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Stock markets and random walks

I was surprised how widespread the misunderstanding of Eugene Fama's observations about the economy was. Fama explained that the QE program is just about buying one type of bonds for others so its effect is similar to removing $100 bills from the circulation and replacing them with a 10 times greater number of $10 bills: the effect is pretty much non-existent.

See also my polemics with the Pig.

Critics of these insights seem to be grouped into two not quite disjoint sets – those who believe that the Feds' permutation games are extremely helpful for reviving the economy and those who believe that those things are extremely dangerous. But despite the apparent differences in the sign, the misunderstanding by both groups has the same origin.

It's hard to summarize what the reason for their misunderstanding is. But I would say that they don't realize that bonds are a kind of "money", too; and they don't understand that the balance sheet isn't "wealth" or "equity" or "debt" because it's just some unphysical number that is immediately subtracted from itself, yielding zero for the quantities that actually matter. So it doesn't matter whether you increase your balance sheet. If you print $50 trillion and lock the bills in the basement, the effect on the economy is zero even though you may boast that someone (you) owes you $50 trillion.

In this post, I want to discuss the claim that you can't beat the stock market – and that the markets are basically efficient. In other words, I will bring you some Mathematica calculations to test some nice quotes by Fama that I fully endorse.

That page is pretty short, so why wouldn't I copy it here:

Eugene Fama Speaks, So We Listen

Eugene Fama, The Living Legend Of Modern Portfolio Theory, Hits On Some Key Points That Every Investor Should Know At Recent IMCA Conference.

- Avoid Active Managers And Their High Fees

“Active management is a zero-sum game before cost, and the winners have to win at the expense of losers,”

- Avoid Any Strategy That Self-Reports Performance (E.G. Hedge Funds)

“I can’t figure out why anyone invests in active management, so asking me about hedge funds is just an extreme version of the same question,”

- The Market Appropriately Prices Assets - Concentrate On What You Can Control, Costs And Taxes

“Since I think everything is appropriately priced, my advice would be to avoid high fees. So you can forget about hedge funds”

- Federal Reserve Tapering Is A Non-Issue For The Long-Term Investor

“The Fed is using one kind of bond to buy another kind of bond. What’s the big deal, and why is anyone taking the Fed seriously?”
Good. Now, can you design some strategies to beat the market? For example, do the stocks move in the random-walk fashion? Can't you just buy the stock that was growing yesterday and make a profit today? Or the other way around?

In this text, I will focus on the session-to-session changes of the stock prices and the correlation between a session-to-session change and the following one. You might test the analogous claims at different timescales and I believe you would probably reach analogous conclusions.

Using Mathematica, we take the 30 stocks in the Dow Jones Industrial Index
a = FinancialData["^DJI", "Members"]
la = Length[a]

{"AXP", "BA", "CAT", "CSCO", "CVX", "DD", "DIS", "GE", "GS", "HD", "IBM", "INTC", "JNJ", "JPM", "KO", "MCD", "MMM", "MRK", "MSFT", "NKE", "PFE", "PG", "T", "TRV", "UNH", "UTX", "V", "VZ", "WMT", "XOM"}
and we list all of their closing prices since January 1st, 2000:
b = Table[FinancialData[a[[i]], "Jan. 1, 2000"], {i, 1, la}]
c = Log[b[[All, All, 2]]]
lc = Length[c[[1]]]

{{{{2000, 1, 3}, 38.25}, {{2000, 1, 4}, 36.8}, ...
Yup, I took the natural logarithm of the prices so that multiplicative changes are transformed to additive ones and they're unbounded in both directions.

Each of the 30 stocks produces 3,479 daily closing prices so the average length between the two sessions is 13.83 years times 365.25 days over 3,479 which is equal to 1.45 days – there is no trading on the weekends and holidays etc.

I calculated the day-to-day (session-to-session) changes
d = c[[All, 2 ;; -1]] - c[[All, 1 ;; -2]]
fd = Flatten[d]
which gave me
lfd = Length[fd]
102,258 session-to-session changes from all 30 stocks. That's a lot of numbers. They went from
{Max[fd], Min[fd]}

{0.298415, -0.359906}
–36 percent to +30 percent growth rate per day (note that these numbers, 0.64 and 1.30, have to be exponentiated to get the actual factor by which the prices grew or dropped). To get rid of some of the extreme events, I eliminated the rates above plus or minus 10 percent:
g = Select[fd + 0.00001*(RandomReal[] - 0.5), Abs[#] < 0.1 &]

Now, what does the histogram of the session-to-session changes look like?
Show[Histogram[g], Plot[3200*Exp[-7000*x^2/2], {x, -0.1, +0.1}]]
Well, it looks like this:

You see that the histogram looks really smooth up to some strange teeth near the daily change zero (some effects of rounding or overrepresentation of zero-changes in sessions that saw no trading? I am not sure about the exact reason but I am confident that there has to be an explanation). The distribution (shown between the rates minus and plus 10 percent) isn't far from a Gaussian one but it is detectably non-Gaussian, too.

I believe that there are three main reasons behind this non-Gaussianity.
  • We're considering session-to-session changes which sometimes represent the change in 24 hours and sometimes in 72 hours (with the weekend) or even more. If we translated the changes to changes in 24 hours (or removed the longer periods altogether), most of the "very high" changes would probably go away.
  • Different stocks may have different widths of the distribution (different volatility) and by adding these differently wide Gaussians, we make the sum decrease slower, too
  • Some of the large changes (jumps and drops of the stock prices) have material, systematic reasons – such large external events occur much more often than what we would expect from a Gaussian distribution
You are invited to quantify how much each of the factors above influences the non-Gaussianity of the outcome – and find other sources of it. Note that the curve drawn on top of the histogram had 7000/2 in the exponent. That is 1/2 times the inverse squared standard deviation. The square root of 1/7000 is 0.012 which means that the root-mean-square average change of the session-to-session stock price in Dow Jones is about 1.2%. Sometimes it goes up, sometimes it goes down, sometimes it's more, sometimes it's less.

