The foreign exchange market is quite decentralized, and I've been thinking recently that it might be convenient for some players in the market for there to be a daily batch auction, perhaps early in the morning in NYC, late morning in London, and evening in Tokyo. Academics often seem to like batch auctions for the thickness (liquidity) they offer, but one of my motivations was the existence of currency derivatives and indexes; there are traders who may be trying to hedge in the spot market against an "end-of-day" risk, and I thought having a batch auction that provided fixes for derivatives would make it easier to avoid some basis risk.
Foreign exchange markets can feel a bit like barter in some ways; if I'm buying pounds from a trader in London, we'll both think of ourselves as the buyer, and if someone in Europe wants to trade dollars for yen, it's not clear whether that's a purchase or a sale.[1] In some ways, a centralized auction alleviates the double-coincidence-of-wants problem and makes barter feasible and even makes money (or, in this case, a vehicle currency) redundant, but there is a complication: consider a trader who enters, into the auction, an order expressing a desire to exchange 10 euros for 900 yen, and suppose the auction determines that the clearing price is 100 yen per euro. A European entering an order to buy 900 yen expects to end up exchanging 9 euros for 900 yen, while a Japanese person entering an order to sell 10 euros expects to exchange 10 euros for 1000 yen. An American may wish to hand over 10 euros and receive 900 yen and to receive the gains from trade in US dollars. An order now should specify the currency of the order, which may be the currency the trader wants to buy, or sell, or something else. In more generality, the trader may express three baskets of currencies, expecting that, if the trade is executed, the trader will give up basket A and receive basket B and some multiple of basket C such that the currency received and the currency provided have the same value at the clearing prices.
Actually determining how to clear the markets turns out to be equivalent to solving a convex optimization problem, at least if currencies are arbitrarily divisible and orders can be partially executed, at least provided that, for each order that executes, the currency associated with that order is provided by some combination of other orders that execute. The solution technique is likely to involve iteratively finding the excess demand for different currencies given different price vectors, and it seems likely that in a practical distributed setting you would want to group orders by currency, where you would first figure out, given the proposed price, which orders execute, the total gains from trade those orders, and how much currency that adds to the demand vector. One potential complication here is created by orders that clear exactly, with no gains from trade, which may end up partially executing; when excess demand of different groups of orders is being aggregated it may be necessary, especially late in the process of finding the execution price, to retain a lot of possible excess demand vectors to aggregate the partial calculations.
[1] This is the source of some confusion regarding options at times; the terms "put" and "call" are similarly poorly defined. In some ways, though, this is clarifying, though I think I should let go of this particular tangent at this point.
Saturday, May 9, 2020
Monday, March 30, 2020
A quick thought on the size of the firm
In times of war, pandemic, or other emergency, particularly when there are quick shifts in the environment, it seems that the sorts of coordination that are amenable to top-down approaches on a large scale become more significant, while the sorts of coordination that they're bad at, or that lower-level coordination is good at, don't change. In Coase's framework, this suggests that the optimal firm size has suddenly gotten larger. (It obviously has other, more political/legal implications as well.)
Tuesday, February 25, 2020
how fed policy works
This post is perhaps on the wrong blog; there's little if anything in this post that I intend to be speculative or even novel. I've been hearing some talk from laymen about fed policy that makes me think that they are thinking about some things very differently from how I, and I think most economists, do, and I'm writing this post as a guide to a framework that's more in the realm of mainstream economics.
Suppose you're in a car on a stunt track, and you're supposed to go up a ramp and jump over a ravine; you need to be going at least some minimum speed when you get to the top of the ramp or you won't make it across. One thing you would want to do, if you're well below that speed, is to start accelerating well before you get to the ramp. If you put the pedal to the metal hundreds of yards out, and someone criticized this decision on the grounds that if you push the gas pedal as hard as you can now, you won't be able to push it any harder when you close within a hundred yards of the ramp, you would think that criticism was nuts.[1] It would sound exactly as nuts as the complaint that cutting the federal reserve policy interest rate in response to a small slowdown in the economy "uses up ammunition", and that the fed should instead "save up ammunition" for if there's a full-blown recession.
Certainly in every economics model I've seen — and (not quite the same thing), I'm pretty sure that almost[2] every economist is quite confident that this is true — it is not the rate cut that is stimulative; it is the low rate that is stimulative. "Low" will depend on context — indeed, a low rate is typically a sign that policy hasn't been stimulative recently — but from a given starting point, lowering the rate sooner will allow stimulation to accumulate longer; trying to postpone the cut will increase the need for stimulus in the future.
