Signal and noise in the eyes of engineers and financiers

When I first got into the MBA program, I took a sort-of personality test which was designed to tell me how my personality matched better different successful professionals in different industry sectors. My results were off the chart for two particular sectors (scoring close to 100/100):

  • Engineers and scientists
  • Investment bankers

What????!!!!

How could these two types of professionals be of the same personality, I wondered out loud to myself, stopping short of feeling insulted.

But I have always loved economics and financial theories, studying them causally by myself over the years of my engineering career. That should have been a clear sign to me were it not for my engineer pride.

Then as I progressed through formal finance curriculum (both at HEC Paris MBA program and in parallel the CFA training), I quickly realized — yes, these two sectors actually require similar personalities (and intellects): objective, analytical, inquisitive, systematic, theory-driven, etc.

Even more, I came to realize that in their trainings and practices the engineers and the financiers even share some common theories and disciplines, among which the dealing with signal and noise is the most revealing discovery I've had.

 

Signal and noise in engineering

One of the most important concepts taught in EE curriculum and used by many communication/circuit design engineers is signal-to-noise ratio (SNR). Or more generally, the relationship between signal and noise.

In general signal is what engineers are trying to protect against noise since only the former carries information. In communication algorithms and circuit designs many a techniques of signal processing have been invented and developed just to optimize the signal-to-noise ratio.

The techniques of signal processing that were invented are both astonishing in number and in its creativity — the CDMA technology that made my former employer, Qualcomm Inc. (QCOM), famous (and rich) even disguises the signal as noise at the transmitter and recovers it out of the noise floor through mathematical calculation at the receiver.

Noise arises from either the nature (e.g. thermal noise), the circuitry (e.g. shot noise) or the processing algorithms (e.g. quantization noise), the way to deal with it is to "describe" it first:

  • Is it stable (stationary)?
  • What is the noise spectrum, i.e. distribution over frequency?
  • Is it stochastic, i.e. distribution over time similar to that over samples?

Depends on the characteristics of the noise, an engineer can try to suppress it from being amplified along with the signal, shape it to different distributions, etc. Whatever they do, it's almost always about maximizing the SNR and therefore optimizing communication quality.

 

Signal and noise in finance

While few people outside of engineering have much idea about the importance of analysis on signal and noise, even fewer outside of finance know that the same applies to finance as well.

In finance, the market is generally regarded as adequately efficient, or at least it's very difficult to profit from any assumed inefficiency. The underlying trend of the market is usually fully expected and priced in. Only new and unexpected informations will change the course of asset prices. This is the famous random walk theory and has been proven to be difficult to invalidate over the decades.

If the market is efficient, the expected asset price trends are then the signal, while daily or weekly price fluctuations due to random walk are the noise.

Like engineering, financiers also spend a lot of time trying to figure out the look of noise, or in financial terminology: volatility. The most liquid securities usually have noise that looks like they're normally distributed, meaning that if you take the daily or weekly return in percentage of a certain security for say 10 years and plot out the distribution, it would look like a normal distribution.

Then the financiers will make perhaps the most critical assumption here: such noise is assumed to be stochastic. This then allows the financiers to use the distribution of the time series to predict the distribution of the price distribution of the next time point.

Probabilistic Programming in Quantitative Finance
Posted by: Thomas Wiecki


The divide

The readers probably have noticed that I have used a lot of "assume" in the past few paragraphs when we shifted the topic to finance.

This is very important.

Unlike engineering where repeatable (either through time or through samples) results are a fundamental part of the industry, in finance one cannot replay the history. There's also only one planet earth as far as we know (and therefore only one sample). And even if you believe in infinite universes and therefore infinite planet earths (samples), it's non-observable and non-investible, therefore useless for the sake of financial practices, e.g. diversifications.

Here lies the greatest divide in engineers and financiers, despite the fact that both employ the same mathematical tools when it comes to dealing signal and noise. Despite this, as I got deeper and deeper in the "dark side", I feel that outstanding engineers and financiers are indeed of the same kind.

Maybe it's just the initial choice of study/career that leads to such a deep divide in later stages of the career. The hatred that many engineers have toward the "non-performing" financiers is maybe but a natural hatred between siblings?

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