I don't believe DH7 really applies here, because the status quo is the steelman of your proposal for change. We already have open-source financial analysis and financial models, and mathematicians do work in the industry. I'm unclear on what concrete changes you're actually proposing here that haven't already been implemented decades ago.
1) I suspect this is the reason why Simons is so unusual, and one of the main stumbling blocks to your plan. Getting to high levels of mathematical skill and achievement takes years, and spending more years learning finance is naturally going to be unappealing. Surely they won't all make $10B, and trying to get folks who've spent their lives getting the famously conservative institution of tenure to give it up for the famously chaotic world of Wall Street seems like a serious challenge.
2) I would agree with this - mathematics is a frame of mind as much as anything, and a pretty useful one. While finance has some elements of the same effect, "anything can be traded" is far less transferrable, and the more specific knowledge base lacks the out-of-field utility of math.
3) True, but then that's true of most fields where people want to do a good job.
4) I'm not convinced of that. One of the good things about finance is how incredibly well incentives are aligned(modulo Congress) - someone who guesses right makes billions, someone who guesses wrong loses billions. Having managers share information and analysis destroys that accountability. It also would tend to encourage groupthink - 20 separate paths of analysis will inherently vary more than one collective pool of analysis. Given that groupthink is a major contributor to bubbles, this seems a real danger.
5) Granted.
6) The primary cost is going to be reduced tax receipts and increased welfare costs, plus the stimulus. The bank bailout actually made a small profit, the auto bailout would probably have happened either way by now, but the damage to the economy(especially the top strata that pays a disproportionate amount of the taxes) really did hurt the government's finances. Also, for ease of data collection, I'm limiting my numbers to the US. Most developed economies will have a similar money lost:GDP ratio(Canada and Japan less, PIIGS more, but it's assumed to work out in the end). All numbers from this wonderful document: http://www.gpo.gov/fdsys/pkg/BUDGET-2014-TAB/pdf/BUDGET-2014-TAB.pdf
Tax receipts: We'll measure these peak-to-peak, so 2000-2007, and use that to establish a trend line. In 2000, the USG took in $2025B, in 2007 it took in $2568B, for an average growth of 3.45%. We'll assume that inflation and population growth are constant over the time period, so the trend will stay flat.
Year Trend Actual Loss
2007 2,568 2,568 0
2008 2,657 2,524 133
2009 2,748 2,105 643
2010 2,843 2,163 680
2011 2,941 2,303 638
2012 3,043 2,450 593
That's a cumulative loss of $2687 billion in tax receipts thus far.
Social spending: It's hard to define "social spending" precisely. Social Security, for example, should remain basically stable during economic change, while food stamps will vary wildly. I'm going to use the "Income Security" function and "Health" function(which is primarily Medicaid - Medicare is separate) to approximate this. There's some stray charges in there(federal employee pensions, occupational health and safety, etc.), but those should be fairly stable modulo recession, and I don't know enough about what precisely is in the categories to get too fine in my distinctions. I'm using the same 3.45% growth assumption.
Year Trend Actual Loss
2007 632 632 0
2008 654 712 -58
2009 677 868 -191
2010 700 991 -291
2011 724 970 -246
2012 749 888 -139
This yields a total of $924 billion in added welfare costs.
Stimulus: The ARRA was estimated at $831B of total costs, though a significant fraction of that has been counted above - $288B was tax cuts, $155B was health spending, and $82B was welfare of various sorts. The remainder is $306 billion on education, infrastructure, and research.
The sum of the above categories is $3917 billion, to the end of FY 2012. However, we also need to factor in the effect of lower interest rates - we're spending less on debt interest today than we were in 2006, despite a 137% increase in the size of the debt. This works out to a $228B savings versus trend(again, assuming 3.45% YOY growth). Throw in a few miscellaneous billions for uncounted programs, we can estimate the cost to date at $3.7 trillion. Final cost will likely be some $6-8 trillion, depending how long this mess continues for.
It's worth noting, though, that if you phrase it in terms of cost to taxpayers, the loss of receipts shouldn't really be counted - after all, it doesn't lose me money to have my taxes go down. Actual new spending as a result of the recession is only about a trillion thus far, the remainder is simply deferred taxes.
(Yes, these numbers are a bit ham-fisted in places. I'm not the CBO, I don't intend to get too far into the details for the sake of an internet discussion. It's a good enough estimate to work with)
someone who guesses right makes billions, someone who guesses wrong loses billions.
Is this accurate?
It seems like there is no ceiling to profits, but a clear floor on losses from the bettor's perspective. If a $100 Billion company bets on a coin toss, it can be $150B bet or a $250B bet and if it wins, it gets $150B or $250B, but if it loses, the company itself is bankrupt, and loses $100B. The portion greater than its value is assumed by its creditors, and doesn't really factor into the decision.
How is my reasoning faulty here?
Note: I completed a PhD in Mathematics from University of Illinois under the direction of Nathan Dunfield in 2011. I worked as a research analyst at GiveWell from April 2012 to May 2013. All views expressed here are my own.
About this post: I've long been interested in ways in which mathematicians can contribute high social value. In this post, I discuss a tentative idea along these lines. My thoughts are very preliminary in nature, and my intent in making this post is to provide a launching point for further exploration of the subject, rather than to persuade.
Recessions as a serious threat to global welfare
In 2008, the US housing bubble popped, precipitating the Great Recession. The costs of this were staggering:
It’s been claimed that recessions cause a drop in prosocial behavior.
All told, the Great Recession had massive negative humanitarian disvalue, and preventing another such recession would have massive humanitarian value.
