Are prices really random?

Exploring market efficiency

It is broadly taught and discussed in financial theory that markets are efficient. According to the most extreme version of this theory, all information (public and private) is swiftly absorbed by the market, rendering technical and fundamental analysis futile in generating excess returns. 

This would mean that prices follow what is called a “random walk”, which implies that the prices and, for that matter, returns are unpredictable. 

However, a closer examination of the claim that prices are truly random reveals a more nuanced reality. In this article, we dig deeper into this theory. 

Black Monday 

Take for example the infamous Black Monday on October 19, 1987. On that day, the Dow Jones index fell 22% on a single day. Yet, this dramatic event was preceded by three consecutive days of market losses, culminating in a total decline of roughly 30% . This can be seen in the data published by the S&P Dow Jones Indices: 

The above table shows that if you had invested $100 on the beginning of Monday 12, by the end of the next monday there would be about 70c on-the-dollar left from that. According to Statista, this has been the worst day in the history of the Dow Jones index.   

Although one day might potentially be seen as an outlier (an event that differs greatly from the entire data set), what are the odds of consecutive falling days?  

In the publication of the third edition of “Technical Analysis – The complete source for Market Finance Technicians”, Charles Kirkpatrick II and Julie R. Dahlquist shed some light on this anomaly by mentioning the following:

For example, the probability of a one-day decline of 10% in the stock market is approximately 1 in 1000. In other words a 10% drop will occur statistically once every four years. If stock returns are independent the probability of two consecutive daily drops of 10% would be the product of the probability of the two independent events. This means, statistically, a 30% three-day drawdown could be expected to occur only once every four million years!      

Technical Analysis – The complete source for Market Finance Technicians

Random Walks

One underlying assumption about the statement above is that the returns have a uniform distribution. This means that each event is seen as independent and with the same probability of occurrence. Which in itself, given the different financial crises is not an assumption that has held through time.

Other studies mentioned in the book, like the one done back in 1988 by both Prof. Andrew W. Lo (MIT) and Prof. Craig MacKinlay (Wharton School of Business), and Didier Sornette (in 2003) show evidence against the Random Walk Hypothesis.

Sornette studies around 14 different market crashes, revealing a  pattern of consecutive days of market decline. This finding starkly contrasts with the statistically expected outcomes of random price movements. It suggests the presence of correlation among sequential returns, indicating that prices are not entirely random.

This concept makes more sense if you take into consideration human behavioural biases, such as “herding”. In this case, individual investors, under the belief that they are making rational decisions, tend to mimic the actions of others. However, the collective behaviour of the "herd" may actually be irrational. We have seen this in bubbles and crises, where prices rise and fall dramatically. Even if the first buys or sells “make sense”, human emotion tends to push this beyond rationality at times and this is reflected in the prices with consecutives positive or negative days. 

While this evidence challenges the notion of randomness, it does not mean that technical analysis will work all the time. However, it does indicate that the profitability of these strategies should not be dismissed as improbable. 

Backtesting 

This revelation calls for rigorous backtesting to identify the indicators or combinations that work best in different scenarios and sectors.

In conclusion, the widely held belief in market efficiency and random price movements merits closer scrutiny. The occurrence of notable events and the presence of correlation among sequential returns highlight the limitations of the randomness assumption. By delving deeper into these patterns, we can refine our understanding of market dynamics and develop more effective investment strategies.