Spero Consulting

Posts Tagged ‘uncertainty management’

We Missed It a Few Months Ago

On the front page of the The ‘Money & Invest­ing’ sec­tion of today’s edi­tion of The Wall Street Jour­nal, there is an arti­cle enti­tled, At SEC a Scholar Who Saw It Com­ing.

The arti­cle is about Henry Hu, who man­ages the newly-​formed Risk, Strat­egy and Finan­cial Inno­va­tion divi­sion at the SEC.

Though he sounds like a good guy, we don’t know much about Mr. Hu, but that’s not why we’re writ­ing. It also men­tions that in Novem­ber, Mr. Wu hired Richard Book­staber to lead staff train­ing and data analy­sis, and that is a good thing. (The print ver­sion incor­rectly iden­ti­fies him as David Bookstaber.)

If you haven’t heard of Mr. Book­staber, he has much knowl­edge and much expe­ri­ence work­ing at large trad­ing firms and hedge funds. In fact, he takes “par­tial credit” for a few of the past crises, includ­ing the Crash of 1987.

Mr. Book­staber is also the author of the 2007 book, A Demon of Our Own Design, which dis­cusses those crises, his roles in them, as well as his approach to risk (and uncer­tainty) management. We highly rec­om­mend the book to any­one in the finan­cial ser­vices indus­try and within par­tic­u­lar roles in other indus­tries, too. For exam­ple, we recently rec­om­mended it to the chief of secu­rity at a large, U.S. based, multi­na­tional that oper­ates fac­to­ries and plants through­out the world.

In the book, Mr. Book­staber makes the excel­lent point that overly-​rigid or overly-​complex risk mon­i­tor­ing and safety sys­tems can actu­ally increase the prob­a­bil­ity of fail­ure and the loss given fail­ure and dis­cusses it both within and out­side of finan­cial ser­vices. (Recently, we made sim­i­lar points in our analy­sis of intel­li­gence fail­ures and bad infor­ma­tion sys­tem design.)

Besides read­ing the book, we also encour­age our read­ers to visit Mr. Bookstaber’s blog, espe­cially to read his tes­ti­mony before Con­gress – the links in the right-​hand col­umn). It is well-​written and not overly-​technical.

Regard­ing risk and uncer­tainty man­age­ment, Mr. Book­staber makes points sim­i­lar to ours, with the main inter­sec­tion being that not every cri­sis is pre­dictable, but thought­ful­ness and con­tin­gency analy­sis goes a long way to mit­i­gat­ing crises. In fact, prepar­ing (rather) gen­eral responses to pos­si­ble, spe­cific crises can pre­pare one for com­pletely unknown ones, too. (See our essay on uncer­tainty man­age­ment and almost any of our posts cat­e­go­rized as uncer­tainty or risk. By the way, we really like our post with the tongue-​in-​cheek title, The Role for Sur­vival­ists and Depres­sives in Uncer­tainty Man­age­ment, because we think that per­son­al­ity traits like skep­ti­cism and pes­simism are under-​weighted and under-​valued in most risk man­age­ment hir­ing process.)

The best that we can tell, we tend to place more empha­sis on stress-​testing and sce­nario analy­sis than he does, but that’s because we think that imag­i­na­tion, like skep­ti­cism, is under-​estimated, too.

One topic where we do dis­agree is his insis­tence that every­one (that mat­ters) under­stands the lim­i­ta­tions of the use of nor­mal dis­tri­b­u­tions in risk mea­sures like VaR (Value at Risk). To explain, 2e’ll try to be con­cise but thor­ough but will err on the side of brevity.

It is well-​known – though not wholly-​agreed-​upon – that assum­ing nor­mal­ity (or log-​normality) mis-​specifies mod­els of returns, and we think that many ‘quants’ do know that, but they use those assump­tions nonethe­less, and that’s for a few reasons:

1. There is no other choice, or no other tractable choice.
2. Depend­ing upon the con­text, it may not mat­ter much.
3. Ease of cal­cu­la­tion and effort. (This is dif­fer­ent than (1).)
4. As a way to reduce mea­sures of risk characteristics.
5. Ease of com­mu­ni­ca­tion to others.

We are very sym­pa­thetic to the first two rea­sons, and being some­what lazy, we are also sym­pa­thetic to the third. However, the fourth rea­son hints at cyn­i­cism and greed and, depend­ing upon who is using the mea­sure, it can be very destruc­tive. Also, if such assump­tions are used for oppor­tunis­tic rea­sons, that can indi­cate the tra­di­tional weak­ness of risk man­age­ment vis-​a-​vis revenue-​generating departments.

