The actual returns you experience from investing in stocks and bonds will not necessarily reflect historical or average returns. As you'll read in any investment prospectus, past performance is not a guarantee of future returns. No one can really predict what will happen in the markets; the past is only a guide. Earlier we discussed the different types of risk and other factors that can affect returns. In this section we'll discuss some of the factors that affect the variability of returns. Predicting Market Performance
There are two prices that are critical for any investor to know: the current price of the investment he or she owns or plans to own, and its future selling price. Despite this, investors are constantly reviewing past pricing history and using it to influence their future investment decisions. Some investors won't buy a stock or index that has risen too sharply because they assume that it's due for a correction, while other investors avoid a falling stock because they fear that it will continue to deteriorate.

Does academic evidence support these types of predictions, based on recent pricing? In this section, we'll look at four different views of the market and learn more about the associated academic research that supports each view. The conclusions will help you better understand how the market functions and perhaps eliminate some of your own biases.

"Don't fight the tape." This widely quoted piece of stock market wisdom warns investors not to get in the way of market trends. The assumption is that the best bet about market movements is that they will continue in the same direction. This concept has its roots in behavioral finance. With so many stocks to choose from, why would investors keep their money in a stock that's falling, as opposed to one that's climbing? (For more insight, see the Behavioral Finance tutorial.)

Studies have found that mutual fund inflows are positively correlated with market returns. Momentum plays a part in the decision to invest and when more people invest, the market goes up, encouraging even more people to buy. It's a positive feedback loop.

A 1993 study by Narasimhan Jegadeesh and Sheridan Titman, "Returns to Buying Winners and Selling Losers," suggests that individual stocks have momentum. They found that stocks that have performed well during the past few months are more likely to continue their outperformance next month. The inverse also applies; stocks that have performed poorly are more likely to continue their poor performance.

However, this study only looked ahead a single month. Over longer periods, the momentum effect appears to reverse. According to a 1985 study by Werner DeBondt and Richard Thaler, "Does the Stock Market Overreact?" stocks that have performed well in the past three to five years are more likely to underperform the market in the next three to five years and vice versa. This suggests that something else is going on: mean reversion.

Mean Reversion
Experienced investors who have seen many market ups and downs often take the view that the market will even out over time. Historically high market prices often discourage these investors from investing, while historically low prices may represent an opportunity.

The tendency of a variable, such as a stock price, to converge on an average value over time is called mean reversion. The phenomenon has been found in several economic indicators, including exchange rates, gross domestic product (GDP), interest rates and unemployment. (For more insight, check out Economic Indicators To Know and Economic Indicators For The Do-It-Yourself Investor.)

The research is still inconclusive about whether stock prices revert to the mean. Some studies show mean reversion in some data sets over some periods, but many others do not. For example, in 2000, Ronald Balvers, Yangru Wu and Erik Gilliland found some evidence of mean reversion over long investment horizons in the relative stock index prices of 18 countries, which they described in the "Journal of Finance."

However, even they weren't completely convinced. They wrote in their study, "A serious obstacle in detecting mean reversion is the absence of reliable long-term series, especially because mean-reversion, if it exists, is thought to be slow and can only be picked up over long horizons."

Given that academia has access to at least 80 years of stock market research, this finding suggests that if the market does have a tendency to mean revert, it is a phenomenon that happens slowly and almost imperceptibly over many years or even decades.

Another possibility is that past returns just don't matter. In 1965, Paul Samuelson studied market returns and found that past pricing trends had no effect on future prices and reasoned that in an efficient market, there should be no such effect. His conclusion was that market prices are martingales.

A martingale is a mathematical series in which the best prediction for the next number is the current number. The concept is used in probability theory to estimate the results of random motion. For example, suppose that you have $50 and bet it all on a coin toss. How much money will you have after the toss? You may have $100 or you may have $0 after the toss, but statistically the best prediction is $50, your original starting position. The prediction of your fortunes after the toss is a martingale. (To learn how this applies to trading, see Forex Trading The Martingale Way.)

In stock option pricing, stock market returns could be assumed to be martingales. According to this theory, the valuation of the option does not depend on the past pricing trend, or on any estimate of future price trends. The current price and the estimated volatility are the only stock-specific inputs.

