If all finance developers around the world were asked to choose the main nightmare they have to face on daily basis, I bet most of them would choose ‘overfitting’. Furthermore, imagine you have to develop an algorithm which has only one ‘ingredient’ to be modelled, only one time-series representing the historical information… Yes, in that case, you’ll need the Synthetic Financial Time Series Generator (SFTSG).

Let’s go for the Currencies

In our last post, we introduced what SFTSG is and its results. It is the perfect tool to fight against overfitting when modelling with financial time series because it leads us to such diversity of scenarios that our models’ robustness clearly improves.

We have worked with Funds and Stocks, but in this post, we want to test its goodness when simulating Currencies. Why Currencies? Because they have to face the main problem already explained in the introduction: we have only one time-series representing the real EURUSD to develop, for example, an overlay program. So in this case, this necessity of enriching the scenarios to train our algorithms clamours the participation of the SFTSFG.

With this in mind, we have synthesised 50 alternative paths of 50 years of the EURUSD using this tool. We have considered the real data representing EURUSD as the time series that has been built as a daily bar of prices that starts at 9 am (UTC+1) and we have taken into account only the close price. Our simulations look like this (real data in black):

Do not be misled by the results of the extremely positive paths because in general, the standards are maintained. We briefly show some results:

Parity and burgers

We want to get an idea of how our simulated paths show an overvaluation or undervaluation of the Euro against the US dollar. Concerning to this topic, we have the option of using any indicator of the Purchasing Power Parity (PPP), which is an economic theory that sets the imbalance between the prices of two currencies through a “basket of goods” approach. According to this theory, two currencies are at par when a basket of goods is priced the same in both countries. In particular, when the good is the McDonald’s Big Mac, we are talking about the Big Mac Index, which has been selected as our benchmark in this post. It is also known as Big Mac PPP and consists on a survey conducted by The Economist that is used to measure the purchasing power parity (PPP) between nations, taking the price of a McDonald’s Big Mac burger as a reference.

Don’t misunderstand us, we know that this is an informal way of measuring the purchasing power parity (PPP). If we would pretend to use it as an axiom, other factors such as work or income of the population should have the same value in different countries. What is more, different countries should have similar gastronomic habits, so please take this indicator as a non-literary one.

An exercise: does the SFTSG add value when simulating Currencies?

Thanks to the open source of The Economist, we obtained the data of the Eurozone PPP Big Mac for the last 18 years. We are going to concentrate on the first half-year of 2018, the latest data we have. At the 17^th of January, The Economist set that the Euro, according to the Big Mac PPP calculations, was undervalued at the rate of 8.3% against the US Dollar. The explanation of this announcement is what follows: at that time the price of this burger was, on average terms, 3.95 euros in the Eurozone. That’s equivalent to 4.84 dollars according to the actual EURUSD rate in those days, which was 1.23. However, this burger’s cost was 5.28 dollars in the US. So the calculations are clear:

If 3.95 euros should have been equivalent to 5.28 US Dollar, the EURUSD rate should have been 1.33 instead of 1.23. That’s why the Euro was undervalued.

In this case, the concrete rate of undervaluation, this means, the value of the Big Mac Index, is 8.3%. This comes from the next simple operation: (4.84-5.28)/5.28 = -8.3%. Furthermore, during the first six months of 2018, the EURUSD didn’t change its behaviour and from January to July, according to this theory, “buying a Big Mac in the Eurozone has been cheaper than what it would be if it cost the same than buying it in the US, so the Euro has remained undervalued against the US Dollar”.

We want to repeat these evaluations with our simulated paths of the EURUSD. We randomly select 1,000 6 month periods of the synthetic series that do not overlap (they are independent). This set is a list of “hypothetical” (but plausible) first 6 months of 2018. We will compare our simulations with the real PPP Big Mac this way: is a Big Mac in the Eurozone too cheap when compared with the US price and therefore our hypothetical currency prices of EURUSD show the euro is undervalued?

The results show extreme cases: most of this random synthetic segments demonstrate an overvaluation or undervaluation maintained during the whole period. In a few cases, the simulated currency pair shows a change in its behaviour that establishes, according to the Big Mac Index, that one of the currencies has passed from being undervalued to be overvalued.

What a simple hamburger can yield…

A priori, we expected more diverse scenarios (under or overvaluation alternation). So we need to further explore whether the SFTSG is helping us to widen the variety of paths enough to improve our models. See you when we have some more answers.