If I were the BRICS Bank, this is how I would design its own Currency (I call it SAMBA — $MB).

Which countries and why would benefit from a BRICS Currency? Let’s look at some data and draw some surprising conclusions.

Photo by Steve Johnson on Unsplash

Introduction

Recently, the New Development Bank (NDB), former known as BRICS Bank, have being increasing discussions about a common currency among the members of the BRICS bloc (link). The bloc, which was established in 2006 with Brazil, Russia, India and China, adding South Africa in 2011 (link), anticipates at least another six countries to join by 2024 (link).

In this post, I want to investigate from the Mathematical point of view what challenges the creation of a new currency should the NDB expect (beside all its political and operational challenges).

In this post you will:

1. Use Python to download data from Yahoo finance and the World Bank
2. Create a weighted index of currencies
3. Analyse the currency risk when pricing bonds (loans) in foreigner exchanges.

Introducing the SAMBA Currency (SMA, $MB)

A currency designed by the NDB will most likely only be an index used to track exchange rates between countries. For that reason, I will focus on the creation of a useful and consistent index. I call that index SAMBA.

The Simplified Accrued Monetary Balance Account (S.A.M.B.A for short and SMB as trading symbol) is my proposed currency index with a solid foundation for NDB adoption as the BRICS currency.

Index Methodology

SAMBA is a basket of currencies weighted by each countries GDP per capita. Here is the simplified mathematical formula definition:

SAMBA methodology

I will ignore the Divisor needed at each new year when the GDPs is updated (changing the weights). In practice one needs to account for that on each rebalancing to avoid artificial jumps. We will not do this here in order to focus on the main points.

Despite its simple definition, SAMBA can be a powerful tool if implemented, as we will see below.

SAMBA Exchange rate in the last 10+ years

One crucial decision on the creation of SAMBA is the currencies that should integrate its basket. Following the initial BRICS formation, I will start SAMBA with the following currencies:

• Brazilian Real (BRL)
• Russian Rubble (RUB)
• Indian Rupee (INR)
• Chinese Yuan (CNY)
• South African Rand (ZAR)

The actual constituents is such a key decision that it makes sense to revisit this point in the future, specially if we want to optimise the basket composition for risk factors. That said, even if this initial choice turns out not to be optimal, I believe that most points in the remainder of these notes would still hold.

Construction SAMBA (SMB)

We will follow the following steps to construct the SAMBA:

1. Let’s get Foreigner Exchange (FX) rates denominated in USD for reference.
2. Let’s gather the yearly GDP per capital of all members for the last 10+ years
3. Let’s compute the GDP per capita weighted FX rate for the Basket (the SAMBA rate)

FX rates using Yahoo Finance

Here is some Python code to retrieve FX rate using Yahoo Finance.

When plotting the normalised time series downloaded from Yahoo Finance, we ca see the following chart:

Performance of BRICS currencies in USD quotes normalised in January of 2010. For example, one CNY cost $0.146 in January of 2010, but cost $0.140 in July of 2023. On the other hand, one BRL cost $0.59 in 2010 but cost $0.21 in 2023. All BRICS currencies depreciated with respect to US Dollar since 2010.

From the plot above we can see that all BRICS currencies depreciate against the US Dollar since 2010. The Chinese Yuan was the best performing, with Brazil and Russia being the worst performers.

If the NDB wants the SAMBA to be an independent currency (even if only as an index), one of its role will be to provide a solid balance sheet where it can provide a floor for SAMBA trading. For that effect, it is OK that USD rates are being used to bootstrap its creation, but moving forward daily quotes and spreads for SAMBA against its main constituents will be a must. The calculation and ability to honour these quotes should fall under NDB, at least in the beginning.

… it is OK that USD rates are being used to bootstrap SAMBA creation, but moving forward daily quotes and spreads for SAMBA against its main constituents will be a must. The calculation and ability to honour these quotes should fall under NDB, at least in the beginning.

GDP Per Capita using the World Bank

In order to use the yearly GDP per capita we will download the data from the World Bank using the following Python code:

The data from the code above looks as follows:

It is worth noting that we are using the World Bank data to calculate SAMBA. This highlights another challenge for the NDB when it comes to its own currency. It is fundamental for the NDB to acquire and validate its own set of data to guarantee SAMBA’s autonomy

It is fundamental for the NDB to acquire and validate its own set of data to guarantee SAMBA’s autonomy

Quoting in SMB

Putting together all the steps above, we can quote not only USD in SMB, but also all BRICS currencies in SMB.

Here is the performance of SMB versus the US Dollar in the last 10 years

SAMBA index against US Dollar. SMB depreciated in the last 10 years against the US Dollar. In January 2010, $1 used to buy around $MB 4. In July of 2023, $1 buys around $MB 10.

Below is the performance of each BRICS FX rate against the SMB. We can see each Currency performance on its own and a 10 year performance

The performance of the BRICS currencies against SMB. On the left we can see the relative performance against all other currencies. On the right we can see the individual absolute performance. Note that the SMB depreciated the most against the Chinese Yuan. The SMB appreciated the most against the Brazilian Real and the Russian Ruble.

