When considering an investment, we ask: “What is the risk?” But what we really mean is: “What can go wrong?” or “How much can we lose?” The uses of the word “risk” in these two contexts are very different.
When we are considering risk in the context of making investments, what we really care about is avoiding sustained losses. To someone who knows nothing about finance, this may seem obvious. But if you have been trained, you will be forced to think about this. Most of us have been indoctrinated into thinking financial risk is price volatility, which is how it is defined in formal finance theory and at most financial institutions and by most financial regulators.
Volatility
Volatility measures how much the price of an asset fluctuates over a defined period. If a share price moves up and down by 10% a day it is more volatile than a share that moves by 1%. On the face of it, this seems like a reasonable proxy for risk, in the sense that presumably the share that moves about much more does so for a reason. Sometimes it is true that price volatility genuinely reflects the probability of a sustained loss, but much of the time it does not. Often, price volatility alone has little information, or what information it has relates to things other than risk.
Consider the following. A rogue journalist at Reuters, the news agency, sends out a fictitious story announcing a terrorist attack in New York. US stocks fall by 15%. The error is subsequently identified by other journalists, Reuters releases a correction and the market returns to its prior level. Volatility of the stock market has just risen dramatically, but it is nonsense to suggest that the risk of owning stocks has changed. Many conventional risk-management tools would dictate that it has; and in order to maintain a stable allocation of risk it would be appropriate to sell stocks!
So why does risk management in finance use the volatility of price to measure risk? One unwitting culprit of this development is Frank Knight, an original and insightful thinker who decided in 1931, quite arbitrarily, to define “risk-taking” as decision-making in circumstances where the probabilities attached to the various outcomes are measurable. “Risk”, in Knight’s terminology, contrasts with his definition of “uncertainty”, which is not measurable. Now this definition is idiosyncratic. It is wrong in the sense that it is not the same idea as we intend in our use of the term “risk” in investment – which is sustained loss – or “risk-taking” as we use it in other contexts. Situations where odds or probability distributions are measurable are just that: situations of measurable probability. They sometimes involve risk-taking if the pay-offs are extreme. They have nothing to do with risk-taking if the pay-offs are highly predictable and steady. Knight was aware of this and just used the words in an idiosyncratic way. This is clear from his understanding of competition and entrepreneurialism. In his highly original work Risk, Uncertainty and Profit, Knight is really trying to draw a very valid distinction between insurance, which exploits diversification, and enterprise, which earns a return or profit from making investments with highly uncertain pay-offs: risk-taking.
Although inaccurate and misleading, the definition of risk-taking as decisions using known, measurable, probability distributions has a great attraction: it permits application of the mathematics of probability. This is why Knight’s definition of risk survives, although it is wrong. In 1951, contemporary financial theory and risk management was invented, by applying the mathematics of probability to investment portfolios. Modern portfolio theory defines investment risk as volatility; and aggregate volatility is derived from the volatility and covariance of the portfolio constituents. In the classic paper Portfolio Selection, Harry Markowitz is very explicit: “The investor does (or should) consider the expected return as a desirable thing, and variance of return an undesirable thing. This rule has many sound points, both as a maxim for, and hypothesis about, investment behaviour” (1952: 77).
As with Knight’s definition of risk, any subtlety in Markowitz’s original ideas is lost in subsequent application by others. His approach can be made consistent with the intuitive meaning of risk.
Markowitz talks of the volatility of expected return and not price. He is explicit that historic return distributions are not appropriate proxies for future return distributions. He also assumes, implicitly, that the holding period of the asset is the same as that used to estimate the variance, an assumption ignored by most risk- management tools. In other words, if I am making a 10-year investment, I should care primarily about the probabilities of the range of outcomes over that 10-year period, and not the probabilities of the range of daily returns.
Of course, in reality the issue is much more complicated because our holding period may be contingent or unknown. It is often the case that we make an investment without a clear view of how long we shall hold it. This prior uncertainty over holding periods is not touched on by Markowitz but is addressed neatly by the concept of sustained loss: if we perceive a loss to be temporary, we may choose to extend our holding period. If a loss is permanent, this option has no value.
Insight lost
The view of diversification Markowitz presents is also a striking example of how mathematical insight gets transposed misleadingly into practice.
For understandable reasons it is often assumed that portfolios containing a large number of different securities provide optimal diversification. Part of the reason we have stock markets is to allow diversification away from the risk associated with an individual company. But what if this risk does not matter very much? What if the risks we really care about affect the whole stock market? Holding the entire universe of stocks is not diversification at all. Now this observation is not inconsistent with Markowitz’s theory of diversification. Markowitz shows that it is preferable to create portfolios with multiple assets that do not have correlated returns in the desired holding period. Buying a large number of securities, or stocks, is only one, very superficial, way to approach this. Observing actual daily, monthly or historic covariance is suggestive but often irrelevant. What matters is the covariance of their return in possible future states, many of which may not be represented in historical data.
