that the bond’s cash flow projection aligns with its most probable redemption date, whether it be at maturity or upon being called.
By following the yield-to-call rule, issuers can make accurate calculations for the bond’s cash flow, ensuring that the correct assumptions are made about when the bond will be retired and how that affects its overall yield.
Below are the circumstances where the yield-to-call shortens the cash flow of the bond to its call date:
- The bond is subject to optional redemption within 5 years of the issuance date and only then if the yield based on the redemption is at least .125% below the yield to maturity.
- The amount of the original issue premium exceeds .25% multiplied by the number of years to the first optional call date.
Example of Analysis Below
The bonds are stepped coupon bonds. A stepped coupon bond, also known as a step-up bond, is a type of bond where the interest rate (coupon) increases at predetermined intervals (e.g., every 5 years) over the life of the bond.
Example of Calculations
No Yield-to-Call Adjustment:
All Bonds Require Yield-to-Call Adjustment:
Some Bonds Require Yield-to-Call Adjustment and Others do not Require Adjustment:
True Interest Cost
The true interest cost (TIC) is the time value calculation of the cost of the transaction to the issuer, considering the underwriter’s discount (i.e., takedown of bonds). It’s the same present value method as the arbitrage yield above except there is no “yield-to-call” adjustment on premium bonds (i.e., the bond series cash flow always goes to maturity).
Example of Calculation
All-In True Interest Cost
The all-in True Interest Cost (all-in TIC) represents the total cost of the transaction to the issuer, considering both the underwriter’s discount (i.e., takedown of bonds) and all the additional cost associated with a bond transaction (e.g., printing cost). It’s the same present value method as the TIC.
Example of Calculation
Bond Years
The number of bond years in an issue is calculated by multiplying the number of years from a specific date (e.g., dated date) to each bond’s maturity by the bond’s maturity value.
Bond years are used in the calculation of the average life of an issuance.
Example of Calculation
Average Life
The number of years to the halfway point of the transaction. The average life reflects the rapidity with which the principal of the issue is expected to be paid.
Example of Calculation
Average Life= 116,000,000/8,000,000
Average Life= 14.5 years
Duration
Duration is a measure of when the principal and interest payments will be received from the issuer. Traders look at the duration of a specific maturity, however, duration can be calculated for the total bond issuance.
Example of Calculation
Conclusion
The intricacies of arbitrage yield are significant in municipal bond financing. From understanding the reasons behind the yield constraint to exploring how the arbitrage yield is calculated, it's clear that this concept plays a critical role in ensuring compliance with federal regulations and maintaining the integrity of tax-exempt bonds.
By grasping these elements, issuers can effectively navigate the complexities of bond transactions and ensure they make informed, compliant financial decisions.
Related Municipal Finance Reading
- Debt Service Calculator for Tax-Exempt Bonds
- Bond Insurance: Making a Marketable Credit Better
- Strategies for Financing New Municipal Capital Projects
Disclaimer: DebtBook does not provide professional services or advice. DebtBook has prepared these materials for general informational and educational purposes, which means we have not tailored the information to your specific circumstances. Please consult your professional advisors before taking action based on any information in these materials. Any use of this information is solely at your own risk
