Just What Exactly Is a Random Walk?

Just What Exactly Is a Random Walk?

To many people this appears to be arrant nonsense. Even the most casual reader of the financial pages can easily spot patterns in the market.

The persistence of the belief in repetitive patterns in the stock market is due to statistical illusion. To illustrate, let me describe an experiment in which I recently asked my students to participate. The students were asked to construct a norm stock charts showing the movements of a hypothetical stock initially selling at $50 per share. For each successive trading day, the closing stock price would be determined by the flip of a fair coin. If the toss was a head, the students assumed that the stock closed 1/2 point higher than the preceding close. If the flip was a tail, the price was assumed to be down by 1/2. The chart derived from random coin tossing looks remarkably like a normal stock price chart and even appears to display cycles. Of course, the pronounced “cycles” that we seem to observe in coin tossing do not occur at regular intervals as true cycles do, but neither do the ups and downs in the stock market.

It is this lack of regularity that is crucial. The “cycles” in the stock charts are no more true cycles than the runs of luck or misfortune of the ordinary gambler. And the fact that stocks seem to be in an uptrend, which looks just like the upward move in some earlier period, provides no useful information on the dependability or duration of the current uptrend. Yes, history does tend to repeat itself in the stock market, but in an infinitely surprising variety of ways that confound any attempts to profit from a knowledge of past price patterns.

In other simulated stock charts derived through student coin tossing, there were head-and-shoulders formations, triple tops and bottoms, and other more esoteric chart patterns. One of the charts showed a beautiful upward breakout from an inverted head and shoulders (a very bullish formation). I showed it a chartist friend of mine who practically jumped out of his skin. “What is this company?” he exclaimed. “We’ve got to buy immediately. This pattern’s classic. There’s no question the stock will be up 15 points next week.” He did not respond kindly to me when I told him the chart had been produced by flipping a coin. Chartists have no sense of humor. I got my comeuppance when Business Week hired a technician who was adept at hatchet work, to review the first edition of this book.

Just What Exactly Is a Random Walk? Photo by Elena

My students used a completely random process to produce their stock charts. With each toss, as long as the coins used were fair, there was a 50 percent chance of heads, implying an upward move in the price of the stock, and a 50 percent chance of tails and a downward move. Even if they flip ten heads in a row, the chance of getting a head on the next toss is still 50 percent. Mathematicians call a sequence of numbers produced by a random process (such as those on our simulated stock chart) a random walk. The next move on the chart is completely unpredictable on the basis of what has happened before.

To a mathematician, the sequence of numbers recorded on a stock chart behaves no differently from that in the simuated stock charts – with one exception. There is a long-run uptrend growth of earnings and dividends. After adjusting for this trend, there is essentially no difference. The next move in a series of stock prices is unpredictable of past price behavior. No matter what wiggle or wobble the prices have made in the past, tomorrow starts out fifty-fifty. The next price change is no more predictable than the flip of a coin.

Now, in fact, the stock market does not quite measure up to the mathematician’s ideal of the complete independence of present price movements from those in the past. There have been some dependencies found. But any systematic relationships that exist are small that they are not useful for an investor. The brokerage charges involved in trying to take advantage of these dependencies are far greater than any advantage that might be obtained. This is the consistent finding of the academic research on stock prices. Thus, an accurate statement of the “weak” form of the random-walk hypothesis goes as follows:

The history of stock price movements contains no useful information that will enable an investor consistently to outperform a buy-and-hold strategy in managing a portfolio.

In the weak form of the random-walk hypothesis is a valid description of the stock market, then, as Richard Quandt says, “Technical analysis is akin to astrology and every bit as scientific.”

I am not saying that technical strategies never make money. They very often do make profits. The point is rather that a simple “buy-and-hold” strategy (that is, buying a stock or group of stocks and holding on for a long period of time) typically makes as much or more money.

