Spero Consulting

Archive for November 12th, 2008

Reg­u­lar read­ers will know that we often crit­i­cize the stu­pid appli­ca­tion of math­e­mat­i­cal mod­els, espe­cially ones related to finance and eco­nom­ics; ergo, our firm’s motto, “Thought Before Calculation.”

In that light, we note that in last Friday’s The Wall Street Jour­nal (Novem­ber 7) the edi­tors excerpted a speech that Michael Crich­ton gave at Cal Tech in 2003, entitled ‘Aliens Cause Global Warm­ing.’ (For those who don’t know, Mr. Crich­ton passed away early last week.)

In the speech, Mr. Crich­ton dis­cussed the Drake equa­tion which attempts to illus­trate the winnowing-​down process of all the plan­ets in the uni­verse to ones that could sup­port life and could send intel­li­gent sig­nals (to us). There are seven vari­ables in the equa­tion, which was the impe­tus of the SETI project and one of the jus­ti­fi­ca­tions for spend­ing funds on it. For SETI, think Jody Fos­ter in the screen ver­sion of the late Carl Sagan’s Con­tact.

Mr. Crich­ton made the excel­lent points that the Drake Equa­tion is a serious-​looking equa­tion and that its seri­ous appear­ance pro­vided poten­tial inves­ti­ga­tors with a veneer of serious, scientific inquiry. This is despite the fact that NONE of the seven vari­ables can ever be known or esti­mated. Thus, the inves­ti­ga­tion was not sci­ence and was/​is not that dif­fer­ent than count­ing the num­ber of angels on the head of a pin. 

Mr. Crich­ton con­cluded that SETI et. al. “is unques­tion­ably a reli­gion.” (Below we argue it is a bad reli­gion – mean­ing a poorly-​considered one.)

More­over, he con­tin­ued his argu­ment by not­ing that with­out legit­i­mate sci­en­tific inquiry and pro­ce­dure, “soon enough garbage began to squeeze through the cracks…” (By this point, the reg­u­lar reader and the astute reader can see where we are headed by this post’s title.)

He went fur­ther to note that the achiev­ing con­sen­sus around a “model” is not sci­ence, and vice versa.

We go fur­ther to argue that such con­sen­sus is not sci­ence, nor even part of science’s broader super-set, reason. 

Yes, we view sci­ence as a sub­set of rea­son – the empir­i­cal part of rea­son. And so, we’d argue that such con­sen­sus is in fact a sub­sti­tute for rea­son. In fact, it fills the entropic chaos of unknow­ing that is the absence of reason. 

Thus, we con­trast such sci­en­tism with more fully-​developed reli­gions like, say, Christianity, which via numer­ous pas­sages, includ­ing the first chap­ter of the Gospel of St. John, defines God as rea­son (logos) and com­mands man to use that same rea­son to be bet­ter than instinc­tual, impul­sive ani­mals amidst the chaos.¹

At first glance, it might seem that the val­u­a­tion (and sub­se­quent real­iza­tion) of mortgage-​backed secu­ri­ties (MBS) and other finan­cial assets has lit­tle in com­mon with the esti­ma­tion of the cur­rent num­ber of intel­li­gi­ble planets.

However, both method­olo­gies require giant leaps of faith when mov­ing from real­ity to a model as both suf­fer from the absence of rel­e­vant data. Other galax­ies and solar sys­tems (and plan­ets) are just too far away to con­sider care­fully, and there are only (rel­a­tively) short his­to­ries of mort­gage prod­ucts and repay­ments avail­able from which one HOPES to extrap­o­late the future, and this is where and why the con­sen­sus arises. 

There are no good mod­els; so, indi­vid­u­als agree to use mod­els already in use (as a val­i­da­tion for their choice). Often, such mod­els first appeared in text­books for entirely dif­fer­ent pur­poses but were used out of convenience.

Mort­gage port­fo­lio, MBS, and CDOs suf­fer a few addi­tional bur­dens not shared by ET’s would-​be friends, including: (1) depen­den­cies and inter­ac­tions between or among bor­row­ers that would seem to be absent with plan­ets; (2) non-stationarities through time with respect to these (and other rel­e­vant) rela­tion­ships; and (3) the inter­ac­tions are endoge­nous as they involve people’s cog­nizant responses through time to eco­nomic con­di­tions and per­sonal cir­cum­stances. (In that sense, it is truly a daunt­ing task.)