But the final point I want to make isn't related to the non-Gaussianity. I want to show you what would happen if you traded with the assumption that
  • the session-to-session change tends to be in the same direction as yesterday (the previous daily change)
  • or, on the contrary, it tends to go in the opposite direction so it mostly cancels the pervious one.
If the first idea is right, it would be clever to buy the stocks that were growing yesterday. If the second idea is right, you should sell or short stocks that were growing yesterday and buy those that were decreasing. You surely get the point. Do you believe in either? Either situation would mean that the stock prices don't follow a random walk – they're non-Markovian. Are they?

Well, let's see. This are the commands that calculate the sum and the difference of two subsequent session-to-session changes of the price:
e1 = (d[[All, 2 ;; -1]] + d[[All, 1 ;; -2]])/Sqrt[2]
e2 = (d[[All, 2 ;; -1]] - d[[All, 1 ;; -2]])/Sqrt[2]
fe1 = Flatten[e1]
fe2 = Flatten[e2]
Recall that "d" contained all the session-to-session changes (the logarithms of the price ratios) so "e1" really counts the changes between today and the day after tomorrow while "e2" is the difference between the Monday-to-Tuesday and Tuesday-to-Wednesday changes. If either of the Markovian ideas is right, the absolute value of the numbers in the "e1" array would be detectably higher than for "e2" or vice versa.

I added the simple factor of the inverse square root of two because a random walk simply predicts that the characteristic change in 2 sessions is equal to the square root of two times the characteristic change in one session. The random walk predicts that "e1" and "e2" will have comparably wide histograms that will be as wide as the histogram of "d" if you add the factor I added.

What is the result? The relevant command is
ee1 = Select[fe1, Abs[#] < 0.1 &] ee2 = Select[fe2, Abs[#] < 0.1 &] Show[Histogram[ee1], Plot[3200*Exp[-3500*x^2], {x, -0.1, +0.1}]] Show[Histogram[ee2], Plot[3200*Exp[-3500*x^2], {x, -0.1, +0.1}]]

and "ee1" looks like this:

On the other hand, "ee2" looks like this:

Visually, all of them are really the same. The distributions are equally wide and they're as wide as the distribution of "d" we started with. It doesn't matter whether you add or subtract the two adjacent session-to-session changes because their signs (and their magnitudes including the sign) are uncorrelated.

Moreover, all three of them look pretty much equally non-Gaussian.

So if you were thinking about borrowing millions of dollars to realize a simple strategy – just buy the stocks that were increasing yesterday (or, on the contrary, buy the stocks that were dropping yesterday) – the histograms above should convince you that you are going to participate in nothing else than a lottery. It is a zero-sum game. Moreover, you may pay some fees which will turn you into a loser in average.

This simple calculation only quantified the comparison of two day-to-day changes of the stock prices and a simple strategy based on correlations of the two adjacent changes at this timescale. You could design other strategies, perhaps more sophisticated (or more contrived) ones, but all of them will ultimately fail. The stock market is a random walk and the deviations from the non-Gaussianity have understandable reasons that don't allow you to make a profit, either (because the motion of individual companies per 24 hours is mostly Gaussian; and the non-Gaussian, larger-than-expected changes are ignited by external events that have both signs and you can't predict them, either).

Even if you found some pattern in the 13.83 years of DJIA data, you would always be at risk that it won't work in the following years. Even if such a pattern were more than a coincidence – if it had some rational reason – you would be at risk that someone else is seeing the pattern as well and will do lots of trades recommended by this strategy before you do them. If that's so, you will already be buying or selling for prices that have increased or decreased and they no longer generate the profit you were hoping for – and they may produce a loss.

The invisible hand of the markets work – and optimizes the prices and economic activity, usually rather quickly. Some traders may detect imperfections of the market behavior and gain profit out of them but the more traders are doing such things, the less profit they may make. The more accurate calculations of the "right price" or "estimated price tomorrow" etc. they are doing, the smaller is the profit margin. The residual deviations from the "right prices" are increasingly random and patternless.

Pretty much all the people who are making a long-term, systematic profit of a similar kind have 1) either been lucky even if they allow the luck to be interpreted as a talent, 2) have some access to some insider information, 3) have a monopoly or near-monopoly in their access to some trading tools (e.g. computers close enough to some servers of a stock exchange, something that gives you a huge advantage in fast trading).

Most other things are superstitions.

The efficient, "fair" character of the prices and the random character of the "deviations" coming from inefficiencies imply that the trading using various strategies is a form of lottery. The profits may be nice but the losses may be also large (not too nice) and if one calculates the expectation value, one may be sure that the fees make the expectation value (more) negative. So with a sufficient number of transactions (e.g. buying and selling a particular stock at times that you believe to be optimized), most of the profits and losses will cancel but no one will return the fees. ;-)

And that's the memo.

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snail feedback (81) :

reader JackSavage said...

Or, as my Dear Old Dad used to say, in a somewhat less complex manner.. "You win some, you lose some!"

reader Luboš Motl said...

Exactly, a good summary. ;-)

reader Eelco Hoogendoorn said...

The only worthwhile kind of trading is insider trading. Unless you know something the average joe smoe does not, you are indeed gambling.

reader lukelea said...

Dear Lubos, You wrote: "This maneuver is expected – and arguably has the desired purpose – to lower the long-term interest rates but the price to pay is the increase of the short-term interest rates."

Lower long-term rates influence a lot of important economic activity. People buy more cars for example and presumably auto manufacturers make more of them. What kinds of off-setting activities do higher short-term rates depress?

Another difference: in times of inflation holders of long-term bonds have no way to protect themselves.

reader Eugene S said...

Skipping right over the math by assuming that it's correct, we come to the "money paragraph":
Pretty much all the people who are making a long-term, systematic profit of a similar kind have 1) either been lucky even if they allow the luck to be interpreted as a talent, 2) have some access to some insider information, 3) have a monopoly or near-monopoly in their access to some trading tools (e.g. computers close enough to some servers of a stock exchange, something that gives you a huge advantage in fast trading).

The first should be non-controversial: if you're a day trader who is turning a profit, you first paid your dues making all the typical mistakes and then learning to avoid them, later you either kept losing money and dropped out or you are making money and staying in the game but by accident.