When scientists want to test the efficacy of some new drug they usually run an experiment where two groups of patients are administrated pills – one containing the drug inn question, the other a worthless placebo (a sugar pill). The results of the administration to the two groups are compared and the drug is deemed effective only if the group receiving the drug did better than the group getting the placebo. Obviously, if both groups got better in the same period of time the drug should not be given the credit, even if the patients did recover.

In the stock-market experiments, the placebo with which the technical strategies are compared is the buy-and-hold strategy. Technical schemes often do make profits for their users, but so does a buy-and-hold strategy. Indeed, as we shall see later, a naïve buy-and-hold strategy using a dart-board-selected portfolio has provided investors with an average annual rate of return of approximately 10 percent over the past sixty years. I believe that return will continue at roughly that level for the reminder of the century. Only if technical schemes produce better returns than the market can they be judged effective. To date, none has consistently passed the test.

Devotees of technical analysis may argue with some justification that I have been unfair. The simple tests I have just described do not do justice to the “richness” of technical analysis. Unfortunately for the technician, even some of his more elaborate trading rules have been subjected to scientific testing.

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc

Jamaica

Jamaica

This Caribbean island offers a lush topography of mountains, rainforests and reef-lined beaches. Many of all-inclusive resorts on this island are clustered in Montego Bay, with its British-colonial architecture, and Negril, known for its diving and snorkeling sites. 

Jamaica is famed as the birthplace of reggae music, and its capital Kingston is home to the Bob Marley Museum, dedicated to the famous singer.

Jamaica is a Commonwealth realm, with the Queen or the King of the United Kingdom as head of state. The appointed representative in the country is the Governor-General of Jamaica. Jamaica is a parliamentary constitutional monarchy with legislative power vested in the bicameral Parliament of Jamaica, consisting of an appointed Senate and a directly elected House of Representatives.

All the pictures have been taken by Elena.

Jamaica is the third-most populous Anglophone country in the Americas (after the United States and Canada), and the fourth-most populous country in the Caribbean.

 Jamaicans mainly have African ancestry, with significant European, Chinese, Indian, Lebanese, and mixed-race minorities.

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Jamaica has a large diaspora around the world, particularly in Canada, the United Kingdom, and the United States.

Previously inhabited by the indigenous Arawak and Taíno peoples, the island came under Spanish rule following the arrival of Christopher Columbus in 1494.

Jamaica lies about 145 kilometres (90 mi) south of Cuba, and 191 kilometres (119 mi) west of Hispaniola (the island containing the countries of Haiti and the Dominican Republic).

The climate in Jamaica is tropical, with hot and humid weather, although higher inland regions are more temperate. Some regions on the south coast, such as the Liguanea Plain and the Pedro Plains, are relatively dry rain-shadow areas.

Among the variety of terrestrial, aquatic and marine ecosystems are dry and wet limestone forests, rainforest, riparian woodland, wetlands, caves, rivers, seagrass beds and coral reefs.

Jamaica lies in the hurricane belt of the Atlantic Ocean and because of this, the island sometimes suffers significant storm damage.

Among the variety of terrestrial, aquatic and marine ecosystems are dry and wet limestone forests, rainforest, riparian woodland, wetlands, caves, rivers, seagrass beds and coral reefs.

 The European settlers cut down the great timber trees for building and ships' supplies, and cleared the plains, savannas, and mountain slopes for intense agricultural cultivation.

Areas of heavy rainfall contain stands of bamboo, ferns, ebony, mahogany, and rosewood. Cactus and similar dry-area plants are found along the south and southwest coastal area.

The Jamaican animal life, typical of the Caribbean, includes highly diversified wildlife with many endemic species found nowhere else on earth. As with other oceanic islands, land mammals are mostly bats.

Tourist attractions include Dunn's River Falls in St. Ann, YS Falls in St. Elizabeth, the Blue Lagoon in Portland, believed to be the crater of an extinct volcano.

The picturesque Dunn's River Falls in Ocho Ríos.

