This page has been archived and commenting is disabled.
The "Mathematical Equation" Of Asset Bubbles
Just when you thought the central planners had everything squared away in a tidy little package (the jobless rate is rising? Sell vol. Not enough iPhone 77.25S are being sold? Sell vol. Ben Bernanke's voice is shaking? Sell more vol. The Russell 2000 is up only 1%? Dump all the vol!), here comes the Harvard-based NBER ( the same people who determine the start and end of recessions), in conjunction with those economic wizards from Princeton, with what is actually an interesting paper discussing the nature of debt (as opposed to equity) bubbles, i.e., "Quiet Bubbles."
In the paper, the authors postulate the following about credit bubbles (an issue that is obviously quite sensitive in a day and age when central banks are responsible for the gross monetization of some 80-100% of government debt/deficits):
"greater optimism leads to less speculative trading as investors view the debt as safe and having limited upside. Debt bubbles are hence quiet—high price comes with low volume. We find the predicted price-volume relationship of credits over the 2003-2007 credit boom."
Sadly, the authors completely ignore the fact that there are some several hundred trillion in credit derivatives where the true impact of credit and interest rate bubble manifests itself, because as far as we recall when AIG blew up courtesy of a few trillion in CDS the outcome was far from quiet, not to mention tens of billions of synthetic structured products (or maybe everyone has forgotten the CDO3s 2006?), as well as one particular entity, the Fed, whose DV01 is now so large at $2.75 billion, the Fed not only will never unwind, but even the tiniest rise in rates will force the Fed to monetize even more as the alternative is a toxic spiral that explodes the Fed's balance sheet. In other words, perfectly logical things than anyone with some practical experience would note but certainly not the Ivory Tower denizens of Harvard and Princeton.
Yet where the paper turns from the merely wrong, to the supremely farcical, is when the authors Harrison Hong and David Sraer, decide to compile a formula that captures and explains the math behind, you know, bubbles - a purely psychological, and utterly irrational, concept, which demonstrates the same hubris best represented by those Marriner Eccles dwelling professors who believe that three programs can correctly predict and forecast the intangible that is the US economy. But hey - at least it has a ton of complex-looking integrals and variances, so it must be correct.
So for anyone who has dreamed of quantifying the irrational human condition, here is the bottom line of the professors' equation (this jumps straight to the conclusion and ignores the preceding several pages of just as meaningless gibberish):
QED indeed: with central planners like this, is it any wonder why the world, the real world - the one which much to the chagrin of Princeton and the Wachowski brothers, can not be explained by an equation or even inequality, is doomed?
Full "proof" for your LOLing pleasure (and the full paper can be found here):
»
- 28133 reads
- Printer-friendly version
- Send to friend
- advertisements -
Yeh, I tried using models like this to forecast Vol in trading FX options a few (well more than a few) years ago.
Got fucked. Use it as only a sideways glance indicator now. Expect the Fed to do the same going forward.
I mean going FORWARD !
Regarding The "Mathematical Equation" Of Asset Bubbles...
Anyone using utility theory to make an argument is bullshitting.
the derivative sigma from negative infinity to positive infinity. yep, they nailed it. so that's how larry summers doubled the harvard endowment. lulz
Without Feynman diagrams I say that formula is bull shit.
Wrong, they propose that the mispricing lives in at least L2. As Mandlebrot demonstrated in Coottner (MIT Press 1964, later republished http://www.amazon.com/s/ref=nb_sb_ss_c_0_19?url=search-alias%3Dstripbook... ), the Cotton Futures Market lives in L 1.7 The fucking assholes always make the same fundamental mistake. And by the way, I am serious about this comment.
Bullshit baffles brains
"If you can't dazzle them with your brilliance, baffle them with your bullshit"
- unknown
WTF?
ask a quant to define the standard deviation of a mispriced asset from its median value; at a 95% confidence level, and he spouts you a whole set of equations with second derivatives to indicate rate of change in bubble formation, based on previous tech data.
But he will never be able to tell you what makes it happen; in terms of human behaviour patterns. The Kairos moment when the thread snaps from elasticity gone plastic.
Difficult to predict human greed and herd instinct; easier to trace the probable fall out once it has happened.