The second and the third are more interesting. I agree but with the proviso that not all "insider information" is illegally obtained. That's what I meant in my earlier comment about Buffett's "social capital" and the momentum he obtains from "network effect". A (near) monopoly on trading tools: yes, shaving off a few microseconds is apparently a genuine competitive advantage that the stock exchanges make you pay through the nose for, but it is also kind of boring, like throwing brute force at a mathematical problem to solve a theorem.

If the news about hiring patterns on Wall Street and in London's City is to be believed, an even more sought-after trading tool is the human brain, but it has to be the right kind of brain and its possessor is called a "quant" (short for quantitative thinker, the type of human who excels in math or physics). The highest-performing hedge funds (~20 percent annual return) are rumored to be hedge funds employing these "big brains" to develop algorithmic trading strategies to beat the competition. (It's difficult to evaluate these rumors because there are no "official" hedge-fund performance rankings.)

But isn't the previous paragraph refuted by point (1), i.e., that there is no strategy guaranteed to make you come out ahead in picking the right stocks to buy or sell? In the long run, that principle should hold. But in the short run, a quant hedge fund should be able to gain an advantage if it hires more big brains before the competition does and is better at maximizing the benefits provided by its human capital.

reader Eelco Hoogendoorn said...

By the way; I think you are correct in agreeing with fama on the effect of QE. That said, changing the yield curve can have substantial effects on the behavior of market participants. Interests coordinates money over time. It can matter quite a bit in the long term if people feel more inclined to spend on short term consumption, or for instance, long term drug development. Any political involvement in the money supply (independent central bank my ass) should be suspected of attempts to cook the books in order to favor the short term (there is always the mythical 'multiplier' to justify short term 'stimulus'). People may hold the current administration responsible for what is happening now. But if we don't have any new medicine 30 years from now, few people will have the attention span to pin it on those responsible.

reader sillybilly said...

I know a perfect strategy - you buy the stocks that are increasing today. :-)

The weird "teeth" near zero are due to -0.00001*(RandomReal[]-0.5)

reader lukelea said...

I have to second that. Some investors are in better position to get important information quicker than others, whether legally or illegally. The fact that Goldman Sachs owns major stores of copper, for example, means they know about changes in demand before those who depend on government surveys. Hedge fund guys hire spys, bribe politicians (with sweetheart deals, etc.) and so it goes.

reader Alexander Ač said...


without going too much into math and equations, question(s) remain(s): "If QE has little or no effect (on the broader economy), WHY are they doing that, and why "tapering" did not happen? Is it just for fun?

Why there was a market sell-of when just a possibility of tapering was mentioned?

But then I agree that central bankers cannot screw the economy much more than it is now...

cheers, Alex

reader john said...

I was going to ask nearly same question. How do you explain success of James Simons and Edward Torp ?

reader Eugene S said...

P.S.: It's unfortunate that the earlier thread had to be closed. But that is inevitable when you have ill-mannered people loudly repeating the same points over and over again.

This is supposed to be a conversation, not a contest to see who shouts loudest and longest. There was one commenter, Scott Sampson, who had interesting things to say, I hope he is not put off from commenting on TRF in the future.

reader Luboš Motl said...

I have answered your questions.

Tapering like QE itself doesn't have and won't have any real detectable effect on the economy, in one way or another.

They're doing it either because they misunderstand economics, or because they want to look important and useful in the eyes of those who misunderstand economics, or both.

There was a market sell-off in many situations when there was no material reason for such an event because there are traders that react irrationally and many of them may do something at the same moment. But they're not making any profit by such irrational reactions and the markets usually quickly undo the deformation of the prices caused by some behavior if it is irrational.

I have never said that the "economy is screwed". The economy of 2013 is the wealthiest and most sophisticated economy the mankind has ever had in its history, since we became humans a few million years ago (when I look at your reasoning, I must correct myself: since *some of us* ceased to be monkeys).

reader Luboš Motl said...

LOL, quite on the contrary, I added the random infinitesimal correction to liquidate the tooth, assuming that the tooth is due to rounding or binning of 0.0000 and nothing else. It actually changed its shape but didn't liquidate it completely.

reader Werdna said...

"removing $100 bills from the circulation and replacing them with a 10
times greater number of $10 bills: the effect is pretty much

I would certainly agree the effect of such a thing in and of itself would not be that large if there were one at all, but the action itself is not free, there is some effort involved in doing something like that. Not likely large relative to the scale of the economy, I would guess naively, but I'd have to work it out to be sure.

There also would probably be some small marginal changes in people's spending habits-in most transactions it's a lot easier to work with the smaller denominations. Again, probably a small effect, but this one is even more tricky, if not impossible, to estimate.

reader Luboš Motl said...

Dear Werdna, there may be changes in people's spending habits but even the sign of it is largely unpredictable. If you only get large banknotes, it may make someone do larger shoppings at all times while someone else may be discouraged to buy anything because he was used to do shoppings only for the small banknotes. ;-)

It is far from clear which of the groups will have a larger effect on the "overall" behavior. The very same comment applies to the swapping of the bonds with various maturity dates etc. Such acts may shake the behavior but the ultimate effect is surely vastly smaller than the magnitude of the money involved - like $80 billion per month - because most of these effects cancel.

And the residue isn't predictable so it's not helpful in any way to shake the economy in a similar way - it has the same change to be helpful and harmful (and it may be even hard to define these adjectives because different people will surely have different opinions on whether it was a good idea to intervene in such a way).

reader RAF III said...

Lubos was not conversing. When he was not ignoring the content of some comments he was willfully, egregiously, and ridiculously misrepresenting them, while at the same time claiming an expertise in economics that he does not possess. I defy you to explain how this:
Dear RAF, it is you, not me, whose completely wrong comments are rooted in Marxism because you are saying that the market economy doesn't work. Marxists also say, just like you, that a price is just an invention of some powerful (rich) people (meant to exploit other people).
- is a reasonable interpretation of this:
Furthermore, prices are determined by supply and demand, not by any
intrinsic 'value' the commodity might possess (which is a Marxist
assumption; how did Pet Rocks succeed?).
Godd luck.

reader Werdna said...

