*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:

- C1: if the spread diverges beyond 1-sigma, bet on mean-reversion.
- C2: if the spread diverges beyond 1-sigma, bet on it getting bigger.
- 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.

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