Please see our ear­lier post for a descrip­tion of the mort­gage pool or port­fo­lio prob­lem. In it, we illus­trate how recent calls for more trans­parency are non sequiturs and sim­plis­tic, but do show a lack of under­stand­ing about the nature of the problem.

It seems that the soci­olo­gies of both plan­e­tary and mort­gage mod­el­ing envi­ron­ments do seem to place a pre­mium on con­sen­sus. While every indi­vid­ual trader or struc­turer may have their own idio­syn­cratic tweaks, most solve val­u­a­tion prob­lems in sim­i­lar man­ners because there just aren’t that many tractable ways to per­form the cal­cu­la­tions. But, as many for­mer traders and struc­tur­ers have dis­cov­ered, choos­ing a method­ol­ogy for its tractabil­ity is very dif­fer­ent than choos­ing one for its applic­a­bil­ity, par­tic­u­larly when the envi­ron­ment changes rapidly or drastically.

In fact, we’d argue that the recent lack of exchange or illiq­uid­ity in these mar­kets results from the real­iza­tion and inter­nal­iza­tion that these mod­els have failed, and no suit­able replace­ment yet has been found; ergo, the paralysis. 

As fur­ther evi­dence of paralysis, today Mr. Paul­son announced the Trea­sury Depart­ment wouldn’t pur­chase any trou­bled assets as part of their TARP efforts. (Recall that the “TA” in TARP stands for “Trou­bled Asset.”) It seems that the gov­ern­ment doesn’t know how to value them, either. We’d have been sur­prised by the announce­ment had we not pre­dicted it six weeks ago.

As always when we dis­cuss these top­ics, we point read­ers to our essay Uncer­tainty Man­age­ment, which presents a broader view of the nature of unknow­ing – far broader than the nar­row empha­sis on risk or mea­sur­able uncer­tainty one typ­i­cally sees.

Finally, as usual, we also note that we have pro­posed a pri­vate solu­tion to the mort­gage cri­sis that uses tax incen­tives – via the equiv­a­lent of accel­er­ated depre­ci­a­tion or invest­ment tax credit – to induce pri­vate pur­chases of the trou­bled assets. We sug­gest Mr. Paul­son con­sider that alternative.

Exclud­ing fools – which we admit pro­vides a non-​trivial exclu­sion – we doubt that finan­cial mod­el­ers or ana­lysts will regain the (mis­placed) self-​confidence they exhib­ited in the calm-​market era prior to mid-​2007. 

In our view, such well-​earned and well-​deserved humil­ity will be ben­e­fi­cial for soci­ety as a whole. Such feel­ings may spur inno­va­tion and increase the level of thought­ful of analy­ses per­formed (rather than rote, pro­ce­dural tasks). Perhaps it may change the struc­ture of contracts.

Per­haps the recent fail­ures will allow senior man­agers to gain effi­cien­cies through the real­iza­tion that irrel­e­vant details are not infor­ma­tion and so many rou­tine tasks and algo­rithms are indeed worth­less – despite the claims of reg­u­la­tors and audi­tors. (Oh, who are we try­ing to kid. The skep­tic in us sug­gests that we’re show­ing our naiveté.)

Jeez, our post from two weeks ago, which noted the sim­i­lar­i­ties between TARP and GARP, makes us seem almost prescient.

Like T.S. Garp, it seems that Mr. Paul­son is jet­ti­son­ing let­ters as he con­tin­ues lonely and aim­less pur­suit. In fact, we’d pre­fer that he take up Mr. Garp’s hobby as it is less dam­ag­ing to the econ­omy and our well-​being than many of Mr. Paulson’s extant actions.

We base our state­ments on today’s announce­ment that the Trea­sury Depart­ment will not pur­chase any Trou­bled Assets: Trea­sury Not Plan­ning to Buy Bad Loans, Assets.

This is one case where we hate to be cor­rect, but it is exactly what we wrote about in Sep­tem­ber and early Octo­ber, when we wrote exhaus­tively that the government’s government-​run “bailout” could not be imple­mented quickly and would fail. (Search, bailout, for exam­ple, for our many posts on the topic.)