Oh I definitely agree it is A) Sure to be small on a relative scale and B) largely unpredictable in either direction.

Of course, even if one could tease out some predictable element of the effects of such a thing, I don't think I like the idea of attempting to steer the economy with it.

reader Luboš Motl said...

Dear John,

Renaissance Technologies has effectively made a bet on a particular pattern that may exist for a decade, namely a bet on a low volatility.

If one assumes that the volatility stays low, it implies some particular deviations from the random walk-based models and one may create money using the assumption that the volatility stays low - people tend to keep things more uniform and more "stable" that chance predicts.

So with some math knowledge how to convert such things to trading decisions (no doubts that they knew how to do such things better than many others), they produced some cool returns, especially in the 1990s.

But those things still depend on assumptions - they're bets and they may break down. And they did break down during the 2008 or so events when the volatility turned to be "higher than average" and Renaissance Technologies exhibited negative returns, too.

Again, I don't have doubts that Jim Simons and pals knows this maths better than almost anyone else but that's not really enough for similar profit potential to stay there.

There were other hedge funds that produced huge losses so you're really cherry-picking if you ask about Jim Simons and Edward Thorp (note the spelling).

reader Eugene S said...

Dear RAF III, it isn't my place to explain the decisions of our host and I won't try. But speaking only for myself, I saw how you egged on the persistent (and annoying, in my evaluation) gold bug and if it were my weblog, I would grow very irritated at you.

reader Luboš Motl said...

But when the supply and demand are balanced, they drive the price towards a particular value that is objectively determined and this is what you are completely unable to see - or unwilling to even consider. So you clearly *are* saying that there's no intrinsic value or price of things and that these things are social constructs.

It seems very hard to talk to folks like you because you are always ready to instantly deny that you wrote something even though it's still clearly written just 10 lines higher. I actually addressed every point you were trying to make and explained to you why it was wrong. You ignored all my points, just offered me nonsensical insults. I wouldn't start with pointing out that your thinking is Marxist in character. It's you who started with that and it was so absurd that I simply had to correct this upside down interpretation of yours.

reader cynholt said...

The US can't seem to taper when it comes to QE, food stamps and war.

I may be mistaken but it all seems like a wilder replay of Johnson's
guns and butter policy of the 60's when Charles De Gaulle smelled a rat
and started demanding gold for his dollar accumulations

reader Alexander Ač said...


I see you are already prepared. Once the economy goes to the toilet big time (see Lehman-like event), you already know who is reposnsible - "monkeys" ;-)



reader Luboš Motl said...

Dear Alexander, indeed, fanatical loons like you represent one of the greatest threats for the economy and the human civilization but even this threat is tiny from the global picture. I am not afraid about the economy's "going to the toilet big time".

I wouldn't even use these big words for the minor downturn we saw after 2008, and be sure that I was heavily exposed to stocks.

reader Alexander Ač said...


if would be nice if "fanatics" like me were holding no debt, were trying to conserve environment, and would care about the long-term habitability of the planet in order not screw over other people. Maybe, just maybe the planet would be a little bit nicer place to live for many people, and for a long time... ;-)



reader cynholt said...

Come on, Lubos, the level of Fama's confusion is stunning! Yes, the Fed
is exchanging short term debt for long term debt -- but the exchange is
not market neutral.

It would be market neutral if the Fed raised short term debt in the
market. But it doesn't. The Fed pays for short term debt with printing
press money. The result of the Fed's activity is more money in the
system, which obviously is not market neutral.

It may be the case that new money is piling up in the system as
excess reserves, and is not being deployed (except to finance Big Bank
trading activity, hence the rise in the stock market). But the process
is far from being market neutral.

What the authorities will not admit -- especially to themselves --
is that they are conducing an experiment, and have no clue how the
experiment will reach some kind of stable outcome.

reader Luboš Motl said...

There is nothing inaccurate about Fama's comments.

It just doesn't matter that the money is being printed! People are obsessed with this "printing of the money". Let me tell you something. When "printing of the money" was used as a slogan for a fiscally irresponsible behavior, it was just a slogan, a huge simplification. There is nothing wrong with printing of the money itself. The wrong behavior only starts when the actual debt is being increased (too much). This doesn't happen at the moment when some banknotes are printed. Or when they are transferred to a box in a bank. The debt is only created when someone (the government, in the case of the public debt) spends the money and promises someone to return the money in the future. That's a mostly irreversible step because it's much harder to "unspend" the money than to spend them. For example, people usually don't get paid for undrinking a pint of beer or having unsex with a prostitute. ;-)

But if you print $50 trillion in banknotes, it's just not a problem.

In the case of quantitative easing, new money is printed but some old (de facto) money is destroyed - the long-term bonds - so the "negative" part of the maneuver exactly answers the positive one. The whole procedure is neutral, at least when it comes to the evaluation of the overall nation-wide effect to the zeroth approximation.

reader Luboš Motl said...

Great to meet someone whose comments make sense. ;-)

reader RAF III said...

No Lubos, What I said was that prices are not determined by some intrinsic value of a commodity but by supply and demand, and that if the money available for purchasing commodities was suddenly increased the prices would go up. That is all - the rest is produced from your imagination. I stated this idea ONCE in the other thread and never repeated it there or anywhere else on your blog. I never mentioned social constructs or any other nonsensical ideas that you inferred.

Supply and demand rarely remain balanced for long in the real world (as opposed to mathematical models) and it is the constant adjustment to such changes, by changing prices, that allows efficient resource allocation. What you describe above is the approach to some stable equilibrium state in a mathematical model, not the actual economy.

