Monday, 20 August 2012

Interpreting Mean Reversion: Mispricing in Irrational Markets

This article builds on the previous two articles in this series, Cyclical Variations in Equity Prices and Mean Reversion and Equity Prices, and interprets mean reversion in equity prices and returns. As with the previous articles, the article below is an excerpt from an academic paper I wrote back in 2001, but I believe the content is still as important today.

Interpreting Mean Reversion

Various theories attempting to explain mean reversion have been laid forward. These theories come in a wide variety and range from “fads, noise traders and rational speculative bubbles” (McQueen (1992)) and year-end tax-motivated trading (Jegadeesh (1991)), to the two competing economic explanations of mispricing in irrational markets versus predictable time variation in security risk premia (Gangopadhyay et al (1996)). Other explanations include irrational overreactions of the market to unexpected and dramatic news events (DeBondt et al (1985)), that reversals are a natural consequence of Bayes’ rule (Cassano (1999)), to the extreme criticism of papers questioning the significance of long-horizon mean reversion and the necessity to explain it (McQueen (1992)). McQueen (1992) also argues that mean reversion found in the earlier papers were due to the Depression and WWII observations, which have large, mean reverting tendencies. This argument is partly supported by Fama et al’s (1988) estimate of lower mean reversion for the period after 1940. Finally, Gangopadhyay (1996) mentions several papers that criticise the earlier papers on statistical grounds, suggesting the results do not really violate the random walk model. When prices are high relative to dividends (or earnings, cashflow, book value, or some other divisor), one of three things must be true: 1. Investors expect dividends to rise in the future, 2. Investors expect returns to be low in the future. Future cash flows are discounted at a lower than usual rate, leading to higher prices. 3. Investors expect prices to rise forever, giving an adequate return even if there is no growth in dividends. If the price/dividend ratio (or any other divisor) is high, either dividends must rise, prices must decline, or the price/dividend ratio must grow explosively (Cochrane (2001)). This research will focus on the two major economic theories mentioned above; mispricing in irrational markets and time varying equity risk premia, the latter will be presented in the next article in this series that will be published later this week.

Mispricing In Irrational Markets

Perhaps the most controversial of the explanations for mean reversion in asset returns is the hypothesis that markets are irrational and shortsighted. Even if controversial, such notions of the markets date back many decades. In his book The General Theory of Employment, Interest and Money, Keynes (1947) observes: “Day-today fluctuation in the profits of existing investments, which are obviously of an ephemeral and non-significant character, tend to have an altogether excessive, and even absurd, influence on the market”. Supporting this argument is the discovery of “anomalies” in stock markets and evidence from the past of aberrant crowd behavior among market participants and even evidence showing that stock prices are influenced by the weather (Saunders (1993)). An anomaly in finance is said to exist if a given return cannot be explained in terms of the efficient market hypothesis and an asset pricing model. Fama (1991) stresses this deficiency and explains that market efficiency per se is not testable but must be tested jointly with some asset pricing model of equilibrium. We can therefore only test whether information is properly reflected in prices in the context of a pricing model that defines the meaning of” properly”. He refers to this as the “joint-hypothesis problem”. This problem arises because it is difficult to explain the return: Does it reflect rational variations in expected returns through time, irrational deviations of price from fundamental value, or does it reflect some combination of the two. The equilibrium model most often used for such purposes is the Capital Asset Pricing Model (CAPM) developed by Sharpe (1964), Lintner (1965) and Mossin (1966), even though it is a static (single-period) model (Merton (1973)). Many of these anomalies may be explained in terms of mean reversion. In an irrational market, mean reversion is thought to occur because prices take long temporary swings away from intrinsic values (Gangopadhyay et al (1996)). This argument is partly based on the notion that markets overreact to information or the state of the market, e.g. they become excessively pessimistic in recessions and turn overly optimistic when the economy is peaking. A recent illustration of overly optimistic behavior is the Internet bubble of the late 1990s and early 2000 which (finally) burst in March 2000. At this stage the stock market had priced in an excessive expected growth in earnings for technology companies. According to I/B/E/S, the long-term earnings growth forecasts for S&P Technology was 25 percent in early 2000 against a long-term historical average of 5 percent. These forecasts were made in response to a positive surprise from actual technology sector earnings during the extended investment boom (Thygesen (2001)). This is illustrative of Lakonishok, Shleifer and Vishny’s (1994) findings that markets and investors have a tendency of extrapolating past growth rates. In their own words, “Investor expectations of future growth appear to have been excessively tied to past growth despite the fact that future growth rates are highly mean reverting”. They further explain that the behavior of putting excessive weight on recent history is a common judgment error in psychological experiments and not just in the stock market. Barsky and De Long (1993) also argue that investors do extrapolate the past. It follows that prices of growth stocks are most likely to reflect the failure of investors to impose mean reversion to long-term growth forecasts.

