### FXE (Euro) input, no ensemble

Our research was motivated by Varadi post here

1.

**Varadi achieved 49% CAGR gain and 56% D_stat in 2010!**!. Quite remarkable. But** with fixed rules and in hindsight, it is easy.**

2.

Varadi is right with his strategy in 2010, but **we prove that in the last 5 years, the relationship is exactly the opposite. So, in the long term, we cannot use a fix rule.** There are periods (2006) when there was negative correlation between the FXE and RUT, but in 2010 there was positive correlation. Luckily, we use an adaptive approach and we train the ANN only on the last 200 days data.

Let’s start from **2005-12-12. That was the FXE inception date.**

If we discretize the input into 2 bins, we have the following function to approximate.

**There is a negative correlation between the FXE and nextDayRUTChange.** If FXE is down, next day the RUT is likely up; if FXE is up, next day the RUT is likely down.

However, note the same chart **using only the last 200 days from today** (2010-12-01)

Varadi was right. **There is a high positive correlation between current day FXE change and next day RUT change.** If FXE is down, next day the RUT is down; if FXE is up, next day the RUT is up.

If we discretize the FXE input change into 4, 6, 10, 20 equal sized bins (starting from 2005-12-12) we get the following charts:

3.

Let’s see a TR (Total Return) chart of the continuous case from 2006 to 2010. (5 years)

At the start (**in 2006), the inverse correlation prevailed and the ANN profited from it. Later in 2008, it changed to the positive correlation. In the transition period, in the period when the regime changed, it is natural that the ANN is very bad at prediction**. It uses the last 200 days for learning, but those samples are from the previous regime. However, **as the new regime behaviour is learned, the ANN shines again.** This is a typical ANN behaviour. The regimes should prevail long enough that we can leverage on the last 200 days info. Of course the 200 days is a parameter and that parameter is found by trial and error in the development of the ANN phase.

**D_stat: 53.44%, TR: 42%, CAGR: 15%**,

Note that **in the last 250 days (last 1 year), it achieved about 70% return. We even beat Varadi in his own game. (with his 49% CAGR)**

🙂

And I bet that in that period we also achieved the 56% D_stat Varadi published.

4.

We run 8 different random experiments. (no ensemble, standalone FF predictors)

The performance of them can be seen for the 2, 4, 6, 10, 20 bins case as well as the continuous case:

5.

The performance plots are here

Notes:

– It suggest that **using the 6 bins version is the best for D_stat, but using non discretization is best for the CAGR**. But **the difference is not significant.**

– As before, **if ANN randomness is the concern, use the 2 bins version.** That is very stable,** even if it doesn’t give the best prediction.** But backtests can be reproduced anytime.

– We were pleasantly **surprised how well the non-discretized (continuous) case performed. It may be that we won’t use discretization in the final predictor.** Note also that **the 6 bins case STD (high) is almost the same as the continuous STD. We observed the same in the CurrDayRutChange version. There is no point of discretizing to 6 bins if it is true. (However, there is a point of 2 bins, if we require stability.)**. We will get back to this after we see an ensemble versions of these backtest.

– The 10 bins case performed very poorly in all 8 experiments!. It is scary, but no explanation yet.

– We also conclude that **the FXE input is a little bit better than the RutCurrDayChange input for prediction power. **

See this of RUT currDayChange input chart for comparison:

For example, the **D_stat, for the 2bins case, the CurrDayRutChange version gives 51.7% (in 12 years backtest) while the FXE input gives 52.28% (in 5 years).** The other measurements (CAGR, TR) are not really comparable, because we performed the FXE test for 5 years instead of 12 years, and in 2008 was a very bad year for almost any adaptive strategy that learns from the past.

– We had about 52% D_stat in the currDayRutChange input case. About 52.5% D_stat in the FXE case. However, **it would be foolish to expect that after we combine the two inputs, we will have an additive 54% D_stat. The reason is that the FXE and currDayChange has some correlation. They are likely to move in tandem.** So, when we aggregate them to a combined input, sometimes, we don’t add extra info to the ANN.

– It is the same as with deterministic rules. Varadi in the aforementioned link achieved 49% CAGR with the deterministic FXE (in hindsight). He also achieved 30% CAGR with the MR player DV2 strategy in 2010.

See link here

However, it doesn’t mean that if we deterministically combine his FXE and DV2 strategy, we will have 49%+30%=79% CAGR.

– **According to Varadi’s experiment, FXE was better than DV2 in prediction (46% vs. 30% CAGR). We also have the same opinion based on the ANN experiments that the FXE input is a little bit better than the RutCurrDayChange input**** for prediction power.**

– Note that our **ANN predictor** is not a rule based deterministic strategy. Rules are easily formed in hindsight. However, it is adaptive. **If things change, it requires some time (100-200 days) to adapt to the new environment, but it adapts after a while.** Therefore, my realistic maximum expectation for our FXE ANN strategy was half of his results: 25% CAGR and 53% D_stat. But as you can see with 70% CAGR, we even beat his numbers in 2010.

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