The simplest model, then, with the fewest possible explicit moving parts, is that there is some "neutral interest rate", not known with full precision and subject to influence from noisy external factors, and that policy is contractionary if the policy rate is higher than it and stimulative if the policy rate is lower than it.[3] If policy is stimulative, that will tend to raise the future neutral interest rate, and if it's contractionary it will tend to lower it. Note that the system — at least parameterized this way — is unstable; if you keep the policy rate fixed forever, the natural rate will either find itself above the policy rate, and will then be pushed higher (by inflationary expectations as aggregate demand picks up), making the policy rate even more stimulative, making it move higher even faster, or the natural rate will find itself below the policy rate, and will similarly move ever lower as a deflationary spiral takes hold. If you're making monetary policy by controlling an interest rate, then, you need to move it in response to noise, pushing it above the natural rate when the natural rate gets high and below it when the natural rate gets low.
And this, then, gets me closer to another comment I hear, which is that long-term interest rates are driven entirely by expectations for future short-term rates, which may in some sense be true, and that therefore the fed has complete control of long-term rates, which is in important ways false, at least where we're talking about real interest rates.[4] I recently mentioned to my class that if you want to know how many jobs there will be in the economy next year, ask an economist, but if you want to know how many jobs there will be in thirty years, you should ask a demographer; similarly, in the short run the fed may have a fair amount of latitude, but if it's avoiding both hyperinflation and depression, an interest rate that's too high now implies a lower range of reasonable policy rate options in the future. Expectations about long-term average future real rates should be formulated (almost) entirely on the basis of economic phenomena, and not on some institutional analysis of the fed or psychological analysis of its governors.
[1] You'd be right.
[2] This is the "Dean almost", wherein I have an excessive aversion to making categorical statements about large groups of people; you can probably drop the "almost".
[3] To be clear, all the standard models could be reduced to this sort of model; they would differ in how (much) outside factors affect the neutral rate, and how stimulative or contractionary deviation from that rate is.
[4] If the fed has a credible inflation target, then control of long-term real rates and control of long-term nominal rates are basically the same.
Suppose you're in a car on a stunt track, and you're supposed to go up a ramp and jump over a ravine; you need to be going at least some minimum speed when you get to the top of the ramp or you won't make it across. One thing you would want to do, if you're well below that speed, is to start accelerating well before you get to the ramp. If you put the pedal to the metal hundreds of yards out, and someone criticized this decision on the grounds that if you push the gas pedal as hard as you can now, you won't be able to push it any harder when you close within a hundred yards of the ramp, you would think that criticism was nuts.[1] It would sound exactly as nuts as the complaint that cutting the federal reserve policy interest rate in response to a small slowdown in the economy "uses up ammunition", and that the fed should instead "save up ammunition" for if there's a full-blown recession.
Certainly in every economics model I've seen — and (not quite the same thing), I'm pretty sure that almost[2] every economist is quite confident that this is true — it is not the rate cut that is stimulative; it is the low rate that is stimulative. "Low" will depend on context — indeed, a low rate is typically a sign that policy hasn't been stimulative recently — but from a given starting point, lowering the rate sooner will allow stimulation to accumulate longer; trying to postpone the cut will increase the need for stimulus in the future.
The simplest model, then, with the fewest possible explicit moving parts, is that there is some "neutral interest rate", not known with full precision and subject to influence from noisy external factors, and that policy is contractionary if the policy rate is higher than it and stimulative if the policy rate is lower than it.[3] If policy is stimulative, that will tend to raise the future neutral interest rate, and if it's contractionary it will tend to lower it. Note that the system — at least parameterized this way — is unstable; if you keep the policy rate fixed forever, the natural rate will either find itself above the policy rate, and will then be pushed higher (by inflationary expectations as aggregate demand picks up), making the policy rate even more stimulative, making it move higher even faster, or the natural rate will find itself below the policy rate, and will similarly move ever lower as a deflationary spiral takes hold. If you're making monetary policy by controlling an interest rate, then, you need to move it in response to noise, pushing it above the natural rate when the natural rate gets high and below it when the natural rate gets low.
And this, then, gets me closer to another comment I hear, which is that long-term interest rates are driven entirely by expectations for future short-term rates, which may in some sense be true, and that therefore the fed has complete control of long-term rates, which is in important ways false, at least where we're talking about real interest rates.[4] I recently mentioned to my class that if you want to know how many jobs there will be in the economy next year, ask an economist, but if you want to know how many jobs there will be in thirty years, you should ask a demographer; similarly, in the short run the fed may have a fair amount of latitude, but if it's avoiding both hyperinflation and depression, an interest rate that's too high now implies a lower range of reasonable policy rate options in the future. Expectations about long-term average future real rates should be formulated (almost) entirely on the basis of economic phenomena, and not on some institutional analysis of the fed or psychological analysis of its governors.
