The Efficient Market Hypothesis (EMH) and Modern Portfolio Theory (MPT) are based on a simple assumption that risk is defined by volatility. According to the theory, investors are risk adverse: they are willing to accept more risk (volatility) for higher payoffs and will accept lower returns for a less volatile investment. The theory is simple and elegant, and can lead further into ingenuous mathematical proofs and equations, which probably has a lot to do with why it has become so widely accepted.

When Markowitz and Sharpe *et al* needed a definition of risk, they chose to define risk as volatility, the greater the volatility of the portfolio, measured either in terms of standard deviation or beta, the greater the risk.

How did these researchers know that volatility was a good measure of risk? They didn't, nor did they do any research to find out. The observation was made that the share market, which is generally thought to be more risky than cash investments, had the highest volatility. The principle was adopted generally without further evidence that volatility was a good way to measure risk.

Economists find this definition of risk compelling, because it is based on an assumption that makes perfect logical sense, that investors *should* be risk adverse, and that in today's well informed, sophisticated markets everyone acts perfectly rationally and takes no risk that is not justified by a bounty of evidence in support.

But the question is still there, why this measure of risk rather than securities analysis as espoused by Graham and Dodd, examining the virtues of each company by a good look at their financial strength, earnings, debt, sales success or many other measures that management use?

One doesn't have to get too far in examining the theory to find big gaps in the logic. Investors are very concerned by downside volatility, but how many object when their portfolio moves up? Volatility is a measure that regards upside movement as equally bad as movement to the downside. What about inflation and the terrible toll it extracts on non-growth assets? Finally, speculative stocks which are extremely volatile do not fit into this mold as they certainly do not give superior returns, as a diversified group or otherwise. Right from the start this definition of risk seemed unrealistic.

Unrealistic or not, an entire generation of investors has grown up with the idea that volatility is risk. Services that rate managed funds examine volatility as a central concern, and "risk adjusted" historic returns are frequently a major factor in determining how many stars a manager is given by the rating services.

There are many problems with the whole concept. For starters there actually isn't any permanent correlation between risk (when defined as volatility) and return. High volatility does not give better results, nor does lower volatility give lesser results.

In 1977, over a decade before Markowitz and Sharpe received their Nobel Prizes for their work on portfolio theory, a paper appeared reviewing the research on risk (J. Michael Murphy, "Efficient Markets, Index Funds, Illusion, and Reality", *Journal of Portfolio Management* (Fall 1977), pp. 5-20.). Some of the conclusions were startling, at least for EMH believers. Murphy cited four studies that found "realised returns appear to be higher than expected low low-risk securities and lower than expected for high-risk securities ... or that the [risk-reward] relationship was far weaker than expected." The author continued on: "Other important studies have concluded that there is not necessarily any *stable* relationship between risk and return; that there often may be virtually no relationship between return achieved and risk taken; and that high volatility unit trusts were not compensated by greater returns". (Italics original)

Another paper (Haugen and Heins, "Risk and the Rate of Return on Financial Assets: Some Old Wine in New Bottles," *Journal of Financial and Quantitative Analysis* (December 1975), pp 775-84) concluded: "The results of our empirical effort do not support the conventional hypothesis that risk - systematic or otherwise - generates a special reward." These papers were published in the mid to late 70s, just as EMH and MPT were really taking off and "revolutionising" the way Wall Street invested money.

The total absence of a correlation between volatility and return for individual stocks is not the only thing that troubles this method and its exponents. Even more fundamental is the failure of volatility measures to remain constant over time. Any options trader will tell you immediately that volatility is not the same from day to day, nor hour to hour or even year to year. Volatility simply does not stay the same for any period of time and varies drastically from one time period to another. Stocks do not have a fixed volatility and hence it is absolutely impossible to use that factor to make meaningful changes to a portfolio unless you know what volatility is going to be; and we are no closer to finding a way to predict volatility than we are to being able to predict the general movement of prices.