We’d also note that it is not too late to attempt a pri­vate solu­tion to the prob­lem. As we men­tioned repeat­edly – includ­ing in ear­lier posts today–the prob­lem is that no one has con­fi­dence in their own val­u­a­tion meth­ods, and that lack of con­fi­dence is jus­ti­fied thus the mort­gage mar­ket is par­a­lyzed. (The broader credit cri­sis also involves a paral­y­sis, but that lack of move­ment relates to dis­trust­ing each other rather than one’s self. Although there is a self-​referential aspect to it that we wrote about in Finan­cial Pro­jec­tion in a Cri­sis.)

How­ever, as we pro­posed in Sep­tem­ber in A Bet­ter Solu­tion (than a gov­ern­ment takeover), pri­vate buy­ers could be induced to pur­chase the trou­bled assets with the proper (and sim­ple) tax incentives. 

Either per­mit buy­ers to imme­di­ately expense their pur­chase price (and then pay low rates on future sales or cash flow realizations) or pro­vide an equiv­a­lent mortgage, investment tax credit.

Such tax incen­tives would pro­vide a cush­ion or mar­gin of error of 30% — 40% of the pur­chase price and would likely be large enough to stim­u­late a sub­stan­tial demand for the mort­gages and the mortgage-​related prod­ucts thereby pro­vid­ing liq­uid­ity with­out the heavy hand of Uncle Sam splash­ing around. (We sus­pect that many traders, struc­tur­ers, and mod­el­ers know that they were/​are wrong, but doubt that it is by an addi­tional, say, 35%.)

Now that our offi­cials seem less in the full-​panic mode than six weeks ago, per­haps they’ll take the time to pon­der or think or con­sider about rea­son­able, sim­ple, and rel­a­tively cheap alter­na­tives to their now dis­carded scheme. We know it is a stretch for many of them, but what else can they do? Garp. Garp. (Or is it rp, rp.)

We haven’t checked the cal­en­dar; so, we ask if the day after Vet­er­ans Day is now cel­e­brated as “Oppo­sites Day.” That’s the sense we get from read­ing the descrip­tions ver­sus the con­tent of James B. Stewart’s weekly col­umn, labeled both “Com­mon Sense” and “Smart­Money” in today’s The Wall Street Jour­nal.

To be frank, we don’t see much com­mon sense or intel­li­gence in his writ­ing in gen­eral, but this week’s col­umn seems espe­cially silly: How Obama Can Fix the Econ­omy.

Can Mr. Stew­art cite a sin­gle instance when via increased gov­ern­men­tal action, a Pres­i­dent has “fixed the economy.”

Ignor­ing the issue of whether we want to live in a soci­ety where power is so con­cen­trated in the exec­u­tive branch that the Pres­i­dent can tin­ker with the econ­omy at will, we can think of no instances when it has worked. Roo­sevelt and the Great Depres­sion has been thor­oughly debunked by Amity Schlaes among oth­ers. Nixon with price con­trols and gas rationing? Hardly. Ger­ald Ford with WIN (Whip Infla­tion Now) but­tons? Uh, no.

In our life­time, the Pres­i­dent who achieved the great­est and most last­ing suc­cess in pos­i­tively influ­enc­ing the health and growth of the econ­omy was the one most in favor of dereg­u­la­tion and the removal of gov­ern­ment influ­ence over enter­prise and the reduc­tion in per­sonal and cor­po­rate tax rates: Ronald Rea­gan. For­tu­nately, much of his influ­ence seems to have lasted many years – until this past September.

Mr. Stew­art claims that “we can for­get about the deficit because one thing we know from the Great Depres­sion and Key­ne­sian eco­nom­ics is that in crises like this the gov­ern­ment has to get out there and spend. World War II pro­duced the biggest deficits as a per­cent­age of GDP …and an end to the Depression.”

Accord­ing to this graph, tech­ni­cally, GDP began grow­ing in 1933, and exclud­ing the reces­sion in 1937 – 38, con­tin­ued to grow in most years. Of course, the bank failures, the stock mar­ket crash, and dust bowl – caused by deci­sions not to plant pre­vi­ously tilled soil – destroyed mas­sive amounts of wealth. It is worth not­ing, because Mr. Stew­ard does not con­sider it, that it took the Dow and the S&P indices until the mid-​1950s to recover to 1929 lev­els. Not only had WWII been over for nearly eight years, but the Korean War had just ended, too; so, we’re not sure of the connection.

Mr. Stew­art then pre­scribes “shoring up the bank­ing and finan­cial sys­tem” and non-​bank par­tic­i­pants, like GMAC and GE Cap­i­tal, too. He writes “These should be good invest­ments since so much of the cri­sis is psy­cho­log­i­cal, and val­ues will rebound when con­fi­dence is restored.”

