So Simple a Caveman Could Do It
Discussion of the current financial crisis is often shrouded in a bunch of pseudo-technical jargon. People, especially intelligent and highly educated people, are often hesitant to ask basic questions. But as Socrates tells us, the beginning of wisdom is a definition of terms.
Imagine you live in a cave in hunter-gatherer society. Og is going to spend the day hunting. You have previously harvested some berries, lived frugally, and now have an extra handful of berries you can give Og to eat while he hunts all day. You and Og make a deal. When he returns from the hunt, he will give you two handfuls of meat. That’s debt. If instead of promising you a fixed amount of meat, you agreed that he would give you a fixed share – say half – of what he brings back to the cave, that’s equity. As an example calculation, if Og takes one handful of berries under such a debt contract and a second handful under such an equity contract, and if he comes back into the cave with, say, 10 handfuls of meat, then he has to give 2 handfuls to the debt holder and 5 handfuls (half of 10) to the equity holder. He is left with 10 – 2 – 5 = 3 handfuls of meat for his dinner. This combination of debt and equity is called his capital structure.
The debt gets paid first; then Og and the equity holders split what’s left, if anything. If Og comes back with less than two handfuls of meat, and hasn’t saved any for a rainy day, then he can’t pay his debt and has defaulted. Note that as Og gets more and more confident about how well his hunting will go that day, the more berries he wants to take in the form of debt rather than equity.
Suppose that Og gives you an IOU for your debt (call this a bond) or for your equity (call this a share of stock). We could refer to the stocks and bonds as, collectively, securities. Suppose your friend in the cave has given a handful of berries to his cousin Ug in return for a promise for some of the meat that Ug brings back to the cave. You might agree to a deal in which you and your friend give each other a half-interest in each other’s securities. Why would you each agree to this? Because there’s a lot of uncertainty in how any one person’s hunt might go on any one particular day, and therefore you’re each more likely to have at least some meat to eat for dinner this way. This is called hedging, and it is one of the primary means by which financial transactions can create value. If you do hedge, you’d be wise to make sure that Og and Ug tend to hunt in different fields and for different animals, so that if one has a bad day, the other is more likely to have a good day. That is, you want to hedge with uncorrelated securities.
As time proceeds some smart people in the cave invent things to make all of this easier. Physical storage and exchange of berries and meat is replaced by money, which is really a kind of general-purpose IOU produced by trusted third-parties. Governments (a.k.a., groups of big guys who like to be charge and have spears) arise to adjudicate and enforce contracts, and eventually monopolize the creation of money. Banks are launched so that you have a safe place to store money, and can pay somebody else to do the work of deciding whether Og or Ug is a better risk for your loans of berries. A corner of the cave is set aside as a securities market for people to trade stocks and bonds under defined rules. One important type of transaction that this securities market permits is “shorting” a stock. This is a deal in which I pay you some money today in return for your promise that I can make you buy a share of Og’s stock from me 90 days from now at today’s price. Therefore, if the price of this stock is lower then than it is now, I can expect to make money and you can expect to lose money, since I should be able to go into the market and buy it at the then-current price and make you buy it from me at today’s higher price. All this financial infrastructure may seem parasitical to the “real” work of hunting animals and gathering berries, but it helps this cave become very wealthy because it serves to make sure that berries are allocated to the best hunters at the right times, and therefore increases the aggregate production of meat.
While this is happening a couple of sharp operators might sit together in a dark corner of the cave, and make a wager about whether Og will default on his bond. In plain English, we would call this a side bet. Though if you wanted to sell this idea to a fairly gullible person who holds Og’s bond, you might make it sound kind of gee-whiz by calling it a Credit Default Swap. If I hold one of Og’s bonds and I take a bet that pays out if Og defaults, then I’ve just hedged my risk.
The bookie who offers me the swap keeps some money on hand, but like all bookies what he really needs is a book of bets that cancel one another out, so that he makes money no matter who wins or loses. The bookie develops a variety of hedging approaches to do this. An illustrative approach is to have his associate quietly go over to the securities exchange and short Og’s stock. Since Og’s stock will tend to fall massively if he is believed to be likely to fail to pay his debts, the bookie will make lots of money on the short sale that he can then use to pay off the swaps. He, in effect, sits on both sides of the bet. Bookies will tend to hire lots of very smart caveman PhDs to develop sophisticated mathematical models to structure these off-setting bets in a way that makes them the most money.