After the event its mathematically definable, its plasticity known; before the event its quantum of exuberance gone viral when change of state occurs.
Humpty Dumpty falls when he falls.
Reminds me of my junior year. If all else fails hit it with a fourier transform and go straight to drinking.
Bernank uses this formula everyday prior to the plung protection team meeting @7:30am est
Ok, let's take a look at this - I'm tired, sozzled, so feel free to shoot me down:
This then limits the speculative resale option of credits.6As a result, a debt bubble has to be smaller and than an equity bubble if there is only this speculative disagreement motive at work. The safer is the debt claim, the more bounded is the upside, the less sensitive its valuation is to disagreement and therefore the lower the resale option and the smaller is the bubble.7
Ok, ouch it's a working paper - fine, call in the editor sooner rather than later.
2.1 There are two assets in the economy. A risk-free asset offers a risk-free rate each period. A risky debt contract with a face value of D has the following payoff at time 2 given by:
Wait: you've just assumed that "risk-free" assets exist.
... lots of stuff I can't post because of .jpg / math formatting
A decrease in D (the riskiness of debt) leads to a decrease in (1) mispricing (2) share turnover and (3) price volatility. [p15] Correct me if I'm wrong, but if we're talking about bubbles here (and Risk), then lower Risk can increase 2) as we've seen with APPL / German Bonds. Flight into safety, yadda yadda?
In the extreme, when D grows to infinity, the credit becomes like an equity, beliefs become relevant for the entire payoff distribution of the asset and the scope for disagreement is maximum. This leads to more binding short-sales constraint at date 1, and hence more volatility and expected turnover... But the bonds that were mispriced during the credit boom of 2003-2007 were investment-grade and in some cases AAA-rated. [page 15 - 16]
That's not how CDOs (CDS / MBS) actually worked; the entire problem was their hybrid nature + the artificial AAA ratings slapped on them!
So a first take-away from our analysis is that the credit bubble had to emanate from the excess optimism of the average investor as opposed to disagreement or speculative resale among investors. [page 16]
"Had to"?!? Again, I'm fairly sure that CDO / MBS were hybrid packages precisely to encourage resale and allow dumping of shitty rated D by mixing it into AAA packages, by the Banks / 'sophisticated' sellers, deliberately [see Congressional hearings].
When investors become more optimistic about the underlying fundamental of the economy, they view debt as being more risk-free with less upside and hence having a smaller resale option.[page 17]
Surely this is set by Bank rates? AAA = lower rates? Otherwise, why else are interest rates currently 0%? Investors don't set the Risk profiles (!!)
Proposition 3. A decrease in G (the riskiness of debt) leads to an increase in (1) mispricing (2) share turnover, and (3) price volatility. [page 17]
Fairly sure they mean increase here, otherwise it makes no logical sense.
In our model, however, when the economy worsens, agents realize that disagreement matters for the pricing of the credit in future periods – which drives up the resale option and subsequently increases volatility and trading volume. [page 18]
Ok, so here's where their model is different from the standard one.
One purpose of this proposition is to show that provided that b is large, i.e. provided that the bubble is large enough, our results that credit bubbles are quieter than equity bubbles is robust to the consideration of shareholders’ limited liability. [page 19]
Hmm.
Page 20-21; working paper, can't see the graphs.
As a consequence, optimism which increases the size of credit and equity bubbles makes credit bubbles quiet but leaves the loudness of equity bubbles unchanged...The fact that credit bubbles are quiet might mean that it was difficult for banks and regulators to see or detect the speculative excesses in contrast to equities. It is interesting to ask whether this quietness might have contributed to why the crash of the credit bubble had more severe consequences than for the crash of the dot-com bubble? [page 21]
Hmm.
1) Dot Com got dumped on the unfortunates; GS etc did the dumping & made bank
2) Fairly sure CDO / MBS was all about attempting to dump once more, and getting caught short, due to the scale of the issue
Appendix: fuck that, I don't have a PHD in Math.
~Figure 2, page 38 is rather telling [CDS]. That doesn't fit their model for a "quiet bubble", at all, surely?
Meh, this little minnow is too tired for this.
