THE SHORT ANSWER
The arbitrage yield is the yield of the bond issue itself, computed under section 148(h) and Treasury Regulation 1.148-4 on the basis of issue price using the economic accrual method, with a consistent compounding interval of one year or less, stated to at least four decimal places. Yield restriction and rebate both measure investments against that yield.
The arbitrage yield is the yield of the bond issue itself, computed under section 148(h) of the Internal Revenue Code and Treasury Regulation 1.148-4, and it is the number the federal arbitrage rules measure invested proceeds against.
This page works through how that yield is computed: the method and its inputs, what payments enter it, how fixed and variable yield issues differ, and why the resulting figure caps what bond proceeds may earn.
It sits inside the broader guide to the federal arbitrage rules for bond proceeds.
What is the arbitrage yield on a bond issue?
The arbitrage yield is the yield on the issue of bonds itself: the annual rate determined on the basis of issue price that the arbitrage rules compare against the yield on invested proceeds.
Section 148(h) of the Internal Revenue Code fixes the basis, by providing that the yield on an issue is determined on the basis of issue price within the meaning of Code sections 1273 and 1274.
Treasury Regulation 1.148-4 supplies the mechanics: yield is computed under the economic accrual method, uses a consistent compounding interval of not more than one year, and is expressed as an annual percentage rate calculated to at least four decimal places.
The regulation's own illustration of that form is 5.2525 percent, and it permits day-count conventions such as 30/360 when they are used consistently.
In the rest of the arbitrage rules this same figure is the bond yield: the materially higher tests in Treasury Regulation 1.148-2(d) are measured against it, and the rebate amount in section 148(f)(2) is compounded at it.
Because the computation is anchored to issue price and solved from the payment schedule, the arbitrage yield is a computed rate, and it is not automatically the coupon rate stated on the face of the bonds.
What goes into the yield computation, and what stays out?
The computation counts the issue's unconditionally payable payments of principal and interest, adds fees for a qualified guarantee and payments under a qualified hedge, and measures all of it against issue price.
For a fixed-yield issue, Treasury Regulation 1.148-4(b)(1)(i) defines the yield as the discount rate at which the present value, as of the issue date, of all unconditionally payable payments of principal, interest and fees for qualified guarantees equals the present value of the aggregate issue price.
Under 1.148-4(b)(2), bonds subject to mandatory or expected early redemption are treated as redeemed on that date for the computation.
Apart from the cases the regulation provides, later unexpected events do not change a fixed-yield issue's computed yield.
On the exclusion side, section 148(h) and Treasury Regulation 1.148-4(b) measure the payments against issue price rather than against the issuer's net proceeds, so the base for the computation is the issue price of the bonds within the meaning of Code sections 1273 and 1274.
Beyond those payments, two additions to the computation are worth naming.
The first is the qualified guarantee: under Treasury Regulation 1.148-4(f)(1), fees properly allocable to a qualified guarantee for an issue, such as bond insurance, are treated as additional interest on that issue, which raises the arbitrage yield.
The treatment is conditioned: the guarantee must satisfy the regulation's requirements in 1.148-4(f)(1) through (4), and those requirements set out an interest-savings expectation, a guarantee in substance and a reasonable charge, along with a limit on the guarantor's use of proceeds.
- Interest savings: the present value of the fees must be expected to be less than the present value of the expected interest savings.
- Guarantee in substance: the arrangement must be a guarantee in substance under the regulation.
- Reasonable charge: the fee must be a reasonable charge.
- Use of proceeds: under 1.148-4(f), the guarantor and related parties may not use more than 10 percent of the proceeds of the guaranteed portion.
Form 8038-T line 27 asks for these fees, and the guide to Form 8038-T covers the filing itself.
The second addition is the qualified hedge: under Treasury Regulation 1.148-4(h)(1), payments made or received by an issuer under a qualified hedge relating to bonds of an issue are taken into account in determining the yield on the issue.
The same paragraph generally treats the hedged bonds as variable-yield bonds, the qualified hedge rules apply only for purposes of Code sections 143(g), 148 and 149(d), and the hedge must be identified on the issuer's books, which Form 8038-G line 41a requests.
