Random Walk Theory: Challenging “Buy and Hold”

I’m going to do something which is perhaps a bit odd for a blogger: I’m going to encourage each and every one of you to read a book that I believe is complete and utter nonsense. The reason for this is the theory behind the book underlies everything behind the current trends in investing towards low-cost, index funds using buy and hold type strategies with ‘stocks for the long run.’ The Random Walk Theory is nearly everywhere in the world of investing; indeed if you trumpet out some boring form of age-based asset allocation I virtually guarantee you believe in it, even if you don’t know it by name.

As a young, bright-eyed eager undergraduate student in economics, I once took a course in financial economics. The course itself appears to have been a bit of a hobby of love for a rather elderly, tenured professor who’s heart was clearly no longer in publishing bullshit in journals (as proper economists are supposed to do) but instead just wanted to talk about stocks and bonds all day. And I have to admit, as a result, his class is one of the more memorable ones I took.

The textbook for the class was “A Random Walk Down Wall Street,” by Princeton professor Burton Malkiel. First published in 1973, the work is a profoundly simple yet amazingly insightful text. I was hooked and became a Malkiel acolyte. I didn’t even fully understand the nerd econometrician humor in the title until later in life when I became a pseudo-statistician, but the pun baked into it made me love it even more. This school of thought would hold sway over me until somewhere around 2014 or 15 when I came to believe the general framework presented on this blog: valuations matter and the business cycle dictates all of your returns.

Nevertheless, I’m recommending everyone reads this book because it is so deeply ingrained in the investment world that I must offer an explicit rebuttal for why I reject that which it advocates. Furthermore I think it is of the utmost importance that every investor prepares their soul before a recession hits. You don’t want to be struggling with your investment ethos when the entire world is going up in an utter shitstorm of ruin. You need to think through what you believe, why you believe it, and have a plan in place for what you will do NOW while things are placid and serene. Understanding random walk theory is thus a cornerstone of that.

Random Walk Theory

So what the hell is a random walk? The analogy I heard in graduate school was imagine a drunken sailor (nothing against sailors) who is staggering out of a pub and will either stumble right or left with equal probability. For his next step, he again stumbles either right or left, and so on and so forth. A random walk is a statistical process which says something will basically go up or down with no ability to discern which way it will move.

As it relates to stocks, this random walk theory therefore implies that everything that can be known about a stock is immediately and already priced in (this is called price efficiency), and all that remains is random fluctuations in price. So, stocks are left to go up and down in equal probability on each day.

An enhancement to the random walk process is “random walk with drift”, whereby the motion of a random variable (see this post to learn about random variables) has a slight upward or downward trend to its motion. This whole process is rather easy to depict in Excel. So, for example, here are the results of 5 different simulations for the current S&P assuming an upward trend of 5% per year but with the current market expectation of volatility:

random walk theory

Random Walk Theory: Investment Application

So, if you can’t predict the direction of the market but it usually goes up, the obvious conclusion is to buy the market and go for “time in the market, not timing in the market.” As an aside, I absolutely detest this phrase as it is some fairy tale bullshit that can get people to buy into a bunch of crap like Bitcoin that is inherently completely useless. I mean, if the market is the market and all, then nobody can be blamed for losses when people make really, really dumb investment decisions. But I digress.

Malkiel cites that most mutual fund managers are unable to best the performance of the S&P 500 over the long haul, and that monkeys throwing darts at a newspaper would result in better performance than most mutual fund managers. And you know what? I completely agree with Malkiel on this point. In the short-run, it is impossible for anyone to consistently time the market. Day to day, month to month, and even year to year moves in stock prices are completely, totally unknowable. Plotting the series of 1 year returns against valuation depicts as much: there is absolutely zero relationship:

Random Walk Theory: Why It Fails

So many people lament that Wall Street has an edge over the little guy and that nobody through their own intelligence can possibly best the titans of finance, but here’s a little secret. Individual investors saving for retirement have one huge luxury over the fund managers: time. Fund managers will quickly be terminated and fired and given their cushy little multimillion dollar golden parachute if they don’t keep pace with the S&P 500. Individual investors, on the other hand, can be picky and choosy about when they are in the market when they have multiple decades of an investment horizon. And it is over the course of decades that the Random Walk Theory completely falls apart.

Robert Shiller won a Nobel Prize in 2013 for proving a very simple relationship: long term returns are nearly entirely dictated by starting valuation. If we look at 10 year returns instead of 1 year returns, we generate a graph which looks anything but random, statistical noise:

The plot of returns against beginning valuation depicts this phenomenon even more starkly:

valuation vs forward return

The relationship between beginning valuation and longterm return could not, therefore, be more clear. But is completely irreconcilable with a world in which stock prices trend upward with noise.