Analysts’ forecasts may also play a role in extrapolating past growth rates. Chopra (1998) argues in his study on the U.S. market that analysts’ are generally too optimistic, that they tend to forecast in a narrow and comfortable range, and that the forecasts are most accurate in an environment of continued strong growth. This extrapolation tends to catch analysts off-guard when economic growth accelerates or decelerates and reverts to its historical pattern. These forecasting weaknesses of security analysts necessarily influence the market assuming their (institutional) clients act on their advice. In addition, bottom-up analysts’ forecasts are usually much higher than that warranted by a top-down analysis, further contributing to overreaction for individual shares and industries. It should also be mentioned that analysts have other agendas that may lead to biased estimates and investment recommendations, such as preserving investment banking relationships with the companies they analyse (See Hooke (1998) for a critical look at this issue).

Lakonishok et al (1994) confirm the tendency of value stocks to outperform growth stocks and relate this tithe extrapolation procedure mentioned above. Campbell (2000) confirms this and explains that this “value effect” may result in part from investors’ irrational extrapolation of poor earnings and their reluctance to hold badly managed companies in declining industries. The superior returns to value stocks over growth stocks are well documented, both in the U.S., internationally and across industries (See for example Basu (1977), Dreman and Berry (1995), Dreman (1998), Dreman and Lufkin (1997, 2000), Fama and French (1996, 1998), Dechow and Sloan (1997), Bauman, Conover and Miller (1999) and Young (2001)).

Positive-feedback traders as discussed by De Long, Shleifer, Summers and Waldmann (1990), may create overreactions by pushing asset prices away from fundamentals. This explanation implies that” trend-chasers” reinforce movements in stock prices even in the absence of fundamental information. It may therefore pay to “jump on the bandwagon and purchase ahead of noise demand”. In this setting, rational speculation can be destabilizing because when rational speculators receive good news and trade on this news, they recognise that the initial price increase will stimulate buying by positive feedback traders tomorrow. Informed rational investors hence buy more today, anticipating price increases tomorrow and so drive prices up today higher than fundamentals warrant.

Arbitrage, one of the fundamental concepts of finance, may also become ineffective in extreme circumstances, when prices diverge far from fundamental values (Shleifer and Vishny (1997)). Due to the risk inherent in arbitrage, it may therefore be unsuccessful in bringing prices back to values based on fundamentals. Recent research by Mitchell, Pulvino, and Stafford (2002) support such limitations of arbitrage in a study on 82 situations where the market value of a company is less than its subsidiary. They show that uncertainty about the distribution of returns, costs and characteristics of the risks limits arbitrage in equity markets. They conclude that market forces are working hard to keep prices at fundamental values but that the effectiveness of these efforts is sometimes limited. Given these limitations of arbitrage,

