Tuesday, January 16, 2018

costly signalling

Thinking about basics again, and it seems like a framework for the basics of costly signalling that is slightly more general than the average textbook version might be of some value.

The basics that an agent has some piece of information that it would like to credibly communicate, and has available a set of possible actions, some of which would directly lead to a lower payoff, but especially if the piece of information were false; as long as my gain from being believed exceeds the cost if my message is true, but is less than the cost if my message is false, then I can credibly and profitably use those actions to communicate my information so that other agents will behave in a way that helps me recoup my signaling cost.[1]

There are a variety of things I might like to incorporate into this, and what I'm particularly contemplating right now is something mechanism designish: if a designer can change the set of actions available and/or their costs, which such changes will improve welfare?  I think that the most interesting thing to note that requires a moment's thought but not a deep analysis is that, while reducing the costs of signalling seems like a good idea, everything falls apart if it becomes cheap to signal the information when it's false — unless the reduction in cost fully compensates you for being unable to communicate credibly, at least.  The clearest beneficial case, then, would be one in which you can make signalling cheaper when it's true, but without reducing the cost of sending a false signal.

I might want the information to be continuous, or at least richer than binary.  In that case, you're likely to get "partially pooling equilibria", such that if the agent wants it to be believed that a parameter is large, the agent behaves with some randomness, with some overlap in behavior between situations in which the parameter is small and when it's in-between, ultimately leading observers to make a higher guess for the value of the parameter when they see a "higher value" sort of signal, but not putting full confidence in it.  The mechanism designer then is likely to face a choice in which a lower cost of signalling in general makes the signals less informative, resulting in some knock-on inefficiency that has to be weighed against the direct cost.

[1] You could also have the cost of signalling be the same, regardless of truth, but the benefits of being believed higher when it's true; again, the sign of the net benefit should be positive if it's true and negative if it's false.

Thursday, January 11, 2018

finance conventions

I've asserted at various times that finance is easy, so they have to invent strange conventions to make it hard.[1]  In his Tuesday column, Matt Levine gave an example, sort of:
The difference is that if you buy a $100 Venezuela 9.25 percent bond a day before the semiannual interest payment is due, and the price is $20, then if it trades clean you pay the seller $20 for the bond plus like $4.60 of accrued interest, while if it trades flat you just pay the seller the $20.
This is correct in some sense, but the emphasis is not what I think a person not steeped in finance conventions would find natural; the way I would put it is
The difference is that if you buy a $100 Venezuela 9.25 percent bond a day before the semiannual interest payment is due, and you want to agree to a price of like $24.60, then if it trades clean you call the price $20 with like $4.60 of accrued interest, while if it trades flat you just call the price $24.60.
The effect of "accrued interest" is to smooth out price drops; for a bond trading at par, the day before a $2 payment, you'll pay $102 (more or less), while the next day you'll pay $100 (because you aren't getting the $2 payment, the seller is), and if it trades "clean" then, by convention, you call it $100 on both days. Stock traders just accept that the day a stock goes "ex-dividend" the price drops, and I think in a day when traders are sitting in front of computers, it's more straightforward to call the price the price instead of adopting weird rules to make it seem to behave differently from how it actually does.

[1] The hardest parts of finance, though, are law.  Conventions are second.

Monday, January 8, 2018

information and interaction

A point that I've made, but that has perhaps been better illustrated by Borges, is that extra information is less information; if you have 4MB of data, from which you need to find the 1k you want, you have, on some level, less information than if you just had the 1k.  (Maybe 12 bits less?  I don't know.)  As a related matter, if I need information from you, we may well be able to transmit it efficiently if we can go back and forth a bit than if not.  If I send one of 2n messages indicating a broad category, and you respond with one of 2m responses to help me clarify my next request, and that request is l bits, and the final answer is k bits, then we've exchanged a total of n+m+l+k bits; if I had to send a single request, I would need to send l bits for each of the 2m responses you might send to my initial message (plus perhaps the n bits as well); my request is 2ml bits, which is huge. If you know I need the information, but have to send it without my request, that's 22mlk bits you have to send me to make sure I get what I want.