Bridging the Random Walk Theory Gap

This section is a bit of a repost of an earlier post, but I describe it again here because its importance is massive and I’m not aware of any other financial blog that attempts to reconcile these two huge facts.

Robert Shiller attributed the divide between short-run efficiency and long-run inefficiency to investor exuberance and sentiment. I believe there is certainly an element to that, but ultimately I believe it is the business cycle that collapses valuations, and my belief is the specific time of recessions cannot be forecast because they are themselves dynamic.

I think people become exuberant not because they are stupid, uneducated, or otherwise simply financially unsavvy, but because they think they have the secret sauce of figuring out when a recession will hit and that they will be able to exit equities before that time period. The difficulty of observing a recession in real time is discussed here for the 2000 recession.

To repeat, I don’t think people are stupid, but I think they think they are stupid enough to believe they will see a recession coming. However, recessions are stochastic events that CANNOT be seen coming.

  • The economy is an extremely dynamic and interrelated system, balancing millions of different markets with their own lead and lag times and adapting at different rates.
  • The economy is run and controlled by humans. Humans are subject to basic emotions of greed, fear, and a particularly nasty herd mentality.
  • Capital markets are too large of a part of life for individuals, companies, and governments to ignore. CEOs and families alike act differently when they have just watched their worth get blown up or interest rates spike by 200 bps.
  • Therefore, capital markets themselves are feeding into the decisions made that impact the real economy, while receiving and reacting themselves dynamically to the activity in the real economy. This can be seen in that interest rates clearly impact both equities and the real economy in a feedback loop.
  • But what ultimately causes a recession? Why does one specific bank failure tilt the wagon over when in another time and place things might be just fine?
  • The underlying decay of the economy (in debt loads, bad investment decisions, etc) reaches a point where it is extremely susceptible to a bank failure or a Fed rate hike. Perhaps it takes a mere 10 percent equity meltdown to set off a crisis. The herd starts to panic.
  • Projects are delayed, workers are gradually furloughed. The effect snowballs and is only seen in the economic data ex-post, much as we see with the fall 2000 and early 2001 data.
  • Therefore, the reason we observe a peak in the stock market 6 months before a recession is because the snowballing effect of equity sell-offs and loss of confidence is itself becoming a recession in a self-fulfilling prophecy. Economic data is only observable ex-post of the severity of the crisis.

The Random Walk Theory: The Final Words

So there it is, I feel an appropriate catharsis and rebuttal to the investment words which I once held near and dear to my heart. I’d encourage you all to go and digest the words that are written by Malkiel. Understand them, take notes, ask me questions. Figure out what you think about the philosophy and whether or not the role of Shiller and business cycle investing are remotely convincing to you. Bridge the gap between the two and come to your own denouement about how exactly you are investing. Plus if you buy the book from the link at the bottom you can help me lose a little less money on this whole blog thing.

Everything in this section is purely my opinion and not a recommendation to buy or sell securities. I have no knowledge of where markets are headed and everything in this post (and on this blog in general) are for informational purposes only. Only you the investor know your own individual circumstances and you should consult with a financial advisor if appropriate. 


5 Responses

  1. w8jcd says:

    “Fund managers will quickly be terminated and fired and given their cushy little multimillion dollar golden parachute if they don’t keep pace with the S&P 500. Individual investors, on the other hand, can be picky and choosy about when they are in the market when they have multiple decades of an investment horizon.”

    Is that really true? If you had a great strategy with a high Sharpe ratio (and the fund’s prospectus allowed it), the manager could borrow money to amplify the reward of the strategy or use derivatives to amplify the reward.

    Another thing: Market timing has historically done poorly. See this resource: https://www.advisorperspectives.com/articles/2016/08/09/how-tactical-allocation-mutual-funds-fared-over-the-last-five-years.pdf

    Thinking about the reasons timing funds and ETFs have done poorly, I can think of: 1) There is extra tax burden associated with timing in a taxable account. This won’t apply to a timing fund held in a retirement account. 2) The trading costs of commissions and slippage are passed on to fund shareholders. 3) This type of fund often comes with high fees. I feel like these factors alone can’t explain the underperformance of timing but I can’t think of the missing factors.

    Note that since with a long-only timing system you are market neutral or invested in bonds a portion of the time, the benchmark is not the S&P 500 but rather the 60/40 balanced fund.

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