Wednesday, January 20, 2010

How Guessing Market Direction Can Be PREDICTABLY Bad for Your Financial Health

"The game is called probability guessing. . . . [S]ubjects are shown a series of cards or lights which can have two colors, say green and red . . . appear[ing] . . . with different probabilities but otherwise without a pattern. . . . The task of the subject, after watching for a while, is to predict whether each new member of the sequence will be red or green. . . . Humans usually try to guess the pattern, and in the process we allow ourselves to be outperformed by a rat. . . ." (excerpt from Leonard Mlodinow's The Drunkard's Walk--How Randomness Rules Our Lives, 2008)

In a stock market context, the probability guessing game described above would read like this: In any given year, the stock market either rises (green) or falls (red). If we look over the past six decades, from 1950 through 2009, we find that during the sequential decades (1950s, 1960s, and so on) the S&P 500 Index rose in 8, 6, 7, 9, 8 and 6 out of the 10 years (using data from Yahoo! Finance). In other words, during a "typical" decade annual stock market returns are "green" about 7 or 8 out of the 10 years, and "red" about 2 or 3 out of the 10 years. Based on these historical data, we can infer that the stock market tends to rise during any particular calendar with a probability of about 75%, and fall with a probability of about 25%. As investors, we, of course, would like to try to predict whether this year (or next year, or any future year for that matter) will be green or red.

For us investors, the million-dollar question is: Should an investor attempt to "time" the market, by investing in stocks during years the market is more likely (in the investor's opinion) to rise and staying out of the market during other years when the market is more likely (again, in the investor's opinion) to fall?

Obviously, if the investor truly has enough information, foresight or precognition to know with a high degree of certainty when the market will rise or fall, then market-timing makes perfect sense and will lead to higher returns. However, what happens if the investor only believes that he knows but actually does not, so that for all practical purposes the investor is really faced with the 75% green versus 25% red probabilities described above? Is any harm done by guessing?

Analogous to the general guessing game Mlodinow mentions in his book, let's consider two strategies:

1. Buy-and-Hold Strategy: Since the market rises during 75% of the years, one could just go long the market by buying an exchange-traded fund tracking the S&P 500 Index (or buying individual stocks), without attempting to time the market at all. A buy-and-hold investor can expect to generate positive returns 75% of the years but must also accept the unavoidable "fact" that the market will typically fall 25% of the time. In this "simpleton" strategy, an investor's long-run win percentage (i.e., the percentage of years the investor's portfolio will show positive returns) is expected to be 75%;

2. Market-Timing Strategy: A presumably more "sophisticated" investor will, through some combination of fundamental and technical analysis and application of his general intelligence and market wisdom, come up with a convincing explanation for why the market is more likely to rise (or fall) during any particular year. Believing he can distinguish beforehand (i.e., predict) which years are among the 75% "green" years when the market will rise and, likewise, which years are among the 25% "red" years when the market will fall, such an investor will want to go long 75% of the time and stay out of (or go short) the market 25% of the time.

If the bright and sophisticated market-timing investor has an "edge" over the the naive and unthinking buy-and-hold simpletons, then he will end up being right more than 75% of the time and will show higher long-run returns. At the other extreme, if it turns out that the market-timer only believes he has an edge but actually does not, one would think that his edge would just vanish and there should be no penalty for guessing, right?

Well, you might think that guessing carries no penalty, but that's actually wrong! Quite counter-intuitively, investors should expect lower returns when they guess. Here's why.

Let p be the (stationary) probability that the the market will rise in a given year, i.e., p = 0.75, representing the 75% "green" probability. Supposing that the market-timer's guesses do not give him any significant edge, his overall win percentage is given by a straightforward weighted-probability calculation:

Market-Timer's Win Percentage
= (Portion of time the market-timer goes long) x (Probability that market rises)
+ (Portion of time the market-timer stays out of market) x (Probabiility that market falls)
= p x p + (1 - p) x (1 - p)
= p2 + (1 - 2p + p2)
= 2p2 - 2p + 1.

On the other hand, the Buy-and-Hold Investor's Win Percentage is just p, as we saw earlier. Consequently, we may write that the expected potential downside of the market-timing strategy versus the buy-and-hold strategy is the difference:

(Buy-and-Hold Investor's Win Percentage) - (Market-Timer's Win Percentage)
= p - (2p2 - 2p + 1)
= -2p2 + 3p - 1
= 2(p - 0.5)(1 - p),

where the last expression is the factored-form equivalent of the quadratic polynomial in the previous line.

