Technical analysis uses past prices and perhaps other past statistics to make investment decisions. Proponents of technical analysis believe that these data contain important information about future movements of the stock market. In practice, all major brokerage firms publish technical commentary on the market and many of the advisory services are based on technical analysis. In his interviews with them, Schwager (1993, 1995) finds that many top traders and fund managers use it. Moreover, Covel (2005), citing examples of large and successful hedge funds, advocates the use of technical analysis exclusively without learning any fundamental information on the market.
Academics, on the other hand, have long been skeptical about the usefulness of technical analysis, despite its widespread acceptance and adoption by practitioners. There are perhaps three reasons. The first reason is that there is no theoretical basis for it, which this paper attempts to provide. The second reason is that earlier theoretical studies often assume a random walk model for the stock price, which completely rules out any profitability from technical trading. The third reason is that earlier empirical findings, such as Cowles (1933) and Fama and Blume (1966), are mixed and inconclusive. Recently, however, Brock, Lakonishok, and LeBaron (1992), and especially Lo, Mamaysky, and Wang (2000), find strong evidence of profitability in technical trading based on more data and more elaborate strategies. These studies stimulated many subsequent academic research on technical analysis, but these later studies focus primarily on the statistical validity of the earlier results (reviewed in more detail in the next section).
Our paper takes a new perspective. We consider the theoretical rationales for using technical analysis in a standard asset allocation problem. An investor chooses how to allocate his wealth optimally between a riskless asset and a risky one which we call stock. For tractability, we focus on the profitability of the simplest and seemingly the most popular technical trading rule the moving average (MA) – which suggests that investors buy the stock when its current price is above its average price over a given period L. The immediate question is what proportion of wealth the investor should allocate into the stock when the MA signals so. Previous studies use an all-or-nothing approach: the investor invests 100% of his wealth into the stock when the MA says ‘buy’, and nothing otherwise. This common and naive use of the MA is, in fact, not optimal from an asset allocation perspective because the optimal amount should be a function of the investor’s risk aversion as well as the degree of predictability of the stock return. Intuitively, if the investor invests an optimal fixed proportion of his money into the stock market, say 80%, when there is no MA signal, he should invest more than 80% when the MA signals a buy, and less otherwise. The 100% allocation is clearly unlikely to be optimal. For a log-utility investor, we solve the problem of allocating the optimal amount of stock explicitly, which provides a clear picture of how the degree of predictability affects the allocation decision given the log-utility risk tolerance. We also solve the optimal investment problem both approximate analytically and via simulations in the more general power-utility case. The results show that the use of the MA can help increase the investor’s utility substantially.
Moreover, given an investment strategy that allocates a fixed proportion of wealth to the stock, we show that the MA rule can be used in conjunction with the fixed rule to yield higher expected utility. In particular, it can improve the expected utility substantially for the popular fixed strategy that follows Markowitz’s (1952) modern portfolio theory and Tobin’s (1958) two-fund separation theorem. Since indexing, a strategy of investing in a well-diversified portfolio of stocks, comprises roughly one-third of the US stock market, and its trend is on the rise worldwide (see, e.g., Bhattacharya and Galpin (2006)), and since popular portfolio optimization strategies (see, e.g., Litterman, 2003, and Meucci, 2005) are also fixed strategies, any improvement over fixed strategies is of practical importance, which might be one of the reasons that technical analysis is widely used in practice.
However, since the MA, as a simple filter of the available information on the stock price, disregards any information on predictive variables, trading strategies related to the MA must be in general dominated by the optimal dynamic strategy, which optimally uses all available information on both the stock price and predictive variables. An argument in favor of the MA could be that the optimal dynamic strategy is difficult for investors at large to implement due to the difficulty of model identification, and due to the cost of collecting and processing information. In particular, it is not easy to find reliable predictive variables, nor are their observations at desired time frequencies readily available in real time. This gives rise to the problem of predictability uncertainty in practice.
Contents
1 Introduction
2 Literature review
3 The model and analytic results
3.1 The model and investment strategies
3.2 Explicit solutions under log-utility
3.2.1 Optimal GMA
3.2.2 Combining a fixed rule with MA
3.2.3 Optimal pure MA
3.3 Analytic solutions under power-utility
- 3.3.1 First-order approximate solutions
3.3.2 Second-order approximate solutions
3.4 Solutions under parameter uncertainty
3.5 Solutions under model uncertainty
3.6 Optimal lags
4 An empirical illustration
4.1 Comparison under complete information
4.2 Comparison under parameter uncertainty
4.3 Comparison under model uncertainty
4.4 The effect of lag lengths
5 Conclusion
A Appendix
A.1 Proof of equations (10), (18) and (19)
A.2 Proof of propositions 1, 2 and 3
A.3 Proof of equation (42)
A.4 Computing the ML estimators
A.5 Proof of proposition 4
A.6 The linear rule
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Technical Analysis: An Asset Allocation Perspective on the Use of Moving Averages
