Sure or Not? Expert Advice on FX exchange rates

TLDR

In the recent past, I had to deal with some FX transfers during some volatile SGDMYR exchange rates.

It felt unnerving at first to make these decisions so I sought out the opinions of various experts. They were all right and wrong to varying degrees.

Instead of making gut decisions on who to trust, I built a simple model to quantify and merge the various expert opinions.

Distilling an Opinion

For each expert, I ask 3 questions:

• What range do you expect the FX rates fall within? (this is q25 and q75)
• Within this range, what do you expect as the average rate? (this is q50)
• If some crazy event happens, what do you expect the highest and lowest it could go? (this is q05 and q95)

This created a nice quantile spread. I felt this was a simple enough method to hold discussions with different people.

Here are some of the expert opinions (names redacted, of course!):

banker = {
	"q05": 3.10,
	"q25": 3.20,
	"median": 3.25,
	"q75": 3.33,
	"q95": 3.35,
	"confidence": 0.50,
}
youtuber = {
	"q05": 2.90,
	"q25": 3.10,
	"median": 3.20,
	"q75": 3.28,
	"q95": 3.30,
	"confidence": 0.25,
}
fx_trader = {
	"q05": 3.20,
	"q25": 3.25,
	"median": 3.28,
	"q75": 3.35,
	"q95": 3.40,
	"confidence": 0.75,
}        

As you can see, the spread is quite significant

• The expected range varies from 3.20 - 3.28. Thats a 2.5% difference between lowest and highest.
• The worse case varies from 2.90 - 3.20. Again, thats a 10% difference!
• The best case varies from 3.30 - 3.40, with a 3% difference.

The biggest takeaway here is to theres greatest uncertainty in how low it will go. The expectation here affects behaviour when the currency is trending downard and there's a time crunch to exchange some currency: wait or bite the bullet?

Building an ExpertOpinion Model

To quantify the expert opinion, I decided on a beta distribution because of its flexibility.

The downside is this is a bounded distribution. I attempted fitting upper and lower bounds with linear and S-curve logistic functions, but in the end, what worked best was simply taking upper and lower quantile and extending it by 0.1....

The objective function was a simple mix of errors at each quantile, with an emphasis on the median and outer bounds.

Here's a stub:

    def _quantile_objective(self, params):
        """
        Enhanced objective function for beta parameter optimization
        incorporating confidence and multiple quantiles
        """
        alpha, beta = params

        # Basic quantile matching
        q25_err = (stats.beta.ppf(0.25, alpha, beta) - self.norm_q25) ** 2
        q75_err = (stats.beta.ppf(0.75, alpha, beta) - self.norm_q75) ** 2
        median_err = (stats.beta.ppf(0.5, alpha, beta) - self.norm_median) ** 4

        confidence_weight = 1 + self.expert.confidence

        # Basic error
        error = median_err**confidence_weight + q25_err + q75_err

        # Add tail quantile matching if available
        q05_err = (
            (stats.beta.ppf(0.05, alpha, beta) - self.norm_q05) ** 4
            if self.norm_q05
            else 0
        )
        error += q05_err**confidence_weight

        q95_err = (
            (stats.beta.ppf(0.95, alpha, beta) - self.norm_q95) ** 4
            if self.norm_q95
            else 0
        )
        error += q95_err**confidence_weight

        # Add shape penalty to prevent "fat" curves
        mode = (alpha - 1) / (alpha + beta - 2) if alpha + beta > 2 else 0.5
        mode_penalty = ((mode - self.norm_median) ** 2) * self.expert.confidence
        # mode_penalty = 0

        # Penalty for extreme parameters (prevents "fat" curves)
        param_penalty = 0.01 * (alpha**2 + beta**2) / (alpha + beta) ** 2
        # param_penalty = 0

        return error + mode_penalty + param_penalty        

For each , I fit a beta distribution to it using numerial optimization and initializing the initial values. The outcome was... acceptable. I found that for the beta distribution, the parameter estimation would "blow up" if the bounds and initalization were not done nicely.

Side Note:

While the curves looked good-enough, it felt like the distribution values didn't feel intuitive.

After some reading, I then tried fitting a skew-normal distribution using mcmc methods. I loved how conceptually intuitive this felt.... however, the results needed more finessing. This now lives in the "someday maybe" pile.

Additional note: half the battle was setting up the correct env for pymc5, but I highly recommend pymc5 over its predecessors. It feels alot leaner.

Aggregating the Models

Great: I've interviewed some experts, converted their opinion to a distribution.... Now comes the exciting part: with N expert opinions, how to aggregate them?

I used a straighforward but effective strategy: empirical sampling approach. A meta-sampler queries the model group and generates an aggregate sample dataset, arbitrarily taking a sample size of 10_000 per expert.

Here's a simple histogram plot:

... and some pocket-summaries:

            fx_rate
mean       3.243234
std        0.102834
min        2.831691
25%        3.184129
50%        3.255911
75%        3.317466
max        3.47799        

Thoughts & Someday Maybe

Some rough edges:

• The min and max are way out of bounds. Intuitively, it feels wrong, but realistically, it could happen... This is also where upper and lower bound setting is so important
• This was useful... to a small extent. Other methods like measuring momentum and volatility were also very insightful.

For future consideration, it would be a simple fun next step to convert this to a bayesian model.

• Treat the expert opinions as a priors
• Treat the previous N days as the observed data
• Generate probabilites for the upcoming window, leading to decisions on when to make an exchange.

WIP Github Repo: https://github.com/lennardong/fx_bayesian