From the factored-form expression, we can easily see that whenever p is in the "physical" range (i.e., consistent with the probabilities indicated by market history for a wide variety of investment time windows) from 0.5 to 1.0, a buy-and-hold investor is expected to outperform any market-timer who is really just guessing without appealing to any special knowledge of market direction. In particular, when p = 0.75 (which is the historical win-percentage for a sequence of annual returns), the Market-Timer's Win Percentage becomes 2(0.75)2 - 2(0.75) + 1 = 0.625, or 62.5%, which is 12.5 percentage points worse than the Buy-and-Hold Win Percentage of 75%.

Therefore, to the extent that a market-timer is "only guessing" (and who can really be so certain?) about market direction, he is (presumably unknowingly) effectively "shooting himself in the foot," following a self-destructive path of degrading his expected returns by staying out of the market 25% of the time (by the way, shorting the market 25% of the time would make matters even worse). Despite his seemingly sophisticated ways, this market-timer can actually be expected to underperform the simpleton buy-and-hold investor in the long-run.

Lesson: Don't attempt to "time the market" unless you are absolutely certain that your market-timing strategy actually works, since your expected downside from "believing without knowing" far exceeds your time spent strategizing, not to mention your trading costs and commissions consumed.

110 Comments:

Anonymous Anonymous said...

Nice article.. thanks

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5:46 AM, January 23, 2010  
Anonymous Paul Poppleton said...

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Blogger HT said...

Nice article. If you're pumping buy and hold the way to maximize profits is to buy things when they are low (funds selling at a discount, blue chips that are at lows historically speaking). I've been looking at California municipal debt lately. Low risk in the longer term, great dividend returns today.
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5:38 AM, February 02, 2010  
Anonymous stock market and investing said...

nice information there, But truly the market is all about probability and somewhat a gamble of prediction and investing on what you have predicted to come. Nevertheless good tips there

5:18 AM, February 03, 2010  
OpenID rlabey said...

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6:05 AM, February 03, 2010  
Anonymous Indian Budget said...

Nice article. If you're pumping buy and hold the way to maximize profits is to buy things when they are low (funds selling at a discount, blue chips that are at lows historically speaking)

6:05 PM, February 05, 2010  
Anonymous nickdrew said...

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10:19 PM, February 07, 2010  
Anonymous stock market for beginners said...

I like this article. Thank you for posting this., :-)

11:26 PM, February 09, 2010  
Anonymous Annuity Guru said...

Timing the market is nearly impossible. However, I think the buy and hold strategy has turned out to be a bad one in the last decade. You simply have to be nimble anymore.

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4:37 AM, February 15, 2010  
Anonymous Arman said...

Nice article. However, as a portfolio manager myself, I would like to comment that market timing is not the only alternative to buying and holding. Indeed, rebalancing a portfolio periodically to match a given risk-return profile can really yield good investment results.

There is a pretty illustrating recent article here:

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That site also has tools you can use to test such strategies yourself.

5:52 AM, February 25, 2010  
Anonymous Team AZ Advisory said...

It's really not good to guess. One must make very well-calculated decisions based on all possible scenarios based on facts.

3:27 PM, February 25, 2010  
Anonymous hyip investment said...

Thank you for sharing this very informative article.

10:55 PM, February 28, 2010  
Anonymous theoharis said...

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7:31 AM, March 03, 2010  
Anonymous Felix said...

Hi! I like your approach, scientific and logical! It would be one that I would take as well. I absolutely agree that we should not guess when investing. It is irresponsible and just plain stupid. However, I would probably come to a different conclusion as yours.

Let's use your model of 25% likelihood of a down market in a particular year. What is the probability of having 2 down years in a row, it would be 0.25 * 0.25 = 6.25%. What is the probability of having 3 down years in a row? 0.25 ^ 3 = 1.6%. If I saw the market go down 3 years in a row, you can bet that I'd re-mortgage my house and put it into an index fund (not that I would use an index fund, but that's another story)! Your model actually shows that market timing is everything!

Buy-and-hold is also a strategy that developed after a long bull market in the 80s and 90s. I would be extremely sorry, if I bought and held during the peak years such as 1972, 2000, 2007. (Using the S&P 500)if I bought in 1972, it would take me 8 years to break-even. In 2000, I would still be down 20% after a decade.