Your objectively determined value can change at a moments notice, e.g. - during a natural disaster, when those selling petrol or flashlights for higher prices will be stupidly accused of gouging.
I've just explained to you in the simplest terms how the market works, and it is not just by driving prices to some equilibrium value. I certainly do not deny the claim that the market works, but unlike you I do know how it works.
The notion that prices are determined by intrinsic value is clearly Marxist, whether you like it or not. But please note that I did not call you a Marxist. Look up for example the labor theory of value.
You did not address my points and hence explained nothing. For example - if banks were (and they are) using new money to purchase stocks would this drive the prices up? ( in fact, this was my only point). Or not? You simply asserted that they were not going up as a result of massive purchases with newly created money and then digressed to tell me about the historical relation between general inflation and GDP when you knew that I was talking about a localized inflation within the stock market.
Your responses to Vangel were equally foolish.

reader john said...

Dear Lubos,

Thanks for your answer. I believe your main arguments are correct that there is no magic formula.

But I don't think that it is "cherry-picking" If I ask about James Simons and Edwart Thorp. If you would choose two hedge funds that could beat market, you would choose the ones managed by best mathematicians or physicists. Considering Thorp's other activities I don't think his success can be considered as luck. Although his strategies may only work for a finite time and possibly wouldn't be efficient now when there are much more hedge funds.

It seems that the key person behind algorithm of Renaissance is Elwyn Berkelamp (a student of Shannon) who was working on Information Theory.

What makes me think that, could there be some properties like entropy, where you can calculate by taking average of all bonds or whatever and predict its future (at least whether it goes up and down). Of course stocks can't compared to 10^23 particles, so that property would have irregularities.

Probably you are right, I just can't be sure because there are some really good scientists involved in.

reader Luboš Motl said...

There is nothing wrong about holding some debt, using the environment to achieve one own's happiness, and to restrict planning to a few years in advance.

The planet couldn't look this fresh and cool if there were never any debt, if the creatures living on the planet didn't try to use the environment for their own survival and happiness, and if they were thinking about some abstract unknown distant future rather than the semi-predictable near future events that matter.

So while you may look holy, all your attitudes actually make the planet a worse place than it would be otherwise, and if you're waiting for a Leftist God who will bless you, you will be disappointed. There is no Leftist God - there are only Leftist Assholes.

reader Luboš Motl said...

Dear John, well, there are great mathematicians in funds that weren't this successful, too.

But even if I agree with the idea that the successful are among the best ones, I wouldn't think it's the canonical choice because I don't really believe that the math skills are capable of doing such things. So for me, the agreement between smartest and richest folks in the industry, if it existed, *is* largely a coincidence.

In particular, I don't think that the "signal' reaches some required thresholds for solid evidence (like 5 sigma, and probably not even 3 sigma), and I predict that in the future, there won't be a clear correlation between best mathematicians and the wealthiest workers in the hedge fund industry.

reader RAF III said...

I didn't ask you to explain the decisions of our host and I didn't expect you to take up my challenge either.

I commend Vangel for his obvious knowledge, perspicacity, and seemingly inexhaustible patience.
It's not your weblog and I don't care about the feelings of passive-aggressive ass kissers.

reader Luboš Motl said...

Dear Luke, it's just not true that you may separate the activities and bonds to short-term ones and long-term ones and it's not true at all that you may say that one of those matters and the other doesn't.

Even for long-term projects, you may fund the thing by borrowing in the short term and when you need to repay in the middle, you may borrow again etc. There's always a flexibility in such things. You must understand that the bonds may be sold before the maturity date as well, in the middle, so they still do act as money of a sort. And new ones may be created.

Moreover, you're completely wrong that the economic activity is decided by long-term bonds only. There are tons of short-term loans that influence much of the activity - and their effect on the GDP growth is faster than the effect from the long-term loans and projects. See e.g. the last graph at

to see that short-term loans are about 1/3 of the loans. And they generally follow the rates pegged to the short-term bonds although many other things influence the actual consumer rate, too.

reader cynholt said...

Taking on and releasing reserves is neutral enough, I suppose. But Fama equates cash reserves with short term debt and says they balance out marketable security long term debt. That only works if the Fed crams those treasuries it is buying down the banker's throats in exchange for their reserves and tells them they can never sell them. Otherwise, their marketable nature will implode the debt market upon release by the Fed in a way that their reserves will not offset. The Fed will take massive losses and pound the debt market if they try to unload in any normal fashion. Which is why they will never be sold by the Fed into the marketplace, but be allowed to mature instead. At well below face value for the mortgage bonds, by the way, the losses the Fed will take are tomorrow's story.

reader cynholt said...

I don't think the Fed is putting upward pressure on short term rates while wanting lower long term rates. That would be an inverted yield curve, which can snap the economy's neck in a half second.

I must have missed something or he did.

reader cynholt said...

I suppose Eugene Fama is at least partially right: it's no big deal from a balance sheet perspective.

But it's a really big deal if the goal is to influence behaviors among capital markets participants (i.e. dump short term credit, buy long term risky assets). In essence the Fed wants you to "buy moar stocks," because academic research supports a causal link between stock prices and nominal economic growth. In order to do that, yields are being suppressed across the yield curve.

Many board members of the Federal Reserve (Bernanke and Yellen the most notable proponents) actually believe this will work, as long as they keep on printing and move these asset values higher. So far, the evidence that this is actually "working" is mixed, at best.

But it doesn't mean the Fed won't keep on trying...

reader cynholt said...

The problem is not the debt, Lobos. At any
fixed level as a percentage of GDP, debt can be sustained forever. The
problem is the increase of debt as a percentage of GDP. It is that
increase which causes ultimately a run on a currency. There is no need
to repay the debt as long as the net increase of debt is growing below
the growth rate of the economy.
It is all about the increase in debt. In other words, the problem is
the corruption of the work ethics. People expect to consume more than
they earn by working.

reader maznak said...

Fair enough, but what is the new wisdom/insight of the research? I have believed Fama´s points for many years, ever since I got my MBA 20 years ago and this is basically what they taught us back then. Stock prices being random walk is the standard, majority opinion ever since I care about the question. Unlike quantum mechanics, there are hidden variables though :)

reader Eric said...

Hi Lubos,
Maybe you can answer my question (even though it is completely unrelated to this post).
It is said that when adding temperature to a CFT, the trace of the energy-momentum tensor stays zero.
How can this be seen?

reader Gene Day said...

