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Investing versus chance and beating the odds

We know that humans have been infatuated with gambling throughout history. Some of the earliest games of chance were forms of a dice game that used the squarish knucklebone of hoofed animals. Gambling was a constant fixture in the lives of both the ancient Greeks and the Romans. Pontius Pilate’s soldiers cast lots for the robe of Christ as he suffered on the cross. In Greek mythology, three brothers rolled dice to decide how to divide the universe. Zeus won the heavens, Poseidon the seas, while Hades, the loser, was sent to hell as master of the underworld.

Our obsession with besting chance has not changed since ancient times. The total known sum of global gambling losses was estimated at US$400 billion in 2017, equivalent to roughly one third of Australia’s annual GDP. Undoubtedly, the actual amount is far higher since Americans are estimated to wager US$150 billion a year on illegal sports betting alone. In Australia, gambling is almost the national pastime. Australians are the biggest gamblers in the world, losing on average $990 per resident adult in 2016, 40% more than runner-up Singapore.

Separating investing from chance

Gambling is part of the human experience, but what separates a random game of chance from the supposedly more highbrow venture of investing? Indeed, the inexorable rise of the passive investment industry is based on the uncomfortable truth that few professional investors outperform the market over long periods.

In the age of Exchange Traded Funds (ETFs) and efficient financial markets, generating investment returns is in fact relatively easy. Over long enough periods, most asset classes generate positive investment returns. Given this, the skill of investing can hardly be thought of as the act of generating positive returns. This is especially the case during periods like the present 9-year equity bull market. Instead, what should separate investing from a random toss of a coin is the skilful assessment, management and bearing of financial risk. The real art of investing should be in generating better returns than what the pre-investment odds would have forecast.

Yet, investment risk remains one of the least talked about aspects of investing. Most investors know what their portfolio returned last year but ask that same investor how much risk they bore to generate those returns and too often, the response is a blank stare.

Given the fundamental principle of investing is ‘risk versus reward’, it is unnerving how little time is spent contemplating risk.

How do we measure risk?

One of the challenges that a wider appreciation of ‘risk’ confronts is that of accounting for the vast range of possible outcomes within financial markets. Most financial risk management becomes a mathematical exercise in quantifying risk based on historical events. This exercise often polarises people. For some, the mathematics provides the only quantifying tools we have to compare the historical ‘riskiness’ of different investment returns.

However, calculating the probability of known historical events only tells us one thing: the probability of events that happened in the past. We cannot quantify the risks that may appear in the future and just as importantly, we cannot quantify the risks that did not appear in the past. Landing safely after skydiving without a reserve parachute does not prove that you will never need one.

Such arguments do not mean that evaluating risk is a futile exercise. Rather, understanding and managing investment risk is both a quantitative exercise and a subjective exercise of skill. The best investors use the framework that quantitative risk management provides to find opportunities that deliver better outcomes than random chance alone.

The risk and return trade-off 

Unfortunately, the mathematics involved in quantifying risk is less straightforward than the mathematics used when calculating returns. If you bought a stock at $1 per share and it goes to $1.50 per share, calculating the investment return is a straightforward exercise. Few of us however, can calculate a standard deviation of returns figure in our head. Too often this means that investors overlook the importance of thinking about risk.

This is a great mistake. All the shortcomings that apply to quantifying risk apply in equal measure to quantifying returns. The first metric we all look at when assessing an investment proposition is what historical returns have been. A skilled investor is one who can form the same sorts of subjective assessments about risk.

The workhorse in most risk measurement exercises is the concept of volatility. In simple terms, the more volatile an investment is - the greater it moves up and down over time – the riskier it is as a proposition. In statistical terms, volatility is a measure of the dispersion of returns around a mean (a standard deviation). Fortunately, it is not necessary to understand statistical mathematics to be able to usefully apply this concept to your investing. Over the long-term, the volatility of global share markets has been 15%. In contrast, the volatility of global bond markets (a much less risky investment class) has been 6%. Long-run average annual returns for global shares have been 5.3%, while for global bonds they have been 3.9%.

Without needing to understand how volatility is calculated, with this information we are now able to put rigour into the idea that investing is a trade-off between risk and reward. The more volatile (risky) an investment is, the greater the returns needed to compensate for taking extra risk.

Taking these concepts to their natural conclusion is the Sharpe Ratio, which is the most widely used metric of risk versus reward in finance. It gives us a simple way of fairly comparing different investment propositions. It effectively shows the ratio of returns divided by their risk (volatility), with a higher ratio indicating better risk-adjusted returns than a lower ratio (a fuller summary of how the Sharpe Ratio works can be found here). Using the above example, the Sharpe Ratios for global share and bond returns are 0.23 and 0.38 respectively, showing that global bonds have delivered better risk-adjusted returns than share markets have.

For Australian investors, a worthwhile data point is that the long-term Sharpe Ratio of the S&P/ASX200 is 0.34.

Conquering luck

The bull market of the past few years has generated returns far greater than the historical long-run average share market return. Hanging over this is one of the most powerful forces in finance, the notion of the return to the mean. Recent double-digit annual returns are not likely to be sustainable in the long run. It is increasingly important for investors to distinguish between the quality of returns rather than only the absolute return numbers.

Many investors today would benefit greatly from a deeper understanding of the concepts of investment risk. In a rising market, an ability to beat random chance is easily overlooked. Yet ultimately, over the long run, the test of an investor is whether they managed to generate returns greater than the risks they took, not whether they made money in a bull market.


Miles Staude of Staude Capital Limited in London is the Portfolio Manager at the Global Value Fund (ASX: GVF). This article is the opinion of the writer and does not consider the circumstances of any individual.

