Risk

Why markets are riskier than you thought.

https://www.pricevaluepartners.com/risk/

“You won’t learn much about capitalism at university. How could you ? Capitalism is a matter of risks and rewards, and a tenured professor doesn’t have much to do with either.”

• Jerry Pournelle.

“For want of a nail, the shoe was lost;

For want of a shoe, the horse was lost;

For want of a horse, the rider was lost;

For want of a rider, the battle was lost;

For want of a battle, the kingdom was lost,

And all for the want of a horseshoe nail.”

• ‘For want of a nail’, Anonymous, 1629.

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One of the most notorious examples of specious science in economics is modern portfolio theory, born under highly questionable circumstances in 1952. Harry Markowitz published his article ‘Portfolio Selection’ – in the Journal of Finance in March of that year. The article would go on to achieve cult status within financial circles.

Markowitz at the time was a young mathematician with no experience of investment. This would not prevent him from advocating the bold investment argument at the heart of his portfolio theory: that a diversified portfolio is always preferable to an undiversified one. This was in turn based on the presumption that “variance of return [volatility] is an undesirable thing” – and a mathematical proof that variance of return may be reduced within a portfolio of stocks and shares by holding a number of different shares.

But even by holding a large number of shares, it is not possible to eliminate variance of returns altogether. Nor is it possible for any one portfolio to exhibit both the maximum return and the minimum variance. As Markowitz wrote, once an investor has achieved effective diversification, then, “There is a rate at which the investor can gain expected return by taking on variance [reducing the number of shares he owns], or reduce variance by giving up expected return [by diversifying his portfolio again].”

Markowitz did not explicitly state that risk and volatility (variance) are the same thing. But as a result of his article, the financial industry would go on to treat volatility and risk as synonymous, and the financial regulators would then join them in that erroneous belief. Thus the more volatility in price that a given investment incurs, the riskier it is. But that is overly simplistic.

Members of the so-called Austrian economic school were on the preferred track. One substantive insight from the Austrians is that risk – whatever risk might even be and however we might define it – is entirely subjective. It is subject to context. Your risk and my risk are not the same. Markowitz assumed that they were. As did the legions of financial professionals who followed in his wake.

Risk is not, realistically, volatility – the extent to which a price wobbles around an average level. Risk is, for example, the possibility that you incur a permanent capital loss. You saved for your retirement and lost everything ? Now that is risk.

Older economists than Markowitz never even dared to define risk. Although there was keen discussion among economists, before World War One, as to what risk might be, and whether it was the same thing as uncertainty, there was complete agreement that whatever risk was, it was probably too complex a thing ever to be fully understood and, crucially, that it was incapable of mathematical calculation.

But Markowitz essentially put a figure on risk. Risk, post Markowitz, equated to the annualised standard deviation of a portfolio’s return – in other words, how much its net asset value wobbled. Not the likelihood of complete financial failure for the portfolio’s owner, but merely the extent to which its net asset value oscillated around a mean.

Peter L. Bernstein, in his history of risk, Against the Gods, suggests that the sea change in attitude towards risk came about because of widespread revulsion at the horrific slaughter of the Second World War. The awful toll on human life bred an attitude that international cooperation could and should be organised so as to prevent any recurrence of that tragedy, and to try and improve the human condition in general. This attitude gave rise to new technocratic international organisations like the United Nations, the World Health Organization and the World Bank.

If science could give us the atom bomb, the thinking went, it could also define risk. Unfortunately it just wasn’t able to identify it properly. Or deploy it within a model that might actually be of use to investors.

Markowitz’s lack of underlying market knowledge is something of a scandal. In Bernstein’s words:

“Markowitz had no interest in equity investment when he first turned his attention to the ideas [in his research note].

“He knew nothing about the stock market. A self-styled ‘nerd’ as a student, he was working in what was then the relatively young field of linear programming..