Warren Buffett did not make most of his money via insider information, although he would not turn up his nose at it. There is at least one other “worthwhile” kind of trading but it is not easy and it does not always work.
It is possible to understand a company’s business and its likely future position relative to its competition. Since there are so many factors at work in most businesses this is a very challenging endeavor but it can be done. Of course if you succeed at it you are doing it at the expense of other shareholders precisely because you know something that
the average joe-shmoe does not.

I have been amazed over the years by the intelligence of the market. It is damn hard to outsmart it. On the average it may be impossible.

reader Mikael said...

Oh, come on,Lubos. To say that there aren't people who can beat the stock market is like saying that there aren't physicists who can write better papers than others. As Gene pointed out the stock price represents the understanding of the avarage Joe. So if you are smarter and work harder in gathering information (by such down to earth activities as reading newspapers) you can for example understand the business of a company better than others and make long term profit by buying their stock (or short selling).
On very short term scales the stock prices may indeed represent a random walk but other scales exist. There are many kinds of insider knowledge and the illegal one represents just one type. Making money at the stock market is not an exact science like physics because besides understanding hard facts you need to understand humans and their behaviour. But it can be done. 5 sigma examples are Warren Buffet or George Soros. Here are some lectures by George Soros which you might want to have a look at.

reader lukelea said...

Warren Buffett is an interesting case. How would Lubos explain his success over such a long period of time, basically his whole life?

reader alejandro rivero said...

The full paper of M.F.M Osborne is here:

BROWNIAN MOTION IN THE STOCK MARKET Operations Research, March-April 1959, p. 145

reader alejandro rivero said...

By the way, if you have connected your adsense account with google analytics, you can get a decent sampling of adsense prices by using a a report with enough granularity, for instance by date and page and filtering number of clicks == 1. The report can be exported as CSV and you can do the same fit to lognormal, finding more or less the same randomness that with stock prices.

reader AJ said...

Somewhat on topic. Interesting interview I heard a couple of days ago with Alan Greenspan marketing his new book. His modelling now includes Keynes' "animal spirits" and "herd mentality", which he formally considered that one could not model.

Punch Line: Increase capital reserves for banks to 20%. Forget all the other regulations that are inexplicable.

reader Michal said...

Dear Lubos, every time you write something about stuff I understand, I have to strongly update my bayesian estimate of your reliability on the topics I do not understand (mainly physics and climate science).

Some of the comments from your readers are actually very good.

And BTW if you are saying that the market moves after QE announcements are irrational and the market quickly corrects itself, you have just found a great arbitrage opportunity and you managed to contradict the second part of your article. Congratulations!

And one more question. Do you seriously believe that these magical market forces that make the market almost efficient work for free?

reader Hockey Schtick said...

Thanks Lubos for these two very interesting posts. Wish I had realized you can't beat the market long ago.

Regarding the Fama assertion of no effect of exchanging long term govt. bonds for short, wouldn't there actually be some benefit to the national debt in that short term bonds carry much lower interest rates than long term debt?

reader Luboš Motl said...

Dear Eric, the trace equals zero in a CFT as an *operator* equation. The vanishing of the state isn't a property of any state; it's a property of the theory - equivalent to the scale invariance of the *theory*. So of course that it stays zero for any thermal - or non-thermal - state.

It's like asking why the stress-energy tensor remains a symmetric tensor in Washington D.C.

reader Luboš Motl said...

Dear Michal, I haven't found any arbitrage opportunity because I don't know in what direction - and to what extent - the irrational reactions are.

These irrational reactions tend to be repeatable a few times but they always break at the end and revert to the opposite reactions. For example, some news about Greece - minor changes in Greece - used to have a huge effect on the euro-dollar exchange rate. At some moment, this influence disappeared and in a different period, it got reverted, rather quickly.

The same thing is about QE. News of the sort "I am Bernanke the master of the sword and I will do great things with QE more than expected" typically raise the stocks. But it may be reverted at any moment. Even if you don't believe that the irrationality of people reverts the sign, you should believe that someone else tries to exploit the arbitrage opportunity because you offered this recommendation yourself. But once people start to do such a thing, the reactions to similar events may be reverted.

Yes, markets set the right prices "for free." They set them because this convergence to the right prices is a consequence of people's - both on the supply and demand side - trying to improve their life and wealth. You might think that these people need to eat to trade and the energy for the food ultimately comes from the Sun ;-) but I am adding these things jokingly because I don't believe that this is what you're asking.

But when it comes to "financially free", of course that the setting of the prices by the markets is free and costs nothing in general. It's always a consequence of having people who are interested in the goods/services/anything-else. Whenever there's someone willing to buy or sell it - in order to have it or get rid of it, not in order to help determine the right prices - the price gets set.

Do you seriously believe that the setting of the prices of things needs to employ paid officials (communist apparatchiks)? I am really stunned how silly things people are ready to believe. If I have described your belief correctly, and I think that I have, then this belief of yours isn't just a disbelief in capitalism and a belief in communism - it would be viewed as a lunacy even in the modern communist parties.

reader Eelco Hoogendoorn said...

Not saying that's the case; the general point is that I share lumos skepticism of the power of the FED; but I am also skeptical of their motives. They do have some tangible powers, and I don't see any reason to have any particular confidence that it is applied in my best interest.

Id like to keep an open mind as to how much I should spend on short term consumption versus long term investments, and I don't particularly fancy a political authority making the decision for me.

reader alejandro rivero said...

A bit of explanation: I am citing Osborne because I am told he is the first one using multiplicative arguments to show an approximately log normal distribution in the stock market. I have not read Bachelier, but elsewhere it is said that he went for a usual additive random walk, and then he really expected a normal, not a log normal distribution. If someone has read the old paper of Bachelier, please tell!

Last, it seems it was Mandelbrot who suggested that the log distribution was not normal but some Levy flight or similar. I have not idea if he tried to suggest some model for it (at least, Orborne tried).

reader Werdna said...

On average it *is* impossible, that's Fama's whole thesis.

Well, impossible to do so *indefinitely* and *consistently*.

reader strictly speaking... said...

