In the world of finance, the relationships between different global economies are crucial for understanding and predicting movements in the markets. One of the fundamental aspects that investors and analysts study is the difference in interest rates between different fiat currencies. This disparity not only reflects the monetary policies of countries but can also influence investor behavior and the direction of capital flows. In this article, we will explore in detail the importance of the difference in interest rates in the context of quantitative finance, and how this relationship can affect the foreign exchange market.

What is the Foreign Exchange market?

The foreign exchange market, also known as Forex (short for Foreign Exchange), is the global decentralized market where the various currencies of the world are traded. Its operation is based on the buying and selling of currencies, with the aim of making profits by speculating on fluctuations in exchange rates between them or obtaining a specific currency to conduct a subsequent transaction.

In this market, a wide variety of actors participate, including central banks, financial institutions, multinational companies, individual investors, and speculators. According to a triennial study conducted by the Bank for International Settlements in 2022, 46.1% of transactions were exclusively between banks, 48.2% were between banks and other types of financial firms, and only 5.7% were between an intermediary and a non-financial company. These transactions totaled an average of 7.5 billion dollars per day. Despite its extreme liquidity, price variation is minimal because its value is associated with the economy that uses that currency. Therefore, high leverage is often offered to operate in the market, sometimes reaching 500:1. The most traded pairs are EUR/USD with a transaction percentage of 22.7%, USD/JPY with 13.5%, and GBP/USD with 9.5%.

The structure of this market differs from the typical one, such as the Nasdaq, where all transactions are intermediated by a single entity. In the case of the foreign exchange market, transactions will be carried out in different entities depending on the size of the transaction, with the broker acting as a counterparty (these brokers are called Market Makers), a bank or financial institution, or even a central bank of a country. These entities are located in countries around the world, so the market is open 24 hours a day from Monday to Friday, closing only on weekends.

The importance of the foreign exchange market lies primarily in facilitating international trade, allowing capital to be converted into foreign currencies to conduct commercial transactions of goods or products between countries. Due to currency fluctuations, companies have also seen the need to conduct transactions for hedging purposes to prevent the risk of depreciation of their local currency or the appreciation of the currency in which they wish to trade foreign products. This makes the foreign exchange market of utmost importance to the largest entities in the world, also reflecting the difference in its nature compared to more traditional markets.

What is an exchange rate or currency pair?

A currency pair in the Forex market is the representation of two different currencies and their relationship. The way currency pairs are expressed is through the abbreviation of the two currencies involved, with the first one being the base currency and the second one being the quote currency. For example, in the EUR/USD pair, the euro (EUR) is the base currency and the US dollar (USD) is the quote currency.

Interpreting a currency pair involves understanding how the value of one currency moves in relation to the other. When we look at a currency pair, the price at which it is quoted indicates how many units of the quote currency are needed to buy one unit of the base currency. For example, if the EUR/USD pair is quoted at 1.20, it means that one euro equals 1.20 US dollars. Technically speaking, all financial assets are traded in pairs, but the quote currency is not usually specified. For example, assets traded in American markets actually quote against the US dollar. Taking Apple's stocks as an example, its pair would be AAPL/USD, with a value at the time of writing the article of $165. This would mean that 165 units of the quote currency (USD) are required to buy one unit of the base asset (Apple stocks). As explained in the article "Absolute and Relative Trend Following" in finance, everything relative and every asset will be reflected relative to another. From that need arises money, as a reference point for asset exchange.

When the price of a currency pair increases, it indicates that the base currency is gaining strength relative to the quote currency, similar to when a company's stocks increase in value relative to the currency they are traded in, known as appreciation. On the other hand, if the price decreases, it means that the base currency is losing value relative to the quote currency, which is called depreciation.

What are interest rates?

Interest rates are one of the fundamental concepts in the world of finance and economics. Basically, they represent the cost of money, that is, the amount paid or received for the use or loan of a certain amount of capital over a specific period of time. When a person, company, or government borrows money, they generally have to pay interest on that loan. Similarly, when someone invests or lends money, they may receive interest as a reward for lending that capital. Interest rates are typically expressed as a percentage and can be fixed or variable.

They play a crucial role in the economy as credit directly depends on the interest rate. Central banks use interest rates as a tool to regulate the money supply in the economy. By increasing or decreasing benchmark interest rates, central banks can influence the amount of money in circulation and control inflation since loans will be reduced, decreasing spending and therefore the demand for products and services. On the other hand, a reduction in interest rates can encourage spending and investment, thereby boosting economic growth. Their impact is also reflected in financial markets. For example, bonds, whose yields are inversely related to interest rates, tend to decrease in value when interest rates rise, and vice versa. In turn, they can influence exchange rates between different currencies; generally, currencies with higher interest rates tend to appreciate relative to currencies with lower interest rates, as they offer higher returns for investors. Additionally, interest rates influence the cost of capital for companies, which can affect their investment and financing decisions.