Mr. Stew­art men­tions Keynes. It is a shame that he didn’t con­sider the quote attrib­uted to him: “The mar­ket can stay irra­tional longer than you can stay sol­vent.” Indeed, Mr. Stew­art may wish to con­sider that mar­kets are one of the places where the psy­cho­log­i­cal becomes the eco­nom­i­cal – where tastes, pref­er­ences, and beliefs are trans­lated into finan­cial val­ues of exchange.

We’re sure that there were many indi­vid­u­als in 1930 who shared Mr. Stewart’s sen­ti­ments today. On aver­age, it would have taken them only about 24 years to real­ize that “value” and change in attitudes.

We do won­der why Mr. Stew­art believes there is value in those firms? It seems that few oth­ers see value in them, par­tic­u­larly GMAC. More­over, why should tax-​payers sub­si­dize inef­fi­cient risk-​takers? When did that became our respon­si­bil­ity (and when was the upside of those gam­bles shared with us)?

Mr. Stew­art goes on to state that we need a com­pre­hen­sive indus­trial pol­icy, and states it won’t be branded social­ism if the gov­ern­ment “man­ages its stakes as though it had a fidu­ciary duty to tax­pay­ers, as opposed to man­age­ment, labor, and other interests.”

Regard­less of whether it is suc­cess­ful or not, if it is not social­ism, then it is at least sta­tism, and the entire gov­ern­ment becomes a huge community-​organizing activ­ity of tak­ing from who are pow­er­less or out-​of-​favor and giv­ing to those who are liked. (Of course, those real­lo­ca­tions of slices also have the effect of severely shrink­ing the size of the prover­bial pie and that’s the big­ger incen­tive prob­lem that Mr. Stew­art doesn’t understand.)

In that regard, we ask: what are the odds that the gov­ern­ment would act on behalf of a gen­eral and dif­fuse group of tax-​payers rather than pan­der to special-​interests of orga­nized busi­ness man­age­ment or labor, etc? We’d put it close to zero and use as evi­dence the polit­i­cal causes of the cur­rent eco­nomic cri­sis, includ­ing Congress’s insis­tence to lend to the uncreditworthy.

We’re get­ting tired; so, rather than dis­sect the remain­ing third of his col­umn, we’ll note that Mr. Stew­art also calls for increased spend­ing on edu­ca­tion, the arts, and infra­struc­ture, includ­ing pour­ing money into pub­lic trans­porta­tion, par­tic­u­larly between air­ports and cities. Pre­sum­ably, he flies a lot and wants us to sub­si­dize his busi­ness trips. In addition, it would seem that he attends unpop­u­lar exhibits and per­for­mances that can’t sup­port themselves.

Many oth­ers have debunked the myth that increases in expen­di­tures improve edu­ca­tion; so, we won’t com­ment on that. We’re more inter­ested learn­ing why we should sup­port his lifestyle? Let him pay for his own bad art.

Finally, he men­tions “trans­parency,” which seems to be this fourth quarter’s buzz­word. Coin­ci­den­tally, although in a slightly dif­fer­ent con­text, in a post ear­lier today, we crit­i­cized the many recent calls for increased trans­parency of finan­cial state­ments and finan­cial infor­ma­tion, par­tic­u­larly as it relates to mortgages.

Those calls and Mr. Stewart’s pre­scrip­tions have much in com­mon, but that com­mon­al­ity involves nei­ther com­mon sense nor smarts. Instead, it is a shared and rather sim­plis­tic, pix­e­lated and chunky view of the world that per­mits pre­scrip­tion with­out thought. That’s not what we want from our physi­cians or com­men­ta­tors, but per­haps we deserve no better.

Recently, we’ve seen many op-​ed essays call­ing for more trans­parency in finan­cial state­ments, par­tic­u­larly with respect to mortgage-​related secu­ri­ties. Many of these essays have been writ­ten by famous and esteemed indi­vid­u­als or their staffs.

In our own idio­syn­cratic, round-​about way, we’ll explain the empty silli­ness of such argu­ments, and we begin by crit­i­ciz­ing the notion that “more is always better.”

Too Much Infor­ma­tion: Unfor­tu­nately, we’ve not read a sin­gle essay that con­tained an intel­li­gent, con­crete argu­ment for why more trans­parency is bet­ter than less – as if trans­parency, in and of itself, is a good (or is inher­ently good).