The fifth rea­son hints that maybe – just maybe – not every­one under­stands the cal­cu­la­tions and assump­tions and their flaws.

We have dealt with very high-​level man­agers at very large firms who are quite igno­rant of the basic char­ac­ter­is­tics of nor­mal dis­tri­b­u­tions. To their credit, a few were quite will­ing to admit as much. (They are the least harm­ful of the bunch.) But given those expe­ri­ences, it is dif­fi­cult to believe that most board direc­tors under­stand the arith­metic; so, it is dif­fi­cult to accept that all senior man­agers (at such firms) under­stand the cal­cu­la­tions; so, it is dif­fi­cult to believe that all other man­agers, traders, sales­men, and investors are knowl­edge­able and well-​informed. (And, boy, could we tell you sto­ries!) The fact that, as Mr. Book­staber points out in his tes­ti­mony, such top­ics appear in text­books is a non sequitur.

When one com­bines cyn­i­cism with mis­com­mu­ni­ca­tion – whether pur­pose­ful or not – there’s a good chance that the orga­ni­za­tion is bear­ing more uncer­tainty and risk that it imag­ines or mea­sures, and that’s not good. So, that fact that “every­one knows” some­thing – even if it that some­thing is true – doesn’t mean that it’s not abused. For exam­ple, pick any vice that every “knows” is wrong but folks do it any­way. The abuse of ille­gal drugs and obe­sity are two anal­o­gous exam­ples. (Oh, by the way, gov­ern­ment reg­u­la­tion doesn’t seem to help much there, either.)

Finally – almost – these last two issues hint at incen­tive prob­lems – both moral haz­ard and adverse selec­tion – that exist within firms, and we’ve writ­ten exten­sively about that, too, e.g., Incen­tives and the Finan­cial Cri­sis and many more.

In sum, while we have never met Mr. Book­staber and likely never will, we are encour­aged to see the SEC hire such a knowl­edge­able and wise per­son. We wish him the best in his new role. (We only wish that we would have done so a few months earlier.)

The physi­cist Michio Kaku has a short opin­ion col­umn in Thursday’s edi­tion of The Wall Street Jour­nal: Jupiter Gets a Black Eye. In it, he men­tions the Jupiter’s recent col­li­sion with a comet or aster­oid – it cre­ated a fire­ball as big as the earth – and then dis­cusses our planet’s vul­ner­a­bil­ity to rel­a­tively large and unknown space objects.

We like the col­umn because it pro­vides a nice – though not com­plete – ana­log of risk man­age­ment at finan­cial insti­tu­tions. Actu­ally, this is one instance where the gov­ern­ment may do it bet­ter. (Wow, we can’t believe that we wrote such a sentence!)

It’s likely that any­one with a web browser and the sophis­ti­ca­tion to access our site knows that there is a dan­ger that satel­lites and space debris within earth’s orbit may crash down upon them. For the most part, those risks are rel­a­tively well-​understood. Gen­er­ally, their effect would be like an idio­syn­cratic finan­cial risk to, say, a par­tic­u­lar firm. All else equal, the satel­lite or its pieces would hit a par­tic­u­lar small region and have lim­ited impact and impli­ca­tions; pos­si­bly, dis­as­trous to a few, but prob­a­bly not to very many. Of course, there is always a pos­si­bil­ity that such a nat­ural (or nearly nat­ural) dis­as­ter could start a chain-​reaction and have far-​ranging polit­i­cal, eco­nom­ics, and social impli­ca­tions beyond that of small, geographically-​isolated incident.

Out­side of the earth’s orbit – but within the solar sys­tem – are about 5,000 near-​earth objects (NEOs) that have also been categorized. These are items reside within the solar sys­tem and orbit the sun, but their orbits may inter­sect with the earth’s orbit and even­tu­ally inter­sect with the earth. Unfor­tu­nately, solar orbits not all con­cen­tric cir­cles or elipses.

Some of the NEOs are small – like man-​made satel­lites in solar orbit – but oth­ers are huge and could cause seri­ous dam­age if not com­plete anni­hi­la­tion of the earth (and its inhab­i­tants). Just look at the sur­face of the moon for some extrater­res­trial evi­dence. The earth has been hit by such items, too, and they’ve been very destruc­tive, e.g., the Tun­guska event. Impacts of smaller items could be viewed as idio­syn­cratic risks, whereas the larger ones – like giant vol­ca­noes that could cover the earth in dust – would be more like sys­temic risks that affect every­one. Over­all, it seems that gen­er­ally, these near-​earth objects are suf­fi­ciently well-​understood that they can be mod­eled with a suf­fi­cient degree of (pre­dic­tive) con­fi­dence. (That if some­thing bad is going to hap­pen, we’ll likely know about it.)

