What Is Ergodicity?

Individual behavior and ensembles

Why are election polls often inaccurate? Why is racism wrong? Why are your assumptions often mistaken? The answers to all these questions and to many others have a lot to do with the non-ergodicity of human ensembles. Many scientists agree that ergodicity is one of the most important concepts in statistics. So, what is it?

Ergodicity is usually described in terms of objective properties of an ensemble of objects, and the discussion often gets lost in mathematical subtleties and thus it is often difficult to understand. Nonetheless, I will describe it in bayesian, subjectivist terms; hopefully this will make the concept very accessible.

Suppose you are concerned with determining what the most visited parks in a city are. One idea is to take a momentary snapshot: to see how many people are this moment in park A, how many are in park B and so on. Another idea is to look at one individual (or few of them) and to follow him for a certain period of time, e.g. a year. Then, you observe how often the individual is going to park A, how often he is going to park B and so on.

Thus, you obtain two different results: one statistical analysis over the entire ensemble of people at a certain moment in time, and one statistical analysis for one person over a certain period of time. The first one may not be representative for a longer period of time, while the second one may not be representative for all the people.

The idea is that an ensemble is ergodic if the two types of statistics give the same result. Many ensembles, like the human populations, are not ergodic.

The importance of ergodicity becomes manifest when you think about how we all infer various things, how we draw some conclusion about something while having information about something else. For example, one goes once to a restaurant and likes the fish and next time he goes to the same restaurant and orders chicken, confident that the chicken will be good. Why is he confident? Or one observes that a newspaper has printed some inaccurate information at one point in time and infers that the newspaper is going to publish inaccurate information in the future. Why are these inferences ok, while others such as "more crimes are committed by black persons than by white persons, therefore each individual black person is not to be trusted" are not ok?

The answer is that the ensemble of articles published in a newspaper is more or less ergodic, while the ensemble of black people is not at all ergodic. If one searches how many mistakes appear in an entire newspaper in one issue, and then searches how many mistakes one news editor does over time, one finds the two results almost identical (not exactly, but nonetheless approximately equal). However, if one takes the number of crimes committed by black people in a certain day divided by the total number of black people, and then follows one random-picked black individual over his life, one would not find that, e.g. each month, this individual commits crimes at the same rate as the crime rate determined over the entire ensemble. Thus, one cannot use ensemble statistics to properly infer what is and what is not probable that a certain individual will do.

Or take an even clearer example: In an election each party gets some percentage of votes, party A gets a%, party B gets b% and so on. However, this does not mean that over the course of their lives each individual votes with party A in a% of elections, with B in b% of elections and so on.

These were examples of why, in some cases - the non-ergodic cases, one cannot use ensemble statistics to infer something about a particular individual. There is also a complementary problem, faced by the scientists doing opinion polls. They gather data from a very small number of individuals and try to infer the characteristics of the entire ensemble. In order to do this as accurately as possible they don't simply pick the individuals at random; they partition the human ensemble on the basis of some criteria (such as age or income) and afterwards they randomly pick individuals inside each partition being careful that each partition is being represented. It is worth noting that the so-called margin of error of the opinion polls is not really a margin of error. This margin of error is computed assuming that the human ensemble (or more precisely, the partitions they establish) is (are) ergodic. But in reality they are not.

A similar problem is faced by scientists in general when they are trying to infer some general statement from various particular experiments. When is a generalization correct and when it isn't? The answer concerns ergodicity. If the generalization is done towards an ergodic ensemble, than it has a good chance of being correct

Milton Friedman's 20 best quotes

Yesterday(2015.8.1) would have been the 103^rd birthday of Milton Friedman, who was one of the most brilliant economists of the last century. In honor of Friedman, here are his 20 best quotes.


