It is a difference of opinion that make horses race. Mark TwainSince the early 1960s a considerable amount of empirical work and not a small amount of computer time has been spent determining whether or not financial markets are efficient. While the evidence in support of the efficient markets model is extensive and, somewhat unique in economics, contradiction is sparse[51], the robustness of any model depends on the span of its applicability. Too often it is assumed that if a hypothesis is proven in one econometric study, that the results hold for all possible scenarios. My objective in this essay, therefore, is to augment the traditional analysis of securities markets with an examination of the efficiency of on-course betting markets.

If securities markets and horse racing seem worlds apart, the difference is more apparent than real and can be largely explained by the stigma society attaches to the latter. Both have common characteristics: a large number of participants; a wide range of publicly available information; and ease of entry. Like securities markets, horse racing provides an opportunity to study the rationale of decision making under conditions of risk and uncertainty. Furthermore, since betting schemes give rise to wager markets with equilibrating functions similar to commodity markets, they afford opportunities for the study of market mechanisms under a widened class of contingency and institutional conditions.[52]

In section one I examine the various empirical tests applied to the securities and horse racing markets. I intend to show that on the whole both markets are efficient, although some inefficiencies persist. In the second section I explore some of the new mathematical and computer techniques used to exploit these inefficiencies to earn super normal profits.

First it is necessary to define what exactly is meant by efficiency. When we speak of market efficiency, we refer not to the efficiency of the services industry, but rather that of information markets. The Efficient Market Hypothesis (EMH) states that at any one point in time, prices reflect all available information. This implies that no amount of data mining can predict future prices. Furthermore an analysis of past or current data cannot identify undervalued stocks. Applying this to the securities markets, the EMH implies that no trading mechanism can consistently beat the market. Hence, for a given level of risk, speculators cannot earn supernormal returns. Similarly, no betting system can consistently earn super normal returns: professional punters, therefore, cannot earn a greater return on betting markets than you or I.

There are varying degrees of market efficiency, with Fama (1965) providing the traditional framework through which the EMH is examined. The weak form simply states that all past information is reflected in current prices. The semi-strong form states that all publicly available information is incorporated in prices, while the strong form, an extension of the first two, states that all information, including insider information, is included in share prices. Each will be examined in turn.

To test for weak form efficiency in security markets one tests the serial
correlation of prices through time. If there is a relationship between prices
in one period and those in the next, then *Corr(P*t-1, *P*t*)*
will be either positive or negative. However, repeated studies [53] have shown that there is a near zero
correlation between stock prices through time. This flies in the face of
technical analysis, and suggests that although in the short run there may be
short lived patterns in price movements, they are unstable and inconsistent.
In the long run, therefore, the best strategy to adopt is a buy and hold
policy.

In considering betting markets, the construction of a weak form test is more difficult. Unlike stocks, there is no history of betting prices to correlate. Instead a more intuitive approach is needed. Snyder (1978) examines the subjective winning probabilities punters assign to horses, at eight different levels of expected return. His findings show that, unlike securities markets, there is a negative relationship between returns and odds. This is accounted for by the utility derived from a bet: punters derive enjoyment from reading the form, riding their luck, and in particular picking long shots to win, thus proving their ability to out-perform the market.[54] Hence, unlike their speculator counterpart, gamblers have different risk preferences: they prefer low probability-high return bets to high probability-low return combinations. This results in what is known as an overlay, whereby smaller proportions are bet on lower-odds horses than their actual chances of winning justifies.

Snyders study, which was compiled from data on over 300,000 horses in more than 30,000 races, shows that at lower odds levels there is a strong bias: punters bet less on favourites than the horses ability merits. This suggests that favourites are good bets and long shots are bad bets. However, when the bookies or tote take is added back in, the bias is not large enough to consistently beat the market. Hence, betting markets, like securities markets, are weak form efficient.