The last cat­e­gory of threats involves extra­so­lar ones. Their num­ber, size, and other char­ac­ter­is­tics are unknown, e.g., whether they have reg­u­lar or irreg­u­lar orbits (or tra­jec­to­ries). They are things things that could crash into the solar sys­tem and and earth with­out warn­ing. Those threats cre­ate plenty of uncer­tainty, but no risk because there is no way to mea­sure them (and risk is noth­ing more than mea­sur­able uncertainty).

That’s not the biggest dif­fer­ence between threats from space and finan­cial calami­ties. Despite what bad mod­el­ers (and bad risk man­agers (and bad chief exec­u­tives)) may tell you, there is a sub­stan­tial amount of immea­sur­able uncer­tainty in trad­ing and invest­ing activ­i­ties, too. The losses asso­ci­ated with either type of uncer­tainty can be indi­vid­u­ally or col­lec­tively devastating.

No, the biggest dif­fer­ence is that with enough mon­i­tor­ing devices, it is pos­si­ble to cat­e­go­rize those phys­i­cal threats and their causes and assign prob­a­bil­i­ties to them. We doubt that it will ever be the case with the coun­ter­vail­ing forces of greed and fear and their psy­cho­log­i­cal and emo­tion causes. That doesn’t mean that uncer­tainty man­age­ment–as it per­tains to the finan­cial mar­kets – is a hope­less cause: only that one should be care­ful and aware that unpre­dicted and unfore­seen and unimag­ined events can indeed happen.

Finally, note that like finan­cial mar­kets and the recent cri­sis, solu­tions to poten­tial threats could be worse than the threat itself. Mr. Kaku men­tions Hollywood’s solu­tion, à la Armaged­don, of attempt­ing to explode a large comet into a bunch of small pieces would make things worse. That would be like hit­ting the earth with a shot­gun blast, rather than with a rifle – pos­si­bly sys­tem­atiz­ing a hard, but idio­syn­cratic risk. That wouldn’t be fun.

We are in the midst of writ­ing a rather long post on the sim­i­lar­i­ties between teenage girls with low blood sugar and daily and intra-​day changes in equity prices. Namely, one can see huge swings in behav­ior, atti­tudes, and mood caused by seem­ingly very minor under­ly­ing events, e.g., “she looked at me the wrong way.” The “she” in this case being an eight-​year-​old sister.

How­ever, we couldn’t com­plete that post because another thought keeps divert­ing our (lim­ited) atten­tion from it.

We were dri­ving with the Chair­man ear­lier today when she men­tioned that the neigh­bor­ing county was hold­ing its fair, and that it was one of the largest county fairs in the state. She went on to explain when­ever she thought of fairs and state fairs she would think of the book, Charlotte’s Web. (We’ve never read it because it was a girls’ book in our youth, and we did not read girls’ books: not then, not now.) As she explained, she par­tic­u­larly liked the chap­ter in which Wilbur the Pig goes to the State Fair, and Tem­ple­ton the Rat tags along in the pig’s cage.

As she explained it, when the rat inves­ti­gated his new sur­round­ings, he thought that he had reached par­adise. He was amazed at the wealth of del­i­ca­cies that he could find on the ground – prob­a­bly things like pop­corn and corn dogs and ice cream cones and maybe deep-​fried Snick­ers bars.

Upon hear­ing that, a ques­tion came imme­di­ately to mind: so, did he stay there?

See, we could imag­ine the rat believ­ing that he had reached the prover­bial land of milk and honey – in this case, half-​eaten corn dogs and ice cream cones as far as the eye could see. It would seem to be an almost lim­it­less sup­ply. Except, except for the fact that state fairs only last for a week or two.

If he decided to stay at the fair­grounds after his swin­ish friend returned to the farm – if that’s where the pig went – then it could eas­ily seem to have been the best deci­sion of his life – for a week or two. Until the cleanup crews came and swept the refuse away, and until he began to face the fol­low­ing 50 weeks of depri­va­tion and hunger.