If the writer knew how hard it is to fool a cattle trader from the country side in Normandy into buying a bad cow, yet he manages to fool the said cattle trader, then he understand how financial markets work and he probably will make a good trader.
Not sure if I'm the cow, and the Math PHD is the trader, or I'm the Trader and the Math PHD is the cow. Looong 36 hrs up.
My formal training screams "Bullshit! Logical error!" all over this, but then again, I'm against level 50 Math Voodoo, so no idea. In any case, all I know is that it bears little resemblance to actual history, which they're trying to model, so we'll call it settled in my book.
Small wonder I prefer howling at the moon...
My brother is a Physics Phd Researcher for French gov and my Cousin a Deen of Math research at Orsay ( I am the idiot). All the family is from the countryside. Once I showed some of the models to my brother and he ask me about some assumptions because that he could not say. I told him that assumptions and explained a bit how it worked. And that things like risk-free asset do not exist and so on and so forth. So I told him those are rubbish and many times there are evidence showing to be rubbish. He also ask me about the variables and if we knew they were continuous or discrete, and so on and so forth. In the end he told me: sounds like a "cat dans une pouque" meaning litteraly: it sounds like a cat in a bag. You do not buy a cat in bag. Any farmer knows that.
Shit! I see this all the time in my textbooks with those nasty proofs! THIS is why a mathematics degree is hard folks! And I only recognise half the notion, but the fact there are integrals (those S's that make people shit themselves) spanning the entire set of real numbers means it is not possible to integrate the expressions in the integrand. You can derive upper bounds and even series to approximate the actual integral but...
The author of this has forgetten the golden rule; solutions are only as good as the people interrupting them. And you can't base formulas around wolly concepts as people's emotions or mispricing (which appears to be a function of 'investor belief'), so all this work is really abstract mathematical wank of which solutions, if there are any, are meaningless...
Do they have an equation for: "I-am-an-idiot-because-my-equation-is-not-verifiable-or-invalidated-everytime-I-try-it-yet-I-still-want-to-show-that-I-know-what-integrals-and-partial-integrals-are-on-my-paper-and-that-I-passed-calculus-I-and-II brilliantly-yet-uselessly-given-economics-is-a-circular-phenomenon-not-an-objective-phenomenon?."
They forgot the end of the equation:
CTRL+P * ? = SHTF
I just use a dartboard.
Aaaah, now I understand. But why is pi used in the formula? Why would you use a circle ratio? Circle Jerk?
Was thinking the same thing. Looks impressive, though.
That's not pi, it's what they call the "expected payoff function."
I generally avoid academic papers in economics (there is much better fiction material out there), so I'm not sure if this is a common notation or if the authors are participating in a bit of trying to baffle them with bullshit.
I generally follow what they're doing with the math, but am of the opinion that formal proofs in economics are only possible if one accepts that the logical framework defined by economists reflects reality, and I do not accept that claim. If people make economic decisions based on the "rational actor" model, I have yet to see any evidence in support of it. Risk-free assets is another doozy. Even physical gold is not risk-free, so I think "risk" models are really just wishful thinking. They can make all the fancy math models they like, but it doesn't make them true.
In the United States, Federal Reserve Chairman Alan Greenspan explained triumphantly to Congress in 1997 that what was so remarkable since 1980 was that labor productivity rose by about 83 percent, but real wages didn’t rise. The Maestro found the explanation to be that workers had taken on enormous mortgage debts, education debts, auto loans, and live on credit-card debt in order to keep up with their neighbors. Testifying before the Senate Banking Committee in February 1997, he explained why wages were rising so slowly despite historically low unemployment levels. Under normal conditions unemployment at the rate then being registered – about 5.4 percent, the same as in the boom years 1967 and 1979 – would have led to rising wage levels as employers competed to hire more workers. However, Chairman Greenspan testified:
As I see it, heightened job insecurity explains a significant part of the restraint on compensation and the consequent muted price inflation.
Surveys of workers have highlighted this extraordinary state of affairs. In 1991, at the bottom of the recession, a survey of workers at large firms indicated that 25 percent feared being laid off. In 1996, despite the sharply lower unemployment rate and the demonstrably tighter labor market . . . 46 percent were fearful of a job layoff.
