### Project Description

Making money with investments is very simple. When owning an asset, or actively managing a portfolio of assets, you will likely be subject to a series of increases (wins) and a series of decreases (losses) in value. If we ensure that both the increases and the decreases are the same size, you only need to “win” 51% of the time, and as time goes on, the value of your account will grow exponentially (or “*compound”). *Simple. The difficult part, is knowing *when* assets will increase in value and when they will decrease. If we were able to forecast these movements in price, we could choose to not participate when they *decrease* and buy them again when they reverse and start to *increase* in value. This is the nature of “*stock picking” *and *speculation*. To speculate in investment, is to make an assumption about a directional movement in price. The most troubling thing about speculation is that you may in fact be extremely successful initially, and then look to repeat your methods, growing in size with each following success. At this time, growing alongside your bets as you ramp up your commitments, is your feeling of confidence that you have pinned-down the *nature of the system*, and then, to your horror, in one month, you are proved wrong. Catastrophically wrong. **Why? **Because nobody can predict price movements, and anyone that says otherwise, its trying to sell you something that mathematics does not buy.

## The Problem

If you flip a regular coin x5 times, what is the statistical likelihood of you getting a result of heads (“T“) five times in a row?

One possible series of outcomes for x5 flips would be

HHHHT

Another could be

TTTTT

Is [HHHHT] more likely than [TTTTT]?

You may have a gut feeling inclination towards thinking that [TTTTT] is less likely. Could you explain why?

For each coin toss there are x2 outcomes only; heads (H) or tails (T). The possible different outcomes for a series of **x5** coin flips could be written as **2**^{5 }or **2^5**, the answer of which being **32**. Accordingly, there is a 1/32 chance of getting a [HHHHT], and there is a 1/32 chance of getting a [TTTTT]. In statistics, this series of results would be described as a “binomial distribution”, whereby there are only two possible, mutually exclusive outcomes. Now, if we were to look at the series of returns of an asset (*lets say a stock*) on a month by month basis then we could assign it a “positive” or a “negative” outcome, based on whether or not it has *increased* or *decreased* in value. As such, we are able to look through the lens of a binomial distribution to calculate the probability of next months returns being positive, right? **Wrong.**

There are two main problems with this approach. Firstly, just because we are able to assign a probability value to an occurrence at a level of “confidence”, there is absolutely nothing to ensure that the distribution will adhere to it. It is theoretically possible that we could do **x10** sets of **x5** coin tosses and flip a heads **each and every time**. Now, if we were to increase the number of observations (*/occurrences)* to **x1000** sets of **x5** coin tosses, we would probably see results closely resembling our predictions- but that doesn’t help the speculator trying to bet on the next toss of the coin. Secondly, you may have noticed that here we are restricting our observation to **x5** coin tosses only. Most investing does not take place over such a short period of time (*e.g the equivalent of x5 tosses could be x5 months of investment returns*), -yet- unless we are able to define the number of observations (*i.e say when the experiment will stop*), we are unable to calculate the probability of events within that window. In reality, investments often existed before you bought them, and continue to exist long after you sell them. Even if you were to be able to define your length of ownership, how would you choose a sample from the investment returns of the asset up until now? Would that sample be sufficiently representative of the asset, or would the data be flawed because it was from a different time when the investment environment was different to what it is now? Lastly, if you have x2 positive results of nominal size, followed by x1 big negative result, you will still have lost money, despite the number of occurrences where you were “correct” being larger. There are a number of issues. This will not however stop you from attempting to make probability judgement in your investments, often without the use of statistics altogether…

## Behavioral Bias

Although global mathematical proficiency is at historical highs among the young, adults are often stumped by basic mathematics when it rears its ugly head in their professional lives. Despite this, we are all guilty of making guesses or placing bets on the likelihood of things happening (*which are very often binomial in nature*) despite not having considered the statistical probability, or even being equipped to do so, should we feel so inclined. Let’s say that a regular coin is flipped in front of you **x6** times and each and every flip produces a “heads”. You are then asked to bet on what the next outcome will be- “heads” or “tails“. **What is the correct, or most probable answer?**

**Again**. You have been beaten by yourself. There is no “correct” or “probable” answer in this example. Nonetheless, you were likely subject to behavioral bias:

Guessed “heads“? – You are the victim of positive recency. The belief that a consistently emergent series of outcomes will repeat again in the near term.