Despite its com­pletely deter­min­is­tic and cycli­cal nature, the “great bust” or ” great depres­sion” or “great famine” or what­ever phrase he would have used to described the clos­ing of the fair, would have seemed com­pletely unpre­dictable and ran­dom. Tem­ple­ton and his other rodent friends, could eas­ily ask, “who could have ever pre­dicted it? or “how could it be my fault?” Of course, it could be that things that seem to be too good to be true, often are.

Now, we are not com­par­ing the recent (and ongo­ing) finan­cial cri­sis with our imag­ined sce­nario of Tem­ple­ton the Rat’s life. In our mind, eco­nomic crises tend to have endoge­nous causes, i.e., they erupt from within the sys­tem – not from an exter­nal source like a nat­ural dis­as­ter or in this case, the pre­dictable end of a two-​week fair.

How­ever, we do think the sce­nario is instruc­tive. To Tem­ple­ton the Rat, the destruc­tion of his new envi­ron­ment would have seemed like a unpre­dictable tsunami. He wouldn’t have known when or if the good times – the fair – would end, and he wouldn’t have known what he didn’t know, i.e., very impor­tant char­ac­ter­is­tics of his environment.

It’s that aspect that is instruc­tive, and it’s why we think that trad­ing and invest­ing firms should increase the scope of their risk man­age­ment func­tions to the broader func­tion of uncer­tainty man­age­ment. “Uncer­tainty” includes the explicit real­iza­tion that (1) not all ran­dom­ness is mea­sur­able risk and (2) seem­ingly incom­pre­hen­si­ble and uncon­sid­ered bad things can happen.

Note how­ever, that just because such things are (cur­rently) incom­pre­hen­si­ble doesn’t mean that (i) that can’t be pro­tected against and (ii) they can’t even­tu­ally be imag­ined through cre­ativ­ity and rea­son. The for­mer is true because ade­quate pro­tec­tion against known harms can also pro­tect against unknown ones; putting your house on stilts pro­tects against known sea­sonal flood­ing and unknown tsunamis. The lat­ter is true because that is the nature of human progress and the expan­sion of knowl­edge through exper­i­men­ta­tion and con­tem­pla­tion: think of humanity’s rel­a­tively recent dis­cov­er­ies of bac­te­ria and viruses. Inter­ested par­ties look­ing for more should read our essay, Uncer­tainty Man­age­ment or our tongue-​in-​cheek post, The Role for Sur­vival­ists and Depres­sives in Uncer­tainty Man­age­ment.

Finally, please note that we chose our title care­fully. It’s a play on the line from the Robert Burns poem, To a Mouse, On Turn­ing Her Up in Her Nest with the Plough. We Angli­cize the line as: “the best laid plans of mice and men often go awry and leave us noth­ing but grief and pain.” We’d add that less thought­ful plans often don’t turn out that well. Read the entire poem on our quotes page.

Despite a few inter­est­ing weeks of activ­ity in the world, we have not posted much lately. That’s because we’ve had a vari­ety of com­puter prob­lems at world head­quar­ters. We woke up last Wednes­day morn­ing to a BSoD or Blue Screen of Death on our desktop/​network server. Our West­ern Dig­i­tal Rap­tor hard drive had failed. It was unbootable and inaccessible.

We replaced it the fol­low­ing day with a big­ger and slightly faster VelociRaptor.

At the same time, we decided to upgrade from Win­dows XP (Media Cen­ter) to Vista Ulti­mate. As we wrote a few months in Walt Moss­berg is Wrong, Again, in our expe­ri­ence Vista tends to be more sta­ble and faster than Win­dows XP. That’s not the sen­ti­ment (or should it be sed­i­ment?) that you’d get from dear old Walt or a vari­ety of other writ­ers or blog­gers, but skep­ti­cism is in order when read­ing “stuff” on the web (except, here, of course, where we have enough skep­ti­cism for our­selves and every­one who visits).

We must admit to mak­ing a mis­take when we pur­chased the new oper­at­ing sys­tem; we bought the 64-​bit ver­sion instead of the 32-​bit ver­sion that we wanted. When it arrived and we noticed the “64”, we fig­ured we’d give it a try, and we have been very pleas­antly sur­prised. Per­haps it’s the new hard drive, but the 64-​bit ver­sion is fast. It is sta­ble, and it has run every 32-​bit appli­ca­tion that we have loaded.

