Tag: quant

Please read Part I for the introduction, Part II for a study of the spread between USDINR and the dollar indices and Part III for a spread-trading back-test on daily returns.

Weekly vs. Daily

In our previous posts, we used daily returns to setup the analysis. However, analyzing daily series on currencies and commodities is problematic. They trade 24/7 in a global marketplace and “closing” prices for commodities and currencies are hard to pin down at a granular level across markets. One way to ameliorate this issue is to use a weekly or a monthly series instead.

Here are the plots of the spreads and p-values from the adf-tests applied to weekly returns:

The back-test results mirror that of the daily series, with bets on momentum carrying through on the USDINR and DTWEXM pairs:

This gives us more confidence in our back-tests. We end our series with the following caveats:

1. Trading the spread involves trading both legs (as discussed in Part III.)
2. One can only buy a currency by selling another. i.e., buying USDINR implies going long USD and short INR.
3. Using the above analysis, if a trade involves buying USDINR in one of the legs, it does not inform anything on relative valuation of USD or INR.

Code and charts on github.

Please read Part I for the introduction and Part II for a study of the spread between USDINR and the dollar indices.

Trading the spread

In Part II, we defined spread = A – βB. When we say “trade the spread” we literally mean going long or short the spread as defined. To actually implement the trade, one would have to create two legs: one that is long USDINR (A) and the other that is short β times one of the dollar indices (B). Since the dollar indices are not something that can be actually traded, the following back-tests are purely a theoretical exercise.

Back-test

We consider three scenarios:

1. C1: if the spread diverges beyond 1-sigma, bet on mean-reversion.
2. C2: if the spread diverges beyond 1-sigma, bet on it getting bigger.
3. D1: if the spread is between the average and 1-sigma, bet on it blowing out.

The first one is pure convergence and the last one is pure divergence. The second one is sort of like momentum – if the spread is already beyond 1-sigma, bet on it further blowing out.

It appears the second scenario, the one that bets on momentum carrying through, is the most profitable. Also, the most profitable pair seems to be USDINR and DTWEXM (Trade Weighted U.S. Dollar Index: Major Currencies).

In the last part in this series, we will run through this analysis for a weekly time-series of these indices.

Code and charts are on github.

Please read Part I for the introduction.

In Part I, we saw that if we force the intercept to be zero during linear regression between two series A and B, we end up with A = βB. In this post, we go one step further and define spread = A – βB

Pair trading

Readers of our posts on pair trading will immediately recognize the above relationships. The idea here is that if we assume USDINR to be dependent on DTWEXB, DTWEXM and DTWEXO indices, then we:

1. calculate the spread between USDINR and each of the indices in turn,
2. check if the spread is ‘stable’ by conducting an adf test on the residuals of the linear fit and checking if the p-value is less than a threshold,
3. if the p-values confirm stability, then we can go long/short the spread whenever it deviates from the mean.

Spreads

When we plot the spreads and p-values, we see that a 50-day period is probably the most suitable time-frame over which to calculate the spread. And, we also observe considerable mean-reversion suggesting that a trading model can be built over it.

In Part III, we will back-test a couple of trading models based on these spreads.

Code and charts are on github.

The St. Louis Fed publishes a number of economic and financial series on its Federal Reserve Economic Data (FRED) database. It is a treasure trove of information for quants. There are a number of currency related time-series in the database. In this post, we will plot the USDINR exchange rate with the trade-weighted indices available on FRED to explore any relationships that there might be between them.

Trade-weighted indices

A trade-weighted dollar index is simply the weighted average of the foreign exchange value of the U.S. dollar against the currencies of a group of U.S. trading partners. The FRED publishes the following such indices:

1. DTWEXB: Includes the Euro Area, Canada, Japan, Mexico, China, United Kingdom, Taiwan, Korea, Singapore, Hong Kong, Malaysia, Brazil, Switzerland, Thailand, Philippines, Australia, Indonesia, India, Israel, Saudi Arabia, Russia, Sweden, Argentina, Venezuela, Chile and Colombia.
2. DTWEXM: Includes the Euro Area, Canada, Japan, United Kingdom, Switzerland, Australia, and Sweden.
3. DTWEXO: Includes Mexico, China, Taiwan, Korea, Singapore, Hong Kong, Malaysia, Brazil, Thailand, Philippines, Indonesia, India, Israel, Saudi Arabia, Russia, Argentina, Venezuela, Chile and Colombia.

Additionally, they also publish the DEXINUS series that is the USDINR exchange rate.

These series go back to the mid-70’s and mid-90’s. However, India was a closed economy with a managed currency for the most parts. So for the rest of this post, we will consider data only from 2005 onward.

Here is how the time-series looks:

Beta between USDINR and the rest

What we are interested in is the relationship between USDINR and the rest of the trade-weighted averages. DTWEXB and DTWEXO have India exposure with the latter made up predominantly of emerging markets. So we should expect a high beta between USDINR and those.

To calculate the beta, we will fit a linear model through USDINR and each of the trade-weighted indices in turn. Also, we will force the intercept to be zero to force the fit.

Here are the betas with a 20-day look-back:

Here are the betas with a 50-day look-back:

The 20-day chart shows that the beta oscillates within a tight band for the most part. This insight can be used to build a mean-reversion model for USDINR.

In Part II, we will explore the spread between USDINR and all three of the indices. Stay tuned!

Code and charts are on github.