We can see that the Chinese Yuan had the best performance of all the BRICS currencies against the SMB. Also we can see that the worst performers were Russia and Brazil. Finally, on January 2010, $1 could buy $MB 4, while in July of 2023, $1 would buy $MB 10.

To certain extent, looking only at the currency exchange performance one could wonder what is the point of a common currency like SAMBA, after all, the Chinese Yuan was the best performer against the dollar, while the Brazilian Real and the Russian Ruble were already the worst performers. What does any one get out of SAMBA? The point of SAMBA is on its decreased currency risk, a topic that we explore in the next section.

Using SAMBA to decrease Currency risk

One of the ripple effects of a common currency like the SAMBA is the business opportunities between companies within its member countries. Imagine a company in South Africa entering a loan contract for ZAR 100,000,000 (~ USD $5M) with one of their suppliers in Brazil. From the Brazilian company point of view, if the contract is fixed in ZAR, the volatility of the pair ZAR-USD will increase the value of the contract (making it more expensive to the South African company). However, if the contract is fixed at USD, all the extra cost from currency risk of the contract stays with with South African company.

A third option to our South African company is to fix the terms of the contract in SAMBA (roughly $MB 60 million for the original loan value). For the Brazilian company, the currency risk of SAMBA is lower than with ZAR-USD (decreasing the cost of the loan for the South African company).

In Summary, fixing loans (issuing bonds) against SAMBA will decrease the currency risk (volatility) of the rates, decreasing the cost of debt to some BRICS members.

Fixing loans (issuing bonds) against SAMBA will decrease the currency risk (volatility) of the rates, decreasing the cost of debt to some BRICS members.

The remaining question is: “Which members would benefit from loans (bonds) denominated in SAMBA?” From a portfolio risk management point of view, any country where its SMB exchange rate risk (volatility) is lower than its USD exchange rate risk (volatility) would benefit from loans (bonds) linked to SAMBA.

From a portfolio risk management point of view, any country where its SMB exchange rate risk (volatility) is lower than its USD exchange rate risk (volatility) would benefit from loans (bonds) linked to SAMBA.

Below we plot the USD vs SMB currency risk (volatility) of the BRICS countries and some of its new members.

Snapshot of Currency Risk (volatility) from 2016 to 2023. All countries above the diagonal dotted line have a lower SMB currency risk than USD. It is worthwhile to see that not all BRICS members would benefit from bonds issues in SMB, which hints to the fact that more than a simple portfolio management strategy is at play when the topic is a NDB currency.

The plot above could help clarify why countries like Argentina are interested in joining the bloc, as its currency exchange has showing much volatility compared to USD, it could benefit of debt raised in a commom currency like SAMBA.

Also, it is worthwhile to see that not all BRICS members would benefit from bonds issues in SMB, specially China. This hints to the fact that more than a simple portfolio management strategy is at play when the topic is a NDB currency.

Finally, it is important to note that the scatterplot above is just a snapshot of a much more complex dynamics that evolve overtime. For that reason, I made a video that follows the risk profile of the BRICS currencies and its new members over the past 10+ years. See the video below:

Conclusion

In these notes I defined the Simplified Accrued Monetary Balance Account (S.A.M.B.A), a GDP per capital weighted currency exchange basket index with potential to be a common currency for the BRICS countries. SAMBA (or a currency index of this form) can be be a powerful tool under the management of the New Development Bank (NDB).

Challenges

Some of the challenges we saw waiting for the NDB when creating a currency like SAMBA were:

• Collecting Its own data: I bootstrapped SAMBA form data in the World Bank database. While that is mostly reliable, one needs to design a strategy when not all data is available in a timely manner.
• Daily quoting of SMB: The daily quoting will require the gathering of data (point above), but also the incorporation of other financial products (like forwards and futures) to be able to safely quote the rates
• Daily Spreads: In my opinion, it would be expected of the NDB to provide a venue of last resource for trades with competitive spreads to be a solid base for this currency.

Steps left out of the Analysis

Index Rebalance: I intentionally left from the rebalancing of the SAMBA index a smoothing factor (often called Divisor). This mishandle should have created an extra volatility on the days of GDP per capita changes. Despite this, all insights and challenges highlighted in these notes are kept unchanged.

Inflation: I also briefly had a look at exchange rates adjusted by inflation and purchase parity, but the impact was so low to overall takeaway messages of the notes that I left this point out of the final version.

Limitations

One big limitation and assumption when analysing the risk using historical data is that the past reflects the future. One should be aware that using ONLY past volatility to assess currency risk is naive, but at the same time, to expect the risk to be much smaller than the observed without a correct vision of the market could be living in denial. In any case, the historical analysis of risk with the health dose of skepticism can be a powerful frame of reference for decision making,

Future

I would love to explore more characteristics of bonds issued on SAMBA. The are two aspects that should be interesting: 1) how different weights to the index can impact the bonds pricing, and 2) how expected aggregated inflation of the members should affect bond prices.

Incorporating transaction volume between countries should also be an interesting way to weight the currencies in the construction of the SAMAB index.

Want more?

— If you want more quantitative finance, look at my Quant-Finance repository with a few notebooks on the topic: https://github.com/mauhcs/quant-finance

— If you want some interesting Math drama look at my rant over the 20th century statistics: The Problem with the 20th Century Null Hypothesis Significance Testing