20) “A society that puts equality before freedom will get neither. A society that puts freedom before equality will get a high degree of both.”
19) “Because we live in a largely free society, we tend to forget how limited is the span of time and the part of the globe for which there has ever been anything like political freedom: the typical state of mankind is tyranny, servitude, and misery. The nineteenth century and early twentieth century in the Western world stand out as striking exceptions to the general trend of historical development. Political freedom in this instance clearly came along with the free market and the development of capitalist institutions. So also did political freedom in the golden age of Greece and in the early days of the Roman era.”
18) “It is one thing to have free immigration to jobs. It is another thing to have free immigration to welfare. And you cannot have both. If you have a welfare state, if you have a state in which every resident is promised a certain minimal level of income, or a minimum level of subsistence, regardless of whether he works or not, produces it or not. Then it really is an impossible thing.”
17) “So that the record of history is absolutely crystal clear. That there is no alternative way, so far discovered, of improving the lot of the ordinary people that can hold a candle to the productive activities that are unleashed by a free enterprise system.”
16) "When everybody owns something, nobody owns it, and nobody has a direct interest in maintaining or improving its condition. That is why buildings in the Soviet Union - like public housing in the United States - look decrepit within a year or two of their construction…"
15) "The great danger to the consumer is the monopoly - whether private or governmental. His most effective protection is free competition at home and free trade throughout the world. The consumer is protected from being exploited by one seller by the existence of another seller from whom he can buy and who is eager to sell to him. Alternative sources of supply protect the consumer far more effectively than all the Ralph Naders of the world."
14) "Two major arguments are offered for introducing socialized medicine in the United States: first, that medical costs are beyond the means of most Americans; second that socialization will somehow reduce costs. The second can be dismissed out of hand -- at least until someone can find some example of an activity that is conducted more economically by the government than private enterprise. As to the first, the people of the country must pay the costs one way or the other; the only question is whether they pay them directly on their own behalf, or indirectly through the mediation of government bureaucrats who will subtract a substantial slice for their own salaries and expenses."
13) "Nothing is so permanent as a temporary government program."
12) "The supporters of tariffs treat it as self-evident that the creation of jobs is a desirable end, in and of itself, regardless of what the persons employed do. That is clearly wrong. If all we want are jobs, we can create any number - for example, have people dig holes and then fill them up again, or perform other useless tasks. Work is sometimes its own reward. Mostly, however, it is the price we pay to get the things we want. Our real objective is not just jobs but productive jobs - jobs that will mean more goods and services to consume."
11) "I am in favor of cutting taxes under any circumstances and for any excuse, for any reason, whenever it's possible."
10) "There is all the difference in the world, however, between two kinds of assistance through government that seem superficially similar: first, 90 percent of us agreeing to impose taxes on ourselves in order to help the bottom 10 percent, and second, 80 percent voting to impose taxes on the top 10 percent to help the bottom 10 percent - William Graham Sumner's famous example of B and C decided what D shall do for A. The first may be wise or unwise, an effective or ineffective way to help the disadvantaged - but it is consistent with belief in both equality of opportunity and liberty. The second seeks equality of outcome and is entirely antithetical to liberty."
9) "When the United States was formed in 1776, it took 19 people on the farm to produce enough food for 20 people. So most of the people had to spend their time and efforts on growing food. Today, it's down to 1% or 2% to produce that food. Now just consider the vast amount of supposed unemployment that was produced by that. But there wasn't really any unemployment produced. What happened was that people who had formerly been tied up working in agriculture were freed by technological developments and improvements to do something else. That enabled us to have a better standard of living and a more extensive range of products."
8) "I want people to take thought about their condition and to recognize that the maintenance of a free society is a very difficult and complicated thing and it requires a self-denying ordinance of the most extreme kind. It requires a willingness to put up with temporary evils on the basis of the subtle and sophisticated understanding that if you step in to do something about them you not only may make them worse, you will spread your tentacles and get bad results elsewhere."
7)“We economists don't know much, but we do know how to create a shortage. If you want to create a shortage of tomatoes, for example, just pass a law that retailers can't sell tomatoes for more than two cents per pound. Instantly you'll have a tomato shortage. It's the same with oil or gas.”
6) “The great virtue of a free market system is that it does not care what color people are; it does not care what their religion is; it only cares whether they can produce something you want to buy. It is the most effective system we have discovered to enable people who hate one another to deal with one another and help one another.”
5) "Workers paying taxes today can derive no assurance from trust funds that they will receive benefits from when they retire. Any assurance derives solely from the willingness of future taxpayers to impose taxes on themselves to pay for benefits that present taxpayers are promising themselves. This one sided 'compact between the generations,’ foisted on generations that cannot give their consent, is a very different thing from a 'trust fund.' It is more like a chain letter."
4) "There are four ways in which you can spend money. You can spend your own money on yourself. When you do that, why then you really watch out what you’re doing, and you try to get the most for your money. Then you can spend your own money on somebody else. For example, I buy a birthday present for someone. Well, then I’m not so careful about the content of the present, but I’m very careful about the cost. Then, I can spend somebody else’s money on myself. And if I spend somebody else’s money on myself, then I’m sure going to have a good lunch! Finally, I can spend somebody else’s money on somebody else. And if I spend somebody else’s money on somebody else, I’m not concerned about how much it is, and I’m not concerned about what I get. And that’s government. And that’s close to 40% of our national income."
3) "Indeed, a major source of objection to a free economy is precisely that it... gives people what they want instead of what a particular group thinks they ought to want. Underlying most arguments against the free market is a lack of belief in freedom itself."
2) "If you put the federal government in charge of the Sahara Desert, in 5 years there'd be a shortage of sand."
1) “I do not believe that the solution to our problem is simply to elect the right people. The important thing is to establish a political climate of opinion which will make it politically profitable for the wrong people to do the right thing. Unless it is politically profitable for the wrong people to do the right thing, the right people will not do the right thing either, or if they try, they will shortly be out of office.”