A martingale in which the next number is more likely to be higher is known as a sub-martingale. In popular literature, this motion is known as a random walk with upward drift. This description is consistent with the more than 80 years of stock market pricing history. Despite many short-term reversals, the overall trend has been consistently higher. (To learn more about random walk, read Financial Concepts: Random Walk.)

If stock returns are essentially random, the best prediction for tomorrow's market price is simply today's price, plus a very small increase. Rather than focusing on past trends and looking for possible momentum or mean reversion, investors should instead concentrate on managing the risk inherent in their volatile investments.

Value Investing
Value investors purchase stock cheaply and expect to be rewarded later. Their hope is that an inefficient market has underpriced the stock, but that the price will adjust over time. The question is does this happen and why would an inefficient market make this adjustment? (For more on value investing, read How To Profit From An Inefficient Market and Is Warren Buffett Really A Value Investor?)

Research suggests that this mispricing and readjustment consistently happens, although it presents very little evidence for why it happens.

In 1964, Gene Fama and Ken French studied decades of stock market history and developed the three-factor model to explain stock market prices. The most significant factor in explaining future price returns was valuation, as measured by the price-to-book ratio. Stocks with low price-to-book ratios delivered significantly better returns than other stocks. (To read more about this ratio, see Value By The Book.)

Valuation ratios tend to move in the same direction, and in 1977, Sanjoy Basu found similar results for stocks with low price-earnings (P/E) ratios. Since then, the same effect has been found in many other studies across dozens of markets. (For more on this, check out Understanding The P/E Ratio.)

However, studies have not explained why the market is consistently mispricing these "value" stocks and then adjusting later. The only conclusion that could be drawn is that these stocks have extra risk for which investors demand additional compensation. (To learn more about this phenomenon, read The Equity-Risk Premium: More Risk For Higher Returns and Calculating The Equity Risk Premium.)

Price is the driver of the valuation ratios; therefore, the findings do support the idea of a mean-reverting stock market. As prices climb, the valuation ratios get higher and, as a result, future predicted returns are lower. However, the market P/E ratio has fluctuated widely over time and has never been a consistent buy or sell signal.

Even after decades of study by the brightest minds in finance, there are no solid answers. The only conclusion that can be drawn is that there may be some momentum effects in the short term and a weak mean reversion effect in the long term.

The current price is a key component of valuation ratios such as P/B and P/E that have been shown to have some predictive power on the future returns of a stock. However, these ratios should not be viewed as specific buy and sell signals, just as factors that have been shown to play a role in increasing or reducing the expected long-term return. (For further reading, see Projected Returns: Honing The Craft.)

Does Higher Risk Really Lead to Higher Returns?
Many widely accepted financial models are built around the premise that investors should expect higher returns if they are willing to accept more risk. But will investing in a portfolio of risky stocks really help increase your investment returns over time?

The Low Down on Low-Volatility Stocks

If modern portfolio theory holds true, a portfolio of risky, highly-volatile stocks should have higher returns than a portfolio of safer, less-volatile stocks. However, stock market researchers are discovering that this may not always be the case. A March 2010 study by Malcolm Baker, Brendan Bradley and Jeffrey Wurgler, published in the Jan/Feb 2011 Financial Analysts Journal and titled, "Benchmarks as Limits to Arbitrage: Understanding the Low-Volatility Anomaly," demonstrated that from January 1968 to December 2008, portfolios of low-risk stocks actually outperformed portfolios of high-risk stocks by a whopping margin.

The study sorted the largest 1,000 U.S. stocks monthly into five different groups based on two widely accepted measures of investment risk. The authors ran the study once using trailing total volatility as a proxy for risk, and again using trailing beta. Over the 41-year period, a dollar invested in the lowest-volatility portfolio of stocks grew to $53.81, while a dollar invested in the highest-volatility portfolio grew to only $7.35. The findings were similar when they grouped stocks based on trailing beta. Over the same period, a dollar invested in the lowest-beta portfolio of stocks grew to $78.66, whereas a dollar invested in the highest-beta portfolio grew to a paltry $4.70. The study assumed no transaction costs.

These results fly in the face of the notion that risk (volatility) and investment returns are always joined at the hip. Over the study period, a low-risk stock investor would have benefited from a more consistent compounding scenario with less exposure to the market's most overvalued stocks. (For related reading on how volatility affects your portfolio, check out Volatility's Impact On Market Returns.)

