Fischer Black’s classic 1986 essay “Noise”

Here is the pdf link, every now and then I feel I should put up an “oldie but goodie.”  This is one of the essays that has influenced my thought the most, noting that Fischer had his own language and could be quite opaque.  Here is the abstract of his 17 pp. essay:

The effects of noise on the world, and on our views of the world, are profound.  Noise in the sense of a large number of small events is often a causal factor much more powerful than a small number of large events can be.  Noise makes trading in financial markets possible, and thus allows us to observe prices for financial assets.  Noise causes markets to be somewhat inefficient, but often prevents us from taking advantage of inefficiencies.  Noise in the form of uncertainty about future tastes and technology by sector causes business cycles, and makes them highly resistant to improvement through government intervention.  Noise in the form of expectations that need not follow rational rules causes inflation to be what it is, at least in the absence of a gold standard or fixed exchange rates.  Noise in the form of uncertainty about what relative prices would be with other exchange rates makes us think incorrectly that changes in exchange rates or inflation rates cause changes in trade or investment flows or economic activity.  Most generally, noise makes it very difficult to test either practical or academic theories about the way that financial or economic markets work.  We are forced to act largely in the dark.

Both of Black’s books are worth studying, as well as the Perry Mehrling biography of Black.


"Noise in the sense of a large number of small events": is that how he persuaded himself that everything must be Gaussian?

"Noise" seems a rather big catch-all.

Don't get me wrong, I think these examples are real, but I see no reason for them to be regular or Gaussian. The prime example:

"Noise in the form of uncertainty about future tastes and technology by sector causes business cycles"

The rise and fall of the hoverboard, etc.

"I see no reason for them to be regular or Gaussian": I wonder whether he thought the Central Limit Theorem implied that 'a large number of small events' would have consequences that followed a Gaussian distribution.

Was 86 pre-Mandelbrot on cotton prices?

Wow that was '63. But it did take some time for chaos, fractals, and long tails to permeate.


Fischer Black (not to be confused with GM Bobby Fischer) is making two points:
(1) in the absence of noise, in the stock market there would be zero transactions made, theoretically (this can be shown mathematically)
(2) he anticipates Nicholas Taleb's "Fooled by Randomness"

Bonus trivia: did central bankers in the 1980s really influence the direction of the US dollar, or was it just them following a trend (noise)? Note the dollar was heading down even before the famous Plaza Accord of September 1985. I would argue the central bankers--who really have very little power in practice--were just following a trend. Likewise for the Louve Accord of Feb 1987, going the other way. Check it out on Fx historical charts and see if you agree.

Thanks for providing a concrete example of the prominence of noise. At first I thought this was random off topic blathering, but then I saw what you are really doing--brilliant!


Yes there is a bridge over the seine, it has on it a printed cretonne and often when I'm there I drink pantocrine as I pantomime a threadbare velvet manumitted manometer.

You're kind of late to my fan club dan1111, but welcome, glad you finally are getting it.

Didn't Brad DeLong make his name by showing how formally how noise traders might cause bubbles? I guess it solves the problem of who is buying overpriced stocks -- a bunch of random fools.

Irony. The large event that occurred 16 years ago has permeated all aspects of the American psyche. We give up so much, for so little in return. The noise can often be instructive.

An observation about the role of noise in potentially making markets more efficient (discussing what happened in the U.S. stock market back on 21 November 2014) when investors suddenly had a significant change in their expectations for a particular point of time in the future:

Since investors have been largely focused on 2014-Q4 in setting stock prices since the Fed's October meeting, stock prices rose significantly on Friday 21 November 2014, and very soon after the market opened, they peaked at 2071.37 before finally fading to close at 2063.50, just 10.75 points above its previous closing value.

As best as we can tell, the one thing that caused investors to suddenly focus on 2014-Q4 and to adjust their expectations for the amount of dividends that S&P 500 companies would pay out for the quarter was China's central bank's surprise action to cut interest rates to stimulate that nation's slowing economy as it approaches recessionary levels.

