This project is inspired by an article on oil-backed foreign exchange. Amid the bullish outlook for crude oil, the currency exchange of oil producing countries would also bounce back. Does this statement really hold? Prior to this article by Bloomberg (or many other similar research), market analysts test the correlation between petrocurrency and oil price, instead of the causality. The issue is that correlation does not equal to causality. Correlation could be a coincidence of a math game. We simply cannot draw the conclusion that oil price moves the currency (the cause can be a third common factor such as inflation). Some researchers even introduce bootstrapping which, unfortunately, destroys the autocorrelation of time series. Thus, it is necessary for us to apply empirical analysis and computer simulation on various petrocurrencies to examine the underlying phenomenon.
The following figure is a global oil production choropleth. The map lists out a couple of petrocurrencies with potential arbitrage opportunities. What can be easily overlooked is that some of the oil exporting economies peg domestic currencies to US dollar. For the central banks, the peg eliminates the volatile currency risk for oil exporting. For the traders, the room for petrocurrency arbitrage is squeezed. So it is crucial to verify the exchange rate regime of any oil exporting country from wikipedia before moving onto any further analysis.
Unfortunately GitHub ReadMe does not support javascript. Click here to be redirected to an interactive version of the oil production choropleth.
The figure below is a global oil production cost curve. Don't ask me why the data is 2015. They said data is the new oil, this is true especially when it comes to oil data. As we can see, the marginal players in this chart are Brazil and UK. Their production cost has reached 90% percentile among these countries. This explains the decade-long inactivity in North Sea oil field. The only feature of Aberdeen has been Angus beef (proudly made in Scotland) since the time of Margaret Thatcher. And for Brazil, I'd say the production cost absolutely has something to do with the corruption probe in Petrobras. Probably it is why iron ore export makes more money than crude oil in Amazon jungles (Vale is de jure privatized yet Petrobras is state-owned). Hence, we will exclude the largest crude oil producer in LATAM from our oil money project.
Okay, enough about bad jokes. You may ask why I talk so much about commodity market at the beginning. If you think quantitative trading is about solving some complex stochastic process on commodity options, prepare to lose a big chunk of money. You simply cannot quantify geopolitical risk or supply disruption by force majeure. Some basic knowledge of underlying commodity is vital to your trading strategy.
In the original article by Bloomberg, the first mention is Norwegian Krone. Norway is one of my favorite places in Europe. Unlike Qatar or Saudi Arabia or any other Gulf/OPEC countries, the government doesn't heavily rely on oil or gas for its gross income (even though Equinor formerly Statoil is still a major player in Oslo Stock Exchange). According to wikipedia, over 60% of GDP is contributed by services in contrast to approximately 30% by industry in 2016 (arguably those services could still be oil-based like Dubai). Norway has established the largest sovereign fund in the world to hedge against oil price decline, ever since the discovery of north sea oil fields. Norway has non-petroleum industries such as fishing, maritime, renewable energy, etc. I doubt if oil price is the major driver of the exchange rate of NOK. I look into international trading statistics of Norway. Apparently, most trading partners are inside European Union. Prior to this report, I include Sterling and Euro into the price evaluation model of NOK. To my surprise, Norway actually does a lot of business with US. Hence, the model regressor consists of EUR, GBP, USD and Brent Crude.
After the selection, we have to choose a base currency to evaluate NOK. It should be a stable entity with free floating FX regime with not much economic tie to Norway. I pick the safe haven currency in East Asia, Japanese Yen. In a released report by OEC, Japan only accounts for less than 2% of exports in 2017 which makes a perfect candidate. Then all regressors in the model would be priced in JPY. Some of you may question why we do not use trade-weighted exchange rate. Indeed, trade-weighted exchange rate is a better choice as it eliminates all other trading partner currencies in the model. The model can solemnly focus on the exporting commodities. However, the pain point is how to construct such exchange rate index. When we talk about trade weights, do we refer to surplus or deficit or total amount of trade? A country can certainly trade with more than 100 partners. Is it reasonable to include every trading partner currency into the weight? Or at what percentile of trade in values do we cut off the list? Why does that percentile make more sense than the others? Constructing a new index is rather state of art than social science. Obviously, it is easier and more efficient to use a non-trading partner currency for evaluation of all the variables. Hence, our regressor variables become EURJPY, GBPJPY, USDJPY and Brent Crude in JPY. Our regressand variable is NOKJPY.
Arguably, the model should involve natural gas (Dutch TTF?) as well. From the website of norskpetroleum, Norway supplies 25% of EU natural gas demand (mainly France and UK). It is interesting that many natural gas contracts are not tied to gas benchmark such as Henry Hub or TTF. In most cases, the price is linked to Brent, sometimes even coal.
Of course, there are other elements that affect NOK. It is widely acknowledged that change of interest rate impacts the foreign exchange significantly. However, the downside of interest rate is its slow response to the financial market. Central bankers assess the overall condition and review their decisions carefully and patiently. The rate hike may only occur after pickup of inflation rate or employment rate. It could be several times one year and silent for the next couple of years. By the time inflation rate is boosted by soaring oil price, NOK has priced that factor in for a long while.