Tests of semi-strong efficiency in securities markets have centred around the
study of events. These events include public announcements, such as a company
reporting a substantial new holding in a subsidiary, and dividend disclosures.
A more interesting example involves testing analyst predictions to determine
whether these can be used to earn excess returns. The Heard on the Street
column in the *Wall Street Journal* publishes analysts tips a week or two
after the opinions were circulated to the analysts clients. The
*Journal*, however,* *is the first wide scale dissemination of such
information. Davies and Canes (1978) examined the differential between
expected and normal returns in the twenty days prior to and subsequent to the
Heard on the Street recommendations. The results show that prices rise in the
final days prior to publication and decline thereafter. As more investors with
knowledge of the analysts predictions enter the market, so demand for the
stocks rise. In response to this prices rise so that the markets anticipate
new information. This suggests that while excess returns cannot be earned
after the announcement, they may be earned prior to publication. However the
residual returns prior to the announcement were between 1% and 2%. Hence, only
if transaction costs were lower than this residual could excess returns be
earned. Securities markets are therefore semi-strong efficient: public
information is rapidly incorporated into, and sometimes even anticipated by,
prices.

An interesting extension of these tests has been to test for market volatility previous to and after events. Roll (1984) looked at the production of orange juice in Florida and the effects of the weather and public announcements. His research shows that there is excess volatility in security markets: prices over react to new information. This highlights an inefficiency in information markets, to which I will return later.

Turning to betting markets, Snyder (1978) states that no satisfactory semi-strong test of horse racing has yet been developed. Like the securities market example above, what is needed is a model which incorporates previous performance data, and allows for the incorporation of new information, be it new weights, jockeys or workout information. This is a point of contention, to which I will return after examining the most stringent form of EMH.

Several studies have analysed mutual funds in the United States, the classic example being Jensen (1968). In this study, the performance of 105 funds were tested over a 19 year period and compared to the market return. Of the 105 funds, only one performed significantly better than the market, while 14 performed significantly worse than the market over the same period. Jensen concluded that securities markets are strong form efficient, and suggested that mutual funds spend less resources conducting technical and fundamental research.

A number of criticisms have been made of Jensens method. First of all he analysed mutual funds and not the individuals who make the arbitrage decisions. Successful analysts manoeuvre regularly through the labour market, and so it is the individual who should be assessed and not the fund. Secondly, and more importantly, Jensen assumes that the market return is the return on the whole market. While portfolio managers can diversify risk, they cannot ensure a market return. Hence the benchmark by which these funds are analysed is arbitrary. Later studies[55], have responded to these criticisms, and while they dont produce the same startling results, they nevertheless support Jensens original hypothesis.

Horse racing is notoriously full of insiders, be they owners, trainers, jockeys or stable lads. Like the securities markets, data on the returns these insiders earn goes largely undocumented. Tests have therefore focused on those who publish their tips. Snyder (1978) tests the returns from the tipsters predictions in the Daily Racing Form and four daily newspapers. His findings show that not one of the tipsters earned a positive return after the bookies take is subtracted, from which Snyder deduces that betting markets are strong form efficient.

This analysis raises a number of difficulties. Firstly, newspaper predictions are made up to 30 hours before the off, so new information is not fully accounted for. Secondly, newspaper tipsters are employed to tip a horse in each race. Professional punters, on the other hand, will often sit a whole race meeting out without placing a single bet. A third deficiency in Snyders methodology is the assumption that newspaper tipsters are examples of insiders on betting markets. In effect many are employed on a part-time basis, and have access only to information that anyone in the general public can obtain. Hence, Snyders strong form test actually tests whether public information only, and not inside information, is incorporated into betting prices. Hence his strong form test should be relegated to a test of the semi strong form.

Similarly, mutual funds are not a satisfactory proxy for those in security
markets with inside information. That analysts better utilise the public
information available to them is not inconsistent with the semi strong form of
EMH. To test for strong market efficiency we are compelled to analyse the
returns of *real* insiders. In the US, shareholders with a substantial
interest in a company, as well as management who own shares, are required to
list their purchases and sales with the Securities Exchange Commission (SEC).
An insider trading on specialised information can be expected to purchase
shares in months prior to price rises. Jaffe (1974) tested for this and found
that these insiders earned greater than normal returns. There is no reason to
assume that substantial shareholders hold superior analytical skills to other
shareholders. It can be deduced, then, that insiders can earn excess market
returns. Hence, securities markets are strong form inefficient.

To recapitulate it has been shown that financial markets are largely efficient. Inefficiencies exist nonetheless. I have, however, highlighted a special subset of players, insiders, who due to their monopoly on information can earn excess returns. It has also been shown that information sometimes is temporarily misreflected in prices, suggesting that those who receive better information quicker are at an advantage. Finally, it has also been shown that there are short lived patterns in share prices. While in the past these were thought to be unstable and inconsistent, a new breed of analyst, armed with superior data, are utilising new statistical, mathematical, and computer techniques to anticipate market reactions to exploit these inefficiencies.