Summers (1986) argue irrational investors who plunge into particular securities may even come to dominate the market. It follows that the returns for past winners and losers are partly temporary in nature (Chan, Jegadeesh and Lakonishok (1996)). De Bondt et al (1985) report substantial weak form inefficiencies and find long-term return reversals, i.e. past winners become future losers and vice versa. Regarding the excessive returns to low P/E strategies, Dreman et al (1995) draw the conclusion that mean reversion account for the major part of the total above-market holding period returns to the lowest P/E group. Excess returns to buying low P/E stocks above that warranted by the underlying risk would be inconsistent with the efficient market hypothesis. An alternative explanation of the out performance of value strategies is that they are fundamentally riskier, i.e. firms under distress who have high financial leverages, and face substantial uncertainty in future profitability (See for example Fama and French (1992) and Chen and Zhang (1998)). Along this path of reasoning is the hypothesis that the high returns to low market to-book investments are compensation for financial distress. However, this argument has not gained support in a number of studies which have found that value strategies are actually less risky than growth strategies. Among the proponents of the latter are De Bondt et al (1987) and De Bondt and Thaler (1989). De Bondt et al (1987) base this argument on the finding that during the test period, the loser portfolio has a bull market beta of 1.39 and a bear market beta of .88. This implies that that the losers go up 13.9 percent when the market goes up 10 percent and fall only 8.8 percent when the market falls 10 percent. Naturally, they interpret this finding rather ironically as not being “too risky” (De Bondt et al (1989)). Lakonishok et al (1994) and Dreman et al (1997) argue that if value strategies are fundamentally riskier, meaning that a risky portfolio has larger swings than the market, this will cause such strategies to outperform in up markets and under perform in down market. Contrary to this belief, both studies conclude that value strategies outperform both in up- and down markets, implying that value strategies are in fact less risky. La Porta (1996) also finds no evidence that low expected growth stocks carry more risk than stocks with high-expected growth. These studies seem to suggest that there must be some other factor(s) than risk which explains these superior returns.

Why do investors then buy growth stocks? The blind extrapolation of historical growth well into the foreseeable future as argued most notably by Lakonishok et al (1994), but also by Dreman (1998), is perhaps the strongest argument and most obvious reason why investors buy growth stocks. The former also offer other appealing explanations for this (irrational) behavior and why even institutional investors may expose themselves to investing in glamour stocks. First, institutions might prefer glamour stocks because they appear to be prudent investments that are easier to justify to sponsors. Such stocks have done well in the past and are thought unlikely to be financially distressed in the near future. Following the hypothesis that the higher return to value stocks is the reward for taking on higher risk, such investments may be easier to justify. Second, most investors, and hence fund managers and sponsors, have shorter time horizons than are required for value strategies to consistently pay off (see comments by Bernstein below). They often cannot afford to under perform the market or their peers for any nontrivial period since this may trigger sponsors to withdraw their funds. After all, the fund management industry is concerned with retaining customers and attaining new ones and might, just as other investors, be overly concerned with short-term profit generation and bonus collection. This study proposes another hypothesis related to the irrational investors argument which could be termed the "lottery effect". Under this theory, investors are thought to throw their money at the biggest potential successes, aware or not of the low probability of consistent, abnormal gains. An investor commenting "why invest in old, boring companies yielding 12 percent a year when I can double my money in months" during the recent bull market, illustrates the psychology underpinning such a theory. One could reasonably assume that such investor behaviour is viable if indeed a successful single growth firm investment yields a far higher return than that of a successful value investment. Intuitively, this seems to be the case when looking at the appreciation of certain technology companies during Internet mania. What would otherwise cause investors to price new, money-loosing companies as high as old, established moneymaking machines? A viable explanation is unrealistic expectations of future cash flow generation and wishful thinking.

In conclusion, there is ample evidence suggesting markets are not always rational, that prices are partly predictable, and that excess returns above that explained by the CAPM are attainable. The latter is evident in the Fama et al (1992) article where they state “We are forced to conclude that the SLB model does not describe the last 50 years of average stock returns”. Whether investment strategies exploiting such inconsistencies are easily implemented, e.g. due to transactions costs and liquidity, is a different story. In the discussion part of the De Bondt et al (1985) paper, Bernstein sums up the issue nicely: “In sum then, the market will naturally provide arbitrage opportunities from long-run inefficiencies, but only a few investors have the necessary psychological attitudes and will accept the necessary investment horizon to perform as true long-term investors”. Finally, Fama (1998) explains that the efficient market hypothesis, like all models, is a faulty description of price formation. Even so, any alternative model has a daunting task and must be able to explain the observed results better than the simple market efficiency story. He holds that a problem in developing an overall perspective on long-term studies is that they rarely test a specific alternative to EMH and instead use a vague hypothesis; market inefficiency. To Fama, this is seen as unacceptable. As mentioned, mean reversion implies predictability of returns. However, predictability is not necessarily inconsistent with the concept of market efficiency if no excess-profit opportunities are available (Balvers, Cosimano and McDonald (1990)).