The path to staying in or leaving the euro for the Greek.

The lovely flow chart from Deutsche Bank Research

(JC) Unit roots in English and Pictures

Monday, April 27, 2015

Unit roots in English and Pictures

After my unit roots redux post, a few people have asked for a nontechnical explanation of what this is all about.

Suppose there is an unexpected movement in any of the data we look at -- inflation, unemployment, GDP, prices, etc.  Now, how does this "shock" affect our best estimate of where this variable will be in the future? The graph shows three possibilities.


First, green or "stationary."  There may be some short lived dynamics, the little hump shape I drew here. Then, given enough time, the variable will return to where we thought it was going all along. For unemployment, suppose your best guess of unemployment in 2050 was 5%. Then you see an upward unexpected 1% spike in today's unemployment. Ouch, that means that we're going back to a recession. But perhaps this news does not change your view of 2050 unemployment at all.

Second, blue or "pure random walk." That's more plausible (though no longer thought to be true) of stock prices. If the price goes up unexpectedly, your expectation of where the (log) price will be in the future goes up one-for-one, for all time.

Third, black, "unit root." This option recognizes the possibility that a shock may give rise to transitory dynamics, and may come back towards, but not all the way towards your previous estimate. As you can see the "unit root" is the same as a combination of a stationary component and a bit of a random walk. Perhaps seeing unemployment rise 1%, you think most of it will work itself out, but that even in the long run labor markets will be sticky and we'll never quite get back.

The "unit root" is most plausible and verified in the data for log GDP. Recessions and expansions have a lot of transitory component that will come back. But there are permanent movements too. Unemployment, being a ratio, strikes me as one that eventually must come back. But it can take a longer time than we usually think, which is interesting.

This is very simplified. A few of the issues:

For GDP the question is whether it will come back to a linear trend extrapolated from past data, not back to a level as I have shown.

Most of the issue is how standard statistical procedures work in these circumstances.

As you can see from the graph, the pure question whether the series will come back in an infinite time period is not really knowable. It could be that the series will come back eventually, but take a very long time. It could be stationary plus a second very slow moving stationary component. This is a statistical problem but not really an economic problem. The appearance of unit roots are economically interesting as they show a lot of "low frequency" movement, series that are coming back slowly -- even if they do come back eventually. The economics of "slumps" and (we hope, someday) "booms" is hot on the agenda, and this is one indication of the fact.

This is all much more interesting if you look at multiple series together. For the canonical example, if you just look at stock prices, they are very very close to a random walk. A price rise or decline are permanent. However, if you see stock prices rise relative to dividends, that's almost entirely stationary. GDP and consumption have a similar relationship. As in the latest recession, if GDP declines with a big consumption decline, that looks pretty darn permanent. GDP declining and people still consuming is much more likely to go away.