Normally, that sort of thing wouldn't amount to much more than what we would describe as a noise event, where the change in stock prices would be relatively short-lived, but this noise event coincided with a change in the fundamental driver of stock prices. That makes it unlike the minor speculative boost in U.S. stock prices following a merger announcement in the biotech industry earlier in the week. And as such, it is a rare example of how noise can actually contribute to the efficiency of setting stock prices, although as we've observed in previous examples, its contribution is most often rationally inefficient.

Most noise is the market's response to the random onset of new information, which shows up in the Brownian motion-like small random changes in stock prices. Larger, Levy flight-like changes in stock prices are often mistaken for noise, but really represent a different phenomenon altogether.

Two comments:

1) "Noise" in one biological sense is variation in a species, a necessary condition for evolution. Thus, one can directly see the connection from evolving natural systems to evolving markets. I wonder to what extent the math/models of the one could inform the other.

2) He's one of the first/only economists I've ever seen to admit that academic economics is over-simplified (due to the inability to include noise without simplifying assumptions thereon) and untestable. I have often made the comparison of classical economics to Astrology - when you get down to it, they're indiscernible.

"I have often made the comparison of classical economics to Astrology – when you get down to it, they’re indiscernible."

As an Aquarian I must stubbornly disagree with your point.

"As an Aquarian"
Fair enough, since my comment compares two antiquarian things!

Reminds me a bit of, whose feast day was last week.

What is the theoretical limit to noise reduction? Tradebook uncertainty. No matter how well informed, we are still uncertain about who was well informed and when. It is the limit because obtaining an aggregate measure of the trades is a serial problem, one at a time can look. The best traders can share uncertainty about the trades is to allow round robin access to traders to check the trade book.

An important point for Fischer Black. Management of trade book uncertainty leads to a quantization effect. If your noise is 5% of trade volume, then your market must be a delivery channel with five bits of accuracy, and we know what that looks like, an encoding graph. The effect occurs because the noise bounds is a bound variance, exceeding the boundary causes a repricing, leading to the optimal economy of scale, a value chain of rank five, for example/..

A recent Masters in Business podcast was an interview with a technical analyst. Her comment was that volume (hence your uncertainty) has become hopelessly opaque with the rise of derivatives and high frequency trading. It is hard to know "in the record" "which trades are real."

Sure, it is simply that first gets tagged onto tradebook uncertainty,which is then has a consensus limit. Pricing is a process like Jim Hamilton;s two peaks in a row, prices are reset when trades vary outside of known noise.

In theory, here is the equivalent problem. At a Cosco store, if the sales manager has gotten inventory variance down to 5%, he did that because he knows the distribution of likely purchases on the floor. If that is a know bound, then the store manager can run the check out with some four counters, each denominated by and upper and lower bound on 'number of items'. At that point, there will be one or two customers in each line.

The new theory eliminates the safe rate concept, term debt. It is replaced by combinatorial limits, as observed when the total number of transactions tend to be minimized. The theory allows us to derive maximum entropy distribution graphs, graph which when driven by uniform random number generates the typical set of trades. We jumped the shark by noting that encoding graphs are optimally queued by definition.

I am glad that's not my job. I could not derive maximum entropy distribution graphs if my life depended on them.

But then you only have to be right a bit more than half the time, and even then, only when people are watching.

“Noise” Ingo R. Titze, Ph.D., in “Noise in the Voice” published originally in the 1997 May/June issue of the Journal of Singing wrote: “A little noise, turned on at the right time, can go a long way toward enlarging the interpretive tool." Indeed, nothing as boring as anything too perfect.
Although I had titled my book “Voice and Noise” before knowing about Titze’s article, I was happily reassured by it that I had made a good choice.

There is a better edition of "Noise" available from Wiley (better photography, copy-pastable text):

When is the Perry Mehrling conversation with Tyler?

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