[1] You'd be right.
[2] This is the "Dean almost", wherein I have an excessive aversion to making categorical statements about large groups of people; you can probably drop the "almost".
[3] To be clear, all the standard models could be reduced to this sort of model; they would differ in how (much) outside factors affect the neutral rate, and how stimulative or contractionary deviation from that rate is.
[4] If the fed has a credible inflation target, then control of long-term real rates and control of long-term nominal rates are basically the same.
Monday, December 30, 2019
counterfactuals, probability, and logic
There's a natural connection between set theory and logic that can be more or less drawn by considering the set of possible universes, and making a correspondence between a binary statement ("watermelon is a fruit") and the set of universes in which it's true. The statement "A and B" is true in exactly those universes in the intersection of the two sets; logical "and" is equivalent to set intersection. "or" is the union. "not" is the complement relative to the set of possible universes. "A implies B" means "either A is false or B is true".[1]
We can extend this common notion of logic and sets by introducing probability theory. For any probability distribution on the set of universes, there's a probability that A is true, and a probability that B is true. If we know (for all elements of the set) that A implies B, then we know that for any probability distribution, the probability that A is true is less than or equal to the probability that B is true; perhaps less obviously, the converse is also true, at least for finite sets of universes: if it is the case that the probability that A is true is less than or equal to the probability that B is true no matter what valid probability distribution is used, then A implies B. If we restrict to one probability distribution, or a proper subset of all possible probability distributions, then there might be more to say; in particular, with one distribution, we can do Bayesian inference, and since P(A|A)=1, we have that if A implies B, P(B|A)=1.
Suppose we ask, "what would have happened if the Axis had won World War II?" To some extent the answer necessarily depends on how we fill out the counterfactual. In settings where we feel as though we have a reasonable answer to a counterfactual question like this, I think it's because we think there is some distribution (or distributions) of universes that is somehow "reasonable", and that, conditional on the information provided in the counterfactual, that answer is more likely than its complement. For questions that are particularly ill-formed[2] may suffer from being conditional on far-fetched possibilities, but also may suffer from conditioning on information that is relatively independent of other interesting information; A is interesting about B if P(B|A) is close to 0 or 1 and substantially different from P(B).
[1] You might ultimately know which universe you're in, or that you're in one of a restricted set of universes, but that's separate from the concerns of formal logic.
[2] I have in mind, in particular, the sort of question my son asks, e.g. "What if a baby beat a grandmaster in chess?", which tend to have the additional flaw that it's not clear what about the proposed reality is being asked.
We can extend this common notion of logic and sets by introducing probability theory. For any probability distribution on the set of universes, there's a probability that A is true, and a probability that B is true. If we know (for all elements of the set) that A implies B, then we know that for any probability distribution, the probability that A is true is less than or equal to the probability that B is true; perhaps less obviously, the converse is also true, at least for finite sets of universes: if it is the case that the probability that A is true is less than or equal to the probability that B is true no matter what valid probability distribution is used, then A implies B. If we restrict to one probability distribution, or a proper subset of all possible probability distributions, then there might be more to say; in particular, with one distribution, we can do Bayesian inference, and since P(A|A)=1, we have that if A implies B, P(B|A)=1.
Suppose we ask, "what would have happened if the Axis had won World War II?" To some extent the answer necessarily depends on how we fill out the counterfactual. In settings where we feel as though we have a reasonable answer to a counterfactual question like this, I think it's because we think there is some distribution (or distributions) of universes that is somehow "reasonable", and that, conditional on the information provided in the counterfactual, that answer is more likely than its complement. For questions that are particularly ill-formed[2] may suffer from being conditional on far-fetched possibilities, but also may suffer from conditioning on information that is relatively independent of other interesting information; A is interesting about B if P(B|A) is close to 0 or 1 and substantially different from P(B).
[1] You might ultimately know which universe you're in, or that you're in one of a restricted set of universes, but that's separate from the concerns of formal logic.
[2] I have in mind, in particular, the sort of question my son asks, e.g. "What if a baby beat a grandmaster in chess?", which tend to have the additional flaw that it's not clear what about the proposed reality is being asked.