Fast Money?
Proponents of behavioral finance have presented the idea that low-risk stocks are a bargain over time because investors irrationally shun them, preferring stocks with a more volatile "lottery style" payoff. Backers of this school of thought also believe that investors have a tendency to identify great "stories" with great stocks. Not surprisingly, these highly touted "story stocks" tend to be among the market's most expensive and most volatile. Overconfidence plays a role here, too. As a whole, investors misjudge their ability to assess when stocks will "pop or drop," making highly volatile stocks appear like a better proposition than they really are. Even the so called "smart money" has a tendency to gravitate toward risky stocks.

Many institutional investors are compensated based on short-term investment performance and their ability to attract new investors. This gives them an incentive to pass up less volatile stocks for riskier ones, especially in the midst of a raging bull market. Whether it is bad habits or disincentives, investors have a tendency to pile into the market's riskiest stocks, which drive down their potential for future gains relative to less volatile ones. Consequently, low-risk stocks tend to outperform over time.

Before You Bet the Farm on Low-Volatility
Before you trade all of your technology stocks in for a portfolio of utilities, keep in mind that like most stock market anomalies, this one probably exists because it is not easy to exploit. A study published in September 2011 by Rodney Sullivan and Xi Li, "The Limits to Arbitrage Revisited: The Low-Risk Anomaly," explored the viability of actually trading the low-volatility stock anomaly from 1962 to 2008. Over the 45-year study period, Sullivan and Li found that "the efficacy of trading the well-known low-volatility stock anomaly is quite limited." Issues cited in the study include the need for frequent portfolio rebalancing and the high transaction costs associated with trading illiquid stocks. According to the study, illiquid stocks are where most of the abnormal returns associated with the low-volatility anomaly are concentrated.

There are a few other issues associated with investing in low-volatility stocks. First, low-volatility stock investing strategies can suffer long periods of underperformance relative to the broader stock market. They also have a tendency to be heavily concentrated in a few sectors like utilities and consumer staples. (Among the methods used to measure volatility, specifically in technical analysis, is calculating average true range. Read more in Measure Volatility With Average True Range.)

The positive relationship between risk and expected returns may hold true when investing across different asset classes, but the same may not always be true when investing within a particular asset class, like stocks. While it is dangerous to assume that you can boost your investment returns simply by investing in a portfolio of risky stocks, it can be equally as dangerous to assume that researchers of the low-volatility stock anomaly have somehow discovered a silver bullet to achieving higher returns.

Stock investors shouldn't overlook the importance of consistency when attempting to compound their investment returns. They should also take into account that the stability of a company's stock price is often a reflection of the true quality of its underlying earnings stream.

Making Sense of Market Anomalies
In the non-investing world, an anomaly is a strange or unusual occurrence. In financial markets, anomalies refer to situations when a security or group of securities performs contrary to the notion of efficient markets, where security prices are said to reflect all available information at any point in time.

With the constant release and rapid dissemination of new information, sometimes efficient markets are hard to achieve and even more difficult to maintain. There are many market anomalies; some occur once and disappear, while others are continuously observed.

Can anyone profit from such strange behavior? Let's look at some popular recurring anomalies and examine whether any attempt to exploit them could be worthwhile.

Calendar Effects
Anomalies that are linked to a particular time are called calendar effects. Some of the most popular calendar effects include the weekend effect, the turn-of-the-month effect, the turn-of-the-year effect and the January effect.

  • Weekend Effect: The weekend effect describes the tendency of stock prices to decrease on Mondays, meaning that closing prices on Monday are lower than closing prices on the previous Friday. For some unknown reason, returns on Mondays have been consistently lower than every other day of the week. In fact, Monday is the only weekday with a negative average rate of return.
Source: Fundamentals of Investments, McGraw Hill, 2006
  • Turn-of-the-Month Effect: The turn-of-the-month effect refers to the tendency of stock prices to rise on the last trading day of the month and the first three trading days of the next month.
Turn of the Month
Rest of Days
Source: Fundamentals of Investments, McGraw Hill, 2006
  • Turn-of-the-Year Effect: The turn-of-the-year effect describes a pattern of increased trading volume and higher stock prices in the last week of December and the first two weeks of January.
Turn of the Year
Rest of Days
Source: Fundamentals of Investments, McGraw Hill, 2006
  • January Effect: Amid the turn-of-the-year market optimism, there is one class of securities that consistently outperforms the rest. Small-company stocks outperform the market and other asset classes during the first two to three weeks of January. This phenomenon is referred to as the January effect. (Keep reading about this effect in January Effect Revives Battered Stocks.)