Again in July 1997 in Congressional testimony, he said that a major factor contributing to the “extraordinary” and “exceptional” U.S. economic performance was “a heightened sense of job insecurity and, as a consequence, subdues wage gains.” Reporter Bob Woodward described him as calling this the “traumatized worker” effect. Their precarious financial situation made them afraid to go on strike or even to complain about working conditions, because if they are fired and miss a payment in their electric utility or phone bill, the interest rate on their credit card jumps to 29 percent. And if they miss a few mortgage payments, they risk losing their home, leaving many workers in fear becoming “one paycheck away from being homeless.” That’s what the debt overhead has achieved for relations between labor and capital.
http://michael-hudson.com/2012/09/financial-conquest-or-clean-state/
Alchemy by the fed, how to make a turd look like gold
brought to you by "Fractured Fairytales"
Print out the formula.
Fold along lines of a and b.
Answer is Fuck
you
Ben!
Just a little somethin I learned in MAD U.
Age'll flatten a man, Wendell.
(Loose Fed + Ponzi banks) x (dumb investors-smarter dumb investors) = Asset bubbles
It looks like arabic.
Without all the throat-clearing.
Mathematics is a Language, one can write science others can write fiction.
So, with the right stimulus, conviction and (mis)understanding one, and well developed language/mathematics skills, one can prove whatever one likes.
It is totally other thing if, whatever is proven, has some relation to the physical, as opposite to an imaginable, reality.
You: "Mathematics is a Language, one can write science others can write fiction."
Me: "Mathematics is a language with which one can write science-fiction."
If that happens to be the secret formula for Coca-Cola, then their secret is pretty fucking safe from me.
Actually, it is the alchemist formula for physical gold. And it does not work because there is no shovel in the equation.
Well, I knew it couldn't be the formula for physical silver --- I did not see one single "only $5 to dig from the ground!" expression in it anywhere.
Yes, I it is obvious that $5/Oz is far too high. Many ounces of silver can be dug for mere pennies(zinc) these days because there are no cost inputs to mining amounting to anything at all. Grow it? Mine it? Titanium ten pad zero key?
If you do all of the math here is the answer you will end up with.
http://www.google.com/imgres?imgurl=http://wall.arche.to.it/wp-content/uploads/scribbles.jpg&imgrefurl=http://wall.arche.to.it/scribble-style-2/scribbles/&h=700&w=641&sz=168&tbnid=-d5LA0zfH-Xg5M:&tbnh=90&tbnw=82&prev=/search%3Fq%3Dimages%2Bof%2Bscribble%26tbm%3Disch%26tbo%3Du&zoom=1&q=images+of+scribble&usg=__c2CWh5InUqeYuoDDyvAAeE0QGEs=&docid=Ulmb8ndNLU6SqM&hl=en&sa=X&ei=DxzmUJjZKIncqwHl1YGYAQ&ved=0CEEQ9QEwBQ&dur=3614
Fucking retards trying use conventional math to solve this. Without dissecting the equations, I would bet it is nothing more than fitting a model to past events. Brilliant. Just brilliant.
QE4EVA X 0 = 0
You are forgetting that between part 3 and part 4, includes a trip to the kahoots. Where the misery meds are dispensed and you leave as you did before QE 1, or even tarp!
The more complext it is, the more they can fudge. This former Quant will give you some good information in layman's terms and gives you the attitudes. Did everyone model those numbers in their brain, of course not:) She makes some very good points on 401k money and how the banks use it when they want as those with such plans she said are called "really dumb investors" and they are not watching like "real" investors are and when they go to retire only part of the money paid in is there. She' right that DE Shaw laid off many in the fact that there's no models to replicate what occurred in the 80s as that happens when everyone gets in the game.
http://ducknetweb.blogspot.com/2012/12/cathy-oneil-mathematicianquant-wa...
Comedy. If everything is less than zero [stuff < 0], then what's the big deal?
