Friday, 6 December 2013


One of the most famous stories about the randomness of markets is the following: One day, Burton Malkiel, one of the leading proponents of the Efficient Market Hypothesis decided to perform an experiment. A hypothetical starting value of a stock was set, and the closing price of each day was determined by the flip of a coin. If for example it was heads, the stock price rose by a point. If it was tails, then it fell by a point. Thus, the probability of the price increasing or decreasing was the same at 50%. When he had accumulated a large set of observations he presented this to a chartist who was unhappy when he found out that it was just a random sequence since he had advised Malkiel to buy. 

A similar graph can be seen below. Using Excel's random numbers generator, I set the price to increase if the number generated was higher than 0.5 and to decrease if the number was less than that. Starting price was 50.

Figure 1
The trend observed here is random, (or quasi-random as most random generators are) and could have just as easily have been downwards. After the first experiment I have to admit I got a bit carried away, which led to the following two graphs:
Figure 2

Figure 3
The graphs compliment the EMH greatly: what appears to be a meaningful trend is in fact random combinations of random numbers. Or are they? In fact, neither Figure 2 nor Figure 3 are random. Figure 2 uses the digits of pi (the known mathematical constant of 3.14159...) with a starting value of 50 and changing signs at each change of decimal. Although some might claim that pi is in fact random (although these people highly doubt it) it is not strictly random in the sense that individual digits are mathematically fixed and not prone to changes.

For those who find it hard to believe that this is not randomness but it follows a "specific" pattern, have a look at Figure 3: this is nothing but Euler's constant which is mathematically anything but random, as it is the limit of (1+1/n)^n as n goes to infinity and can be approximated by
Thus, even though the trend appears to be random, it is in fact just as deterministic as 1,2,3,4.

Why the whole fuss about this the reader may ask. Well, since the mid 1960's when Fama published his Efficient Market Hypothesis paper, many have been promoting that markets are in fact random and cannot be predicted. I would beg to differ. Although markets do reflect information, and no-one can doubt that, I think we can safely say that they are not random in their reactions. Just like the two graphs above, what appears to be random may be just that we have no information about it yet. Even though the sequence of numbers like pi or e are relatively easy to spot using modern-day computers, its sequence is not one which we can follow in the long-run.

Don't get me wrong here: no full predictability exists in the markets. They are driven by information as already said, and some information is indeed random (e.g. natural catastrophes, etc) while other is not. If all information was random then there wouldn't be people betting on the collapse of Lehman Brothers or shorting Mortgage-Backed Securities (MBS) (Michael Lewis's "The Big Short" provides an interesting read on those who managed to short before the sub-prime lending crisis).

To some extent, markets can be predictable. Not to everyone and not every person making a prediction will be correct all of the time. In fact, most investors understand what if they are correct 60-70% of the time they will become extremely successful. Timing is hard. As Nassim Nicholas Taleb says, nothing is easier than to say "we could have seen this coming" after the event. As stated before, there are things which are random and there are others which are not. Nevertheless, stating that markets are random because you cannot understand them is the same as a hunter blaming everyone else but himself because he cannot shoot well enough to catch his prey.

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