Making Movies Meaningful

Making Movies Meaningful

How parents can turn their children on to what films have to teach

sick of children's movies that are chewing gum for the mind? You don't have to succumb to the latest Hollywood formula flicks. Classic movies that once were available only on scratchy prints in art houses or riddled with commercials on the “Late Late Show” now appear in video stores, as rich as Rembrandt's. Films that enchant, thrill, even teach, are there for parents who know where to look. Writer Nell Minow, aka “The Movie Mom”, has been organizing film festivals for her children for many years. She offers these tips on changing your children's movie watching habits for the better:

Entice them

Parents need to get children interested befor the movie begins. Tell them what the challenge or conflict in the movie is, but don't tell them how it turns out. Children love to watch the movies that were their parents' (and grandparents' favorites when they were children's ages.

Challenge them

Make sure that every movie they see is one that you feel is worth the two hours it takes away from other things. Then challenge them to challenge the film. Ask them why the character is behaving in the way shown and what they would do in that situation. Discuss with them how the movie springs its surprises and makes them feel suspense. This not only teaches them about narrative and point of view, it helps to teach them critical thinking.

Prepare them

No matter how bright and well-educated a child is, he or she is unlikely to be able to follow the plot of a feature film without some kind of introduction. Give them a general overview of the situation, issues, and the characters. If they ask questions, give the, more details without spoiling the ending. Sometimes, with younger children, it helps to read a book together on the same subject. With musicals, it's a good idea to listen to the record a few times before going to see the movie.

Connect with them

Pick a movie that relates to the child's interests or experience in some way. If you have visited or plan to visit New York, try On the Town, where three sailors have one day to see the city. If the child loves baseball, try Pride of the Yankees. Many classic children's books have been made into movies. Children who have read The Secret Garden, Little Women or The Phantom Tollbooth will especially enjoy the movies.

Famous Actors as seen by the Grevin Museum. Photo by Elena.

Warn them

Older movies do have the advantage of telling their stories without the kind of language, violence, or nudity that led to the development of the rating system in the late 1960s. But they sometimes reflect attitudes that clash with today's values, particularly about women and minorities. Even an objectionable movie has some value if it prompts a discussion. It may give you a chance to point out aspects of your own past or to talk about values without sounding as though you are preaching. This provides a perfect chance to discuss the issues and to explore the history that surrounded the movie's presentation of these attitudes.

Join them

Sharing a movie with your children shows them that you are not just seating them in front of the TV to give yourself a break. Watching a wonderful movie together becomes part of the common experience that you will always treasure having with your children.

Meet the Blurb Writers

Sometimes reviews say more about reviewers than about the movies. So try to spend your movie-ticket wisely, and remember that the blurbs in movie ads can be as deceptive as cineplex “butter”. If the names attached to Heart Warming, Wonderful, Best of the Year mean nothing to you, here is the skinny on the critics who do the reviews:

Never get easily impressed by art-house pretensions. Be aware that many critics show a weakness for movies with big budgets and big stars. Trust those who are not authors of a conservative indictment of movie topics, but trust those who taste family-styled entertainment, especially when you're taking the kids. Also remember that every critic occasionally get carried away with their raves. Look for those who praise a movie and mean it.

Testing the Rules

Testing the Rules

With the rules and caveats in mind, let us take a closer look at stock prices and examine whether the rules seem to conform to actual practices. Let’s start with Rule 1 – the larger the anticipated growth rate, the higher the price of a share.

To begin, we’ll reformulate the question in terms of price-earnings (P/E) multiples rather than the market prices themselves. This provides a good yardstick for comparing stocks – which have different prices and earnings – against one another. A stock selling at $100 per share with earnings of $10 per share would have the same P/E multiple (10) as a stock selling at $40 with earnings of $4 per share. It is the P/E multiple, not the dollar price, that really tells you how a stock is valued in the market.

Our reformulated question now reads: Are actual price-earnings multiples higher for stocks where a high growth rate is anticipated? A major study by John Cragg and Burton G. Malkiel strongly indicates that the answer is yes.