I kind of got to thinking about this in the context of the Mars rover, for which two-way communication is possible, but with latency.  If the latency doubles, to the extent that analogues for n and l are appreciable, you've basically just halved the rate of information transmission; the ability to recover from that latency by transmitting extra information on spec is basically negligible.

Sunday, December 31, 2017

college football playoffs

I have noted previously somewhere, though possibly not here, that the aim in choosing four football teams to participate in a playoff shouldn't be to pick the four teams that are thought best by some consensus, but to choose the four teams that are thought most likely to be the best team; if there are different reasonable ways of analyzing the season, and all of them indicate that a particular team is the third best, I'm not as interested in including that team as a team that some people reasonably argue is sixth and others argue is the best team in the country.
Team, Conf, RecordMASSAGAPCFPS&Ptotal
Clemson ACC 12-1121173.643
Alabama SEC 11-1614422.167
Ohio St B10 11-2445511.9
Georgia SEC 12-1233331.833
Oklahoma B12 12-1352281.658
Wisconsin B10 12-1576660.843
Penn St B10 10-2769950.732
Auburn SEC 10-38877100.636
Washington P12 10-2189121140.591
UCF AAC 12-01016101290.457

I have taken here five different rankings — Massey and Sagarin, which are good, solid computer rankings based on the final score and outcome of games, S&P, which uses play-by-play data and sometimes produces very different results than other systems, and AP and the College Football Playoff committee, which aggregate expert human opinions in very different processes — and I have added the multiplicative inverse of each ordinal ranking. Thus Ohio State, which the S&P really likes, is listed above Georgia, which is broadly regarded as about third, because I'm more interested in getting each system's top team and, to a lesser extent, top two teams near the top than getting anybody's third place team near the top.

It's possible that the S&P, as callers to a radio sports show might assert, is just the crazy ramblings of statheads with no real appreciation of football, but shouldn't that — as those same callers might assert — be settled on the field?

Friday, December 8, 2017

bowl eligibility

66 "FBS" teams had at least 6 wins against other FBS teams during the regular season; these teams are eligible to go to bowl games.  (Teams can count one win against an FCS team for bowl eligibility, but that would have involved extra work for me, especially as I'm reusing code I wrote years ago.  Laziness also led me to declare any game in December "post-season".)  Mississippi only won 5 games against FBS teams, but played fewer than 5 games against FBS teams that aren't bowl-eligible; they beat 2 teams that are bowl-eligible, and only lost to one that isn't — Arkansas.  If I make Mississippi eligible, then Arkansas beat one bowl-eligible team, and lost to no ineligible teams.

If we adopt this as the rule — you're bowl-eligible if you win at least 6 FBS games, or if you beat more teams that are bowl-eligible than lose to teams that aren't, recursing as necessary — there are 14 additional teams that gain bowl-eligibility:  Utah, Texas Tech, Mississippi, Minnesota, Nebraska, Florida St, Colorado, California Vanderbilt, Tennessee, Syracuse, Maryland, Florida, and Arkansas. the last six in particular only had 3 FBS wins each, but since almost every FBS team they played was bowl-eligible, they get strength-of-schedule credit.

Monday, August 14, 2017

backward-bending supply of nonperishable commodities

What I'm writing here is probably less novel than its presentation, but I find this a useful way to think about it.  (It will seem a bit technical, but I'm going to use language fairly loosely where I can while preserving the idea.)

Hotelling noted that, in some expected-value sense, the price of oil reserves should increase at the rate of interest in equilibrium.  If the market interest rate is lower than the rate of a particular producer — if the producer faces higher borrowing costs (perhaps as a poor credit risk) and/or faces a liquidity constraint — then that producer will want to produce more now (even while producing less later).  If a country forms rigid spending plans in anticipation of selling oil at a particular price, lower prices tend to induce exactly those liquidity shocks and credit risks that make money comparatively more urgent to them.

There are two things I'm trying to highlight here: one is that non-perishability and trade-offs through time are crucial to this effect, and I think that gets buried in some formulations of this observation.  The other is that this is a "liquidity" issue more than a "solvency" issue, or, more to the point, perhaps, that the increase in production in the face of lower prices doesn't increase the producer's wealth as measured using the "market" interest rate.  A patient producer wouldn't respond this way; a producer responds this way only in a context of (implicit or explicit) leverage, or at least the coming due of various dollar-denominated obligations.

Friday, June 2, 2017

liquidity, ETFs, and price indices

One of the big topics I see running through my current and planned research is the idea of prices as essentially emergent phenomena that have a less precise existence in a lot of contexts than we often pretend.  Transactions have precise prices; offers to transact have precise prices.  Assets with centralized, fairly liquid markets have fairly precise prices; a firm offer to sell at a particular price more or less refutes any price higher than it, and a firm offer to buy (a bid) at a particular price more or less refutes any lower price, so two such offers close to each other, especially with large sizes, pretty well pin down the market price of even a moderately sized trade.  Smaller cap stocks often have only loosely defined prices.  Real estate generally has something an appraiser pulled out of his

Corporate bonds don't have liquid markets, or centralized ones (even in the sense that stocks do under Reg NMS).  Corporate bonds are an important asset class, and there are price indices that attempt to give a sense of whether the prices are going up or down and by how much.  There are various ways of doing this, and they aren't uniformly terrible; many of these indices are in some reasonable sense more or less correct, to about the degree that such a thing can be correct.  There are some contexts in which they run into the problem that they're weighted sums of numbers that don't actually exist, though.

Exchange-traded funds (ETFs) are more or less, as the name has it, exchange-traded shares of mutual funds.  Unlike closed-ended funds, the number of shares is variable, and essentially determined by the market; unlike open-ended funds, most of the activity consists of buyers buying existing shares from sellers.  Unlike either, at least in their most common configuration, their holdings are publicly known and basically static; a share of the fund may represent .08 shares of one stock, .03 shares of another, and so on.  The ETF has a sponsor, and a redemption size; if the redemption size is 75,000 shares, and you go to the sponsor with 75,000 shares of the fund, the sponsor will exchange them for 6,000 shares of the first stock, 2,250 of the second, and so on; conversely, if you take those underlying stocks to the sponsor you can receive 75,000 shares of the fund in their place.  Even if all the stocks involved have very liquid markets, you can occasionally have a small difference between the price at which the ETF is trading and the weighted sums of the prices of the underlying stocks, but if the difference gets at all appreciable big institutional investors will start buying whichever is cheap and selling whichever is expensive and the sponsor will end up creating or redeeming shares.  Because everyone knows this is likely to happen, it doesn't need to happen very often; if traders believe that a big purchase or sale of ETF shares is a short-term event, they may sell or buy, partially hedging with a subset of the underlying basket, in the expectation that the prices will return to parity.  (If you google something like "stabilizing speculation gold points" you can probably find a description of how this worked under the gold standard when the "sponsor" was a central bank and gold was being exchanged for currency.)

Once in a while ETFs need to change their holdings; an ETF that tracks the S&P 500 stock index adjusts its holdings when the constituents of the index change.  In the case of bond funds in particular, bonds will mature every now and then, and rather than just pay out the cash some new issue is typically added to the fund and the fund continues its existence.  There are bond ETFs, though, and they work in ways that are mostly unsurprising.  In the case of corporate bond ETFs in particular, though, the underlying securities often lack liquid markets, and often only really trade once or twice a week; the ETFs are often a lot more liquid than many of the underlying issues, which is big part of the value that the ETFs add.

Curiously, though, there are some people who are troubled by this, particularly where the ETF is attempting to track a bond index.  Even if the ETF itself is liquid (and thus has a fairly well-defined price), the price of the ETF may fail to track the index. This is a failure of the index, not the ETF.  Indeed, one great value the ETF is adding in this scenario is that it is giving a better measure of the index; a lot of "incorrect" values for the basket are being "refuted", including possibly one calculated by the index methodology, which most likely (in this scenario) is leaning too heavily on stale prices — too much pretense that the "price" of a bond that hasn't traded since Tuesday is the price at which it traded on Tuesday.

I would propose, in fact, that where an index (basket) might accommodate a more liquid market than many of its constituents, that the best way to define the index may be as the "price" of an associated ETF.  There are ways of tracking repeated sales (the Case-Shiller index does a pretty good job of this), but most of the time, if there's a clear conflict between the price of the ETF and the calculated value of the index, I'm better that the price of the ETF is more current and more correct.