From a purely scientific standpoint, it is true that the likelihood of a person starting to invest in those years is low. However, the world is a little more complex. I, myself started investing in 2000, exactly when the market was peaking. Why was that? Was it just pure bad luck? The answer is an emphatic NO! I was young and was just starting to earn money. I saw a lot of my friends making a good amount of money investing in stocks. What did I do? I also started investing, but in a blind manner. Usually, a lot of beginners get sucked in during a market craze when everyone is making a killing. So, it's no surprise that I lost a lot of money!

Anyway, thanks for taking a scientific approach to investing and sorry for ranting!

7:20 AM, March 06, 2010  
Anonymous Eric said...

Great piece. Might as well flip a coin, eh?

2:18 PM, March 06, 2010  
Blogger Joanne said...

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11:56 PM, March 08, 2010  
Blogger Mitchel Husky said...

Thanks for this clear, mathematical way of looking at things. I agree that if the market goes up more often than down, and the market timer is nothing more than a random guesser, the buy-and-holder will do better. However, given the current macro economic trends where the US is flooded in debts and many productive activities are moving overseas, it is debatable whether the US market portfolio will still hold the 75% winning percentage. Perhaps, the buy-and-holder would like to add foreign assets to his portfolio in order to diversify away the US specific risks. Or the market timer would still like to time the market and hedge his bets in belief of his insights?

10:24 AM, March 13, 2010  
Anonymous Don | High Yield EFT said...

Ya, you should never make huge financial decisions based on a guess. You might as well take all that money you are investing and throw it down on a craps table at the casino.

Doesn't make sense to me why people do that, but whatever.

8:32 PM, March 17, 2010  
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6:31 PM, March 21, 2010  
Anonymous PeopleString said...

I agree, timing the market is nearly impossible, future market price movements is hard to predict, it's just a form of gambling based on pure chance,
but interesting article, thanks!

8:00 AM, March 23, 2010  
Anonymous simpleinvest said...

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11:08 AM, March 24, 2010  
Blogger Robert Wasilewski said...

I'm not sure whether the article is as informative as your readers believe. The problem is not to guess on January 1 of each year whether the market will rise or not. The problem involves magnitude and is not necessarily based on calendar time.
If the only thing you felt confident about over the past 5 years was that on 1/1/2009 the market was cheap from a long run perspective you hit a home run! If you recognized that the bankruptcy of Lehman was a time to raise cash you hit a homerun.
The point is that it is not a game where on 1/1 of each year we guess "green" or "red".

7:21 AM, March 30, 2010  
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5:33 AM, April 06, 2010  
Anonymous Carl said...

Any guess work is inevitably bad in my opinion. Blind guesswork can lead to unforeseen stress, much of which can be avoided or at least anticipated with educated guesswork. Unforeseen stress inhibits logical judgment, a necessary for analyzing markets.

12:59 PM, April 06, 2010  
Anonymous Apex Investment Corporation said...

more delay or stop you cash flow then less profit we receive.so time holding policy is not good for growth.your blog is very interesting and knowlegeable.
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2:03 AM, April 14, 2010  
Blogger Peter said...

That is really a nice mathematical theory you have there. Perhaps market is really unpredictable. I was wondering if you could help me with my fish tank accessories business. Should I predict the market or just let it work on its own?

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8:26 AM, April 16, 2010  
Anonymous learn online trading said...

Yes whenever I have a gut feeling about the market it does tend to be wronf. When I use proper indicators then (although not right all the time) I tend to do ok.

2:39 PM, April 24, 2010  
Anonymous Investment Resource said...

Its always simple to avoid bad predictions by looking at the fact the economy is suffering from. Look at the stability of your economy and then think of investing financially in any field of life.

3:02 AM, May 06, 2010  
Blogger amaurosis.fugax said...

Your article is based on a lot of assumptions and you don't have the slightest clue about probabilities. Fat tails or black swans are responsible for most of the significant movements in the stock market. It took the stock market 10 years to reach over 12000 and it dropped back to 6-7000 within a few weeks. There is no probability involved. Stop searching for patterns as these fat tails cannot be modeled. Try and protect your money and be conservative with it rather than rely too much on your phoney assumtions.

3:07 AM, June 09, 2010  
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buy and hold is probably totally passe and it is now ever more important to manage our risks in an uncertain environment..

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Blogger Synthetic Convert Guy said...

Wow this is a very good and well written article. I have been amazed over the years to see so many people who honestly think they are able to prdict the direction of the market. To this day I still am fascinated with the popularity of the ongoing carousel of so-called investment gurus who can predict the direction of the market.

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