I hope this helps.

Links for finance

* Asset management 

Economists :: (Fund management) Will invest for food_20140503

브레튼우즈체제의 변천과 새로운 국제경제질서의 모색

브레튼우즈체제의 변천과 새로운 국제경제질서의 모색

http://ajaja77.egloos.com/viewer/4801806 (퍼온 글)
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글로벌시사경제 세 번째 주제로 브레튼우즈체제의 성립과 변천과정 및 현재 논의되고 있는 새로운 국제경제질서의 모색과정에 대해 알아보기로 한다. 헤겔은 [법철학] 서문에서 미네르바의 부엉이는 황혼녁에 날기 시작한다고 했다. 지성과 지혜의 상징인 미네르바의 부엉이가 황혼이 되어서야 날아오른다는 말은, 모든 사회적인 현상과 사건들은 그 사태의 끝 무렵이 되어서야 정확하게 그 실체를 알 수 있게 된다는 의미다. 모든 지식과 지혜란 사회적 현상에 앞서 존재하는 것이 아니라 후에 그것을 분석하고 판단하는 잣대일 뿐이라는 소극적인 표현으로 이해할 수도 있다. 1944년 제2차 세계대전이 끝나기 직전에 성립한 브레튼우즈체제는 그간 몇 차례에 걸친 보완에도 불구하고, 글로벌화의 진전과 서브프라임사태에서 촉발된 미국의 금융위기, 현재 진행중인 유럽의 경제위기 등과 맞물려 그 황혼기를 맞고 있다. 

1. 브레튼우즈체제의 성립 배경

제1차 세계대전 이전까지 국제통화제도의 근간은 금본위제였다. 즉 모든 국가의 통화가치를 일정량의 금에 고정시키고, 이를 통해 각 국간 통화의 교환비율이 결정되는 고정환율제도였다. 1차 세계대전이후 대공황의 여파로 극도의 혼란속에서 금본위제도는 흔들리게 되고, 각 국은 관세장벽을 높이고, 수입할당제, 수입허가제 등의 보호주의적 성격의 무역규제수단을  도입하게 되었다. 또한 각 국은 경쟁적으로 환율의 평가절하를 단행하여 국제경제의 불안정성은 확대일로에 있었다. 1940년대에 들어서도 세계경제는 국제유동성부족과 외환통제의 보편화 등으로 금본위제는 붕괴되고, 국제통화제도는 위기에 직면하게 되어 새로운 국제경제질서에 대한 논의가 시작되었다.. 

이러한 혼란속에 1943년 4월 영국정부는 새로운 국제경제질서의 확립을 위해 ‘국제청산동맹안’(Keynes 안)을 발표하였고, 뒤이어 같은 해 7월 미국정부는 ‘연합국 안정기금 예비초안’(White안)을 발표하였다. 이를 계기로 논의가 본격화 되어, 1944년 7월 미국 뉴햄프셔주 브레튼우즈의 마운트 워싱턴 호텔에서 44개국 대표가 모여 통화금융회의가 개최되었고, 브레튼우즈협정이 체결되었다. 이듬해인 1945년 12월 30개국이 서명함으로써, 브레튼우즈체제는 정식 출범하게 되었다. 

2.브레튼우즈체제의 기본구조

브레튼우즈체제의 기본 골격은 크게 세 가지로 요약할 수 있다. 첫째, 금본위제도의 붕괴이후 혼란에 빠진 외환 및 금융시장의 안정을 회복하는 것, 둘째, 보호주의적 성격의 각종 무역규제를 철폐하여 국가간 무역을 활성화시키며, 셋째 전쟁관련국의 전후부흥과 개발도상국의 개발을 위한 지원이 그 주요 내용이다.

이러한 목표를 달성하기 위해, 국제통화제도를 관장하고 각 국에 필요한 외화를 공급하는 기구로 국제통화기금(IMF), 전후부흥과 후진국개발을 위한 국제부흥개발은행(IBRD)을 설립하였고, 무역활성화를 위한 기구로 관세 및 무역에 관한 일반협정(GATT)를 출범시켰다. 