Another important element is economic activity, GDP Year-on-Year growth. Inadequate amount of the data is its biggest flaw. GDP is usually released by statistics bureau quarterly. Forex market is agile and it moves every weekday 24/7. We cannot trade only 4 days a year and stay put for the rest of 246 days. Some indicators are seen as early signs, such as active oil rigs or social financing. These indicators are released on a monthly basis, slightly better than GDP.
Thus, Brent and other currency pairs are undisputedly better inputs to reflect whether NOK is undervalued or overvalued at the moment.
The data of the past five years is collected from Thomson Reuters (now called Refinitiv). We denote the time horizon before 2017-04-25 as training period. We use that period to fit a regression model. From 2017-04-25 to the end of our dataset is defined as testing period. We use our model from training horizon to predict "reasonable" range of the value of NOK in testing horizon. This is a standard practice called cross validation by data scientists. Economists call it out-of-sample data for forward testing and in-sample data for backtesting. The regression result comes out as below. We have a pretty high R squared. All T stats and F stats seem to be significant. I have to take back my words. Brent shows a major influence on NOK which implies Norway still heavily depends on petrochemical industry. As the summary suggests, there could be multicollinearity (condition number is large and R squared is large). Obviously, Brent crude and US dollar should be negatively correlated. Most commodity future contracts are priced in US dollar. When US dollar appreciates or depreciates, the underlying commodity price is likely to go the opposite direction. There could be a cointegration relationship between Sterling and Euro for pre-Brexit time as well.
In this case, we will use elastic net regression to implement regularization. Elastic net is a statistics/machine learning technique that consists of both Lasso (L1) and Ridge (L2) regression to act as a penalty. Ideally it is a perfect tool for multicollinearity issues.
Before backtesting, we ought to set up thresholds for signal generation. One sigma two-sided range is the common practice in statistical arbitrage. When actual NOK price goes above the upper threshold (larger than one sigma), we take a short position. We hold the belief that NOK is overvalued and it should fall back to its normal range very soon. Vice versa. However, the model is based on historical data. No models can precisely predict the future from the past. Our estimation is most likely to be overfitted and fail very quickly in the near future. We need to set up some thresholds for stop orders. When the model breaks, we could clear our positions and exit the trades gracefully. In that case, let's use another golden rule in statistics, two sigmas with 95% confidence interval, to do the trick. If NOK deviates 2 sigmas away from our fitted value, we need to realize the model is broken and we shall exit the trades right away. The figures below show the initial trading strategy. They demonstrate the positions of our statistical arbitrage and the actual price movement against the fitted value within confidence intervals.
To our surprise, there is a strong momentum after our model breaks. The momentum is independent of the selection of our training horizon. In another word, no matter which period we use as training horizon, the strong momentum always follows through right after the model breaks. The failure of this model doesn't really upset me. On the contrary, it is a blessing in disguise. What I see is an opportunity for trend following strategy! We will get back to that very soon.
What also interests me is why the model fails after 2017/11/15. Well, there is no way that a universal model can exist and work forever. Most models have short memory due to the dynamic environment of macroeconomics and geo-politics. Based on adaptive market hypothesis developed by Professor Andrew Lo from MIT, the players in the market are always evolving along with the fast-paced environment. Therefore, we should anticipate our model to lose its power sooner or later. Still, what is the cause of the break? For a quantamental analysis, we have only completed the quant part. I would not get into too much of rigorous and boring part of the fundamentals. Instead, I intend to bring up a short but insightful discussion here. What could possibly be the reason of this dramatic change? Could it be that Saudi and Iran endorsed an extension of oil production cap to boost up the oil price on that particular date? Or Donald Trump got elected as POTUS so he would encourage a weak US dollar and lift up restrictions on oil export as promised during his campaign? If we consider the price of NOK as a stochastic process, we can decompose NOK price into long term trend and short term random disturbance. Well, apparently short term is dominated by Brent Crude. It partially justifies our model. What really drives the long term trend though?
Ta-da, its Euro. As Norway is in EEA, its economic tie with EU totally dominates the long term trend of NOK. From the normalized figure, we clearly see the trend of both NOK and EUR are somewhat correlated. To get a formal conclusion, we need a cointegration test. Nevertheless, there is no Johansen Test in statsmodel package (not on the date when the first draft of oil money was finished, but there is now). We would have to use Engle-Granger two step test. I have to honorably mention that this method is co-developed by the mentor of my mentor, Robert F. Engle, a Nobel Laureate! Unfortunately, we can't get any confirmation of cointegration from the test. The residual of the first step regression is not stationary under Augmented Dickey-Fuller Test. Sometimes we have to use the old fashion way to make a qualitative judgement, rule of thumb. Most researchers in big organizations recalibrate their forecast with policy or experience or consensus views or simply instinct (as an insider, I guarantee you this is 100% true). This is the moment that I exercise my sacred right to declare that EUR is the driver of NOK's long term trend!