Wednesday, November 27, 2019
trading on the blockchain
Bitcoin is regarded as a digital currency, to some extent, but I often find it useful to think of blockchain as a system for indelibly publishing messages. In the case of bitcoin, these messages are largely of the form "I am taking the bitcoin I got from [provenance] and giving X of it to [bitcoin address] and Y of it to [other bitcoin address]", and as part of the system of maintaining the blockchain it is verified that the sender has bitcoin from that provenance in a quantity that is no less than X+Y.
Actually buying bitcoin involves, as do all transactions, two legs: you give someone dollars or euros or pizza, and they publish a message on the blockchain publicly relinquishing some bitcoin to you. There are exchanges that get together people who want to trade dollars for bitcoin and people who want to trade bitcoin for dollars. When a match is found, the dollars are conveyed in some usual dollar-conveyance manner, and a bitcoin conveyance is published on bitcoin's blockchain. I'm starting, though, to sort of envision a system in which the blockchain itself serves as the exchange.
Consider a blockchain on which the messages took the form of "I trade W units of asset A and X units of asset B, from [provenances], for Y units of asset C and Z units of asset D." The process of incorporating a new block of such messages into the blockchain would require verifying that the person submitting the message has at least W units of A and X of B from the stated provenances, and also verifying that the entire block gives up at least as much of every asset as it conveys. If there is a very small set of prices that clear the market, then calculating how to put such trades together into a valid block gets computationally hard if a lot of these bids are very close to worth zero, but if there aren't too many assets, and there are a fair number of orders that give up a nonnegligible amount of value for some set of market prices, it becomes practically tractable, and certainly sufficiently tractable to reasonably incorporate into the "proof of work" that is part of bitcoin mining.
There are two big technological barriers that occur to me: the simpler one is that there has to be a way to cancel an order that doesn't get executed. It seems to me that bitcoin must have a way to deal with this — that, if I publish "I give Sam 2 bitcoins" and it doesn't go through within a reasonable amount of time that there must be a way to withdraw it or for it to expire — but I don't know what it is. Probably the message should include some sort of timestamp and/or expiration time, along with a hash of the message that includes the expiration. An actual cancel may be impossible.
The other, perhaps bigger, issue, is how the assets get on the relevant blockchain in the first place. If the only messages convey bitcoin, and all bitcoin originate at some level of indirection from bitcoin mining, then you have a fully closed system, and it's all fine. I can really only trade things that are on the blockchain, and for this to be useful they have to be able to somehow get there.
One possibility goes back to an older idea I had, and one that I later came to be was largely Ripple's initial idea, which is essentially to let each person have an asset that they can create out of thin air, simply by being them. I can trade "Dean's dollars" in any quantity for anything I can persuade other people to sell me; the problem is just in getting them accepted.. The provenance is just me. Other people can then trade them as they will, once I have put them out there. Maybe some of my friends would be willing to accept a certain amount of Dean's dollars among themselves; widespread acceptance would probably only come to a few currencies issued by a few people who are in some sense trusted (perhaps trusted to back their currency at some ratio with some basket of off-blockchain asset). You could imagine State Street publishing a list of blockchain addresses it maintains in which it promises to keep the "currency" of each address linked to a corresponding ETF.
Actually buying bitcoin involves, as do all transactions, two legs: you give someone dollars or euros or pizza, and they publish a message on the blockchain publicly relinquishing some bitcoin to you. There are exchanges that get together people who want to trade dollars for bitcoin and people who want to trade bitcoin for dollars. When a match is found, the dollars are conveyed in some usual dollar-conveyance manner, and a bitcoin conveyance is published on bitcoin's blockchain. I'm starting, though, to sort of envision a system in which the blockchain itself serves as the exchange.
Consider a blockchain on which the messages took the form of "I trade W units of asset A and X units of asset B, from [provenances], for Y units of asset C and Z units of asset D." The process of incorporating a new block of such messages into the blockchain would require verifying that the person submitting the message has at least W units of A and X of B from the stated provenances, and also verifying that the entire block gives up at least as much of every asset as it conveys. If there is a very small set of prices that clear the market, then calculating how to put such trades together into a valid block gets computationally hard if a lot of these bids are very close to worth zero, but if there aren't too many assets, and there are a fair number of orders that give up a nonnegligible amount of value for some set of market prices, it becomes practically tractable, and certainly sufficiently tractable to reasonably incorporate into the "proof of work" that is part of bitcoin mining.
There are two big technological barriers that occur to me: the simpler one is that there has to be a way to cancel an order that doesn't get executed. It seems to me that bitcoin must have a way to deal with this — that, if I publish "I give Sam 2 bitcoins" and it doesn't go through within a reasonable amount of time that there must be a way to withdraw it or for it to expire — but I don't know what it is. Probably the message should include some sort of timestamp and/or expiration time, along with a hash of the message that includes the expiration. An actual cancel may be impossible.
