Cross-Currency Asset Swaps for Comparing Brazilian Corporate Bonds

# Simplified Cross Currency and Interest Rate Swap Method - USD YTMs to BRL Floating-Rate YTMs


# Simplified Cross Currency and Interest Rate Swap Method - USD YTMs to BRL Floating-Rate YTMs












Good afternoon,

I work in the financial markets and I am trying to better understand how to convert USD bond yields of Brazilian companies into BRL yields, so that I can compare them with local benchmarks such as DI, IPCA, and finally with the yields of the same companies' instruments traded in the domestic market.

[Comment: DI is Brazil's interbank deposit rate, the main reference for floating-rate instruments locally. IPCA is the official inflation index. Many local instruments are indexed either to DI or to IPCA.]

My goal is to understand whether the bond issued by the same company is paying more or less than its debentures, CRIs, or CRAs in the local market.

[Comment: Debentures, CRIs (Receivables Certificates related to real estate), and CRAs (related to agribusiness) are common corporate fixed-income instruments in Brazil.]

As far as I understand, the "Curva Dólar x Pré" (Dollar vs. Fixed Rate Curve) published by B3 (the Brazilian Stock Exchange) — commonly referred to as "CDP" — represents the implicit future appreciation of the US dollar embedded within the DI futures curve.

Thus, a "back-of-the-envelope" calculation I have been doing is to add the return of the CDP over the bond yield, across the bond’s maturity period. After that, I subtract the DI futures curve to arrive at the bond’s equivalent “DI+” rate.

[Comment: "DI+" means the spread over the DI rate, a common way to express local fixed-income yields.]

To get to an “IPCA+” rate, I subtract the implied inflation from the DI-adjusted rate.

[Comment: “IPCA+” is the spread over inflation — i.e., real interest rates — and a common metric for comparing fixed income investments in Brazil.]

I know that this method provides an imperfect approximation because, in theory, the correct approach would be to convert all the bond’s cash flows into BRL using the forward FX curve, and then calculate the equivalent BRL yield from there. However, even with a Bloomberg Terminal, this becomes nearly impractical and hard to maintain, due to the sheer amount of data I would need to process to cover the entire universe of bonds I’m analyzing.

[Comment: The more precise method would be a full multi-curve cash flow projection with forward FX hedging, but this is often operationally complex.]

I have seen some reports from BTG [Pactual, a major Brazilian investment bank] that refer to the "FRA curve" for doing these swaps, but they explain the methodology in a rather elusive way, and the whole process is a black box. Besides that, I’m not entirely sure what kind of “FRA” they are referring to, since there is more than one type.

I would guess they are referring to the "Cupom Cambial" (DDI), but in that case, I understand that their methodology would be different from mine, essentially decomposing the DDI from the bond’s YTM.

[Comment: "Cupom Cambial" refers to the implied interest rate differential embedded in non-deliverable forward FX contracts, often measured by the DDI curve (Interbank Deposit rate for Dollar operations).]

Does anyone have experience with this kind of operation and could give me some guidance? I’d be happy to share some of my knowledge and spreadsheets in exchange.

P.S.: when I say "subtract" or "add" interest rates, I mean I'm "decompounding" or "compounding" them ;)

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/83546

I think I have an idea of what you're trying to analyze. I'll edit if I missed something.

Suppose you own an asset that promises to pay some fixed amount of U.S. dollars and for the purpose of this answer, that you completely ignore credit risk, e.g. U.S. treasury or agency bond. Suppose further that you don't really want exposure to US dollar interest rates, for starters (we'll get to the multi-currency case momentarily).

So you enter into a swap where one leg is you paying the counterparty whatever cash flows you get from your asset and the other leg is the counterparty paying you SOFR + spread. If your asset amortizes or gets prepaid, the remaining notional of the swap is reduced accordingly. (And, once again, we'll disregard the credit risk.) But how much is the fair spread?