Beta, as defined by Sharpe, Lintner and Mossin were shown to have no predictive power. The beta defined for one period differs drastically to that in the next and there is no way of using beta to predict future volatility.

Barr Rosenberg, a well respected researcher proposed a more sophisticated multifactor beta, including a large number of other inputs besides volatility to measure risk. These betas, called "Barr's Bionic Betas" proved as worthless as previous definitions in portfolio construction. Other betas were examined but none proved to have any usefulness at all for anything besides providing work for market statisticians.

The Capital Asset Pricing Model is based entirely on beta. Without a reliable beta you can't have CAPM any more than a value investor can buy stocks without knowing anything about assets or earnings. Somehow all this managed to be ignored until Eugene Fama, one of the original researchers who in 1973 had been right at the centre of the development of the Efficient Market Hypothesis, put out a new paper on risk and return in 1992. (Fama and French, "The Cross-Section of Expected Stock Returns" *Journal of Finance* 67 (1992), pp 427-465). Fama and French examined 9,500 stocks between 1963 and 1990, concluding that a stock's risk, measured by beta, was not a reliable predictor of performance. Fama stated "beta as the sole variable in explaining returns on stocks ... is dead. ... What we are saying is that over the last 50 years, knowing the volatility of an equity doesn't tell you much about the stock's return."

This was like the Pope announcing that there is no God, anyone who knows what a central role Fama's early 1970s work on EMH and MPT played would appreciate that this was an astounding development. As the *Chicago Tribune* put it: "Some of its best-known adherents have now become detractors."

If not volatility, then what? "What investors really get paid for is holding dogs." said Fama's coworker French. Their research found that stocks with lower price to earnings ratios and price to book ratios, as well as smaller capitalisation companies provided the highest returns over time. Stocks are more positively related to these measurements than to beta or other similar risk criteria.

Fama's words "beta is dead" reverberated around the world. As one finance professor put is in discussing the Fama and French findings:

Modern finance today resembles a Meso-American religion, one in which the high priest not only sacrifices the followers - but even the church itself. The field has been so indoctrinated and dogmatised that only those who promoted the leading model from the start are allowed to destroy it.Other measures were developed do adjust returns by volatility to devise "risk adjusted" returns. I might return 40% over a few years but if I do this with sufficiently high volatility then someone who invested in treasury bills would have better risk adjusted returns. Remember that volatility, in its usual definition, is no different for upside or downside movements. If I achieved this with results ranging between +1% and +100% in any given year, but with no down years at all, then on the basis of that track record my strategy was obviously a risky one. Many contrarian and value investors whose track records include very little downside volatility but tend to make a lot of money when markets bounce have very poor "risk adjusted" returns as a result of this thinking.

Beta gives the appearance of a highly sophisticated mathematical formula but in reality it is data mining, looking at history you can find a number of factors that seem to be correlated, but these correlations are more often than not sheer coincidence. This is very bad science. I learned while doing my own studies that it is wrong to confuse correlation with causality, and wrong to just assume that correlations can be extrapolated to the future. Perhaps other researchers in finance and economics should study for a degree in the physical sciences as I did, maybe they don't teach this concept in economics.

Modern Portfolio Theory is based on a number of assumptions. Mathematically you would expect any conclusions to be drawn from the model to be correct as long as the assumptions are correct. In science we develop basic theories and understand basic principles. As long as the fundamental pieces fit, equations can be manipulated to provide new insights. This is why now that quantum mechanics and relativity are fairly well understood a large proportion of scientific discovery is purely mathematical. As long as the theory is correct you can make new discoveries by putting the theory into a mathematical model and giving it all a good shake. Physicists have found hundreds of subatomic particles that were originally predicted and described in complete detail by mathematics.