Now, consider the dynamics that might occur in this cave if you had a string of very good hunting seasons.
Hunters start to borrow more and more berries and enjoy much nicer meals while hunting. The hunters shift their capital structures to increasing amounts of debt versus equity. Less adept hunters see that they can succeed, and begin to hunt instead of gathering berries. Smart bankers observe that lending is very profitable, and compete to provide more and more loans to hunters, with terms that are more and more favorable to the hunters. This enables the banks to make more money, and they can use this to offer higher interest rates to depositors. Banks who think this is too risky and don’t make bigger and bigger loans will have less profits to use to pay higher interest rates to attract deposits, and will therefore tend to shrink. Bankers also realize that the odds of every depositor showing up on one day to demand their money is almost zero, so they can hold a lower and lower proportion of deposits actually on hand, which enables them to make more loans which enables them to offer higher interest rates and attract more deposits. They see that this is risky, but like making more loans, if they don’t do this, they will not have the profits to pay competitive interest rates to prospective depositors, so very few people will deposit with them, and therefore they will lose business.
Of course, there is a great solution to all this risk the banks are taking on: They can buy swaps to hedge this risk. They and the bookies who provide these swaps call it “credit insurance” because this makes everybody feel better. The business of providing swaps is very lucrative, because the hunting is so good that they almost never have to pay off. Like the banks, the bookies begin to be forced by competition to take larger and larger risks, which require ever more sophisticated models. Large banks and other financial institutions begin offer swaps because they are so profitable, and because the detailed hedging strategies embedded in them are so hard to understand that the banks that buy them rely on the brand name of the provider to feel safe.
What happens if we then get a string of bad hunting seasons because the weather changes? The worst hunters can’t bring in any meat, and many good hunters have borrowed so much that they can’t make their debt payments. Lots of bank hedging strategies start to fail because previously uncorrelated hunting performance across different fields and animal types suddenly become correlated – the weather gets worse everywhere at once. Defaults start to rise substantially across all portfolios, but the banks aren’t worried at first, since they have “insured” the debt.
But when the providers of swaps are called upon to pay off, they realize they have a huge problem. Lots of the other people over at the securities exchange are also shorting the same equities at the same time for the same reasons, because so much debt has been insured in this way. They know that they all will have to sell. This would drive down the price of the offsetting equities too rapidly to be able to execute the short-selling strategy that they rely upon to be able to pay the bank.
An invisible crisis becomes visible when a major swaps provider projects that it won’t be able to meet its contracts, and threatens to declare bankruptcy (let’s call them, oh, AIG). Suddenly all the bankers confront a horrible realization: Their credit insurance was an illusion. If more than a tiny fraction of market participants rely on it, then as soon as it is needed, it isn’t there. Banks all simultaneously foresee that if even one large provider of swaps goes bankrupt, it could create a chain reaction. Banks that were depending on that provider’s swaps will not have sufficient funds to pay depositors, and will go bankrupt. Other banks that have lent money to this bank will suddenly be short on money. Since nobody has clarity on how exposed various banks are to swaps or similar instruments – either directly, or because they have more standard loans out to banks that are exposed to them – depositors of even highly conservative banks begin to withdraw money. No bank holds enough money to make good on all depositors’ claims at once. Realizing this, depositors scramble to get their money out before their bank goes under. A series of bank runs start. Banks begin to stop making normal business operating loans to hunters in order to conserve capital and protect themselves against runs. More hunters can’t get berries to eat while hunting, so they hunt less, and defaults increase further. This leads to more defaults by providers of swaps, which in turn leads to more bank runs and more constriction of lending, and so on. In short, financial contagion ensues, leading to an enormous economic contraction.
Unfortunately, all of us in the developed world appear to be living in a cave that is teetering on the edge of such a catastrophe right now.
Brilliant. Nice job, jim.
Could you clarify this?:“But when the providers of swaps are called upon to pay off, they realize they have a huge problem. Lots of the other people over at the securities exchange are also shorting the same equities at the same time for the same reasons, because so much debt has been insured in this way. They know that they all will have to sell. This would drive down the price of the offsetting equities too rapidly to be able to execute the short-selling strategy that they rely upon to be able to pay the bank.”