“One day, while waiting to see his professor to discuss a topic for his doctoral dissertation, Markowitz struck up a conversation with a stock broker sharing the waiting room who urged him to apply linear programming to the problems investors face in the stock market. Markowitz’s professor seconded the broker’s suggestion enthusiastically, though he himself knew so little about the stock market that he could not advise Markowitz on how or where to begin his project.”

To a man with a hammer, everything looks like a nail. To a mathematician with no market experience, why not assume that equations can solve everything ?

Following Markowitz, the world of finance cheerfully adopted the volatility of historic returns as an appropriate proxy for risk. Based upon this idea, the Capital Asset Pricing Model (CAPM) was developed. CAPM would beget the Efficient Market Hypothesis (EMH). EMH would beget a statistical measure widely used by portfolio managers called value-at-risk.

The CAPM model is still alive and well and being taught to brand new generations of fund managers, and CFA candidates, despite the fact that it is pure nonsense. It can be defined by the following equation:

r = Rf + Beta x (RM – Rf)

Where:

• r is the expected return on a security

• Rf is the risk-free rate (i.e. cash)

• Beta is the overall market risk

• RM is the return from the appropriate asset class

Where to begin with the flaws here? There is no longer any risk free rate, if indeed there ever was one. The policies of QE and NIRP (Negative Interest Rate Policy), not to mention constant inflationism, have essentially killed off the risk-free rate.

We can also ask whether beta is an appropriate, accurate or measurable proxy for market risk. And whether it’s remotely sensible to boil down risk per se to an easily calculable figure.

We can also consider some of the additional assumptions that CAPM requires:

• Investors are all identical.

• Investors are all equally risk-averse, profit-maximising individuals (a life form known as homo economicus that has never been glimpsed in the real world).

• All investors have access to all available information about the market simultaneously.

• Market returns obey a model of normal distribution.

• Asset markets are frictionless, information is costless, trading is costless, and the borrowing and lending rates are identical.

• There are no such things as taxes, regulations or restrictions on short selling.

The financial theory behind CAPM doesn’t hold up in any approximation to a normal financial market; it doesn’t work in theory or in practice. Building on the work of Harry Markowitz, the CAPM was the creation of Jack Treynor, William Sharpe, John Lintner and Jan Mossin. Sharpe, Markowitz and Merton Miller would go on to receive the 1990 Nobel Memorial Prize in Economics – always a dangerous sign – for their contribution to financial economics. Fischer Black and Myron Scholes would go on to develop the so-called Black-Scholes model for derivative pricing in 1973.

Bad economics. Overly crude modelling. Widespread adoption within the financial services industry. What could possibly go wrong ? First the Long-Term Capital Management collapse and then the financial crisis of 2007/8 showed exactly what.

Adherence to flawed economic models helped trigger the credit crisis. Adherence to questionable economic theories dictated our authorities’ response to the credit crisis. What if the authorities were simply wrong? Trillions of dollars, pounds and euros have been spent on quantitative easing and extraordinary monetary stimulus since the bankruptcy of Lehman Brothers.

It is by no means clear that those trillions have been well spent.

The failure of LTCM in 1998 can be traced back to Markowitz. The market volatility experienced in stock, bond and currency markets in August 1998 should, according to Finance World’s standard risk models, never have occurred.

On 4th August of that year, the Dow Jones Industrial Average fell by 3.5%. Three weeks later, as the news out of Russia got worse, stocks fell by 4.4%. On 31st August, they fell by 6.8%. Other asset classes fared worse – notably bonds. Bank bonds fell by a third in value relative to Treasuries. LTCM was on the wrong side of both trades (it was long credit and short government debt, in all markets, using leverage of 200:1).

Standard risk modelling theory had estimated the odds of that final, 31st August collapse at one in 20 million – something that, if you traded daily for almost 100,000 years, you would not expect to encounter once. The odds of experiencing three such declines in the same month were even more minute – roughly one in 500 billion. In the parlance of risk modelling and the normal distribution curve of standard deviation (the bell curve), August 1998 was a succession of fat tails. Or was it?