이렇게 출범한 브레튼우즈체제는, 국제통화제도의 본질적 기능인 국제유동성공급을 위해 금환본위제를 기본으로 하고, 국제수지 조정메카니즘으로 조정가능 고정환율제를 채택하였고, 일시적 유동성부족의 문제를 해결하기위해 특별인출권제도(SDR, special drawing rights)를 두었다.   

금환본위제란, 미국이 은행국으로서의 역할을 담당하고, 달러를 기축통화(key currency)로 지정하여 금 1온스(31.1g)당 35달러로 고정시키며, 각 국은 자국통화를 금 또는 달러에 고정시키고 미국은 각 국이 보유한 달러에 대한 금태환을 보장하는 고정환율제이다. 따라서 브레튼우즈체제하에서의 국제유동성의 공급은 금산출량과 달러의 공급수준에 의해 증감하게 된다.다음으로 조정가능 고정환율제란, 원칙적으로 각 국 통화의 환평가를 상하 1%이내에서 변동할 수 있게 고정시키고, 근본적 불균형(fundamental disequilibrium)이 발생한 경우에 한해, IMF와 협의하여 10%이내에서 환평가를 변경할 수 있도록 한 제도이다.

마지막으로 특별인출권이란, IMF회원국은 사전에 각 국의 경제규모에 따라 정해진 범위내에서, 국제수지악화 등 일시적 유동성부족을 해결하기위해 담보없이 외화를 인출할 수 있는 권리를 말한다.

3. 브레튼우즈체제의 문제점

제2차 세계대전이 연합국의 승리로 끝나면서 미국의 영향력이 전례없이 커지면서 호기롭게 시작한 브레튼우즈체제는 로버트 트리핀(R, Triffin)지적한 것처럼, 유동성과 신뢰성의 딜레마를 포함한 몇가지 문제를 내재한 불안한 출발이었다.

첫째, 국제유동성의 문제를 지적할 수 있다. 앞에서 살펴본 것처럼 브레튼우즈체제하에서의 국제유동성의 공급은 화폐용 금의 추가적 공급과 기축통화국의 국제수지적자, 국제통화기금에 의한 신용창출에 의해서 가능하다. 그런데 화폐용 금의 산출량과 국제통화기금에 의한 신용창출은 제한적일 수밖에 없어, 결국 기축통화국의 국제수지적자에 의존하는 부분이 클 수밖에 없다. 세계경제의 팽창과 더불어 국제유동성을 지속적으로 증가시키기 위해서는 기축통화국인 미국의 국제수지적자를 통해 달러를 공급해야한다. 그러나 지속적으로 국제수지의 적자가 누적되면 미국 달러에 대한 신뢰성은 하락하게 되는 문제, 즉 트리핀이 지적한 유동성 공급과 신뢰성간의 딜레마에 봉착하게 된다. 

둘째, 조정가능 고정환율제의 채택과 관련된 문제도 지적 된다. 원칙적으로 각 국은 환율을 금과 달러에 고정시키게 되어 있으므로, 각 국의 경제사정에 따른 환율변경의 가능성은 그만큼 작아진다. 따라서 국제수지의 불균형이 발생하였을 경우 적자국은 물가하락과 소득수준의 감소로, 흑자국은 물가상승과 소득수준의 증대로 귀결되어, 환평가의 조정이 필요하게 되지만 각 국의 이해관계가 상반되어 환평가의 대칭적 조정을 어렵게 한다. 또 근본적 불균형이 발생하였을 경우에 한해 환율조정을 가능하게 한 조항도, 그 개념이 불명확하여 조정에 소요되는 시간을 지연시키고, 이로 인한 환투기를 유발하여, 각 국 정부로 하여금 IMF의 기본목적과는 달리 무역이나 외환에 대한 직접적 통제를 통해 문제를 해결하려는 동기를 부여한다는 점에서 문제로 지적된다.

