Theories can't count cost of risk

(Published in the South China Morning Post on 19 November 2006)

Risk. It's a word thrown around so frequently in the investment world there's risk-adjusted, systematic risk, specific risk, and we all know that beta, alpha, cost of equity and the Sharpe Ratio have something to do with it. But what is it actually?

In the 1950s, the early pioneers of modern portfolio theory (MPT), such as Harry Markowitz, Merton Miller and William Sharpe, asked themselves this question when they came up with the simple hypothesis that investors get rewarded (with higher returns) for taking on greater risk. For this idea to go any further, though, they had to have a way of quantifiably measuring risk.

They came up with a simple, if controversial, solution: risk (of any asset) can be measured by the standard deviation of historic returns (of that asset). In other words, the more volatile the returns from a given asset the more risky it is.

From this simple assumption - and several others, such as markets being efficient, that one measure of risk applies to all investors, that there are no transaction costs - grew MPT and its flagship, the risk-gauging capital asset pricing model, to this day the cornerstones of the financial economics curriculum in schools, investment associations and financial institutions.

For their work in the field of understanding how asset prices behave, Dr Markowitz, Dr Miller and Dr Sharpe shared the 1990 Nobel Prize in economics. Building upon MPT and work by Robert C. Merton and others, Fisher Black and Myron Scholes published a paper in 1973 introducing the options pricing model that bears their name. Its basic assumption is equities move randomly; that is, their returns are distributed according to the normal bell curve, which charts the frequency of random walk outcomes.

The model assumes that volatility does not change much, and prices options as a function of the historic volatility of the underlying asset.

This worked well in normal market conditions, where changes in volatility were gradual, but if volatility abruptly increased it would break down. Dr Merton and Dr Scholes - members of the team that in 1994 established the ill-fated Long-Term Capital Management (LTCM) hedge fund received the Nobel Prize in 1997 for this and other work.

Best-selling financial author Roger Lowenstein, in When Genius Failed, his excellent book on the US$4 billion collapse of LTCM, said: "Every investment bank, every trading floor on Wall Street, was staffed by young, intelligent PhDs, who had studied under Dr Merton, Dr Scholes or their disciples. The same firms that spent tens of millions of dollars per year on expensive research analysts - i.e. stock pickers - staffed their trading desks with finance majors who put capital at risk on the assumption the market was efficient, meaning that stock prices were ever correct and therefore that stock picking was a fraud."

It is now known that a significant portion of the instructions on Black Monday, October 19, 1987, to sell large blocks of shares came from black box, or automated, trading programs into which the Black-Scholes model had been built. The initial fall in markets caused by Germany's unexpected interest rate increase - and the associated rise in volatility - triggered a self-fulfilling wave of computer-driven panic. The programs were spitting out sell instructions assuming the increased volatility was highly unusual - which in the real world it was not - further increasing volatility and causing more sell instructions.

In the aftermath of the 1987 crash, Harvard economics professor Lawrence Summers, later a United States treasury secretary, remarked to The Wall Street Journal: "The efficient market hypothesis is the most remarkable error in the history of economic theory."

And all of this from the simple assumption that volatility equaled risk. What went wrong?

The dictionary definition of risk is the possibility of loss.

Applied to financial markets, risk should mean the probability that an investment - whether a portfolio or an individual asset - will perform worse than expected.

But whose expectation? After all, expectation is a subjective quantity. In investing, expectation belongs to the investor. Everyone is entitled to have a different expectation for their investments. It is ludicrous to suggest that Warren Buffett and a day trader would see eye to eye on a particular stock, especially if they were both holding it at the same time. One would want the stock to grow at a steady pace over many years, while the other would be happy with a half-point bump before lunch. Yet MPT posits they should see eye to eye, defining risk as the objective historic volatility of a given stock. Furthermore, asset price returns are not normally distributed. In the real world, the supposedly well-distributed curve has a lump at each end, known as the fat tail (see chart). The tails describe extreme events - such as Russia's 1998 debt default that brutally exposed LTCM's weakness – which are not as rare as the theory says they should be.

The ultimate irony about short-lived LTCM - the penultimate one being its name - is that two of its partners, Dr Merton and Dr Scholes, proponents of the Efficient Market Theory, built a model to take advantage of arbitrage opportunities created by market inefficiencies.

These are not new observations, but the speed at which old-established theories are debunked is agonisingly slow. The likes of Mr Buffett who I suspect does not calculate his risks by looking at historic stock price movements - must hope the pace of change remains slow and that the Nobel committee continues to bestow its awards on academics sitting in their ivory towers, far removed from the messy world of nuts, bolts and corporate profits.

So what is the point of all this? My advice is to throw away the textbooks and accept that, at least for most investors, there is no point in worrying about volatility. On the contrary, you should learn to welcome it, as your shares can't go up without it. The only sure fact is that over periods of 10 years or more, markets tend to go up, and that most of this appreciation will be due to rising corporate profits.

Ultimately, the only reliable model of the real world is the world itself. As University of Chicago economist Eugene Fama – often thought of as the father of Efficient Market Theory - famously remarked, life always has a fat tail.