Question

1.Answer the following review questions about the actual market efficiency.

a.What is mean reversion? How might an investor use mean reversion to earn above-average returns?

b.What is excess volatility? How might an investor use excess volatility to earn above-average returns?

Answer 1

Mean reversion Is the tendency for stocks that have recently been earning high returns to experience low returns in the future and for stocks that have recently been earning low returns to earn high returns in the future.

Or

ean reversion is the theory suggesting that prices and returns eventually move back toward the mean or average. This mean or average can be the historical average of the price or return, or another relevant average such as the growth in the economy or the average return of an industry.

This theory has led to many investing strategies involving the purchase or sale of stocks or other securities whose recent performances have greatly differed from their historical averages. However, a change in returns could be a sign that the company no longer has the same prospects it once did, in which case it is less likely that mean reversion will occur.

Percent returns and prices are not the only measures considered mean reverting; interest rates or even the price-earnings ratio of a company can be subject to this phenomenon.

A reversion involves the return of any condition back to a previous state. In cases of mean reversion, the thought is that any price that strays far from the long-term norm will again return, reverting to its understood state. The theory is focused on the reversion of only relatively extreme changes, as normal growth or other fluctuations are an expected part of the paradigm.

The mean reversion theory is used as part of a statistical analysis of market conditions, and can be part of an overall trading strategy. It applies well to the ideas of buying low and selling high, by hoping to identify abnormal activity that will, theoretically, revert back to a normal pattern.

The return to a normal pattern is not guaranteed, as an unexpected high or low could be an indication of a shift in the norm. Such events could include, but are not limited to, new product releases or developments on the positive side, or recalls and lawsuits on the negative side.

Even with extreme events, it is possible a security will experience a mean reversion. As with most market activity, there are few guarantees on how particular events will or will not affect the overall appeal of particular securities.

Excess volatility Is selling stocks when they are above their fundamental values and buying them when they are below their fundamental values. Attempts to use this trading strategy have not been consistently able to produce above-average returns. In other words Too big changes in stock prices compared to changes of their fundamentals like corporate earnings, dividends, interest rates

The excess volatility puzzle, identified by Shiller (1981) and LeRoy and Porter (1981), has gained much attention over the past three decades. Surprisingly, unlike other financial anomalies in the literature, few papers have attempted to explore profitable trading rules implied by excess volatility. Dumas (2003) makes the following remark:

“If there is excessive volatility, one can argue that this is evidence of financial market inefficiency. In that case, one should be able to develop some ‘volatility arbitrage’ that would reap profits. In particular, if the reason for excess volatility is irrationality of one or several categories of traders, one should be able to find a way for rational traders to take advantage of their behavior ”

But Dumas (2003) immediately points out that “[t]hat is not easy to conceive”. In this article, we will provide such an effort and investigate the relation between excess volatility and the cross-section of stock returns.

Shiller (1981) defines excess volatility as the volatility of the equity market that cannot be justified by variation in subsequent dividends. Since the information that investors use to forecast future dividends is unobservable in nature, researchers often examine the excess volatility puzzle by comparing the realized stock price volatility to the volatility bounds. These bounds are formalized based on the ex-post present values derived from some discount-rate models. However, the empirical methodologies employed in the volatility test literature have been under extensive critiques ever since Shiller (1981). For example, Cochrane (1991) criticizes that the volatility tests are only tests of specific discount-rate models; they do not have any advantage over other empirical methods such as return-forecasting regressions or Euler equations and cannot tell much about the market efficiency or inefficiency.

This issue of unobservable information becomes even more disturbing when we try to identify profitable opportunities implied by excess volatility. We cannot use any ex-post information—such as ex-post dividend distributions, which are often utilized in the volatility test literature—to quantify excess volatility. Thus, some innovative method must be attempted in order to accomplish the challenging task that is posited by Dumas (2003).

We go back to the literature for possible clues to quantify excess volatility. First, Shiller (1981) states that the short-term stock market volatility is too excessive to be explained by the subsequent variation in the economic fundamentals. In the longer horizon, however, the extra volatility should fade away as more real information about economic growth, corporate earnings, and changes in the business condition are factored into the stock price. Second, French and Roll (1986) propose that if trading noises are the source that causes excess volatility in daily returns, the variance of long-horizon returns should be less than the cumulated variance of daily returns. They find that mispricing can be responsible for 4–12% of the variance in daily returns on average. Third, Fama (1990) and Schwert (1990) provide abundant empirical evidence that the fluctuation in stock returns over longer holding horizons can be explained more by variation in the subsequent real activities. They argue that since economic information is usually spread over many previous periods, the cumulative economic information can be better captured by the longer-term stock returns.

Although the classical studies listed above have various research aims on their own, they share the same view that the economic fundamentals are more correctly reflected by longer-horizon stock returns. Thus, the difference between the volatility of short- and long-horizon returns can be very informative for quantifying excess volatility.