The other, perhaps bigger, issue, is how the assets get on the relevant blockchain in the first place. If the only messages convey bitcoin, and all bitcoin originate at some level of indirection from bitcoin mining, then you have a fully closed system, and it's all fine. I can really only trade things that are on the blockchain, and for this to be useful they have to be able to somehow get there.
One possibility goes back to an older idea I had, and one that I later came to be was largely Ripple's initial idea, which is essentially to let each person have an asset that they can create out of thin air, simply by being them. I can trade "Dean's dollars" in any quantity for anything I can persuade other people to sell me; the problem is just in getting them accepted.. The provenance is just me. Other people can then trade them as they will, once I have put them out there. Maybe some of my friends would be willing to accept a certain amount of Dean's dollars among themselves; widespread acceptance would probably only come to a few currencies issued by a few people who are in some sense trusted (perhaps trusted to back their currency at some ratio with some basket of off-blockchain asset). You could imagine State Street publishing a list of blockchain addresses it maintains in which it promises to keep the "currency" of each address linked to a corresponding ETF.
Thursday, August 8, 2019
bond ratings
Matt Levine mentions a front-page Wall Street Journal article in today's newsletter, and notes, interestingly,
The rational equilibrium story you'd like to tell, provided you have a degree from the University of Chicago, is that an issuer would pay for a credible bond rating because bond buyers are risk-averse and will, on average, underpay for a bond that would be rated (say) BBB+ if it is instead unrated because they don't know that it should be rated BBB+. Because I'm in recent possession of an "ambiguity" hammer, I see an "ambiguity" nail here; "BBB+" is itself essentially a probability of default, and while one can construct purely Bayesian models with risk-averse agents in which credibly revealing additional information is of positive value to sellers, I look at this and wonder whether ambiguity aversion, in which buyers don't know the right probability and are more willing to take on quantified than unquantified risks, can play an additional role.
[1] There's some level on which "one more level of rationality than the conventional wisdom" makes a lot of sense; this suggests as a rule of thumb that you should try to be two levels more rational than the conventional wisdom, provided you have a good idea what that is.
Moody’s Corp., for instance, gave lower grades to some tranches of commercial mortgage-backed securities than its competitors did, with the result that “by 2015, issuers ‘essentially stopped soliciting our ratings’ on those slices.” And investors priced those tranches accordingly:So this looks like one more level of rationality than in what I perceive to be the conventional wisdom: in particular, the issuers do have an incentive to solicit more credible, less lenient ratings, but they don't realize (or act on) them.[1]
Investors demanded higher yields on triple-B portions of deals without Moody’s ratings than on triple-B slices that included Moody’s during 2011 to 2014, according to a Journal analysis of Commercial Mortgage Alert data. The difference was about three-tenths of a percentage point more, on average, than benchmark triple-B rated CMBS—which means it was costlier to borrow than comparably rated debt.
The rational equilibrium story you'd like to tell, provided you have a degree from the University of Chicago, is that an issuer would pay for a credible bond rating because bond buyers are risk-averse and will, on average, underpay for a bond that would be rated (say) BBB+ if it is instead unrated because they don't know that it should be rated BBB+. Because I'm in recent possession of an "ambiguity" hammer, I see an "ambiguity" nail here; "BBB+" is itself essentially a probability of default, and while one can construct purely Bayesian models with risk-averse agents in which credibly revealing additional information is of positive value to sellers, I look at this and wonder whether ambiguity aversion, in which buyers don't know the right probability and are more willing to take on quantified than unquantified risks, can play an additional role.
[1] There's some level on which "one more level of rationality than the conventional wisdom" makes a lot of sense; this suggests as a rule of thumb that you should try to be two levels more rational than the conventional wisdom, provided you have a good idea what that is.
Monday, August 5, 2019
money supply and the business cycle
I ended my previous post with the suggestion that the ability to borrow be viewed as part of the money supply; it's worth noting that this is even more pro-cyclical[1] than usual measures of the money supply.
[1] As far as I know. Fact-checking isn't strictly opposed to the spirit of this blog, but while this is an assertion I'm making based on intuition that is less informed than most of the assertions I make here, I don't feel like trying to figure out whether it's true.
[1] As far as I know. Fact-checking isn't strictly opposed to the spirit of this blog, but while this is an assertion I'm making based on intuition that is less informed than most of the assertions I make here, I don't feel like trying to figure out whether it's true.
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