그 외에도 신인의 문제나 기축통화인 달러의 평가가치 변동이 미국의 경제적 상황에 따라 영향을 받게 되어있어, 미국의 경제적 상황에 따라 세계경제가 지나치게 영향을 받을 수 있다는 점도 문제로 지적되어 왔고, 이러한 염려는 최근의 서브프라임 모기지관련 미국발 금융위가가 전세계로 급속히 확산되는 과정에서 확인될 수 있었다.  

4. 브레튼우즈체제의 변천과정

1960년대 들어 미국의 만성적인 국제수지 누증으로 브레튼우즈체제는 구조적 모순을 노출하게 되었다. 미국 국제수지적자의 누적과 베트남전 전비조달을 위한 통화량 증발로 인해 인플레이션이 가속화 되고, 달러화의 가치가 급락하게 되어, 미국에 대해 금태환을 요구하는 국가들이 늘어나면서 금보유량이 급감하여 1971년 8월 닉슨 대통령이 금태환정지를 발표하여 브레튼우즈체제는 붕괴의 조짐을 보이게 되었다.

이러한 혼란을 수습하기 위하여, 1971년 12월 18일 선진 10개국 재무장관들이 워싱턴소재의 스미소니언박물관에서 금태환 정지로 붕괴된 고정환율제도의 부활을 위한 논의를 하였다. 그 결과, 달러의 금태환을 계속유지하고, 달러의 평가절하를 인정하며, 환율변동폭을 기존의 1%에서 2.25%로 확대시키고, 달러 외에 기축통화를 도입한다는 내용을 포함하고 있었다. 이 협정을 브레튼우즈체제의 연장선상에서 스미소니언체제라고도 한다. 

그러나 스미소니언체제는 1973년 오일쇼크로 인한 2차 달러화 평가절하로 비교적 단명하게 되었고, 국제통화체제는 혼란을 거듭하다가, 1976년 1월 자메이카의 수도 킹스턴에서 열린 제5차 IMF잠정위원회에서 그간의 논의결과를 바탕으로 새로운 협정문을 발표하였다. 킹스턴체제로 불려지는 합의문의 주요내용은, 고정환율을 포기하고 변동환율제도를 인정한 것,통화로서 금의 역할을 축소하고 궁극적으로 금을 폐화시키고, 대외준비자산으로서 미달러화 대신 SDR 기축준비자산화한 것, IMF의 신용제도를 확충하고 그 이용조건을 개선한 것 등이 포함된다. 

5.새로운 경제질서의 모색

이상에서 간단히 살펴본 것처럼 국제통화제도는 금본위제 → 브레튼우즈체제 → 스미소니언체제 → 킹스턴체제를 거쳐 현재에 이르고 있다. 그러나 세계화의 급속한 진전과 더불어 급변한 글로벌 경제환경에 적절히 대응하지 못한 채 브레튼우즈체제는 사실상 붕괴되었고, 현재의 혼란상을 극복하기 위한 새로운 국제경제질서에 대한 논의가 활발히 이루어지고 있다.영국 고든총리는, 2008년 미국발 금융위기 사태의 원인인 자유화된 금융시장의 병폐를 척결하고 새로운 자본주의 체제를 구축하기 위한 방안으로 종전의 달러기축통화체제인 브레튼우즈체제에서 다국 기축통화체제로의 전환을 촉구하면서 신브레튼우즈구상을 발표하였다.

이와 관련하여 현재 논의되고 있는 주요 내용은, 국제 표준의 새로운 회계기준의 채택을 통한 투명성 확보, 국가별로 이뤄지고 있는 현행 금융감독체제를 개혁하여 IMF를 포함한 새 국제 금융감시기구의 창설, 금융위기 조기경보시스템의 확립 등으로 정리해볼 수 있다.

뿐만아니라, 기존의 브레튼우즈체제를 강화하고 신흥국을 참여시키기를 선호하는 미국의 주장과, 브릭스(BRICS) 및 아시아의 의견이 서로 대립하면서 신브레튼우즈체제는 난항을 겪고 있는 것이 현실이다.

