How to calculate interests in Brazil (CDI) - Part 4

After discussing what "CDI" and "percentage of CDI" are, to finalize this topic we will talk about the "margin over CDI".

In the USD market, US Libor loans are often negotiated on a Libor + margin basis. "Margin over CDI" is the equivalent to Libor + margin in Brazil. One should probably ask: if these two are equivalent, why do we need a post about this topic?

Answer is: although these two are equivalent, the calculation process is not.

Formula for calculating interests using "margin over CDI" follows below:

Similarly to the numeric example provided in my previous post, the calculation process for "margin over CDI" starts with the daily compounding of the CDI.

Assuming that we have a loan of 100,000 BRL at CDI + 1% and that the CDI for the first day of the loan is 11%, then the interests calculation for this first day would be:

Balance of your loan at day one: 100,045.37 BRL

Assuming that the CDI for day two is 11,25%, interests calculation should be:

Balance of your loan at day two: 100,091.66 BRL

After one month (21 business days), the balance of your loan should be 100,961.10 BRL:

Interested in more information about the CDI and how financial products using this rate are calculated? Send me an email: mmatsmoto@gmail.com

How to calculate interests in Brazil (CDI) - Part 3

Do you know what "percentage of CDI" means? No? You're not the only one...😃

In Brazil, investments, derivatives, loans and other financial contracts are often negotiated using as contractual rate (or reference rate) "percentage of CDI". But, what exactly is "percentage of CDI"?

As previously discussed here, CDI is the average rate at which Brazilian banks are willing to borrow/lend to each other for one day. This is the benchmark rate for the BRL domestic market.

"Percentage of CDI" is the discount/premium over the regular CDI rate. For example, when a bank extends a loan to a customer at 120% of the CDI, this means that the cost of this loan is 20% higher than the regular CDI rate. On a deposit transaction at 90% of the CDI, the yield on this investment is 10% lower than the regular CDI.

Negotiating interest rates using "percentage of CDI" is a specificity of the BRL domestic market. Market professionals often say this is related to historical reasons, mostly linked to the super high inflation (and consequently high interest rates) we used to have in the country some decades ago. Since prices and interest rates used to oscillate significantly on a daily (even intraday) basis, negotiating a fixed margin over the benchmark rate was not a reliable metric (imagine a margin of 1% over a rate of 10% and, on the following day, 1% over a rate of 100%). Percentage of CDI provides a return that varies depending on the prevailing interest rate levels, what worked better at that time for investors.

Coming down to math, this is the formula for calculating interests using "percentage of CDI":

Similarly to the numeric example provided in my last post, the calculation process for "percentage of CDI" starts with the daily compounding of the CDI.

Assuming that we have an investment of 100,000 BRL at 90% of CDI and that the CDI for the first day of the investment period is 11%, then the interests calculation for this first day would be:

Balance of your investment at day one: 100,037.28 BRL

Assuming that CDI for day two is 11,25%, interests calculation should be:

Balance of your investment at day two: 100,075.38 BRL

After one month (21 business days), the balance of your investment should be 100,789.35 BRL:

Interested in more information about the CDI and how financial products using this rate are calculated? Send me an email: mmatsmoto@gmail.com

How to calculate interests in Brazil (CDI) - Part 2

After all the technical explanations and mathematical formulas, the best is to have a numeric example to make it cristal clear, right?

First, let´s get started using the standard formula for interests calculation:

 

As explained in my previous post, the CDI is an interest rate published on a daily basis that must be compounded for the calculation of interests amounts.

First step for the compounding process is the calculation of the daily interests. Assuming that the CDI for the first day of the investment period is 11%, then the interests calculation for a 100,000 BRL investment would be:

Balance of your investment at day one: 100,041.42 BRL

Assuming that CDI for day two is 11,25%, interests calculation should be:

Balance of your investment at day two: 100,083.75 BRL

After one month (21 business days), the balance of your investment should be 100,877.42 BRL:

Interested in more information about the CDI and how financial products using this rate are calculated? Send me an email: mmatsmoto@gmail.com

How to calculate interests in Brazil (CDI)

CDI - Definition

First of all, what is the so called CDI (terminology commonly used in the Brazilian market)?

In portuguese, CDI stands for "certificado de deposito interbancário" - free translation to english: interbank certificate of deposit. CDI is the average rate at which the Brazilian banks are willing to borrow/lend to each other for one day. This market is also called "interbank money market".

The equivalente to the CDI in the American market can be considered to be the FED Fund rate.

This rate is calculated by CETIP and published on a daily basis on the site https://www.cetip.com.br/?lang=en-us

Why Brazil uses the CDI

Before 1994 (year when Plano Real - economic plan that managed to control hyper inflation in the country - was launched),  Brazil used to suffered from extremely high inflation - CPI in the 12-months prior to the Plano Real was almost 5,000%!!!!. Due to this, long term planning was not possible, with most of the people trying to simply either buy something (cars, real estate, even groceries) as soon as they had some money or invest their money exclusively in short term investments - economic plans attempting to control inflation often confiscated the investments in financial products from the population, thus when investing in such products the population required the ability to exit at any moment if they suspected an economic plan was about to be implemented.

This problematic economic history created a "short term culture" in the economy, where people avoided long term planning and transactions are mostly referenced to the overnight interest rates - the CDI. Recently there were some discussions about why we still use the CDI and potential alternatives for this index. Tentatives were unsuccessful and CDI is still the major reference for the Brazilian economy what regards to nominal interest rates in local currency.


Calculation using the CDI

CDI is a rate expressed in an anual basis that uses the exponential business days day count convention. But...what exactly this means?

This means that (1) the CDI is a rate valid for business days only - weekends are not included in the day-counting process, and one year is considered to have 252 business days - and that (2) the calculation formula uses compounded interest calculation - differently from the international market where linear interest calculation is used. This calculation method compares to the IOS swaps, where the floating rate is reset on a daily basis.

If you make an investment with interest income referenced to the CDI, your income should be calculated as follows:

 There are, however, some transactions where variations of the CDI are negotiated, which are (1) the percentage of the CDI, and (2) a margin over the CDI. Each of those require a specific formula for the correct calculation of the interest amounts.

(1) Percentage of the CDI: no specific reason why Brazil uses this convention, but it is often used in loan transactions and deposits.

Interest amount should use the following formula:

(2) Margin over CDI: typically loan transactions use this convention, where a margin over the base rate is applicable for the calculation of the interest amounts. Formula for the interest amount as follows:

Interested in more information about the CDI and how financial products using this rate are calculated? Send me an email: mmatsmoto@gmail.com

First post

Hello there!

Interested in learning more about the brazilian financial market? If your answer is yes, then you´re in the right place!

I´m an experienced professional with over 15 years working in the Brazilian, American and European financial markets, taking senior positions in risk management, product structuring, trading and sales.

This blog is intended to approach subjects related to transactions regularly seen in the financial markets, such as derivatives, investments, structured products and even analysis and perspectives about the financial markets, always focusing on the Brazilian market and explaining the specificities of its products.

I hope you enjoy this blog!