A Simple FOREX Model

TDLR: There is an arbitrage opportunity between XAU, GBP, and USD.

I used the Bank of England’s currency exchange data from 2015 to create a model between the price of gold (XAU) in GBP (XAU GBP) and XAU in USD (XAU USD). Graphing both, we can see that it most likely has a linear relationship.

With XAU USD as the regressor against XAU GBP, the model returned an R² of 88.53% with σ² = 185.05. In a quick and rough summary, we see the exchange rate should be β_1, which is .8853, the exchange rate of USD GBP.

To improve the model, we can take the GBP USD price and add it as a regressor. We get an R² of .9990 and σ² = 1.61. This is a near-perfect model. When graphing the residuals plot, we see hardly any outliers and scattered data points scattered without clustering.

This model was frustrating to me on the surface since there is an economic theory saying that a currency will have the same value anywhere — parity. A way to think of this is if two pawn shops are next to each other if one offers widgets for sale at $1 and the one next door will but them at $2, then it would be a good idea to but as much, sell next door, and keep up the process until the prices are equal. The same applies to the currency market. Since the model is not perfect, we see a minimal opportunity for arbitrage; however, since it is not equal, and the model’s R² is not a perfect 1.000, money can be made in thoery.

At the time this is written I do not have any financial postions. I am not offering this article as investment advice. I am not a fincial advisor. There is a risk involved. Every investment has risk that I do not assume for you. It should not be assumed that the information provided will be profitable or that it will not result in losses. Previous information shared is not an indicative of future returns. You are responsible for making your own investment research and decisions.