ANZ Finance blog | Algorithms in Finance?| McGraw Hill Australia New Zealand

Algorithms in Finance? That’s Nothing New!

Published 15 January 2021

By Dr Peter J Phillips, Associate Professor (Finance & Banking) University of Southern Queensland

Tech Titans -- McGraw Hill ANZ Finance Blog -- Australia and New Zealand

I wonder how many people believe that the markets are purely random, that anything could happen. And I wonder how those people make financial decisions. If it’s purely random and anything could happen, does a decision even matter? One thing seems certain to me. If you know that the financial markets have a structure you will make your decisions in a different way to those who believe that there is no structure at all.

Structure does not mean predictability. Although researchers have found a predictable component in asset prices (we will discuss that another time), investments are fundamentally risky prospects. They are characterised by a range of outcomes (returns) and each outcome occurs with some probability. A basic approximation of what to expect in the future is the average of what has happened in the past. The actual return might be higher or lower. This variability is the nature of risk.

The average return and the variability of returns are two measurable statistics that contain within them the first glimpses of structure. If one asset has a higher average return than another and yet the variability of returns (risk) is the same, traders will buy the former and sell the latter. This equalises the returns and ensures that each asset yields a return commensurate with its risk. Since the risk is the same, the returns should be same.

"An algorithm is just a set of steps, a recipe, to be followed to solve a problem"

This simple relationship is a flexible glue that holds the markets together. On its foundation rests all modern finance theory and every trading strategy from the simplest buy-and-hold approach to the most sophisticated trading strategies used by quantitative analysts at the most innovative hedge funds. Including the use of algorithms.

An algorithm is just a set of steps, a recipe, to be followed to solve a problem. If you like, the steps can be written in programming language to tell a computer how to solve the problem. While the use of algorithms might seem to be a characteristic of 21st century finance, their use can be traced back to the 1950s (at least).

In the early 1950s, Harry M. Markowitz was a student at the University of Chicago. He realised that investors do not simply flock to the asset or portfolio that has the highest average return. They consider the risk. He wondered how risk could be calculated and realised that the variability of returns was a natural measure. The more variable the asset’s returns, the wider the range of outcomes that the investor might experience. What is risk if not the chance of an unexpected outcome? Assets with higher average returns should have more variable returns. This is a formal expression of the adage, more risk, more reward.

If Markowitz had stopped there, we might never have heard of him. But he didn’t stop there. He proceeded to build Modern Portfolio Theory, which arranges the average (mean) return and variability (variance) of every individual asset and portfolio in the economic system into a formal statistical structure. What he did was to work out, using mathematics and statistics, the nature of the flexible glue that holds the financial markets together.

"He invented an algorithm that rests at the heart of the structure of modern finance theory"

If he stopped there, we certainly would have heard of him. But he didn’t stop there either. He invented an algorithm that rests at the heart of the structure of modern finance theory. It’s called the critical line algorithm.

A portfolio is a collection of assets. The proportion that any asset makes up of the total portfolio is called its ‘weight’. If 50 percent of the value of a portfolio is made up of IBM shares, then IBM has a weight of 50 percent (or 0.50) in that portfolio. If the other 50 percent is made up of Chevron shares, then Chevron also has a weight of 0.50.

Each asset in the portfolio has its own average return and variability and these combine to produce the portfolio’s average return and variability. Say that you have formed a portfolio, a collection of assets, with IBM weighted 0.50 and Chevron weighted 0.50. The portfolio has an average return and risk. Is there any way that you can rearrange the weights, taking Chevron up to 0.60 and IBM down to 0.40 or IBM up to 0.90 and Chevron down to 0.10 such that the portfolio produces the maximum return at your desired level of risk? Yes. And Markowitz’ critical line algorithm is the series of steps that you need to follow or, more likely, tell your computer to follow.

If the financial markets were purely random, if there was no structure, there would be no algorithms. Markowitz revealed an important part of this structure and designed an algorithm that would operate within it. This was in 1952.

Discussion Question

Discuss the use of variance or standard deviation (i.e. measures of variability) as a measurement of risk in finance. Does variability encompass what you consider to be the nature of risk?

Further Reading

Chapter 7 of the textbook touches on the topic of technical analysis, which is the attempt to identify and profit from trends in share prices. An important thing to consider when thinking about technical analysis is that buying and selling based on technical analysis should yield a positive average return over time, since it involves risk. The question is, was the return commensurate with the risks that were taken?