A year beforehand, the Dow had fallen by 7.7% in a single day.

Probability: one in 50 billion. In July 2002, the Dow recorded three separate, steep falls within seven trading sessions. Probability: one in four trillion.

On 19th October 1987, the Dow fell by 29.2%. Based on the standard financial theory, the probability of the October 1987 crash was less than one in 10⁵⁰ – odds so small that they have no meaning whatsoever in reality.

Let’s consider further the normal distribution curve of standard deviation – the bell curve. The bell curve shows variation in probability distributions.

Consider the adult male population in the USA. The average height of an American male adult is roughly 70 inches. The standard deviation from average height is two inches. So 68% of all American men are between 68 and 72 inches tall (that is, they stand within one standard deviation either side of the mean). 95% of all American men are between 66 and 74 inches tall (within two standard deviations either side of the mean). And so on.

The standard bell curve doesn’t disprove the existence of giants or dwarves – rather, it simply suggests that their populations are going to be very small. Which, in real life, is precisely the case. But in the financial markets, the standard bell curve does not exist. It is not a good map for those navigating financial market reality.

Between 1916 and 2003, for example, the daily index price movements of the Dow Jones Industrial Average do not fit neatly on the bell curve. The tails are too fat. Theory suggests that over that time period, there should have been 58 days when the Dow moved more than 3.4%.

In fact, there were over 1,000 of those events. Theory predicts six days of index swings beyond 4.5%. In fact, there were 366 of them.

Index price swings of more than 7% should, according to theory, come once every 300,000 years. In reality, the 20th Century saw 48 separate occasions of them.

It looks very much as if the bell curve and the normal distribution, which form part of standard financial theory, are not an appropriate way to predict market movements.

Markowitz didn’t deserve his Nobel Memorial Prize in Economic Sciences. That award should have gone instead to the Polish-born scientist and mathematician Benoit Mandelbrot. But Mandelbrot died in 2010, so will sadly never get his chance.

Mandelbrot, father of the Mandelbrot set, of never-ending fractals, is co-author, with Richard Hudson, of a book entitled The (Mis)Behaviour of Markets. Mandelbrot’s book is, to the bestselling author and financial theorist Nassim Nicholas Taleb, “The deepest and most realistic finance book ever published.”

If you happen to look at price records, as Mandelbrot did, especially in relation to the market in cotton, you find a different kind of distribution to that of the bell curve. The tails in the market price curve do not flatten out into irrelevance. Rather, they follow a power law that happens to be quite common in nature.

In a power law relationship, a relative change in one quantity triggers a proportional relative change in another. If you double the length of a square, for example, its total area is multiplied not by two times, but by four.

The same type of power law holds for income distributions (the so-called Pareto principle, the 80-20 rule, shows that roughly 20% of the population accounts for 80% of its wealth). And it also holds, somewhat ominously for those who believe in stable or easily controllable markets, for earthquakes, volcanic eruptions, landslides, and forest fires.

Unlike Markowitz, who conjured up a square theory in blissful intellectual isolation and then hammered it into the round hole of the market, with little bits of relevance flying off the theory each time, Mandelbrot developed his own theories having already spent a good deal of time assessing historical prices. Here are some of his conclusions:

Rule 1: Markets are riskier than we think. And certainly riskier than conventional financial theory thinks.

Price movements do not happily track the bell curve. Extreme price swings are not the exception. They are the norm.

Rule 2: Trouble runs in streaks.

Or as Shakespeare put it, “When sorrows come, they come not single spies/ But in battalions!” Market turbulence does not arise out of a clear blue sky and then disappear. It tends to cluster. A wild market open may well be followed by an equally desperate full trading session. A chaotic Monday may well be followed by an even more chaotic Tuesday.

Rule 3: Markets have their own personality.