The move away from LIBOR left this area with its own transition rule: under 26 CFR 1.1001-6(c)(1)(iv), adopted in T.D. 9961, a covered modification of a qualified hedge, or of the tax-advantaged bonds the hedge is integrated with, is treated as not terminating the qualified hedge, provided the modified hedge still qualifies within a 90-day window.
Whether a particular modification fits that treatment is a technical tax question for bond counsel.
| Component | How it enters the yield computation | Where the rule is |
|---|---|---|
| Principal and interest | Unconditionally payable payments, present-valued to the aggregate issue price as of the issue date | Treas. Reg. 1.148-4(b)(1)(i) |
| Qualified guarantee fees | Treated as additional interest, if the guarantee meets the requirements of 1.148-4(f) | Treas. Reg. 1.148-4(f)(1) |
| Qualified hedge payments | Taken into account in the yield on the hedged bonds | Treas. Reg. 1.148-4(h)(1) |
| Early redemption | Bonds subject to mandatory or expected early redemption are treated as redeemed on that date | Treas. Reg. 1.148-4(b)(2) |
How does the calculation differ for fixed and variable yield issues?
Treasury Regulation 1.148-4 computes the two differently: 1.148-4(b) governs fixed-yield issues, whose yield is computed once as of the issue date, and 1.148-4(c) governs variable-yield issues, whose yield is computed separately for each computation period.
For a fixed-yield issue, the discount rate is solved once against the unconditionally payable payments of principal, interest and qualified guarantee fees, and later unexpected events do not change it except as the regulation provides.
For a variable-yield issue, the yield is determined for each computation period rather than fixed at issuance.
Qualified hedges are the bridge between the two: once payments under a qualified hedge enter the computation under 1.148-4(h)(1), the hedged bonds are generally treated as variable-yield bonds.
| Fixed-yield issue | Variable-yield issue | |
|---|---|---|
| Where the rule is | Treas. Reg. 1.148-4(b) | Treas. Reg. 1.148-4(c) |
| When the yield is computed | Once, as of the issue date | Separately for each computation period |
| What changes the analysis | Mandatory or expected early redemption built into the payment schedule, 1.148-4(b)(2) | Payments under a qualified hedge generally make the bonds variable-yield, 1.148-4(h)(1) |
The split matters for reinvestment planning because the tolerance tests on the investment side key off the issue's yield, so the analysis of what a fund may earn starts with knowing which computation its bonds follow.
Why does the arbitrage yield cap what investments can earn?
The arbitrage yield caps investment yield because both arbitrage regimes measure investments against it: outside the exceptions, proceeds may not be invested at a yield materially higher than the bond yield, and the rebate computation compounds earnings against the bond yield as well.
For most investments, Treasury Regulation 1.148-2(d)(2)(i) treats a yield as materially higher when it exceeds the bond yield by more than one-eighth of 1 percentage point, which is 12.5 basis points.
Where yield-restricted investments within one class are subject to different materially higher definitions, the definition that produces the lowest permitted yield applies to the whole class under 1.148-2(d)(1).
The measurement itself runs class by class: yield is computed separately for each class of investments under Treasury Regulation 1.148-5(b)(2)(i), yields within a class are blended, and the yields on investments in different classes are not blended.
Valuation follows its own rules, with yield-restricted nonpurpose investments generally valued at present value under 1.148-5(d)(2), and investments held past a temporary period may be treated as purchased at fair market value at the end of that period under 1.148-5(b)(3).
The yield restriction rules and the temporary periods that defer them have their own pages.
The bond yield also reaches purpose investments: IRS Publication 5005 notes that fees charged by the conduit issuer can raise the effective yield on a conduit loan, which is a purpose investment, and that conduit issuers generally must keep the loan yield from exceeding the bond yield by more than the permitted spread.
The permitted spread for program investments is 1.5 percentage points under Treasury Regulation 1.148-2(d)(2)(iii), and other purpose investments fall under the general one-eighth standard.
Conduit issues carry this as a fee question on the loan side, and the guide for conduit issuers takes it up in full.