The Academy of Lagado:
Gulliver visits the academy, where he meets a man engaged in a project to extract sunbeams from cucumbers. He also meets a scientist trying to turn excrement back into food. Another is attempting to turn ice into gunpowder and is writing a treatise about the malleability of fire, hoping to have it published. An architect is designing a way to build houses from the roof down, and a blind master is teaching his blind apprentices to mix colors for painters according to smell and touch. An agronomist is designing a method of plowing fields with hogs by first burying food in the ground and then letting the hogs loose to dig it out. A doctor in another room tries to cure patients by blowing air through them. Gulliver leaves him trying to revive a dog that he has killed by supposedly curing it in this way.
On the other side of the academy there are people engaged in speculative learning. One professor has a class full of boys working from a machine that produces random sets of words. Using this machine, the teacher claims, anyone can write a book on philosophy or politics. A linguist in another room is attempting to remove all the elements of language except nouns. Such pruning, he claims, would make language more concise and prolong lives, since every word spoken is detrimental to the human body. Since nouns are only things, furthermore, it would be even easier to carry things and never speak at all. Another professor tries to teach mathematics by having his students eat wafers that have mathematical proofs written on them.
Sweeft!!!
Whatever happened to the classic PV=NrT? Lemme play with this, for grins...
Let's assume that:
1. P = Pressure, but here P = the Pressure Velocity of fiat money (No, not the car FIAT!)
2. V = Volume of the 'Asset' bubble.
3. N = Avogardro's Number (1 Mole), but here it is some FED constant. Size of Money Supply, that is not a constant anymore. :-(
4. r = constant, but here it's also some arbitrary Wall St. constant (by JPM, GS, etc.)
5. T = Temperature, but here it's the 'heat' of the Market price. At hi values of T, the Market gets "frothy".
So...
The V increases if we increase T. V is proportional to N, r and T.
If we (the market) reduces V, then this can be offset by corresponding increases on the r.h. side of the equation, aka "Manipulation"
QED.
+1 for Avogardro Number = some FED constant.......like, the "coefficient of the FED = 1 < N < oo
If you accept that the basic assumption of continuous functions generalizes out the lumpiness of the actual 'real world' numbers, and omit the Bernanke effect as not relevant, and assume Corzine isn't a gnome, that politicians always tell the truth, do the right thing and are smarter than all of us all the time, this is sufficiently troothy to give these bungholes their issue of Princeton TP.
This equation is no doubt as reliable as the one that was developed by the Ph.D. economists that started LTCM, in which they claimed to have found a way to quantify and eliminate risk in the market. Economics is a soft science and these charlatans should have minimal impact on any govermental policies.
last time i checked
that looks like the equation of a super massive black hole
E(This Paper) = 0
Nassim Taleb would have a good chuckle at this.
HEY, that's the integral for "on a long enough timeline the survival rate for everyone drops to zero"
SIMPLIFIED:
FED ASSHOLE PLUS PRINTER = BUBBLE
Pushing mathematical constructs to infinity is pointless if the underlying premise if flawed. The risk-capital structure relationship is a complex function in and of itself that this whole calculus salad fails to account for.
I prefer Didier Sornette's model - much simpler and you don't need a Ph.D. in math to understand it. Sornette characterizes bubbles by "super-exponential growth". There is a very easy test for this - the time it takes for the asset or debt to double is decreasing with time. The US Federal Debt is a very simple example of a "debt bubble" meeting this criterion.
"There is a very easy test for this - the time it takes for the asset or debt to double is decreasing with time."
So when do the derivatives finally blow?
86 those morons out of the country.
Fucking nimrods. It's a disgrace to math to have these clowns pretending they know something.
Interesting.
Hey, you forgot to carry the 1. FYI
Duly noted. Thanks.
Where's the graph?
Now here's the mathmatical equation for 'quantitative easing'
your savings + your disposable income = your really screwed
Now here's the formula for sovereign debt crisis:
money printing + stimulus = buy gold and silver
Now lets see the result for those of you buy and holders/401K ginnypigs:
long term bear market + economic illiteracy = you'll be deep in the negative when you retire.
As you can clearly see from this comprehensive exercise in arithmetic, I was indeed a high school mathlete
I found an error in the formula!
... and no, I'm not going to tell where it is!
Ben, you're fucked. I'm not :-)
While I agree an open system as complex as the US economy cannot be represented by a model that includes some mathematical eqns utterly incomprehensible to the average Joe on Main street, I do feel that mathematical tools help because they try to bring some sanity and objectiveness into the study of economics which is in turn, a system that is largely a function of the sum total of man's emotional makeup.