The father of value investing, Benjamin Graham, famously created the manic depressive character Mr. Market to account for the stock market’s constant oscillations between greed and fear. But when individual investors, institutional fund managers, hedge funds, day traders and sovereign wealth funds come together in a real marketplace, a new kind of market personality emerges – both greater than, and different from, the sum of its constituent parts.

Mandelbrot suggests that market prices are determined by endogenous effects specific to the inner workings of those markets, rather than by exogenous, external events. For example, his analysis of cotton prices during the last century showed the same broad pattern of price variability when prices were unregulated as they did in the 1930s when cotton prices were regulated as part of Roosevelt’s New Deal.

Rule 4: Markets mislead.

In Mandelbrot’s words, “Patterns are the fool’s gold of financial markets.” The workings of random chance create patterns, and human beings are pattern recognition experts. We see patterns even where none exist, and financial markets are especially prone to statistical mirages. Following from this, bubbles and crashes are inherent to financial markets and “the inevitable consequence of the human need to find patterns in the patternless.”

Rule 5: Market time is relative.

Just as the market has its own personality, so it has its own time signature. Professional traders often speak of a fast or slow market, depending on their assessment of volatility at the time in question.

In a fast market, things like market-, stop- or limit orders have limited utility. Prices don’t necessarily glide smoothly within narrow ranges. Sometimes they gap down or leap up, effortlessly vaulting beyond price limits presumed to protect portfolios from ruin.

Traditional economists – if they’ve thought about them at all – have tended to treat the financial markets as a kind of closed system that obeys rigid and pre-set natural laws. Mandelbrot showed that the financial markets are altogether wilder than that. Another class of economists would recognise the inherent unpredictability of financial markets and the broader economy, and give them both the respect they deserved – the so-called Austrian School.

But back to the topic of risk. Most geopolitical forecasters would likely not have foreseen the US/Israeli attacks on Iran that began in February 2026. Any that did would probably not have foreseen the secondary impact on the prices of natural gas and LNG and nitrogen-based fertilizers. Short version: the US and Israel attack Iran – and millions of people internationally now face the prospect of widespread crop failure, of higher food prices, and of starving to death.

As investors we didn’t foresee Operation Epic Fury. But we did recognise the insoluble build-up of US (and international) government debt and the seemingly inevitable inflationist response. So we were and are positioned accordingly: overweight precious metals and commodities; hugely underweight ‘growth’ stocks; no exposure whatsoever to government bonds.

In the mid-6th century BC, Croesus, the wealthy king of Lydia, consulted the Oracle of Delphi before deciding whether to attack the Persian Empire led by Cyrus the Great. He asked if he should cross the Halys River (the border) and wage war.

The high priestess replied with the cryptic prophecy:

“If Croesus crosses the Halys River, a great empire will be destroyed.”

Croesus interpreted this favourably, assuming it meant he would destroy the Persian Empire.

Encouraged, he entered battle.

In reality, the “great empire” destroyed was Lydia itself. Croesus was defeated and captured, and his kingdom was destroyed.

One wonders whether any of President Trump’s advisers have been the beneficiaries of a classical education.

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As you may know, we also manage bespoke investment portfolios for private clients internationally. We would be delighted to help you too. Because of the current heightened market volatility we are offering a completely free financial review, with no strings attached, to see if our value-oriented approach might benefit your portfolio – with no obligation at all:

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Tim Price is co-manager of the VT Price Value Portfolio and author of ‘Investing through the Looking Glass: a rational guide to irrational financial markets’. You can access a full archive of these weekly investment commentaries here. You can listen to our regular ‘State of the Markets’ podcasts, with Paul Rodriguez of ThinkTrading.com, here. Email us: info@pricevaluepartners.com.

Price Value Partners manage investment portfolios for private clients. We also manage the VT Price Value Portfolio, an unconstrained global fund investing in Benjamin Graham-style value stocks and real assets, and also in systematic trend-following funds.