— Glenn · Oct 14, 03:47 PM · #
Excellent piece of writing, Jim.
— scritic · Oct 14, 03:54 PM · #
Glenn / scritic:
Thanks very much.
I have an article in the upcoming National Review that goes into this in some detail, but it’s very much like what actually happened on October 19, 1987 when “portfolio insurance” rather than “credit insurance” contributed to a 22.6% market decline in 7 hours.
In short form, suppose I’ve set up an algorithm that buys a short contract (bets that a stock will decline) as soon as a related security declines slightly. If a billion short contracts are bought and sold each hour, and I’m buying one, my action has no measurable impact on the price of the short contract, and I’ve hedged my loss on the original stock. But suppose, instead, that all billion short contracts on this security are being bought by a group of traders applying the same algorithm that I am using. Then there are only sellers, and no buyers, and the price has no bottom. Somewhere between “one” and “a billion”, this becomes a precipice. What works for one market participant to decrease risk, when applied on a market-wide basis actually increases risk.
— Jim Manzi · Oct 14, 04:15 PM · #
This is tremendously helpful, Jim — I’m in your debt!
— Alan Jacobs · Oct 14, 05:33 PM · #
Where’s the cavemen CRA to blame?!?
I like this. One big conceptual step I had to force myself to take was seeing that “Robinson Crusoe” models could, in their simplicity, explain quite a bit, even more than big model.
If I may be so bold, if you are looking at the algorithm slide part of what has happened – I’d recommend glancing at Professor Lo’s “What Happened To The Quants In August 2007?” paper that’s out on the net. One way to read it is that the same 6 big players were all chasing the same, well-documented, mean-reversion trends with ‘algorithmic trading’ – however, due to their market influences, the moment one of them stopped playing the game the rest were all screwed – to unwind the position did the opposite of what they were chasing, forcing others to unwind at a loss. The worst kind of Nash equilibrium to get oneself into…
— rortybomb · Oct 14, 05:37 PM · #
rortybomb:
Thanks for the pointer. Lo is an exceptionally clear writer, and it’s a neat piece of analysis.
The hypothesized proximate cause was an unwind. They further hypothesize that if you go back in the chain of causation, this unwind was caused by a margin call or “risk reduction” (ha ha) by the fund that initiated the avalanche. This is, I think, a decomposition of the “external shock applied to monolithic algortihmic trading dominated market leads to collapse” into “external shock causes one particpant in monolithic algorithmic trading dominated market to unwind position that leads to collapse”.
I actually have an article in the upcoming National Review that makes the point that the feared credit collapse from “credit isnurance” is very similar to what Lo describes, and what happened on October 19, 1987 in the futures and equity markets – only a vast scale.
— Jim Manzi · Oct 14, 06:15 PM · #
If I’m reading you right, the hedging algorithm monoculture creates a stampede of traders, all seeking the same side of short contracts on the endangered company. Too many shortsellers start chasing too few counterparties. Even those traders initially willing to be counterparties get out of the way when they see the oversupply of shortsellers annihilating the security. The stock evaporates too quickly for the insurers to establish a sufficient short position and they have to face their obligations hedge-less. Thus the next domino falls.
Do I understand your narrative correctly?
— Glenn · Oct 14, 07:40 PM · #
Jim, expand this, keeping it even more rooted in your caveman setting (you shortcutted to the creation of banks, money, etc., it seemed to me); get someone to make you cute illustrations of Og the Hunter, Gah the Banker, and Otoo the credit swap bookie; sell it to a publisher; and make oodles of money in this uncertain marketplace! Great work.
— Chris Floyd · Oct 14, 08:17 PM · #
Glenn:
Yes.
— Jim Manzi · Oct 14, 08:28 PM · #
Since the fact that the banks making the highest-risk investments had the greatest ability to offer attractive interest rates, and thus increase their stock price/market share/etc., what could individual banks have done to limit their own complicity in this mess? Or could it only have come from regulation or a third-party?
— Freddie · Oct 14, 09:14 PM · #
“One important type of transaction that this securities market permits is “shorting” a stock. This is a deal in which I pay you some money today in return for your promise that I can make you buy a share of Og’s stock from me 90 days from now at today’s price.”
Isn’t that buying a put option contract at a strike price of today’s price?
That’s still effectively an action with a “short” view, but isn’t the actual act of shorting borrowing the security, selling it today, then buying it back at some later time and returning the security?