그러나 글로벌 경제위기는 날로 심화되고 새로운 국제경제질서에 대한 세계적 요구는 급속히 확산되고 있어, 머지않아 브레튼우즈체제를 대체할 새로운 국제경제질서가 등장할 것은 틀림없는 사실이다. 첫 부분에서 언급한 것처럼, 황혼녁에 날개짓을 하면서 힘차게 날아오를 새로운 부엉이를 상상하며, 우리는 새국제경제질서 창조의 현장 목격자가 될 수 있는 좋은 기회를 부여받았다. 수험생들로서는 이러한 흐름속에서 관련 뉴스를 해석해보는 것도 큰 도움이 될 것이다.

Market Liquidity and Funding Liquidity

Understanding Liquidity Risk

By David Harper  

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Related Searches: Four Financial Statements, Ratio Analysis, Cash Flow Statement, Statement of Owners Equity, Accounting

Before the global financial crisis (GFC), liquidity risk was not on everybody's radar. Financial models routinely omitted liquidity risk. But the GCF has prompted a renewal to understand liquidity risk. One reason is because there was a consensus that the crisis included a run on the shadow (non-depository) banking system - providers of short-term financing, notably in the repo market - systematically withdrew liquidity; they did this indirectly but undeniably by increasing collateral haircuts. After the GFC, all major financial institutions and governments are acutely aware of the risk that liquidity withdrawal can be a nasty accomplice in transmitting shocks through the system (or even exacerbating contagion). (For more on liquidity, check out Understanding Financial Liquidity.) TUTORIAL: Liquidity Measurement Ratios

What is liquidity risk?
Liquidity risk is divided into two types: funding liquidity risk (aka cash-flow risk) and market liquidity risk (aka asset/product risk).

• Funding (cash flow) liquidity risk is the chief concern of a corporate treasurer who asks: can we pay our bills, can we fund our liabilities? A classic indicator of funding liquidity risk is the current ratio (current assets/current liabilities), or for that matter, the quick ratio. A line of credit (LOC) would be a classic mitigant.
   
• Market (asset) liquidity risk is asset illiquidity. This is an inability to easily exit a position. For example, we may own real estate but, owing to bad market conditions, it can only be sold imminently at a "fire sale" price. The asset surely has value, but as buyers have temporarily evaporated, the value cannot be realized. Consider its virtual opposite, a U.S. Treasury bond. True, a U.S. Treasury bond is considered almost risk-free as few imagine the U.S. government will default. But additionally, this bond has extremely low liquidity risk: its owner can easily exit the position at the prevailing market price. Small positions in S&P 500 stocks are similarly liquid. They can be quickly exited at the market price. But positions in many other asset classes, especially in alternative assets, cannot be exited with ease. In fact, we might even define alternative assets as those with high liquidity risk!

Market liquidity risk can be a function of the following:

• The market microstructure. Exchanges (e.g., commodity futures) are typically "deep markets," but many over-the-counter (OTC) markets are "thin."
   
• Asset type: simple assets are more liquid than complex assets. For example, in the crisis, CDOs-squared (CDO^2 are structured notes collateralized by CDO tranches) become especially illiquid due to their complexity.
   
• Substitution (is the asset fungible?): If a position can be easily replaced with another instrument, the substitution costs are low and the liquidity tends to be higher.
   
• Time horizon: If the seller has urgency, this tends to exacerbate the liquidity risk. If a seller is patient, then liquidity risk is less of a threat.

Note a common feature of both types of liquidity risk: in a sense, they both involve "not enough time." Illiquidity is generally a problem that can be solved with more time! (To learn more about risk, read Determining Risk And The Risk Pyramid.)

Figure 1: Measures of Market Liquidity

Measures of Market Liquidity Risk
There are at least three perspectives on market liquidity (see Figure 1). The most popular and crudest measure is the bid-ask spread; this is also called width. A low or narrow bid-ask spread is said to be "tight" and tends to reflect a more liquid market. Depth refers to the ability of the market to absorb the sale (exit) of a position. An individual investor who sells shares of Google, for example, is not likely to impact the share price; on the other hand, an institutional investor selling a large block of shares in a small capitalization company will probably cause the price to fall. Finally, resiliency refers to the market's ability to bounce back from temporarily incorrect prices. To summarize:

• The bid-ask spread measures liquidity in the price dimension and it is a feature of the market not the seller (or the seller's position). Financial models that incorporate bid-ask spread adjust for exogenous liquidity and are exogenous liquidity models.
   