If you have Bloomberg terminal, you can play with the ASW (asset swap) function. There are some variations of how exactly you configure the swap, but they're not very important. Under the hood, the function calculates the fair values of each leg of the swap and solves for the spread that makes them equal. You can do it yourself in Excel etc if you have the market data (i.e. the discount curves).

Now, suppose that you're accounting is in a different currency, and you don't want the exposure to the USD exchange rate. You can likewise solve for spreads where you will pay the USD cash flows of the asset (fixed or floating now) and receive the cash flows in your desired currency, i.e. SONIA / EURIBOR / €STR / SARON / CDOR / whatever + spread. You can also receive fixed in another currency if you really want to, and then you'd solve for the fixed coupon. The calculation may use a simple interest rate parity, or may include adjustments for the different cost of funding (i.e. cross-currency swap basis), different volatilities of interest rates (if the two legs have very different VaRs / capital costs), etc.

Many accounting frameworks allow such asset swaps to be booked as hedges for the asset if some conditions are met.

An additional twist in Brazil (and many other emerging or frontier markets) is that there's a large difference between yields of onshore / local law versus offshore / external law assets. The yield that offshore BRL bonds pay differs from the onshore NTN-F bonds pay. Cupom Cambial that you mention is the Brazil onshore USD interest rate (the spread between the overnight interbank deposit interest rate and the exchange rate variation prior to maturity of the DDI contract - Trying to understand brazil derivatives market - there also used to be onshore NTN-D bonds, but they have all matured ). A few other countries have their own onshore hard currency interest rates. Maybe these will become more common as the trade wars rage on.

I suppose you could price a swap where external USD is exchanged for onshore USD + spread. I'm not sure if Bloomberg ASW would understand it, but in Excel it should be easy as long as you have the curves.

Brazil has more creative variety than most countries when it comes to payoff formulas in the local currency - reais. @Akdemy may want to comment, but I don't think Bloomberg ASW / SWPM support all of the varieties of payoffs that I've seen in Brazil:

- CDI + spread accrued daily

- CDI accrued daily and a spread added once at the end of the coupon period.

- CDI $\times$ gearing (which would become problematic if the rates went negative)

- IPC-A is Índice Nacional de Preços ao Consumidor Amplo - the Extended National Consumer Price Index, very similar to the retail CPI in the US. There are inflation-linked instruments similar to US TIPS, where every cash flows - principal and interest - is multiplied by index at payment / index at inception - for example NTN-B bonds. You could swap into fixed IPC-A - adjusted cash flows. But there are also some instruments where the interest is IPCA + spread, and the principal is not inflation-adjusted.

- IGP-M is the wholesale inflation index, more correlated to fx rates than IPC-A. NTN-C bonds are fixed-coupon bonds inflation-linked using this index.

If ASW can project all the variations of cash flows that you really need, then just use the terminal and convert to a benchmark of your choice, like the spread for DI+, otherwise you may have to project the cash flows yourself and solve for spreads or fixed coupons. If you have some ideas about probabilities of default and losses given default, you could try to analyze these instruments as credit rather than pure rates.

If some corporate debt issuer has several outstanding offshore / external law / eurobonds in currencies like USD / EUR / GBP / CHF, and even "offshore non-deliverable BRL", then you'd expect all these bonds, especially with similar maturities, to have similar asset swap spreads, and also Z-spreads. But onshore / local-law instruments, are not pari passu with the eurobonds, but rather have additional risks, such as the transferability risk discussed in the answer cited above, for which investors would want to be compensated. Instead of the back of the envelope approximate you mention, asset swap spread / Z-spreads using curves like Brazil onshore USD, or NTN-B yield curve (for IPC-A adjusted instruments), might make more sense for rich / cheap / relative value comparisons.

If you have Bloomberg terminal, I would asking first checking what's missing there, i.e.

- market data (such as Brazil onshore USD curve or NTN-B and even NTN-C yield curves)

- ability to project cash flows - examples of onshore instruments where CSHF doesn't project the right cash flows, hence ASW, YAS, etc cannot solve for spreads

then give your list to Bloomberg: start with F1 F1 and they'll escalate to the right team.