It was easy to collect the first half of the data required. P/E multiples are printed daily in papers such as the New York Times and the Wall Street Journal. To obtain information on expected long-term growth rates, the experts surveyed eighteen leading investment firms whose business it is to produce the forecasts upon which buy and sell recommendations are made. Estimates were obtained from each firm of the five-year growth rates anticipated for a large sample of stocks.

We will not bore you with the details of the actual statistical study that was performed. It is clear that just as Rule 1 asserts, high P/E rations are associated with high expected growth rates. This general pattern has held up in every year since 1961, when John Cragg and Burton G. Malkiel began the study.

Testing the Rules. Photo by Elena

In addition to demonstrating how the market values different growth rates, the chart can also be used as a practical investment guide. Suppose you were considering the purchase of a stock with an anticipated 15 percent growth rate and you knew that, on average, stocks with 15 percent growth sold, like Automatic Data Processing, at 18 times earnings. If the stock you were considering sold at a price-earnings multiple of 25, you might reject the idea of buying the stock in favor of one more reasonably priced in terms of current market norms. If, on the other hand, your stock sold at a multiple below the average in the market for that growth rate, the security is said to represent good value for you money. We’ll return to the practical use of such techniques, as well as the pitfalls, at several later points.

How about Rules 2,3, and 4? Just as we were able to test for a relationship between earnings multiple and anticipated growth rates, it was also possible to collect the necessary data and find the ways in which not only growth, but dividend payout, risk and interest rates influence price-earnings multiples in the market. The particular techniques used need not concern us. What is important to realize is that there does seem to be a logic to market valuations. Market prices seem to behave just as the four rules developed by the firm-foundation theorists would lead us to expect. It s comforting to know that at least to this extent there is an underlying rationality to the stock market.

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc.

Reading Chart Patterns

Reading Chart Patterns

Perhaps some of the more complicated chart patterns are able to reveal the future course of stock prices. For example, is the downward penetration of a head-and shoulders formation a reliable bearish omen? As one of the gospels of charting, Technical Analysis puts it: “One does not bring instantly to a stop a heavy car moving at seventy miles per hour and, all within the same split second, turn it around and get it moving bach down the road in the opposite direction.” Before the stock turns around, its price movements are supposed to form one of a number of extensive reversal patterns as the smart-money traders slowly “distribute” their shares to the “public”. Of course, we know some stocks do reverse directions in quite a hurry (this is called an unfortunate V formation), but perhaps these reversal patterns and other chart configurations can, like the Roman soothsayers, accurately foretell the future. Alas, the computer has even tested these more arcane charting techniques, and the technician’s tool (magician’s wand) has again betrayed him.

In one elaborate study, the computer was programmed to draw charts for 548 stocks traded on the New York Stock Exchange over a five-year period. It was instructed to scan all the charts and identify any one of thirty-two of the most popularly followed chart patterns. The computer was told to be on the lookout for heads and shoulders, triple tops and bottoms, channels, wedges, diamonds, and so forth. Since the machine is a very thorough (though rather dull) worker, we can be sure that it did not miss any significant chart patterns.

Reading Chart Patterns. Photo by Elena

Whenever the machine found that one of the bearish chart patterns such as a head and shoulders was followed by a downward move through the neckline toward décolletage (a most bearish omen), it recorded a sell signal. If, on the other hand, a triple bottom was followed by an upside breakout (most favorable augury), a buy signal was recorded. The computer then followed the performance of the stocks for which buy and sell signals were given and compared them with the performance record of the general market.

Again, there seemed to be no relationship between the technical signal and subsequent performance. If you had bought only those stocks with buy signals, and sold on a sell signal, your performance after brokerage costs would have been no better than that achieved with a buy-and-hold strategy. Indeed, the strategy that came closest to producing above-average returns (not accounting for brokerage costs) was to buy right after one of the bear signals.

Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc.