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.

Wednesday, March 8, 2017

business cycles through the years

Tens of thousands of years ago, "productivity" was pretty much a function of weather, and "business cycles", insofar as the term can be applied, followed productivity very closely, both in time and in linear correlation.  In the last couple centuries of the second millennium, a drop in expected future demand led to a pullback in investments, both in capital and in new labor relationships, resulting in unemployment, resulting in a drop in demand.  That we aren't living in caves eating berries owes much to our stockpile of capital, both physical and intellectual, but the greater the share of our economy that is devoted to producing durable goods (including capital), the more sensitive our near-term production is to expectations of slightly less near-term production, leading both to a greater variation in production resulting from a particular exogenous fluctuation in productivity and to a greater variation in production resulting from nothing at all.

I think I've mentioned a couple of times that I believe the most underappreciated macroeconomic stylized fact of my lifetime is the doubling of the portion of GDP going to depreciation, and I've even suggested (I believe) that this is part of why the 1990 and 2000 recessions were long and shallow rather than sharp and steep; perhaps without the shift away from producing long-duration capital, the 2008-2009 collapse would have been closer to the scale of 1929-1933, better response by the Federal Reserve notwithstanding.  Perhaps this is related to the general deceleration in growth over that time; perhaps it will also, though, improve our ability to make forecasts going forward, insofar as they depend more on "fundamentals" and less on self-fulfilling expectations.