The correlation of returns is not written in the past and predetermined; it depends on what happens. If, for example, the stock exchange is suspended for 10 years, the return over that 10-year period of a portfolio of 1,000 publicly listed stocks will be perfectly correlated, and a portfolio with one publicly listed stock and one privately owned stock will be better diversified. Or consider what may be a more plausible concern: that rising commodity prices act as a constraint on the profitability of non- resource companies in the developed world. A portfolio consisting of the equity of the five lowest-cost producers of resources in the world could provide a negatively correlated positive return relative to a portfolio with a large number of stocks.
These examples are entirely consistent with Markowitz’s theory, but structuring portfolios to account for these views would find little useful information from historic prices and correlations. Why, then, are historic volatilities and covariances the basis of risk management? They can be insightful, but for many relevant scenarios they arenot. They are used because they are conveniently measurable.
Covariance matters
The inherent need for judgement about prospective returns and plausible scenarios cannot be reduced to historic measures of price volatility and covariance. A very similar observation is made in one of the earliest reviews of Markowitz’s work, by A. D. Roy, who had developed a similar theory at roughly the same time: “Dr Markowitz presses for a precision in the specification of both motives and of expectations which it seems unlikely that any existing investor can reasonably be expected to possess or to express coherently” (quoted by Bernstein 1992: 63–4). I agree. The main insight from Markowitz (and much of the finance theory that develops subsequently) is simply that covariance matters. And we often forget this: encouraging employees to own shares in the company they work for involves a very high concentration of risk; if the firm goes bust, you lose much of your wealth as well as your income.
Warren Buffett is often presented as opposing diversification. This is an implausible starting-point given that he owns one of the world’s largest insurance companies. But he does not pursue portfolio diversification through a large number of stock holdings. As someone with expert knowledge of industry profitability and principal-agent problems, the two main risks he sees are loss of competitive advantage and management misallocating capital. Buying a large number of businesses is a very inefficient way to diversify these two risks if you understand industry economics and can identify good custodians of your capital. Buffett is in fact constructing better diversified portfolios with fewer stocks.
Keynes was making a similar point when he said: “To suppose that safety-first consists in having a small gamble in a large number of different [companies] where I have no information to reach a good judgement, as compared to a substantial stake in a company where one’s information is adequate, strikes me as a travesty of investment policy.” (Quoted by Bernstein 1992: 48)
My own perspective is that the value of modern portfolio theory is almost entirely theoretical. I am not suggesting that innovative quantitative approaches cannot be devised to deal with some of these critical subtleties. I expect that they already have by a tiny minority of highly thoughtful individuals. But the mechanical and simplistic application of these ideas that is prevalent in the literature and practice of risk management is detrimental to a true understanding of risk. To draw a contrast with physics: in physics formal theories and empirical estimates are far superior to everyday language at describing many physical phenomena.
The opposite is often true in risk management: thoughtful judgement, informed by theory and evidence, is frequently superior to purely quantitative procedures. Subprime mortgage debt and many structured credits had extremely low volatility but were extremely risky, which is why a great many investors avoided them, and many banks using “sophisticated” risk management tools did not. Asian equities had relatively low volatility prior to the Asian crisis, when they were extremely risky, and very high volatility after the Asian crisis, although their risk properties (measured by corporate leverage and governance) were greatly improved. Equity volatility was extremely high in 1999 and 2000, a phase during which a great many equity investors subsequently incurred predictable and near permanent losses, but lower than equity volatility in early 2003, a phase after which equity returns were predictably higher.
Volatility of price is not a measure of the probability of sustained loss. Aggregate risk management at financial institutions should aim at sustained loss mitigation under conditions of very limited knowledge.
Risk managers, which includes any investors, should always be aware of how much might be permanently lost in plausible scenarios. This requires keeping it simple, and being pessimistic when you sense collective optimism. With respect to the latter, the biggest difficulty is finding those who agree with you.
REFERENCES
Bernstein, P. 1992. Capital Ideas. Hoboken, NJ: Wiley.
Markowitz, H. 1952. “Portfolio Selection”. Journal of Finance 7(1): 77–91.
ABOUT THE AUTHOR
Eric Lonergan is a macro hedge fund manager at M&G Investments and a member of the investment team of Episode. He is also author of ‘Money’, published by Acumen.