Earning within the cap is not the whole test either: IRS Publication 5271 puts it directly, the yield restriction rules may allow the issuer to earn the arbitrage, but the rebate rules may not allow the issuer to keep it.
The rebate amount is itself a bond-yield computation: under section 148(f)(2) and Treasury Regulation 1.148-3(b) and (c), it is the excess of the future value of all receipts on nonpurpose investments over the future value of all payments on them, with future values compounded at the bond yield, using the same compounding interval and conventions as the bond yield.
Gains and losses on a disposition count in that computation under section 148(f)(4)(A)(i), and the rebate calculation page works through the arithmetic.
The bond yield even sets the target for correcting a misinvested escrow: IRM 7.2.3.4.3, the IRS's published VCAP standard for identified violations in tax-exempt bonds, covers an escrow party's failure to timely reinvest proceeds of a refunding issue when investments mature, giving the example of a matured guaranteed investment contract that is not reinvested in zero-percent time deposit SLGS.
A request made within 60 days of the next required computation date after the failure resolves by paying the amount needed to reduce the escrow's yield to the bond yield, plus interest, and a request within six calendar months after that date substitutes 110 percent.
IRM guidance is internal IRS procedure and resolution terms vary by the facts, so an actual failure calls for bond counsel and tax counsel.
Each test above starts from the issue's computed yield, and the site's arbitrage yield calculator performs this computation from an issue's own terms.
For proceeds already invested, mGIC can check your proceeds against the rules and show where a fund stands against the issue's yield and its temporary periods.
mGIC is an independent, SEC-registered municipal advisor and Bidding Agent paid by the winning provider rather than the issuer, and a free, no-obligation reinvestment review is the place to start that conversation.
Which computation applies to a given issue, and how its funds test against it, is a legal and tax conclusion that belongs to bond counsel and tax counsel.
Frequently asked questions
Is the arbitrage yield the same as the coupon rate?
Not automatically. The arbitrage yield is a computed rate: section 148(h) and Treasury Regulation 1.148-4 determine it on the basis of issue price under the economic accrual method, so it is not automatically the coupon rate stated on the face of the bonds.
Does bond insurance change the arbitrage yield?
It can. Under Treas. Reg. 1.148-4(f)(1), fees properly allocable to a qualified guarantee, such as bond insurance, are treated as additional interest on the issue, which raises the arbitrage yield, provided the guarantee meets the interest-savings, guarantee-in-substance and reasonable-charge requirements.
How many decimal places must the arbitrage yield be stated to?
Treasury Regulation 1.148-4 requires the yield to be expressed as an annual percentage rate calculated to at least four decimal places, with 5.2525 percent as the regulation's own example.
Do payments under an interest rate swap change the arbitrage yield?
Payments made or received under a qualified hedge are taken into account in determining the yield on the hedged bonds under Treas. Reg. 1.148-4(h)(1), and those bonds are generally treated as variable-yield bonds. Whether a particular swap is a qualified hedge is a technical question for bond counsel.
Where does the arbitrage yield show up in the rebate computation?
It is the compounding rate: under section 148(f)(2) and Treas. Reg. 1.148-3, the rebate amount is the excess of the future value of receipts over the future value of payments on nonpurpose investments, with future values compounded at the bond yield.
Sources
- 26 CFR 1.148-4, Yield on an issue of bonds
- 26 CFR 1.148-2, General arbitrage yield restriction rules
- 26 CFR 1.148-5, Yield and valuation of investments
- 26 CFR 1.148-3, General arbitrage rebate rules
- eCFR 26 CFR 1.1001-6
- IRS Publication 5271, Complying with Arbitrage Requirements
- IRM 7.2.3, Tax Exempt Bonds Voluntary Closing Agreement Program
- IRS Publication 5005, Your Responsibilities as a Conduit Issuer
This page is general educational information about municipal finance and federal and state rules as of the date shown. It is not legal, tax or investment advice, and it is not a recommendation about any particular investment. Product availability, legality and suitability depend on the issuer, jurisdiction, governing documents and transaction-specific facts. Final legal and tax determinations remain with the issuer's bond counsel, tax counsel and other advisors.
