Three of these projects have been concerned in some way with attempts to trade financial markets aggressively, based on the analysis of past information. It is important to bear in mind that there some limitations to this methodology:
1. It assumes future is like the past. The vahdity o f this assumption is debatable as some factors are obviously changing - the automation o f exchanges, new financial products, new currencies, and changes to legal and pohtical constraints to name but a few. The question is “are the important characteristics of markets changing slowly enough for the analysis of data histories to be useful?” What is deemed
“important”, and “slow enough” are clearly dependent on factors such as the experimental technique chosen and what the objectives are.
2. Financial markets are not scientific test beds: a single market price path is available, and data migrates in-sample extremely rapidly [King96]. For instance, if a section o f market history is used for testing a trading rule, then it is invahd to use any information from that experiment on any subsequent trading rule test that uses that same period o f market history - to do so would be to effectively use information from the future in the second experiment.
3. There are also significant problems with the vahdation o f trading rules, as for each market only a single price series is available to conduct experiments on. Consequently it is very difficult to make robust empirical assessments o f whether a rule works or not. For instance, before accounting for trading costs, it would be expected that half of all possible utterly bogus (i.e. zero information) trading rules would appear to make a profit at the end o f the test run. However, it is often not clear from inspection whether a rule has information processing capabihties or not. Rules can be required to perform acceptably across disjoint test sets, but as extra constraints are imposed on the characteristics of the cumulative profit and lost curve, such as tolerable draw-down, rule longevity, or rule apphcabihty across markets, the experiment begins to be propehed into the realm of curve-fitting. The only answer is to carry out out-sample testing on completely uncontaminated data for reasonable periods o f time.
8.6.1 Financial Anomalies - A Consistent Story
The experiments presented in this thesis provide evidence both for and against the EMH. From the survey of the hterature that was presented earher, this is not a surprising outcome. However, the evidence can be arranged in an attempt to form coherent picture. In particular, the BuU-Bear results and some o f the points presented in Chapter 7 can be brought together into a common explanatory framework that can account for several anomahes of financial theory.
It can be seen from Peters' work[Pete91] that in general, most traded securities have significant non-random aspects to the price dynamics, and exhibit trending behaviour. This is in confiict with the econometric assumption that the movement of market prices
follows a random walk. This assumption of the price following a random walk is also in conflict with the idea that it is possible to reliably profit from price bubbles.
A reasonable inference from Arthur’s work[Arth95] is that relaxing assumptions of homogeneous expectations leads to financial markets rallying and crashing, and the market’s volatility exhibiting GARCH behaviour. That markets display GARCH behaviour is an econometric construct, but that is in fact anomalous to the assumptions of financial theory.
The most important result of this thesis is that the Bull-Bear trading engine works better on longer maturity markets. See Figure 8.1. This effect has been demonstrated to 86% confidence, and there is no econometric explanation for this result. It is clear from analysing the rules that most are momentum based.
Figure 8.1: P/L gradient vs. Market Maturity: US Treasury Futures
& c 0) ■B
2
O ) 40% 35% 30% 25% 20% 15% 10% 5% 0% 1.5 2 1 -0.5 0 0.5 1log (market maturity)
This maturity effect can be incorporated into a non-hnear, behavioural view of markets that is consistent with Arthur’s and Peters’ work. Markets trend - this is not really under dispute but is proved by Peters. If assumptions of homogenous expectations are dispensed with then price bubbles occur (and the simulation takes on behavioural qualities displayed by "real" markets). The Bull-Bear trading engine profits from going with price movements. Longer maturity markets are more volatile*, and so bubbles can be larger in these markets. As the Bull-Bear engine profits from going with price
’ The price of the bond is the sum of the coupon payments over its lifetime and the return of the principal. However, these cashflows must be discounted at the current market rates, and the longer the bond, the larger the number of payments that need discounting, and so interest rate changes have a greater effect on the prices of long bonds.
bubbles, it works better in the longer maturity markets. This view o f financial markets is summarised in Table 8.2.