Good explanation overall, by the way. The lack of focus on CDSes in most discussions about the crisis as, if not the cause, then the multiplier of the crisis is very troubling, especially since there’s what, 55 trillion worth of these things out there?
— Winston Chang · Oct 14, 09:50 PM · #
Thanks! This helped clarify a few things, I’ll pass it on to my friends and readers (I like to pretend the latter is a larger distinct group from the former).
— Greg Sanders · Oct 14, 10:33 PM · #
An interesting explanation of an unstable system. Thank god Cheney/Bush/McCain and the Christian Socialist Party had some available remedies. Seriously, why was this instability not predicted by a relatively simple mathematical model running in Monte Carlo mode?
— creighton burrell · Oct 14, 10:42 PM · #
Perhaps I’m overlooking something obvious or making an equally obvious mistake, but you begin the third paragraph with the sentence: “The debt gets paid first; then Og and the equity holders split what’s left, if anything.”
This is a description of the equation that appears two sentences above: “He is left with 10 – 2 – 5 = 3.”
The 2 is the debt. This is taken from the 10.
But if “Og and the equity holders SPLIT WHAT’S LEFT” they’d be splitting 8, no? That’s what’s left, 8. Half of 8 is 4 (not 5). This leaves Og with 4 (not 3.)
So either the equation should be 10 – 2 – 4 = 3 or the sentence should read something like “The debt gets paid first; then THE EQUITY HOLDER GETS A SUM EQUAL TO HALF OF THE ORIGINAL AMOUNT OG BRINGS BACK.” Right?
Because the equation you give isn’t a 50% split of “WHAT’S LEFT,” which would be half of 8 (4). Rather it’s half of the original amount, which would be half of 10 (5).
Am I missing something? Doing something dumb?
— ML · Oct 14, 10:50 PM · #
Congratulations on this. I was expecting the panicked cave dwellers to all turn to the guys with spears for help — who realize that with everyone starving and mistrustful of one another, NEW guys with spears could come in and take over the cave — and who are the only ones with the powered to tell everyone, “Okay, each and every one of you give us a third of your berries, and we’ll pay off enough of the hunter’s debts to the banks that it’s worthwhile for those banks to start loaning those berries to the hunters so they can go hunting again. And we’ll put a few of the bookies heads on pikes to remind you all not to get cute in the future.”
— Bram R · Oct 14, 10:56 PM · #
Sorry I stupidly cut-n-pasted without changing the final amount. It should, of course, read:
“So either the equation should be 10 – 2 – 4 = 4 or the sentence should read something like “The debt gets paid first; then THE EQUITY HOLDER GETS A SUM EQUAL TO HALF OF THE ORIGINAL AMOUNT OG BRINGS BACK.” Right?”
10 – 2 – 4 = 4
— ML · Oct 14, 10:58 PM · #
Freddie:
Only government regulation (as far as I can see) can dampen the boom-and-bust cycle. In the forthcoming NR article I referenced earlier in the comments, I argue that such regulations should focus on compartmentalizing risk, rather than trying to dampen economy-wide business cycles.
— Jim Manzi · Oct 14, 11:05 PM · #
Bram R:
Yes, well, this is the disaster scenario that makes financial contagion look pretty mild in comparison.
— Jim Manzi · Oct 14, 11:11 PM · #
Winston:
Thanks. Since most people have heard of “shorting” a stock, and have at least a vague sense of what it means, I wanted to describe the simplest mechanism for betting on its decline.
— Jim Manzi · Oct 14, 11:13 PM · #
ML:
Sorry if this was ambiguous. I said “split”, not “split evenly”.
— Jim Manzi · Oct 14, 11:13 PM · #
creighton:
That’s a question with a very long answer.
In short form, because what probability of a bunch of bad hunting seasons should you put into your MC simulation? If you used only the last few years, you would project almost no probability of collapse. If you used very long periods, you might or might not see this. Who is to say what is the “right” period of observation to establish the relevant probability distribution? Lots of people would have been arguing that we had moved to a “permamnet plateau” of better weather, others that tried-and-true distributions of weather over the past century were right, and others would argue that had accurate climate forecasting models indicating that we “know” weather will actually improve in the future. Who’s right?
This is essentially a restatement of the philosophical problem of induction. Taleb has made a second career out of writing books like “Fooled by Randomness” and “The Black Swan” about this issue.