More pre­cisely, in all of these arti­cles, the value of trans­parency is assumed, and the assump­tion seems to be implicit and sub­con­scious (uncon­scious?) rather than some­thing arrived at via seri­ous delib­er­a­tion. (Hint: we can’t recall any of these essays that bother to define trans­parency. Pre­sum­ably, it is like pornog­ra­phy: you know it when you see it.)

In that half-​assed way, these recent prompts for more trans­parency have much in com­mon with the slightly older admo­ni­tions to elim­i­nate mark-​to-​market account­ing.¹

In their the­o­ries, many econ­o­mists – includ­ing, yours truly – have shown that more trans­parency, which often means more pre­cise infor­ma­tion, is not always bet­ter than less; in fact, it can make things strictly worse. Such seem­ingly patho­log­i­cal results are actu­ally rather com­mon in a vari­ety of social set­tings, includ­ing some markets, and arise for a num­ber of reasons, including risk-​sharing and incen­tives, where more infor­ma­tion can affect an agent’s behav­ior and actions or efforts thereby reduc­ing social wel­fare and/​or exac­er­bat­ing incen­tive problems.

For exam­ple (and this is a gross gen­er­al­iza­tion of the results with­out spec­i­fy­ing any of the nec­es­sary assumptions) in Kan­odia, Singh and Spero (JAR, 2005), we show that it is bet­ter to keep two unknown vari­ables as unknowns rather than know only one with per­fect pre­ci­sion. Think of it in the fol­low­ing way: sup­pose there are two ran­dom vari­ables – one that is some­what in the person’s con­trol and the other, which is not.

If the one under his influ­ence is known per­fectly, he’ll overem­pha­size it. If the other one is known per­fectly, then he’ll right­fully con­clude that the noisy sig­nal of his effort will be over­looked in favor of the other vari­able so he’ll do lit­tle. The for­mer cre­ates over-​exertion and the lat­ter cre­ates under-​exertion and both are socially dam­ag­ing; thus, one can find a happy medium in less extreme cases where nei­ther vari­able is known with total pre­ci­sion. (It should remind one of Goldilocks.)

Now, let’s be very clear that one need not be an econ­o­mist to know that more infor­ma­tion or trans­parency is not always bet­ter. For exam­ple, how does the reader answer ques­tions from a spouse, rel­a­tive, or friend when asked some­thing like, “Do you like my new hair­cut?” or “Does this dress make me look fat?”

In addi­tion, there are other cases where another party reveals per­sonal details with too much pre­ci­sion. In fact, we as a soci­ety have the col­lo­qui­al­ism, “Too much infor­ma­tion!” for just such cases where you’ll never again look at the revealer in the same man­ner and sub­se­quently rue­fully won­der, “why did they have to tell me that?”

Details Are Not Infor­ma­tion: this is a par­tic­u­larly apt time to repeat our admo­ni­tion that details are not infor­ma­tion. Back in April, we posted a long essay on the dif­fer­ence between details and infor­ma­tion or use­ful facts. (Use­ful facts are ones that might cause a deci­sion to change as the fact is real­ized.) Our point in that essay was to dis­tin­guish between keep­ing track of a lot of nec­es­sary data – as in data pro­cess­ing – and the quite dif­fer­ent task of pro­vid­ing use­ful infor­ma­tion to decision-makers. If one leaves sys­tems design to sys­tems peo­ple, one will likely get the for­mer and not much of the lat­ter. More­over, if the decision-​maker can’t design the sys­tem – not the pro­gram­ming – then his or her com­pe­tence at decision-​making should be jus­ti­fi­ably questioned.

The same dis­tinc­tion between details and infor­ma­tion holds true with finan­cial assets, too. More trans­parency can mean an inun­da­tion of book-​keeping and account details, which may pro­vide no infor­ma­tion or which may require expert judg­ment to (sift through to) become infor­ma­tion. In either case, the recip­i­ent of the data dump may not “see the for­est for the trees.“² So, one may have all the facts, but no abil­ity to orga­nize them – much like a child writ­ing a term paper.

And, that, of course, illus­trates the silli­ness of call­ing for more trans­parency for mortgage-​related secu­ri­ties. The big­ger prob­lem is that with every datum about every mort­gage in a pool, there is still no easy way to value them.