Correlation between Interest Rates and Currency Pairs

To observe the relationship, the major currencies that make up the majority of the major pairs (known as "majors" in English) and crosses have been selected: EUR, GBP, USD, JPY, AUD, CAD, NZD, and CHF. Each one represents an economy or group of economies, and the pairs formed by their combinations will be studied.

class Currencies(enum.Enum):
    EUR: str = 'zona-euro'
    GBP: str = 'uk'
    USD: str = 'usa'
    JPY: str = 'japon'
    AUD: str = 'australia'
    CAD: str = 'canada'
    NZD: str = 'nueva-zelanda'
    CHF: str = 'suiza'

The price data for these pairs will be obtained from Yahoo Finance using the yfinance API, developed by Ran Aroussi. On the other hand, interest rate data will be obtained by webscraping from Expansion. For all this, the following libraries will be imported:

import enum
import itertools
import datetime as dt

import matplotlib.pyplot as plt
import pandas as pd

import plotly.graph_objects as go
from plotly.subplots import make_subplots

import yfinance as yf

We will continue with the definition of the function responsible for calculating the difference between interest rates and the correlation between it and the exchange rate. To do this, the first step will be to divide and obtain the two currencies of the currency pair in order to download the data and calculate the interest rate difference correctly. Subsequently, the correlation will be calculated.

def getRelation(data:pd.DataFrame, pair:str, show_plot:bool=True) -> float:
    
    curr1: str = pair[:3]
    curr2: str = pair[3:]
    
    if curr1 == curr2:
        return 1
    
    if curr1 not in df_tipos:
        raise ValueError(f'{curr1} is not in the dataframe given')
    if curr2 not in df_tipos:
        raise ValueError(f'{curr2} is not in the dataframe given')
    
    temp: pd.DataFrame = data[[curr1, curr2]].copy()
    temp['Diff'] = df_tipos[curr1] - df_tipos[curr2]
    temp['Price'] = yf.download(f'{pair}=X', start=temp.index.min(), 
                            end=temp.index.max(), progress=False)['Close']
    temp.dropna(inplace=True)
    
    correlation: float = temp['Diff'].corr(temp['Price'])
    
    if show_plot:
        plot(temp, curr1, curr2, correlation)

    return correlation

Finally, we will download the interest rate data and iterate over all possible combinations between the currencies we have previously selected.

exp: Expansion = Expansion()
df_tipos: pd.DataFrame = exp.interestRates(currencies=list(Currencies.__members__.values()))

pairs: list = list(itertools.product(*[Currencies.__members__.keys(), 
                                        Currencies.__members__.keys()]))
correlations: dict = {}
for pair in [f'{p[0]}{p[1]}' for p in pairs if p[0] != p[1]]:
    correlations[pair] = getRelation(df_tipos, pair)

In the following figure, you can see both the price of the EUR/USD pair and the fluctuation of the difference between US and European interest rates. There seems to be a certain relationship between them, although it is the interest rates that tend to react to price fluctuations and not the other way around. This may be because it is the tool used by central banks to regulate the economy. Furthermore, with a correlation of nearly 0.55, the trends often appear to be quite synchronized.

In the following table, the correlation for the pairs formed by the chosen economies can be seen. First, it is observed that most of the correlations are positive, with only 5 negative values, indicating a general association between the difference in interest rates and the exchange rate. This finding is consistent with the theory of interest rate parity, which suggests that investors tend to move their capital towards economies with higher interest rates, which in turn can influence the demand for the currency and therefore its relative value in the foreign exchange market. The highest correlation would be for the GBP/CAD pair, while the most negative is found in the CHF/CAD pair. This could be due to specific economic and political factors affecting these currencies. It could be studied the possibility of implementing a market filter for an operational strategy based on this idea to see if this information really adds any value.

Conclusion

After analyzing the correlation between the interest rate differential of two economies and their exchange rate, several significant conclusions can be drawn. The relationship between these two factors is of vital importance in the world of finance and the global economy, and understanding it properly can be key to making informed decisions in financial markets.

In general, a positive correlation is observed between the interest rate differential and the exchange rate. This means that when the difference between the interest rates of two economies increases, it is likely that the exchange rate between their currencies will also increase, and vice versa. However, there are also cases where the correlation between the interest rate differential and the exchange rate is negative. This may be due to a variety of factors, such as expectations about future changes in monetary policy, unexpected economic events, or central bank interventions. These cases underline the complexity of the foreign exchange market and the importance of considering a wide range of factors when analyzing the relationships between interest rates and exchange rates.

Furthermore, it is observed that the strength and direction of the correlation may vary between different currency pairs. Some pairs may show a stronger and more consistent correlation between the interest rate differential and the exchange rate, while in others, the relationship may be less pronounced or even reversed. This variability highlights the importance of conducting detailed and specific analysis for each currency pair before making investment decisions.