So what assumptions and fundamentals does Modern Portfolio Theory rely on? There are ten of them which are particular doozies. The following are key concepts around which MPT has been constructed:

- There are no transaction costs in buying and selling securities. There is no brokerage, no spread between bidding and asking prices. You pay no taxes of any kind and only "risk" plays a part in determining which securities an investor will buy.
- An investor can take any position of any size in any security he wishes. No one can move the market and liquidity is infinite. You can buy a trillion dollars worth of stock in a small speculative mining stock or buy one cent worth of Berkshire Hathaway. Nothing stops you from taking positions of any size in any security.
- The investor does not consider taxes when making investment decisions, and is indifferent to receiving dividends or capital gains.
- Investors are rational and risk adverse. They are completely aware of all risk entailed in an investment and will take positions based on a determination of risk, demanding a higher return for accepting greater volatility.
- Investors, as a group, look at risk-return relationships over the same time horizon. A short term speculator and a long term investor have exactly the same motivations, time horizon and profit target. Regardless of who you are, you will always give an investment the same amount of time to work out and volatility will be your only concern.
- Investors, as a group, have similar views on how they measure risk. All investors have the same information and will buy or sell based on an identical assessment of the investment and all expect the same thing from the investment. A seller will be motivated to sell only because another security has a level of volatility corresponding to their desired return. A buyer will make a purchase because this security has a level of risk corresponding to the return that he wants.
- Investors seek to control risk only by the diversification of their holdings.
- All assets, including human capital, can be bought and sold on the market.
- Investors can lend or borrow at the 91-day T-bill rate - the risk-free rate - and can also sell short without restriction.
- Politics and investor psychology have no effect on the markets.

Investors are not rational, they go for "hot" sectors and markets boom and bust regularly because of speculative excesses. Many people will buy stocks based only on rumour or hunches, the market for thinly traded issues would be wiped out if people really appreciated the true situation of the companies being traded.

Who could argue that a day trader and Warren Buffett would see eye to eye on the outlook of a stock. Does a long term investor buy the same stocks as a trader?

Only the government can borrow at the T-bill rate. No other investor in the world can borrow money at these rates unless they have some special concession. Short selling is illegal or severely restricted in many countries.

Three hundred years of Tulipomania, South Seas bubbles, Real Estate rushes, gold rushes, concept stocks, junk bond busts, dot coms and Asian Crises have shown that politics and psychology have a major effect on markets.

But don't let any of this dissuade you from believing in Modern Portfolio Theory or looking up tables of beta and alpha for various stocks. After all, almost every university throughout the world still teaches MPT to finance and economics students, fund rating services such as Morningstar allocate stars based to a large degree on "risk adjusted" returns, fund managers structure their portfolios based on the Capital Asset Pricing Model, which is a key part of Modern Portfolio Theory, and financial planners do their best to pigeonhole clients into one of five "risk profiles" where all but the most "aggressive" permanently devote large proportions of their portfolio to "low risk" investments such as cash and bonds, even though we do know that taxes and inflation make these classic loser's investments.

MPT is enshrined to the point that it is included in legislation. Risk profiles are an essential part of financial planning, and if I, as a financial planner, were to recommend a portfolio made entirely of stocks, I would probably be sued successfully if the market fell, even if the investor had a very long term outlook. ASIC requires diversification and require us to provide our clients with volumes of data calculated with the Capital Asset Pricing Model. The Diploma of Financial Planning, as well as many similar industry qualifications for those who wish to be advisers or analysts or portfolio managers teaches the Efficient Market Hypothesis and MPT as gospel.

The "prudent man rule", a concept where a fiduciary (professional funds manager) is obliged to invest in "safe" assets is based on a definition of risk that only goes as far as maintaining dollar amounts of a portfolio, even if purchasing power is lost. In our rush to protect funds, we find that a volatility definition of risk is important, and even though inflation and taxes may well destroy an investor's real wealth, as long as dollars are preserved a fiduciary can be said to have acted prudently; hence the popularity of bonds and cash in long term portfolios.

What is this "statistical significance" and most importantly, what sort of performance does one need to turn in to achieve a statistically significant result?

