A Random Market?

I received a copy of Burton Malkiel’s famous book “A Random Walk Down Wall Street” 15 years ago.  The book lays out the case for why stock market investment returns are random and passive investing is preferred over trying to beat the market.  It strongly supports the efficient market hypothesis.

At least this is why I’ve heard, because I never actually read it.  Now that I’m writing a blog about randomness in markets, I probably should get around to reading it, but the idea has always seemed ridiculous.  I mean really, markets are random and efficient.  They sure don’t feel that way.

However, I’ve looked long and hard to find any kind of edge, something which indicates investment returns can be predicted.  I can’t find it.¹   I’m not the only one either. Plenty of people smarter than myself have investigated this question, only to come up with the same conclusion. Returns always look random.

But here’s the interesting thing about randomness – It looks identical to a non-random process for an observer that is ignorant of the cause.  Let’s think about a coin flip.  We all view a coin flip as random.  However, if you know at any point during the flip which side is up, how fast the coin is rotating, and how long until the coin lands, you can develop an accurate heads or tails estimate .  It’s all physics.  The result isn’t actually random, we are just ignorant of the information needed to understand the system.²   And yet, coin flips are perfectly modeled by “randomness”.  

Therefore, you can believe:

1. Markets are not random
2. However, no one actually knows what causes stocks to change price
3. Therefore, It’s best to view the markets as random until someone figures out why they are not.³

So in a way, I’m fine with Mr. Malkiel’s assertion the markets are random.  Until we figure out more, it works as good model.  However, I do not agree with the second part of his assertion proclaiming preference for investing passively.

Math Games showed that optimal strategies for random games exist. Just because you can’t “predict anything”, does not mean you should give up and settle on buy and hold. Even in the face of unpredictable outcomes, mathematically optimal strategies still exist.   You can profit from randomness.⁴

The Framework

So with this in mind, let us build a new framework for investing in a random market.

Let’s imagine that an investment in a stock is actually a repeated series of bets.  Everyday, you make a bet in a stock.  Historically, the stock has returned 0.04% per day on average.  So we will simplify the game to a 50% chance of earning 1.54% and a 50% chance of losing 1.46%⁵ (averaging 0.04%). 

Every day you have the choice to end the game and sell all your stock, reduce your exposure by selling some stock, or if you have extra money, buy more stock to increase your bet.  If you leave everything alone, the bets repeats with the entirety of your payout from the day before.  Within the construct of a random market, this is the proper way to view stock returns.

Play this game, you will expect to average 10.6% each year (arithmetic average), but will instead only see 7.5% each year compounded (geometric average).  Over a year, you would make 252 separate bets.  Over 20 years, 5040 bets. Over a lifetime of investing- say 50 years- 12600 bets.  The math behind repetition will drive your outcome, yet very few truly focus on this idea.

Relationship to Current Investment Strategies

I have a working theory that most investment strategies can be described through the lens of repetition, and their success (or failure) can also be explained through this construct.  In the prior post, I outlined various betting games, and ended the post by asking how those games relate to various investment strategies.  Understanding the framework above, lets re-consider that question.  Yes, the games have a negative geometric return and the framework above does not, but the principles are still the same.  I will describe the reasoning behind each strategy in later posts.

Which game represents buy and hold?  Game #3 (the worst game).

Which game(s) represents index investing?  A weak version of Game #6

Which game(s) represents traditional portfolio construction?  A mix of Game #6 and Game #7

Which game(s) represents trend following?  This one is tricky.  It’s a mix of game #2 and game #6.

Which game represents factor investing (smart beta)? A poorly constructed game #6. 

Which game represents Geometric Balancing? A dynamic version of Game #6.

Which game represents the best strategy? Game #6

1-Some people claim “momentum” as evidence against random markets.  I am not sold.  “Momentum” exhibits many warning signs of not being real, which I will divulge in later posts.

2-I’m fairly certain you could create and app on a smart phone to predict a coin flip.  Assuming you enter the start value of heads or tails on the thumb, the app could predict within a couple seconds of leaving the thumb a highly reliable heads or tails estimate for the coin landing on a pillow, assuming all were within the view of the camera.

3-I consider this a “Schrodinger’s Market” statement.  Its best to view markets as both random and non-random simultaneously, until someone observes the non-random characteristics, whereupon the random view will cease to exist.

4-A sharp reader probably thinks, yes, but you know the exact odds in per-defined “game”.  The odds and payout in the market are unknown.  This is very true.  But you can make fairly accurate estimates and approximations of the investment odds, and with the factors of safety to protect from your mistakes, still gain advantages of using a mathematically correct strategy.

5-It is more appropriate to say a distribution somewhat similar to a normal distribution with a standard deviation of 1.5%.  But I’m simplifying it to make this clearer as it doesn’t change the concepts.  And yes I know stock returns are not normal, but baby steps.