The answer is...............................................................................................42!
Yes, but did you make a profit today?
The author's are right. The problem with the credit markets in 2007 was a bubble in housing, not credit and (as is always the case) bankers fantasizing that collateral is what a mortgage should be based on.
The authors note that you can't really speculate on debt, which is correct. There's a ceiling. The problem arose in the creation of mortgage backed securites that could not be unraveled and became illiquid.
The authors also nail the simple idea that institutional markets have a huge long bas and institutions, being buy only guys, limit the amount of sellers. This long only management makes funds more risky than the actual investments in the funds.
If you chart an open ended government bond fund against a closed end one you see this. Normally they track together.
The lesson from this is a car is not a car when it turns into a driveway. The bubble was in housing not debt, and the culprit was the rising price of oil. (Which is another discussion) The problem with AIG was that it was a straw man. AIG was like jesus. It took away the sins of the world. Had AIG been allowed to go under, the counterparties would have held the bag. THEN you would have had 1000 ;points of Lehman.
I'm still lacking the capabilities to unpack the math, so mind if I ask some questions?
The problem with the credit markets in 2007 was a bubble in housing, not credit
At what point does the provision of credit to obviously high-Risk "investors" (i.e. mortgage owners) not constitute making said housing bubble? Yes, house prices were vastly over-inflated [same as we've seen all over the developed world, in particular Spain / Ireland] but surely this was accelerated and created by over-easy credit?
There's an argument to be had that banks etc were forced politically to provide easy credit (or at least, extremely encouraged via Central Banks - Greenspan etc), but this doesn't stop the originator of the problem being credit. Ok, you can break this into different classes of credit, but the big institutional investors must surely have been aware of the fundamental basis for the burgeoning rise in mortgages?
Simple and easy information check: # of people in a State vrs # real estate leases. The % rise would have told you instantly that a larger segment of the population were getting mortgages, even without looking at the average income levels stated [which, again, we all know were fudged in many cases].
The authors note that you can't really speculate on debt, which is correct. There's a ceiling. The problem arose in the creation of mortgage backed securites that could not be unraveled and became illiquid.
You can speculate on debt - see here. In fact, you could argue that a lot of private equity firms speculate on the debt provisions of existing entities when they take on failing businesses to 'turn over'. Without factoring in the (potential) debt load of companies, they cannot function and they certainly don't provide 100% of the cash-for-purchase themselves. They are able to raise funds by offering the (potential) debt load of said companies as "collateral" for their take-over.
(As an aside: if you know, for instance, that the Central Bank interest rates are 0%, and you know that quantative easing is happening, then you might not call it "speculating"; rather "a dead cert".)
As I noted above, those securities (CDOs etc) were designed so that tranches of Risky Debt were tied to AAA Risks so that they could be sold on; they were designed so that high Risk Debt was "balanced" by low Risk debt, and they were designed so that unravelling the three tiers of the packages was impossible.
The infamous "shitty deal".
The authors also nail the simple idea that institutional markets have a huge long bas and institutions, being buy only guys, limit the amount of sellers. This long only management makes funds more risky than the actual investments in the funds.
By this, I presume you're talking about the institutional investors [the insurance / pension funds listed page 21 onwards] who were buying off GS etc. I'd accept this analysis then, but it doesn't seem to be a huge insight, unless I've missed something.
The bubble was in housing not debt, and the culprit was the rising price of oil.
Again, due to the provision of credit, I'm not sure how you can argue that housing wasn't actually purely credit driven; oil prices, yes, that's another conversation.
Anyhow, I'd be interested to hear your thoughts on this.
Once u get over 16 trillion in debt this formula explains how u fuck urself:
FUR/16=u4Q
The equation probably makes sense if:
G = gas prices
D = Total Debt
C = Cost to buy off a Senator and MSM reporter
P = Real Price of food, after a CPI bullshit adjustment
T = Size of the Fed Balance Sheet in Trillions
x,y = Lying and stealing coordinates of the Wall Street profit function
And naturally, everything is capable of going to infinity.
lol