— Jim Manzi · Oct 14, 11:19 PM · #
Creighton: actually, this event was forecast. Paulson (John, the conventional hedge fund manager, not Hank the new global HF manager…) captured a lot of it. It’s systematic – thus Minsky forecast it in the sense that this kind of thing is inevitable. Santa Fe Institute models forecast it. Hell, Krugman forecast it in 2005 and was roundly lambasted by the conservative press…
— Dave · Oct 14, 11:31 PM · #
Og’s head hurts.
— Og · Oct 14, 11:35 PM · #
Jim,
Do you have evidence that the algorithms used by CDS sellers involved shorting stock and how big of an influence that was? For example, Morgan Stanley’s short interest wasn’t that much. It was quite easy to sell short the stock at any time.
— travis · Oct 15, 12:19 AM · #
That Monte Carlo example, in caveman terms, is fantastic.
creighton:
If anything people rely too much on monte carlo – if you are familiar with the technique: in broad, broad strokes, estimates for subprime defaults were around 3-5%, with saavy risk managers at 8%, and Doomsayers around 12% (Those are massive numbers mind you – 3% of this in context).
Last I’ve seen, the numbers turned out to be around 18% defaults. That is so far in the extreme of the distribution tail it should happen once every tens of thousands of years; nowhere near enough to think through in banking terms, much less convince people to lose money to capitalize against.
At let’s not even talk about estimating the distribution of the default of your counterparty’s counterparty holding the meat of a tail-risk insurance device. How do you even begin to get a correlation?
The more I think through this, the more nash equilibrium shows up. Once someone offered the returns on these risks (especially on the ‘alpha’ return), others would have to in order to compete – they are measured on the same metric, and there’s only lost customers to playing it safe. You caught this with “the bookies begin to be forced by competition to take larger and larger risks.”
— rortybomb · Oct 15, 01:56 AM · #
There’s one fundamental element missing in the cavemen model: fiat money and inflation. To correlate to what actually happened, the model should include a massive issuing of monetary units. That expansion of money would give way to higher prices and (this is critical) an altered relative price structure: the meat-berries exchange rate would go up, which would lead to overinvestment in meat procurement at the expense of other activities and (again critical) savings. During an initial phase, anyone with exposure to the meat business (hunters (meat), bondholders (bonds), stockholders (stocks), bookies (CDS), banks (loans), etc) would do great compared to anyone else, since the assets they own are overvalued and do not reflect the actual risk (those mathematical risk models are distorted by the spurious monetary signal). But beyond a certain threshold it would become apparent that those high prices and perceived low risks are a monetary artifact, and, meanwhile, the price of everything else would begin to catch up with the price of meat. If the FED of the Caves wants to avoid a runaway inflation problem, it has to restrict the growth of money (picture 2005-2006), and, a little later, the house of cards comes crashing down (summer of 2007). The FED of the Caves might attempt to inflate the price of meat again, but would only achieve raising the price of other things (commodities in 2007-2008), making things worse and merely postponing the day of reckoning (today).
— Keyah · Oct 15, 01:57 AM · #
Jim,
The problem of induction that you refer to is, once again, a function of monetary policy making. The FED has guaranteed since, at least, 1996 that no crisis could provoke any kind of shock to the system, no matter how small, shocks that would’ve “burned the undergrowth” of leverage. For at least 12 years the FED has chased away any black swan that appeared on the horizon: LTCM in 1998, the dot com bubble in 2001-2002, the Bear bailout this year, etc, to the point of allowing agents to believe that there were no black swans. Hence the runaway condition that you and rortybomb posit that exits in the absence of regulation: agents chasing market share into systemic calamity. Without monetary distortions agents would balance market share and profits against the risk of going under, a risk that the FED basically defined down to zero through monetary tricks.
The question is: how can be monetary distortions avoided? At a minimun, the FED should become like the Bundesbank of yesteryear: extirpate politics from the institution (no more “presidential cycles”, and no more playing kingmaker like Greenspan did), adopt a strict Austrian interpretation of the bussines cycle and focus on monetary stability to the exclusion of any other goal. A more radical approach would be to discard the fiat money experiment altogether and adopt a commodity based monetary system (berries, anyone?).
— Keyah · Oct 15, 02:56 AM · #
Nice.
