# A distracted walk with Technical Analysis

In the last blog post I wrote about random walks modeled with a Brownian motion, and then criticized the typical use of this model in finance, where we find it with a fixed drift term. A fixed drift term is too much of a simplification I argue, and propose that we should rather be open to incorporate a time dependent drift term.

In this post I’ll look at technical analysis and how it relates to our random walk. Technical analysis tends to get slaughtered quickly in the context of an overly simplified Brownian motion modeled reality. Let’s see if that holds with a time dependent drift..

There’s something called a rational investor, or homo economicus, in the academic world of finance. This is a mythical creature that no one’s ever meet, but the rational investor is critical for our simplification of the real world. Without homo economicus, it breaks down.

So let’s look at some of the characteristics of homo economicus:

- Consistently rational
- Narrowly self-interested
- Optimal approach

Within such a framework we would define the drift term in our Brownian motion as always being positive. Because, if it was negative, no rational investor with an optimal approach and his or her self-interest intact, would ever invest in such an asset.

So how can the stock market ever go down, if this is the case? Well, that’s simply down to the fact of our error term, which is normally distributed. A quick recap from the last post, and we can define an asset’s price movement like having a constant drift of 10% with a volatility of 20%. Isolating on the pure drift, removing the error term, and we find an ever increasing asset price.

Even if you’d say a fixed drift is too simplistic, you’d still never let it go negative. Because that speaks against the fundamental concepts that it is built upon.

So there we have it: If you limit your reality to an always positive drift, the best possible strategy is a buy and hold, because the only thing making the price move down is an error term following a normal distribution with mean zero. And since there’s no memory in the error term, there is simply no point trying to outsmart the Brownian motion.

## What a simple little world they’ve created

Financial markets are not a physical property. It’s a social artifact of humans interacting.

And to constraint yourself to homo economicus is a simplification taken too far. It’s time to move on..

It is clear that greed, panic and irrationalities rule even the most “professional actors” of financial markets. It is therefore completely reasonable to assume that sometimes the drift isn’t positive. And if that is the case, an asset will have price tops and bottoms, from which you can sell high and buy low. The challenge is to find the function for this drift, isolating it from all the noise we still have in there.

Moving on to technical analysis specifically. There’s certainly a lot of bull shit within technical analysis, let’s not forget that. But if you think about the simpler concepts, like a moving average, what exactly is a moving average? It is what we’d call a low pass filter.

So if there is a function to the drift, that can go negative at times, but is obstructed by higher frequency noise, a low pass filter, or moving average, is to be fair, a good initial approach for detecting it.

The question we need to ask ourselves, is, does this low pass filter allow us to jump onto the trend fast enough? Or is the natural lag of a low pass filter simply too great for us to use it to our benefit?

What about another technical analysis concept called support and resistance?

I think it’s perfectly reasonable to assume that an asset has an intrinsic value, and we can imagine this value staying fixed for some period. If the stock market is a voting machine, the stock price should cluster around this value as it reaches some majority consensus. This thereby creates what we could assume is a support or resistance level. It would be like having a zero drift, and the only reason we’re moving around the intrinsic value is due to market noise. Again the challenge is to isolate the drift term.