David Dreman wrote about this in Contrarian Investment Strategies: The Next Generation in a section entitled "The Vanishing Support for EMH", so just how does a person go about proving that they can outperform the market, to the satisfaction of all parties?

The biggest problem with statistical significance is that it is a weak tool when there is very little data available. Statistics was designed for use with large sets of numbers, you want thousands of data points in your survey and simply put most money managers haven't been in the industry long enough to have thousands of quarterly performance figures out just yet!

When you have smaller data sets, you need to be looking for larger differences to be flagged as statistically significant. When you have one million data points you won't need very much of an outperformance to show up on a researcher's screen at the 95% confidence level (generally regarded as the minimum acceptable level of statistical significance), so when someone has clocked up 250,000 years worth of quarterly data it will be blindingly obvious to even the statisticians that his long term average return was pretty good! For most managers that have a career of maybe 30 years, that is only 120 data points. You need to be looking for a very severe outperformance to get good statistical significance with a track record so short.

One of the most important studies upon which the Efficient Market Hypothesis first drew support used a technique by Jensen (one of the important mutual fund investigators). One study showed that using the Jensen technique out of 115 funds only one demonstrated superior performance.

To even show up on the screen, the manager had to have a past performance beating the market by no less than 5.83% annually for 14 years! Books get written about guys that manage to outperform the market by only a couple of percent (ie John Neff, Peter Lynch), so I think it would be fair to say that this test of performance is unrealistic. Only someone in the league of Buffett or Templeton could hope to show up with such a high cutoff, and then you'll just get a few remaining sour grapes claiming that since only two people in history have ever achieved this performance it probably just comes down to dumb luck.

In another study using risk adjustment techniques the researchers showed that at the 95% confidence level it was impossible to tell whether a portfolio that was up 90% over ten years had outperformed one that was down 3%. (!!) They noted that given a reasonable level of annual outperformance and volatility, it takes about 70 years of quarterly data to achieve statistical significance at the 95% level.

Lawrence Summers, later Deputy Secretary of the Treasury of the United States under the Clinton administration estimated that it would require 50,000 years of data to disprove the Efficient Market Hypothesis to the satisfaction of the stalwarts.

The mere existence of Warren Buffett and John Templeton does prove that it is possible to select stocks and earn a higher return than an index fund. On a more practical level though, it is very clear that there aren't many of these people around, and it is also clear that identifying such individuals in advance (when selecting a fund manager to put your money with) is very hard.

Moderate academics acknowledge that there are inefficiencies, "free lunches" as some put them, in market prices. What few people doubt though is that spotting them requires more skill than most people have and that for the most part stocks are efficiently priced most of the time. As one researcher put it, there may be free lunches but you'll starve to death waiting for them.

One hedge fund manager I spoke to the other day had these words to say, "we find that 80% of all stocks are efficiently priced, we look for the 20% that aren't." It is fair to say that the majority of stocks are efficiently priced and that an index fund will thus be a relatively efficient vehicle. Maybe this hedge fund manager can identify the 20%, maybe he can't. The question that we as investors need to think about is whether we feel confident that the managers we invest with (or us, if you DIY) can successfully identify the 20% of incorrectly priced stocks and profit from them. Some can, obviously, but knowing if our strategy will work in advance, given that most active strategies don't, is the million dollar question.

A second question is whether these inefficiencies are really so profitable that they are even worth going for once identified. If your active strategy leads to more frequent realisations of capital gains then the loss of tax efficiency might do more harm than your strategy does good.

While I do encourage readers to study the great investors, I also encourage anyone that does not, after much honest self assessment, feel that they are not quite up to Buffett's standards, to consider an indexed approach instead.

I personally do keep an eye out for free lunches, but in the mean time I am happy enough to leave most of my money invested across a variety of index funds, including in particular value index funds. In the next article, I'll bring you a little closer to the state of the art in Modern Portfolio Theory. Chuck out your CAPM and burst your beta, the truly chic academics are now seeking to explain why value stocks outperform, given that they aren't actually more volatile.