The three datasets you plotted look very Lorentzian. Have you tried fitting a Lorentz distribution instead of a Gaussian?

reader Luboš Motl said...

Hi, I agree with the visual impression but no, I haven't because, as I said, these "overall" distributions have at least three reasons why they decrease slower than the Gaussian and the isolated distributions for real 24-hour jumps; isolated companies etc. - might be much closer to Gaussians. A composition of Gaussians of different widths always creates this softer decrease at infinity.

So the real distribution is surely not exactly Lorentzian or any other canonical function while I agree that it would probably be a better fit for the curve we're seeing.

reader cynholt said...

Taper is now just keeping the heroin IV drip the same. Junkie indexes now demand exponential increases, not just the paltry $85 billion a month maintenance dosage.

reader Werdna said...

First, it needs to be understood that there is nothing about efficient markets that prevents a single investor, for a finite time, pursuing a strategy that beats the market. 100 years is as far removed from infinity as 1 year is. It is less likely, and the class of people who do so is significantly smaller. But it is not impossible.

Second, Warren Buffet can frequently beat the market for finite periods of time, but he can't *always* beat the market for an *infinite* period of time.

reader Michal said...

Lubos, thanks for this lengthy answer. It is really nice of you how much time you spend talking with your readers (not everybody does that). On the other hand, it is sad to see how stubbornly you refuse to admit that it is you who is wrong. So stubbornly that your brain somehow refuses to process even pretty straightforward arguments and chooses to misinterpret them instead.

Regarding the proposed arbitrage regarding the “irrational” market moves after FED announcements. It seems that you are thinking about predicting the direction of this “irrational” move. But this is not what I am talking about. I am proposing betting on the reversion back to “where the prices should be”. Which you claim happens “rather quickly”. You see, there is a clear directionality in your forecast and it is really easy to bet on these reversion events (your whole life savings are small enough that they will find a buyer in a millisecond).

You also cannot be further from the truth thinking that I believe in communistic apparatchiks setting the “correct prices”. There are no apparatchiks, just people like me who systematically profit on finding mispriced stocks. You say it is the “completely impersonal mechanism “ or “pure mathematics” that “guarantees that the sellers can't overcome the right price (much)”. Well that’s one way to look at it. But it is also a lot of very personal professionals who step in to buy if the sellers push the price too much. Why would they do it if not for a profit?

The fact that you were not able to find any arbitrage opportunity using your extremely crude method doesn’t mean that there are none.

BTW somewhere else you claim that “Renaissance Technologies has effectively made a bet on a particular pattern that may exist for a decade, namely a bet on a low volatility.” Do you realize that their Medallion Fund is around for well more than two decades that have been anything else than low volatility? (I am sure you know some people who work there, try to show this blog post to them)

reader scooby said...

"A composition of Gaussians of different widths always creates this softer decrease at infinity".

Hum, no, or perhaps I misunderstand you, but if the stock returns, for different stocks, were independent and normally distributed then their sum would also be normally distributed. There is a large body of work dealing with the fat tailed distributions in finance, and other stylized facts of the financial markets. First Mandelbro, and later Fama, argued that price changes can be modeled by a stable Paretian distribution with an exponent less than 2. Other distributions for stock returns are the Logistic distribution, the Scaled-t distributon, the Exponential Power distribution etc..

reader Rehbock said...

... Lubos probably right about this from what I gather in above link on Quant funds, but on physics for sure right.

reader OldLb said...

The problem with your argument and Fama, is that QE in the US hasn't been just buying treasuries. They have been buying other debts as well. It's not just rearranging the government's debts.

reader OldLb said...

There is a problem with debt. The problem arises when there aren't assets to back up the debt.

A good example is Bernie Maddoff. He owed investors, but spent their assets paying one off without telling them.

Then when they wanted their cash. he defaulted.

The same is true of governments. They have no assets to back up their debts. Not even the idea that the state owns you (the slave argument) makes an asset, since the cost of keeping the slave happy is higher than the income they generate. They are liabilities.

Where Lubos's arguments fall down, is that he's excluding things from the argument. Take Fama. Are they rearranging debt? Yes. Is that the only thing they are doing? Nope. But that bit's been excluded.

Similarly, what are the effects of rearranging the debt. It's not neutral.It depresses debt payments now, at the expense of massive debt payments in the future. If you ignore things, you can come up with any justification for actions or inactions.

reader Luboš Motl said...

Cash itself - banknotes - are "debt" of a sort. Debt is necessary for any economy to work.

The QE manipulations *are* just rearranging the debt, that's Fama's point and he is right.

reader Luboš Motl said...

Cash itself - banknotes - are "debt" of a sort, too. Debt is necessary for any economy to work.

The QE manipulations *are* just rearranging the debt, that's Fama's point and he is right.

reader RAF III said...

Here are some ideas on arbitrage from quants:
Is this physics, finance, or something else?
I choose something else.
Quants have made money from finding temporarily exploitable opportunities and their strategies fail when others catch on or circumstances change.
The discussion about beating the market is mathematics, not economics, and is no deeper than the fact that no betting strategy can profit from successive tosses of a fair coin. However, if one can observe and calculate the trajectory before placing bets, one can win. A similar thing has actually been done with roulette.

reader OldLb said...

Not the case.

If I buy your debts, I'm becoming more endebted

They have bought mortgage debt as part of QE.

That increases the governments debts.

GIven the state has no assets that can pay the debt, the end result is that they are going to screw people in the future.

QE is all about postponing the reckoning, not preventing that day.

reader Luboš Motl said...

I agree with you and be sure that if you think that I have written anything that contradicts your elementary remarks, you have misunderstood something.

reader OldLb said...

Not the case and easy to show that this is wrong - depending on the boundary.

So lets that the US government. Your claim is that the government has just rearranged its debt. In other words that its debts are constant.

So which number do we need to check to see if you are right? It's the total debt. If that debt is constant, then I will accept that they have just rearranged their debts.

Oh dear. They had to increase the debt ceiling. The debt has gone up. The US government hasn't rearranged their debt, they have increased it.

reader RAF III said...

Here are some arbitrage ideas from quants:

Are these physics, finance, or something else?

