Many people wonder whether algorithmic trading the way we do – in the timeframe of minutes, days, or weeks – can really work, since they often relate this to high frequency trading, expensive IT equipment, or a hedge fund with hundreds of PhDs. In this article I would like to discuss first on a theoretical basis and then a bit more practical why and how it can work.

## The efficient market hypothesis

Let’s start with a quote from Wikipedia:

*The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to “beat the market” consistently on a risk-adjusted basis since market prices should only react to new information.*

**Eugen Fama** together with **Robert J. Shiller** und **Lars Peter Hansen** even received a Nobel Price “for their empirical analysis of asset prices”. One of the consequences was that investors came to the conclusion that managed funds cannot beat the market and therefore ETFs (exchange traded funds) who have lower costs became very popular of the last years. This **Nobel Price** was awarded in 2013, but the actual work of the scientists was done many years before.

**Econophysics** tries to combine the scientific know-how of statistical physics and econometrics

## How can physics help to understand market efficiency?

Recently the interdisciplinary field of “**econophysics**” has emerged, trying to combine the scientific know-how of statistical physics and econometric. One concept which was borrowed from thermodynamics and later used a lot in information science was **entropy**. Most of you probably never heard of entropy and the ones who did at school or university still are a bit scared, since it is one of the hardest things to understand in physics (besides quantum mechanics or the theory of relativity).

I would like to explain it in a somewhat simple way, so that you can understand why entropy is important for us and how it relates to the original question “Can algorithmic trading really work?”, since it can’t if Fama was correct.

**Entropy measures how much information is included in data.** In physics it is typically used to measure the degree of information in a system. There entropy is important, since a physics law states that in a closed system chaos will always increase and never decrease, if no energy from outside is added to the system. That is also the reason why the room of your kids becomes messier every day, if you do not put energy into cleaning it up. (Never let your kids know that this is a law of physics .)

The same concept of entropy can be used to measure the degree of information that is included in the price history of a stock or commodity. According to Fama there should be no information included, but such information (also often called alpha like in alphamonda) is needed to enable algorithmic trading to work.

In two scientific papers **Luciano Zunino et.al.** studied whether there is information in the markets. In the first one they looked at stock markets and compared different ones. They used entropy to measure their information content. The result was very interesting. They could show that emerging markets have a lower entropy than developed ones. This is a very interesting finding, since it shows

- that
**markets are not totally efficient**, but include information which can be harvested, and - even show that
**emerging markets contain more information than developed ones**, which is very much what you would expect

In a second paper they then studied the commodity markets to understand whether there is some information included. As expected, they also **found that information is included in the commodity markets** and even could rank their efficiency. They found that silver and copper have the highest market efficiency and wheat and corn the lowest one.

Thus, from a theoretical perspective on, we clearly can say that Fama was not totally correct. There is information contained in todays market and this can be harvested with algorithmic trading.

## What does the real trading data tell us?

In the graph below you can see an equity curve over the period of approx. two years which includes the sum of all algorithmic strategies traded live by me over that period.

To understand this graph a bit better and for full disclosure, there the assumptions:

**95% of trades included are live trades**, 5% are simulated trades. This is due to the fact that I did not trade when I was on vacation and still wanted to include the data or that a strategy broke and still was included for some time to supervise it,- this includes strategies which worked all the time and also
**a few which were broken**. Yes, this happens with algorithmic trading and it is important to have statistical tools to detect it early. Nevertheless, you can see that even with broken strategies included the equity curve does not suffer too much, - there is
**no position sizing**on portfolio level included, but only where it is built into strategies already. Some strategies can decide under which market conditions to trade one, two or even three contracts. In real live on top of this you may add classical position sizing like fixed fractional or fixed ratio. This is not included in that chart, and - 95% of strategies were break-out strategies. The other ones were intermarket ones, which I also traded for some time.

## Conclusion: Algorithmic Trading can and does work

What can we learn from this? My take, and you may not be surprised, **algorithmic trading can and does work**. Theoretically I could show you that the efficient market hypothesis is not fully valid, but there is information contained in the markets. Also practically the breakout strategies made money, worked most of the time and are robust.

There is always a certain risk associated with trading, a profit can never be guaranteed. Please read the disclaimer below for more details.

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