• Position size, relative to the market, is a feature of the seller. Models that use this are measuring liquidity in the quantity dimension and are generally known as endogenous liquidity models.
   
• Resiliency measures liquidity in the time dimensions and such models are currently rare.

At one extreme, high market liquidity would be characterized by an owner of a small position relative to a deep market who is exiting into a tight bid-ask spread and a highly resilient market.

What about volume?
Trading volume is a popular measure of liquidity, but it is now considered to be a flawed indicator. High trading volume does not necessarily imply high liquidity. The Flash Crash of May 6, 2010 proved this with painful, concrete examples. In that case, according to the SEC, sell algorithms (program trades) were feeding orders into the system faster than they could be executed. Volume jumped but many backlog orders were not filled. As the SEC wrote, "especially in times of significant volatility, high trading volume is not necessarily a reliable indicator of market liquidity."

A Common Method for Incorporating Liquidity Risk
In the case of exogenous liquidity risk, one approach is to use the bid-ask spread to directly adjust the metric. Please note: risk models are different than valuation models and this method assumes there are observable bid/ask prices.

Let's illustrate with value at risk (VaR). Assume the daily volatility of a $1,000,000 position is 1.0%. The position has positive expected return (aka drift), but as our horizon is daily we will bring our tiny daily expected return down to zero (a common practice). So let the expected daily return equal zero. If the returns are normally distributed, then the one-tailed deviate at 5.0% is 1.65; that is, the 5% left tail of normal distribution is 1.65 standard deviations to the left of mean. In excel, we can get this result with =NORM.S.INV(5%) = -1.645.

The 95% value at risk (VaR) is given by:

$1,000,000 * 1.0% volatility * 1.65 = $16,500

Under these assumptions, we can say "only 1/20 days (5% of the time) do we expect the daily loss to exceed $16,500." But this does not adjust for liquidity.

Let's assume the position is in a single stock where the ask price is $20.40 and the bid price is $19.60. In percentage terms the spread (%) = ($20.40 - $19.60)/$20 = 4.0%. The full spread represents the cost of a round trip: buying and selling the stock. But, as we are only interested in the liquidity cost if we need to exit (sell) the position, the liquidity adjustment consists of adding one-half (0.5) the spread. In the case of VaR, we have:

Liquidity cost (LC) = 0.5 * spread

Liquidity-adjusted VaR (LVaR) = position ($) * [-drift (%) + volatility *deviate + LC], or

Liquidity-adjusted VaR (LVaR) = position ($) * [-drift (%) + volatility *deviate + 0.5 * spread],

In our example,

LVaR = $1,000,000 * [-0% + 1.0% * 1.65 + 0.5 * 4.0%] = $36,500

In this way, the liquidity adjustment increases the VaR by one-half the spread ($1,000,000 * 2% = +$20,000).

The Bottom Line
Liquidity risk can be parsed into funding (cash-flow) or market (asset) liquidity risk. Funding liquidity tends to manifest as a credit risk: inability to fund liabilities produces defaults. Market liquidity risk manifests as market risk: inability to sell an asset drives its market price down, or worse, renders the market price indecipherable. Market liquidity risk is a problem created by the interaction of the seller and buyers in the marketplace. If the seller's position is large relative to the market, this is called endogenous liquidity risk (a feature of the seller). If the marketplace has withdrawn buyers, this is called exogenous liquidity risk (a characteristic of the market which is a collection of buyers); a typical indicator here is an abnormally wide bid-ask spread.

A common way to include market liquidity risk in a financial risk model (not necessarily a valuation model) is to adjust or "penalize" the measure by adding/subtracting one-half the bid-ask spread. (For more on Value at Risk, see An Introduction To Value at Risk (VAR).)

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Filed Under: Balance Sheet, Financial Statements, International Trade, Liquidity, Liquidity Ratio, Macroeconomics, OTC Bulletin Board