Well, I am not an economist (even though my work has a lot to do with them). I do not expect to really find out what happened on 2017/11/15 through our quantamental analysis. Let's call it an end to this twist (if you are an economics-savvy person who is eager to know more, feel free to read this paper by the Central Bank of Norway). In fact, we can simplify our model to NOK driven by Brent. From an econometrician's perspective, it does not sound like a good idea. Every coefficient of the model is statistically significant. Adding more variables does not worsen AIC, BIC or adjusted R squared. There is no incentive for us to remove variables as more information in the model is always better. From a trader's perspective, the requirement is a universal model. Ideally, the model contains two variables, one is the underlying petrocurrency, the other is the local crude oil contract. In this sense, the reduced form model can be replicated to any petrocurrency without too much focus on analyzing trade partners or exporting products. The argument here could be, is linear regression model too naïve? Nick Patterson, a cold war cryptographer who later worked in Renaissance Technologies, said (check here for the original version of 45-minute-long interview),
One tool that Renaissance uses is simple regression with one target and one independent.
It's simple, but effective if you know how to avoid mistakes just waiting to be made.
In the world of modelling, the identification is far more important than the estimation. As long as we find an element with causal effect, there is no need for fancy spatial time series analysis when we can solve everything in its simplest form. We will take the trader's perspective in the following context.
Next, let's take a look at the portfolio performance. So far so good, we actually make a few bucks from statistical arbitrage. Interestingly, after we place the stop order, I decide to add an extra position to see what would happen if we follow the trend. In the figure below, we could see the downwards momentum doesn't stop until two months later (probably another major event in financial market).
Wow, did we just discover a momentum trading strategy! We started off this project to seek for a statistical arbitrage opportunity between crude price and petrocurrency. What we got in the end is an entry signal of momentum trading strategy. Also, we found out Euro is the major and long term influence on Norwegian Krone, and Brent Crude is the short term disturbance. My explanation for our discovery is that, when the model breaks, there must be something fundamental that change investors' outlook in NOK or Brent, e.g. an increase in north sea refinery capacity limit. That sort of change is supposed to last for quite a while which offers us a chance for trend following (this is how CTA makes money).
Here are the rules of our latest momentum trading strategy.
- The first step is always about regression. Run linear regression on NOKJPY and Brent in JPY of the past 50 data points. If the R squared exceeds 70%, the model is deemed as valid, which has successfully verified the petrocurrency status of Norwegian Krone for the past 50 trading days. Then the forecast derived from the model becomes reliable.
- Calculate the standard deviation of the residual. Set +/- two sigma from the predicted price as the threshold to trigger trading signals. If the actual price sits above the upper threshold, the position is net long. If the actual price sits below the lower threshold, the position is net short.
- Once the trade is executed, a counter will start as well. It will keep track of how long the position has been held. If the holding period exceeds 10 days, the position will be cleared. Because the underlying momentum could have vanished into the thin air after such a long time.
- Meanwhile, if the absolute spread between the current price and the entry price exceeds preset limit, which is 0.5 points by default, the position will be cleared to claim profit/loss. The preset spread limit varies along with each individual's risk averse level. When the market gets too volatile, it is sensible to reduce the risk exposure.
- After the position gets cleared, the model has to be recalibrated by the latest 50 data points. Now that a trade cycle has completed, the whole thing goes back to the first step. So on and so forth.
As shown in the portfolio performance, each momentum takes different length of time to decay. Holding the position too short may not reach the peak of the asset price. On the other hand, Holding the position too long may surpass the peak and head towards the lower side of the profit curve.
Nonetheless, we are not satisfied with the return. We are greedy creatures. 2% return? Why don't we deposit the money into the current account and get some risk free interest (Norges Bank interest rate at 1% as on the 30th of April, 2019)? We certainly need to tune the parameters, such as different holding period and stop loss/profit point (even the amount of backtesting data points or acceptable R squared level), to maximize the return. After several attempts, we have gathered the below statistics. In average, the return is around 2%, positively skewed. Yet, extreme values can go as far as -6% to 6%. Needless to say, 6% is the goal.
The heatmap below is the visualization of return using different parameters. The darker the tile is, the more money you make. From the chart, you can easily tell stop profit/loss point doesn't have much explanatory power on the return. The return is more correlated with the length of holding period. It makes sense since this is a trend following strategy. The optimal holding period to maximize the return appears to be 9 trading days. The optimal stop loss/profit point is more flexible, which could range from 0.6 to 1.05.
It turns out that our momentum trading is much more robust and profitable than our original idea of statistical arbitrage. But does it work on any other petrocurrencies? Unfortunately, Norway is one of the largest oil producing countries with floating FX regime. The rest are US, Russia and Canada. US dollar is a totally different case. Petroleum business only takes up a very small share in US economy even including shale boom in Permian Basin.