Question?
If those berries were made into juice, and some of that juice were to be sent to hunters of another cave and not all meat comes back to this cave and not all of the juice (offshoring)
how much juice would have to be lost before hunters could not go hunting for this cave?
— Brian · Oct 15, 01:11 PM · #
Travis:
To my knowledge there has been no trading meltdown (a la October 19, 1987) in the securities used to hedge CDS. We should all hope it doesn’t, as it is the prospect of such a meltdown that is so fearsome.
Trading strategies that back swaps are proprietary, which is one of the things that makes them so opaque. But look at it this way, while nobody knows the exact value of CDS outstanding, it is generally estimated to be about $60 trillion. This is more than 4X US GDP and about equal to the total value of financial assets that currently exist in the US. The only way to issue this volume of swaps (other, I guess, than outright fraud) is to have a hedged trading strategy.
I gave shorting a linked basket of equities as one example of such a strategy, but was very careful to say:
The dynamics defined by an algorithmic trading approach that works for one player but leads to collapse if followed by the whole market will be the same under various such strategies.
— Jim Manzi · Oct 15, 01:28 PM · #
Dave:
Sure, it was forecast. Other forecasts were that it would not happen (at least at this time and in this way). In retrospect, we know who was right, but that doesn’t help a whole lot.
The rock-and-hard-place problem here is this. On one hand, we need markets in order to forecast future events and value assets in the face of uncertainty, rather than mere risk. Without them, we can’t grow the economy nearly as fast. Real markets always have busts. (This is why, by the way, “forecasting” that “this market is headed for a crash” doesn’t get you a whole lot of donuts.) In the very long-run, these busts are just part of a system that grows faster and better. But on the other hand, the busts that real markets always create can produce sufficient political instability to undermine the legal, political and social basis of the market order. There’s no perfect, and probably no very good, solution to this, but just muddling through.
— Jim Manzi · Oct 15, 01:33 PM · #
keyah:
Well the various ways the guys with spears can take berries and meat without paying for them is a mansion with many rooms.
But imagine that there is no money, only berries and meat. The same dynamics would still lead to the same outcome.
— Jim Manzi · Oct 15, 01:38 PM · #
Sounds like the movie Trading Places with Eddie Murphy…When the 2 rich Wall Street bothers explain (to the then poor Murphy) what they do for a living with big Wall Street lingo, he turns around and says, “I see, you guys are a bunch of bookies.” When Wall Street went on its greed inspired run…they all became a bunch of bookies and build a house of cards they must have know was going to collapse. Someone should be going to jail!!!!
— luis · Oct 15, 02:00 PM · #
Jim,
I gather that you interpret inflation fundamentally as a tax, i. e. something the guys with spears do to get meat and berries for free. And that is correct. But it has far more pernicious consequences: it alters the price structure, distorts the perception of risk and thus modifies decisions about consumption, investment and savings.
You ask us to imagine a cavemen economy without money. But that is the problem. A model without money is simply not a valid model. As Friedman said, money is what matters (to what degree Friedman was right in general, is a matter for another debate; but the aphorism stands).
P. S.: I’m writing to you from Spain. I’ve been reading you over at NRO and elsewhere for quite some time. At a time of systemic silliness, intellectual hysteria and headless chickens running all over the place, you’re a voice of reason and sanity.
— Keyah · Oct 15, 02:39 PM · #
Chris Floyd wrote: “Jim, expand this, keeping it even more rooted in your caveman setting (you shortcutted to the creation of banks, money, etc., it seemed to me); get someone to make you cute illustrations of Og the Hunter, Gah the Banker, and Otoo the credit swap bookie; sell it to a publisher; and make oodles of money in this uncertain marketplace!”
I agree — a whole book explaining economic concepts in terms of cavemen? Maybe there’s already something like this out there, but if so, I’ve never heard of it. I would buy it.
— LP · Oct 15, 08:30 PM · #
The book idea is a good one. Look over How Things Work for inspiration.
— Adam Greenwood · Oct 15, 09:17 PM · #
Jim,
Part of the problem with the huge numbers being thrown around for derivatives is that there is a lot of double counting. Here’s an article that attempts to get a handle on the numbers. Unfortunately, I don’t know whether to trust their conclusions…
http://www.slate.com/id/2202263/
— travis · Oct 15, 11:13 PM · #