Table 8.2: Market Models
Conventional Financial View New View
Markets are random Markets trend (Hurst exponents > 0.5) Expectations are homogeneous Expectations are heterogeneous
GARCH is anomalous GARCH natural consequence
Bubbles are anomalous Bubbles are natural consequence
Long maturity markets are noisier Bubbles can be larger in long maturity markets BuU-Bear result inexpUcable BuU-Bear exploits bubbles
8.6.2 But don’t overdo it
It is important not to neglect the evidence against rejecting the EMH:
1. The Genetic Algorithms for Trade Filtering project demonstrates that charts have information content, but this is not under dispute. What is unresolved is whether they contain sufficient information to out-perform a buy-and-hold strategy. This is indeterminable from the available information, and so the EMH cannot be rejected from this information.
2. The Continually Adaptive Trading Engine makes returns approximately 100 basis points (1%) over LIBOR. It is unclear whether this constitutes beating the market or not: if the markets are efficient, one should not be able to make money by borrowing in the interbank loan markets, and then simply investing it in the stock market, thus borrowing at around 5% and then making about 10% on stocks. For this reason, it is unclear whether making super-LIBOR returns is beating the market or not.
3. The BuU-Bear Trading Engine fails to operate on commodities. This is consistent with the market being efficient. The analysis impUcations o f the system’s behaviour on gold is ambiguous: the system failed to work, as is consistent with the EMH, but also behaves completely systematicaUy which is not. However, for reasons explained in Section 6.9.2, this system cannot simply be traded the other way. Each of these results are either consistent with the EMH, or insufficient to reject it.
8.6.3 Conclusions on the Efficient Market Hypothesis
The ultimate conclusion o f this discussion of the Efficient Market Hypothesis must be that it is untrue. Just as Fortune concluded[Fort91], that there is overwhelming empirical evidence against the EMH. Tests of the EMH usually fail to reject it if the test in question is somehow derived from financial theory in the first place. Tests that have roots in ideas different from finance often find a hole in the theory.
The work presented here finds yet more holes in the EMH:
1. The Bull-Bear Trading Engine successfully trades most Government bond futures markets;
2. The presence o f some relationship between the effectiveness of momentum based trading systems and market maturity has been demonstrated to 86% confidence. 3. The Continually Adaptive Trading Engine appears to out-perform LIBOR.
There is a body o f hterature already in existence sufficient to refiite the EMH, and although work presented in this thesis makes a valuable contribution to this stance, it is insufficient to end the debate once and for ah.
One reason for this hes in whether the experiments are “useful refutations” o f the EMH or not. An experiment may punch a hole in the EMH, but if it enables investors to underperform the market, then the economists are rightly ahowed to say “So W hat?”. A simhar response would greet any failures of the EMH that cannot be exploited once transaction costs have been taken into account. However, if an experiment makes excess returns then other problems arise - an example of this is the risk adjusting of returns (Section 6.11.2). These experiments are underpinned by auxhiary assumptions that leave the final state o f the discussion in a pecuhar state. As Fama wrote in summary in one o f his papers[Fama90] “Whether the combined explanatory power of the variables - about 58% o f the variance of annual returns - is good or bad news for market efficiency is left for the reader to judge”.
Markets are not efficient, but they are sufficiently efficient for the EMH to be a working assumption - it is not a trivial process to devise a speculative trading system that systematically extracts profits from the markets. As Malkiel[Malk88] notes, there is a great deal o f evidence supporting both sides of the argument, and “reports o f the
death of the Efficient Market Hypothesis appear premature”. However, this statement was made 10 years ago, but the same academic jousting is taking place and options are still priced with variants of the Black-Scholes pricing formulae.
Some of the results presented in the course of this thesis suggest that the EMH is untrue. A large number o f papers have been pubhshed in reputable journals by competent researchers that demonstrate that the EMH is invahd. A hypothesis cannot be restored to health by a second body of hterature that shows that it has not been refuted[Cham92], and so as a result o f these investigations, it must be concluded that the EMH is invahd.