Transparent financial analysis as a possible solution
There are actors in finance who accurately predicted that there was a housing bubble that was on the brink of popping, and who bet heavily against subprime mortgages, reaping enormous profits as a result. The most prominent example is John Paulson, who made $3.7 billion in a 2007 alone, starting from a base of less than $1 billion. There are less extreme examples that are nevertheless very striking.
It’s difficult to determine the relative roles that skill and luck played in these peoples’ success, and the situation is further obscured by hindsight bias. Nevertheless, it seems possible that the financial success of Paulson and others was a consequence of careful analysis and shrewdness, and that other people of sufficiently high intellectual caliber and rationality would have been able to predict it as well.
As is always the case in finance, those who recognized the impending pop of the housing bubble kept their analysis secret, because sharing it would have allowed others to partially close the arbitrage opportunity, reducing the potential to profit. If these people had made their thinking public, it could have resulted in other people betting against the housing bubble earlier on, popped the housing bubble when it was smaller, possibly substantially lessening the severity of the ensuing recession. While there were people who publicly voiced concern, a large number of people would have had a bigger impact
This suggests that transparent financial analysis by intellectual elites could carry massive humanitarian value.
Mathematicians as unusually well positioned to perform such analysis
In the course of my graduate school days, I became familiar with mathematical community. There’s a wide cultural gulf between pure math and finance. My experience was that mathematicians generally view finance as “dirty business,” on account of:
I believe that this gulf has led to a potential opportunity being overlooked: mathematicians may be ideally suited to perform transparent financial analysis that reduces damage from financial bubbles.
This idea occurred to me a few weeks ago. Ideas for philanthropic interventions generally fall apart upon closer examination, and so I wasn’t too optimistic about it holding up. So I was surprised when Neal Koblitz (co-creator of elliptic curve cryptography) raised the same idea in unrelated correspondence:
If mathematicians had been noticing the dubious ways that people in the financial world were claiming to be applying mathematics, and if they had publicly and loudly criticized the misuse of mathematics, then the world might have been spared the collapse of 2008 (or, rather, it wouldn't have been as bad). If mathematicians could have played a role stopping the credit-derivatives bubble before it got out of hand, the economic value of doing that would have been in the trillions of dollars.
When an idea occurs to two people independently, the case for it being a good idea is strengthened. Moreover, Koblitz has a long history of involvement with humanitarian efforts and so can be expected to have perspective on them.
Some reasons why mathematicians seem unusually well suited to the task are:
Transferable Skills — Most mathematicians are unfamiliar with some of most important tools used in finance: statistics, data analysis & programming. But there’s a historical track record of mathematicians being able to pick up these skills and use them to powerful effect. James Simons transitioned from differential geometry to quantitative finance, and became one of the most successful hedge fund managers ever. Cathy O’Neil did a PhD in algebraic number theory under Barry Mazur’s direction, and got a job at DE Shaw, which is one of the most prestigious hedge funds. Mathematicians who are motivated to learn these skills are well positioned to do so.
There are other skills that are very important for successful financial analysis – in particular, one has to have a good eye for empirical data. This is a skill that’s not directly transferable, but it still seems likely that a nontrivial fraction of mathematicians could develop high facility with it.
Intellectual Caliber — The mathematics community has a very dense concentration of intellectual power. James Simons offers a direct point of comparison between math and finance:
Simons won the Oswald Veblan Prize in Geometry before leaving academia to start Renaissance Technologies. There are 25 living mathematicians who have won this prize. The prize is awarded exclusively for work in geometry/topology, and if one looks more broadly at all mathematical fields, one can generate a list of about 100 living mathematicians who were at least as accomplished as Simons at the same age.
After leaving academia, Simons made $10 billion in quantitative finance. What I find most interesting about this is that the situation is not that Simons succeeded where other mathematicians of the same caliber had failed – rather, Simons is virtually the only pure mathematician of his caliber to have left academia. This raises the possibility that there are a handful of elite mathematicians who could make much better financial predictions than most present day actors in finance. Less accomplished but capable mathematicians may also do very well.
Cautiousness — Mathematicians are naturally intellectually conservative, as they spend much of their time rigorously examining arguments for flaws. Thus, they’re unusually unlikely to succumb to greed and fear, which are factors that are thought to play a large role in the behavior of financial markets, and which lead to speculative bubbles. This is corroborated by some of Cathy O’Neil’s remarks on finance.
Implications
The above considerations suggest that mathematicians could contribute enormous social value by engaging in transparent financial analysis.
Many mathematicians who I know wish that they could contribute more social value. In the essay Is there beauty in mathematical theories?, the great mathematician Robert Langlands wrote:
In a letter to A.-M.Legendre of 1830, which I came across while preparing this lecture, Jacobi famously wrote
It is true that Mr. Fourier thought that the principal goal of mathematics was their public utility and their use in explaining natural phenomena. A philosopher like him should have known that the only goal of Science is the honor of the human spirit, and that as such, a question in number theory is worth a question concerning the system of the world.
I am not sure it is so easy. I have given a great deal of my life to matters closely related to the theory of numbers, but the honor of the human spirit is, perhaps, too doubtful and too suspect a notion to serve as vindication. […] Moreover, the appeal to the common welfare as a goal of mathematics is, if not then at least now, often abusive. So it is not easy to find an apology for a life in mathematics.
A fair number of mathematicians don’t have any choice but to do pure math. Gromov wrote:
You become a mathematician, a slave of this insatiable hunger of your brain, of everybody's brain, for making structures of everything that goes into it.
I'm very sympathetic to Gromov's remark, and I think that for people who constituted in this way, it’s probably best not to try to suppress these urges, as such attempts tend to be unsustainable and result in lower contributions to global welfare rather than higher ones.
But for mathematicians who are:
there may be a major opportunity to contribute enormous social value by conducting transparent high quality financial analysis.
This question warrants further investigation.