Guessed “tails“? – You are the victim of negative recency. The belief that because a particular outcome has been emergent in recent observations, the other outcome is about to make a….*outcome-back!*

In the context of the stock market, a scathing observer could label the “positive recency” group the “suckers” and the “negative recency” group the “contrarians”. In reality, they both lose money using an identical method, and are both motivated by the “outcomes” of recent months in their decision making. This form of speculation is baseless, and without mathematical foundation. *It is however, very easy to sell…*

## Efficient Market and Random Walk

To add more fuel to the fire, we have academic work going back to the year 1900 (*namely, French mathematician Louis Bachelier*) that is now commonly referred to as the “**random walk hypothesis**“.

The hypothesis explains that movements in price are random, and unpredictable- like the steps of a drunk. Presently, the random walk hypothesis is summarised and explained by the widely acknowledged “**e****fficient**** market** **hypothesis**“.* *This theory states that financial markets are ‘efficient’ and that prices already reflect all available information, and as such, prices adjust and update rapidly without error. This is said to be true of current information (*i.e after an earnings announcement*) but also future information and prospects (*i.e earnings growth, or dividend payouts*). There is no way you can ‘beat the system’ because the discrepancies in market price and value will only exist for a microscopically small window of time. (*There are exceptions to this rule when looking at markets that are smaller, less developed, or more esoteric in nature, e.g emerging markets, micro cap, private equity, indexes based on proprietary selection criteria, etc., so index trackers can only take you so far….*)

As such, only “new” information will move stock prices, and the advent of the introduction of that new information is unknown. Because of this, **future movements in stock prices are also unknown**, and thus random. The basis of the efficient market hypothesis is that the market consists of many rational investors who are constantly reading the news and react quickly to any new significant information about a security- the majority of whom are also “professional” and not amateurs investors. This can be seen in full effect in the realm of high frequency trading (HFT) where computer algorithms operate rules-based strategies to arbitrage these windows of opportunity away until they cease to exist. There are of course criticisms of EMH, but we have yet to see an investment manager pilot a successful strategy that openly contradicts its premise.

**So,** if it is **a)** impossible to predict what the next outcome is, based on previous outcomes unless we define, or restrict our number of observations (*/time invested) *and **b)** even when limiting our number of observations, we are told that the system producing the outcomes is by nature “random”, then how are we able to meaningfully predict price?

## The Solution

You’re not still falling for it, are you? This is the bottom line. **You cannot consistently and successfully predict the price movements of assets**. Now, there is evidence to suggest that the prices of publicly traded securities are *mean-reverting* – i.e they are statistically likely to return to their long-term ‘average’ prices once they divert away from them, but the degree to which this is actionable for an active investor is very much case by case. At the top of the list of factors that undermine this as a ‘method’ for investing, is that mean-reversion theory provides no apparatus to measure the time-frame within which the price will ‘revert’ or come back. Economist John Maynard Keynes summarised this risk very well, “The market can remain irrational longer than you can remain solvent”…

You are now hopefully immune to the stock-picking gurus and unscrupulous **financial advisors** that claim to have an omniscient understanding of the stock market. Unless you are highly proficient in mathematics and programming* (and also willing to dedicate a few years before you find your algorithmic trading feet*) you should put price on the back burner entirely and accept that good investment returns are the reward of a good **asset-allocation** **methodology**. There is no shortcut and no voodoo. Pick a basket of quality assets that have agreeable volatility|reward profiles and liquidity, ensure that the grouped assets produce the desired degree of market correlation for the portfolio as a whole, and manage allocation drift once a year. Owning a robust portfolio of assets that you understand will serve you well over the long-term. In the short-term, leave the millisecond two-tick price wars to the computers.

[ Sources ]

– A Random Walk Down Wall Street, Burton Malkiel

– Binomial Distribution Handbook for Scientists and Engineers, Elart von Collani

– The Efficient Market Hypothesis and Its Application to Stock Markets, Sebastian Harder