I would choose 'something else'.

The discussion about beating the market is mathematics, not economics. It is no more deep than the fact that no betting strategy can profit from successive tosses of a fair coin. However, if one can observe the trajectory of the coin and place bets before it lands, one can win. This has actually been done at roulette tables.

reader RAF III said...

You might research Permanent Open Market Operations.

reader RAF III said...

Here are some arbitrage ideas from quants:

Are these physics, finance, or something else?

I would choose 'something else'.

The discussion about beating the market is mathematics, not economics. It is no more deep than the fact that no betting strategy can profit from successive tosses of a fair coin. However, if one can observe the trajectory of the coin and place bets before it lands, one can win. This has actually been done at roulette tables.

reader RAFIII said...

Here are some arbitrage ideas from quants:

Are these physics, finance, or something else?

I would choose 'something else'.

The discussion about beating the market is mathematics, not economics. It is no more deep than the fact that no betting strategy can profit from successive tosses of a fair coin. However, if one can observe the trajectory of the coin and place bets before it lands, one can win. This has actually been done at roulette tables.

reader Luboš Motl said...

The increase of the debt ceiling has nothing to do with the quantitative easing. The ceiling was raised dozens of times decades before anyone would even think about a thing like quantitative easing.

I am just trying to explain to everyone - clearly, completely unsuccessfully - that the debt and all other important overall measures of the economy stay constant in the QE operation because one form of debt is replaced by another. This should be clear to every kid in the kindergarten who is not completely dense.

reader OldLb said...

It's because you are not specifying the boundary around the debt. If you want the physics analogy, think entropy. What's a closed system?

Unless you define the boundary of your system, you are being completely imprecise.

Hence when I and other say, look the government has done more than rearrange its debt, we are 100%. It's because we have specified the boundary of the system, which is the government.

Here's another example to show how flawed the argument is.

Consider the island with two people. As it stands there is no debt.

A loans B some money. What happens to the amount of debt? Does it go up? Is it just rearranging the debt? Debt is increased.

reader Jon said...

A simple thought experiment about QE: suppose the Fed buys every traded asset; are you sure the effect is just swapping cash vs near-cash? No indeed that isn't imaginable; inflation would surely rise.

Second, when the Fed changes policy direction regarding QE, the impact appears in the markets, and it appears in the inflation data. Ergo, QE is quite effective.

What's not effective is the steady jawboning by the Fed that they will make QE a temporary injection even as NGDP grows at 4%: that signals the Fed views output as being on target, and thus we've languished for years with elevated unemployment.

reader Luboš Motl said...

Stocks and most traded papers are neither cash nor near-cash. They are not the debt of the government. They are percentage of a particular privately owned company allowing the owner of the stock to co-decide about the company and to pick a part of the income (dividends).

The relative price between stocks and cash or stocks and near-cash (bonds) has an objective meaning signalling something about the ability of the companies to produce profit by their own activity.

If the Fed were buying just some stocks, it would surely distort the market. If it were buying all stocks, it would just redefine the currency by producing inflation - because the banknotes used to buy the stocks *are* the new debt but the stocks that would be bought were *not* the government debt and it wasn't even liquidated.

The fact that the stock buying program would surely influence inflation does *not* mean that the bond buying program influences inflation, it doesn't.

reader Rehbock said...

But like all gambling only the house wins in the long term unless
They make money the old fashioned way, they cheat. Quants can exploit short term fluctuations but it will catch up with them in long run for the reasons developed. For longer term profitability it seems we always find out that something was rigged.

reader RAF III said...

No, they don't cheat. They identify market, or trading, inefficiencies and exploit them. When others learn about this the quants advantage disappears. When the quants fail to realize this they can lose a great deal.
Knowing what you are doing is not cheating. Nothing is rigged and, like the tossing of a coin, there is no house.

reader Rehbock said...

The market is the house every trade profits the traders and their bosses the fund managers. We are placing the bets through them.
The use of insider information is cheating. That was the link.
The exploiting of skill isn't but if you look at history when funds have made far more than average for a long time .
The most honest and careful investors and funds can make a good return but will also suffer losses when the market turns. Look at what happened to quants when the random change hits wrong.

reader Jon said...

Why are long bonds cash like but equity is not? Why are stocks not "debt" like? Both are liabilities of companies and they must have yield to have value. Though gov't bonds and bank notes are both 'debt' of the gov't on a consolidated basis, the gov't cannot auction perpetual debt at zero yield. Meanwhile short-term bills can be auctioned at near zero yield. Yet CASH is perpetual. So, cash is different than all of these things. It has no yield, yet is perpetual.

So we come back to an old point, temporary injections of cash--cash that the Fed is expected to call back shortly are not different than bills but, injections of cash perceived to be permanent are different. Such cash determines the price-level, and so is not neutral.

reader Luboš Motl said...

Sorry, you're completely confused. Stocks have nothing whatsoever to do with "being debt" of any sort. Stocks are not a debt of the company. Stocks are the company itself. If one owns stocks, it's just an administrative way to describe that one is owning (parts of) the company itself. Stocks (companies), like anything else, belong to someone, and he may buy, sell these assets and use the acquired money to repay debt, or he may borrow (create debt) if he wants to buy stocks but the existence of stocks or companies isn't any sign of any debt being anywhere. The company could have been produced without using any debt whatsoever and when it was built, the creator of the company could sell parts of the company by printing stocks. Nothing to do with debt. There is no liability anywhere.

It becomes meaningless to talk and think about the economy if you can't distinguish debt from stocks.

reader RAF III said...

Your analogy is flawed. A casino fixes the odds in it's favor, trading firms charge a fee for their services.
I'm sorry, but I couldn't read the link, but would be happy to do so if you could provide a translation or summary.

Anyone will take a loss if they bet on an outcome which does not occur. So what?

Can you explain why the use of insider information is cheating? And what you mean by insider information?

Except for the extremely rare situations where others have a right to know I see nothing wrong with this. One might as well say that fitter, stronger, faster athletes are cheating and should somehow be handicapped. Do grandmasters have insider information which explains their ability to beat 20 average players while blindfolded?