Philip Carman
August 26, 2018

On an analysis of what he and Miles have written, Peter, you'd have to agree with Ashley! His analysis is more reliable ... Miles takes one example and bases an hypothesis upon it.

Miles Staude
August 27, 2018

I’m sorry Philip, I don’t know what you mean. Perhaps you could explain a bit further?

August 25, 2018

Thanks Miles for taking the time and effort to respond in detail! Yes i see your point too. I was quite influenced by Howard Marks' book The Most Important Thing, and he be-labours this point that volatility is not risk. I know it is not his idea originally, and I also appreciate volatility is widely used across the industry by longer-term managers to measure risk. I think Marks makes the suggestion it is probably so widely used because it is measureable, and fits the academic theory to plug into Black-Scholes formulae, etc. In the same way the measureability of returns makes them front and centre for most investors, as you rightly pointed out.

Further on the flash crash... I mostly follow a traditional fixed asset allocation strategy with ETF's. During the US election, when it first became apparent on exit polls in Australian hours that Trump might be the winner, global equities plunged by 5% or more. I happened to look at my allocation, and noticed I needed to buy some global equities (VGS) to re-balance my weightings to target. The next day after Trump had won and soothed everyone with his speech (perhaps prematurely soothed), VGS had bounced back 5% or more and my spreadsheet said I should sell the VGS i just bought and realise a quick profit. Simply following a mechanical, textbook investment strategy appears to deliver a return here. I'm not sure how you would view that quality of such a return, risk-adjusted. The short-term volatility was very high, so did I gamble recklessly to make 5% overnight. Or was I just following a disciplined, tried and true investment approach and making a very low risk profit from one of Mr Market's moodswings?

Anyway, I take your point, it depends on how you calculate volatility and returns, over what period. So maybe it just means long-term investors like myself need to make sure we're looking at metrics on an appropriate time-scale. And perhaps another aspect is risk needs to be taken more seriously but accepting that there will be some qualitative aspects that are hard to quantify, as much as we would like to bring everything back to numbers?

August 23, 2018

Agreed we all need to think more about risk, and how much risk went into generating returns. But volatility may not be appropriate, just because it's measureable.

Risk = volatility --> short-term trader
Risk = chance of permanent capital loss --> long-term investor ??

Flash crashes create a lot of volatility and that is risky if you're a big computer doing algorithmic trading. But if you're a mere mortal who blinked and missed all that exciting price action, was there any risk?

Miles Staude
August 25, 2018

Hi Adrian,

When it comes to looking at financial markets, one of my guiding principles is the old proverb that runs: “in the land of the blind, the one-eyed man is king”. Nobody has a perfect crystal ball for assessing or forecasting financial markets. I think the correct way to think about the risk tools that are available to us then, is to accept that they (like everything else) are not going to provide a silver bullet that will answer all our questions. Rather, like most things, they provide us with some useful yet imperfect tools, with which we can better analyse and think about a very important issue.

These risk tools are in fact used by many large and long-term professional fund management groups and not the preserve of shorter-term traders.

As an interesting aside. With regards to your example about a flash crash - and to try and expand upon my general point that many investors are inclined to be far more critical of risk calculations than they are of return calculations – if you measured volatility over the period of “flash crash” it would indeed be very high. Similarly, if you measured returns over this same period, your losses would also be very high. If you are a longer-term investor, measuring returns over a long period of time, then a flash crash would have very little impact on your return figures. The same is also true if you measured your volatility over the same longer period.


Peter Thorhill
August 23, 2018

On this occasion I agree wholeheartedly with Ashley.

Miles Staude
August 25, 2018

Hi Peter,

See my comment above.


August 23, 2018

Quoting Sharpe ratios to 2 decimal places compounds the problems with the maths behind the ratio – it has many unrealistic assumptions.

Also, need to specify the measurement period in some of the claims about risk-adjusted returns of bonds versus shares because it depends on the period selected. For example, the past 3 decades of disinflation have delivered artificially high and unsustainable returns for bonds. Try that for the previous 3 decades…

It’s important because people retiring now are probably facing the next great structural phase of rising interest rates – so the next 3 decades will be more or less the reverse of the past 3 decades.

Miles Staude
August 25, 2018

Hi Ashley,

I agree with your point that we should never be seduced into thinking that financial metrics which look very precise are in fact able to provide us with perfect answers. In this case I used two decimal places because the absolute numbers are quite low, and I was only presenting two numbers in total.

In terms of the general short fallings of the Sharpe Ratio, or indeed other common risk metrics like volatility, the assumptions that go into these are no more or less realistic than the assumptions that go into other aspects of financial mathematics, like say, return calculations. In terms of the well-trodden statistical debates over issues like normal distributions and kurtosis, these are perfectly good areas to consider. However, these parts of a statistical debate are very much second order effects within an overall analysis.

While the Sharpe Ratio is not perfect, ignoring a proper analysis of risk because the mathematics cannot provide us with a perfect answer is a far greater mistake, in my view.
In my experience, I have found that many investors often ignore thinking about risk because the mathematics can seem a bit more involved. I’ve always believed that is a real shame, even a modest understanding of how to analytically think about risk would add a lot to the arsenal of these investors. Moreover, these days, the mathematics are not beyond anybody with a little patience and web browser.

Could I ask you and Peter below a question. Do either of you measure the historical returns of your various investments? If you do, what do you use this information for? And, further, do you undertake a similar analytical exercise of what your historical risk has been, or may be in the future? There are a large number of tools available out there. The Sharpe Ratio and measuring volatility are just two of these.



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