In a study on our attitudes to risk, Tversky (1988) demonstrates that we are non-linear in our thinking: we are risk averse when expecting a gain and risk seeking when facing a loss.[56] This is consistent with Gruens (1976) analysis of betting markets. He concludes that gamblers, when facing a loss, are especially risk seeking. Recent analyses of securities markets have now shifted from looking at stock behaviour to analysing the behaviour patterns of people. Market theorists are now looking for slight non-linearitys in markets, as a means of anticipating future prices. One theory, GARCH (Generalised Auto-Regressive Conditional Heteroskedacity) assumes volatility in stock markets is clustered. In times of high volatility markets are contrarian, a point Keynes first highlighted in the thirties. GARCH theory, however, concentrates on clusters of low volatility, where it anticipates that trends last longer than an examination of market fundamentals suggest. Investors often wait until they see a price rising before they purchase. Hence a rising price is a bandwagon, with herds of investors entering the market, second guessing each other. If we are non-linear in thinking, then technical analysis is justified.

If statistics are helping us understand market movements, then mathematics will
help us anticipate them. The new breed of market analyst is now looking to
chaos theory as a means of predicting financial markets. If markets trend in
one direction longer, then prices do not follow in a random walk as stated by
EMH. Instead of following the normal Gaussian distribution, returns on
financial markets are leptokurtotic. A leptokurtotic distribution is one in
which the occurrence of event, *E*t, is a function of *E*t-1. A
study by Peters (1991), which analyses S&P 500 price changes in the period
1928-1989, shows that securities markets are highly leptokurtotic. This
implies that information is not immediately reflected in stock prices, a direct
attack on the semi-strong form of the EMH.

If securities markets are leptokurtotic in distribution, then fractal theory can be used to predict future prices. A fractal is an object with a non integer number of dimensions. An example is a piece of crumpled paper which is estimated to have 2.5 fractal dimensions: in parts it looks two dimensional and in others it appears three dimensional. Any one point in a fractal is a function of those surrounding it. Similarly, in a leptokurtotic financial market, any one price is a function of previous prices. Peters estimates that the S&P 500 index has 2.3 fractal dimensions. This implies that as few as three variables can accurately predict market movements. However, markets are in a perpetual state of change and so these three variables are constantly changing. Chaos theory seems better at explaining financial markets than predicting them. Nevertheless, in times of low volatility, pockets of predictability arise, permitting the potentially successful exploitation of chaos theory. This is where neural networks enter the frame.

A neural network is a system of computers which learn by trial and error. Developed to mimic natural evolution, these super computers breed: those networks which are most productive survive, and generate new sibling networks. Those computers which are least productive are shut down, their power being used to develop the new siblings. Neural networks are the perfect complement to chaos theory, given their ability to learn quickly and develop. However, they are not without fault. Firstly, neural networks tend to overfit data: leave them processing long enough, and theyll find a relationship between planetary movements and stock prices; a relationship which can only be coincidental.[57] Secondly, neural networks are a black box: they offer predictions without rationale. Now while most traders act on little more than a gut feeling, investors of the future are unlikely to place their hard earned cash in the hands of a breeding computer.

Despite these criticisms, Fidelity, the largest Mutual Fund company in the world, have seven funds utilising neural networks. One of the funds has consistently beaten the S&P index by between 2% and 7% per quarter for the last three years. Yet the market has been rising consistently during those three years. Neural networks are not good at revising their predictions and so when market conditions change, successful neural networks of the past will have to be replaced with newer models. However, the question remains as to when the optimal time to stop using a neural network is.

Efficient markets imply analysts who adopt a passive strategy of picking stocks are as likely to be as successful as those who pursue an active policy of research and analysis. Yet, as the Grossman-Stiglitz paradox outlines, if everyone adopted a passive strategy, some securities would be undervalued and opportunities for successful technical and fundamental analysis would arise. One thing is clear, however. Computer trading software is as heterogeneous as traders. Hence, the use of computers in stock analysis extends to the public (Primitive Neural Networks can now be purchased for PCs to be run at home), entry to the securities markets will rise. This will increase liquidity and, in the long run, reduce costs thus making markets more efficient.

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