    Occasionally, the turn-of-the-year effect and the January effect may be addressed as the same trend, because much of the January effect can be attributed to the returns of small-company stocks.

Why Do Calendar Effects Occur?
So, what's with Mondays? Why are turning days better than any other days? It has been jokingly suggested that people are happier heading into the weekend and not so happy heading back to work on Mondays, but there is no universally accepted reason for the negative returns on Mondays.

Unfortunately, this is the case for many calendar anomalies. However, the January effect may have the most valid explanation. It is often attributed to the turn of the tax calendar; investors sell off stocks at year's end to cash in gains and sell losing stocks to offset their gains for tax purposes. Once the New Year begins, there is a rush back into the market and particularly into small-cap stocks.

Announcements and Anomalies
Not all anomalies are related to the time of week, month or year. Some are linked to the announcement of information regarding stock splits, earnings, and mergers and acquisitions.

  • Stock Split Effect: Stock splits increase the number of shares outstanding and decrease the value of each outstanding share, with a net effect of zero on the company's market capitalization. However, before and after a company announces a stock split, the stock price normally rises. The increase in price is known as the stock split effect.

    Many companies issue stock splits when their stock has risen to a price that may be too expensive for the average investor. As such, stock splits are often viewed by investors as a signal that the company's stock will continue to rise. Empirical evidence suggests that the signal is correct. (For related reading, see Understanding Stock Splits.)

  • Short-Term Price Drift: After announcements, stock prices react and often continue to move in the same direction. For example, if a positive earnings surprise is announced, the stock price may immediately move higher. Short-term price drift occurs when stock price movements related to the announcement continue long after the announcement.

    Short-term price drift occurs because information may not be immediately reflected in the stock's price.

  • Merger Arbitrage: When companies announce a merger or acquisition, the value of the company being acquired tends to rise while the value of the bidding firm tends to fall. Merger arbitrage plays on potential mispricing after the announcement of a merger or acquisition.

    The bid submitted for an acquisition may not be an accurate reflection of the target firm's intrinsic value; this represents the market anomaly that arbitrageurs aim to exploit. Arbitrageurs aim to take advantage of the pattern that bidders usually offer premium rates to purchase target firms. (To read more about M&As, see The Merger - What To Do When Companies Converge and Biggest Merger and Acquisition Disasters.)

Superstitious Indicators
Aside from anomalies, there are some nonmarket signals that some people believe will accurately indicate the direction of the market. Here is a short list of superstitious market indicators:

  • The Super Bowl Indicator: When a team from the old American Football League wins the game, the market will close lower for the year. When an old National Football League team wins, the market will end the year higher. Silly as it may seem, the Super Bowl indicator was correct more than 80% of the time over a 40-year period ending in 2008. However, the indicator has one limitation: it contains no allowance for an expansion-team victory.

  • The Hemline Indicator: The market rises and falls with the length of skirts. Sometimes this indicator is referred to as the "bare knees, bull market" theory. To its merit, the hemline indicator was accurate in 1987, when designers switched from miniskirts to floor-length skirts just before the market crashed. A similar change also took place in 1929, but many argue as to which came first, the crash or the hemline shifts.

  • The Aspirin Indicator: Stock prices and aspirin production are inversely related. This indicator suggests that when the market is rising, fewer people need aspirin to heal market-induced headaches. Lower aspirin sales should indicate a rising market. (See more superstitious anomalies at World's Wackiest Stock Indicators.)

Why Do Anomalies Persist?
These effects are called anomalies for a reason: they should not occur and they definitely should not persist. No one knows exactly why anomalies happen. People have offered several different opinions, but many of the anomalies have no conclusive explanations. There seems to be a chicken-or-the-egg scenario with them too - which came first is highly debatable.

Profiting From Anomalies
It is highly unlikely that anyone could consistently profit from exploiting anomalies. The first problem lies in the need for history to repeat itself. Second, even if the anomalies recurred like clockwork, once trading costs and taxes are taken into account, profits could dwindle or disappear. Finally, any returns will have to be risk-adjusted to determine whether trading on the anomaly allowed an investor to beat the market. (For related reading, see Market Cycles: The Key To Maximum Returns and The Stock Cycle: What Goes Up Must Come Down.)

Capital Market Efficiency

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