The issue isn’t the details, it is how to com­bine cur­rent and past details to deter­mine value and risk in the future, and it is very likely a per­fect method is unknow­able. So…

Value Matters, BUT There’s No Trans­par­ent Way to Find It: let’s illus­trate the notion in to a fairly high level of detail (for a blog post). We’ll ignore the “water­fall” aspect of real mortgage-​backed secu­ri­ties and CDOs where dif­fer­ent classes of secu­rity hold­ers have dif­fer­ent pri­or­ity claims on the cash flows because those claims are not the con­found­ing fac­tors – the intere­la­tion­ships of the mort­gages are.

So, imag­ine a pool of T thou­sand mort­gages going down the first col­umn of a spread­sheet. Fur­ther, sup­pose that the next 360 columns rep­re­sent months, m, so, the row t and col­umn m inter­sec­tion is the amount of cash received from bor­rower t in month m. Now that cell will actu­ally be a func­tion of any num­ber of fac­tors, includ­ing inter­est rates which affect whether the mort­gage is repaid early; the person’s wealth and income which deter­mine whether the bor­rower declares bank­ruptcy, the rela­tion­ship between the value of the col­lat­eral and the loan bal­ance, etc. We could go on and on, but the point is that each cell could take any num­ber of val­ues depend­ing upon many dif­fer­ent factors.

One page of the spread­sheet would then rep­re­sent one entire sce­nario of how cash is received from all T thou­sand mort­gages over the next thirty years.

At issue for val­u­a­tion (and risk mod­el­ing) is how to com­bine out­comes across all mort­gages. The cells are clearly related within a row, i.e., a borrower’s sta­tus in one month will affect cash flows in later months.

But, cash flows are also related within columns – phe­nom­ena, like a hur­ri­cane, may con­tem­po­ra­ne­ously affect more than one bor­rower – and across columns, too. For exam­ple, someone’s default in month m may make another’s default in month m + n more likely. So, the big­ger issue is: how does one relate bor­row­ers across time and space to arrive at a dis­tri­b­u­tion of cash flows. (Note: we mean “space” lit­er­ally because com­mu­nity and regional effects mat­ter – the inter-​row action, sometimes.)

One could gen­er­ate any num­ber of sce­nar­ios or pages, but, of course, the issue for val­u­a­tion (and risk) are which com­bi­na­tions in the numer­ous T x 360 grid are more (or less) likely (and how wide is the range of pos­si­ble outcomes)?

In other words, the prob­lem lays with deter­min­ing the joint dis­tri­b­u­tions across bor­row­ers and time. As we see it, there is no cor­rect method, but there is an infin­ity of incor­rect meth­ods, espe­cially ones that rely only on his­tor­i­cal rela­tion­ships, par­tic­u­larly very short histories.

Those incor­rect meth­ods include many that were imple­mented in recent years. As we see it, many of those meth­ods were imple­mented because they were solv­able, not because they were accu­rate. Unfor­tu­nately, those weak­nesses (inac­cu­ra­cies) were obscured by the rel­a­tive calm­ness of the mar­kets, includ­ing the near-​Ponzi-​like schemes of dif­fer­ent banks buy­ing the secu­ri­ties to re-​securitize them yet another time.

So, we ask those writ­ers urg­ing more trans­parency: exactly how would it help us find a price in the above exam­ple? Our illus­tra­tion high­lights the rea­son why there is a lack of buy­ers. There are data aplenty. What is lack­ing is a quan­tifi­able notion of the future.

That, dear reader, is why we devel­oped and wrote about an alter­na­tive solu­tion to TARP. One that involved the use of invest­ment tax cred­its or cash-​basis account­ing (to per­mit the imme­di­ate expense of the pur­chase price) to sub­si­dize and cush­ion the risk of pur­chas­ing these con­glom­er­a­tions of cash flows. It would pro­vide pri­vate buy­ers with an imme­di­ate ben­e­fit of 30% — 40% of the pur­chase price, which seems large enough to per­mit room for error.

As always, we encour­age vis­i­tors to read our essay, Uncer­tainty Man­age­ment, which dis­cusses the notions of mea­sur­a­bil­ity (quan­tifi­a­bil­ity) and immea­sur­a­bil­ity by dis­tin­guish­ing between the broader idea of uncer­tainty and the nar­rower idea of risk. In that regard, the num­ber and cost of mis-​specification errors related to our ongo­ing cri­sis may be the great­est in any period in history.

We’ll prob­a­bly edit this again in the near future.

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