Many blog­gers and writ­ers have com­plained about the lack of 64-​bit dri­vers, but many of those com­plaints seem to be sev­eral years old, i.e., from 2006 or so. So far, we’ve had no prob­lems installing any of our hard­ware, includ­ing an older USB, HDTV tuner; an Epson R1900 printer, and a Canon MP830 mul­ti­func­tion device. We have one rather eso­teric piece of equip­ment left to install – a Graph­tec Robo Pro 5000 – but based upon what we read on-​line (oh dear) we think it will work, too.

Vista 64-​bit pro­vides a few other advan­tages over 32-​bit Win­dows, too. We’re finally able to use all 6GB of our installed mem­ory, so there is less hard-​drive caching, and 64-​bit oper­at­ing sys­tems are sup­pos­edly less sus­cep­ti­ble to 32-​bit viruses. (We have no per­sonal expe­ri­ence with that claim, but it makes sense to us.)

Despite being dis­rup­tive and time-​consuming, the crash wasn’t a total loss. Our sys­tems are stronger and bet­ter than they were. (Hah! Don’t you wish the same were true of the finan­cial system!) After almost of week of use, we only wish we had made the same “mis­take” dur­ing the recent pur­chase our two portable workstations.

Speak­ing of which, unfor­tu­nately, the desktop’s hard drive fail­ure was only 0ne-​half of our hard drive problems.

For a few weeks, our M4400 lap­top has been behav­ing badly with fre­quent, unex­plained crashes. After we fin­ished repair­ing the desktop, the con­di­tion of laptop’s hard drive wors­ened; how­ever, unlike the desk­top drive, the lap­top drive isn’t com­pletely dead, but it quite a nuisance.

Now that the replace­ment hard drive has arrived from Dell, we’ll spend the rest of the day rein­stalling our pro­grams. We should be back to post­ing our view­points either tonight or tomorrow.

By the way, we’re quite happy to have installed Nor­ton 360 backup. It worked auto­mat­i­cally and well on both machines, and spared us a lot of mis­ery and irri­ta­tion and time and money.

There’s an excel­lent opin­ion col­umn in yesterday’s (May 28) edi­tion of The Wall Street Jour­nal. It is Crazy Com­pen­sa­tion and the Cri­sis by Alan S. Blinder.

Why do we write that it is “excel­lent” the dear reader may ask?

Well, for the obvi­ous (and self-​serving) rea­son that we have been writ­ing the same cri­tiques on these pages for much of the past year or so.

Mr. Blinder iden­ti­fies sev­eral prob­lems that cre­ated the poten­tial for the cri­sis and its sub­se­quent real­iza­tion.¹ We will cat­e­go­rize the prob­lems that he iden­ti­fies as:

1. Wrong legal form/​organization struc­ture for some firms,
2. Incom­pe­tent boards, and
3. Lax con­trols and poorly-​designed incentives.

He treats them in a dif­fer­ent order than we list them; we’re going from top-​to-​bottom, which is con­sis­tent with Our Con­trol Frame­work. Clearly, the three cat­e­gories are related. For exam­ple, see our pop­u­lar post, SOX’s Roles in the Finan­cial Cri­sis of ‘08, which hits on all three top­ics, and crit­i­cizes gov­ern­ment reg­u­la­tion to boot. In our mind, they all pro­vide evi­dence of the fallen nature of man. (We’re not com­plain­ing about that nature. We accept it in our­self and, to a lesser extent, in oth­ers. We’re only try­ing to profit from it.)

Wrong Legal Form/​Organization Structure

We wrote about this on Sep­tem­ber 26, 2008, when we asked Will Invest­ment Banks Go the Way of the Dinosaur? In that post we spec­u­lated that part­ner­ships may make a come­back because “They pro­vide con­trol mech­a­nisms and lev­els of over­sight and scrutiny that seem dif­fi­cult to dupli­cate in pub­lic corporations.”

Mr. Blinder made explicit what was implicit in our post: the dif­fer­ence between one’s level of risk-​taking when man­ag­ing OPM (Other People’s Money) ver­sus what he refers to as MOM (My Own Money), or one’s own money.² Those fac­ing unlim­ited per­sonal losses tend to be more con­ser­v­a­tive than those with lim­ited losses.

In Jan­u­ary, in a cri­tique of The Wall Street Jour­nal’s edi­to­r­ial board, What Did They Expect?, we wrote, “We also dis­agree with their [the edi­to­r­ial board’s] assess­ment that “com­pen­sa­tion lev­els are a busi­ness judg­ment made under the pres­sure of com­pe­ti­tion.” That might be true if the firms were part­ner­ships or oth­er­wise privately-​owned, there was no agency costs, and there was no self-​dealing, i.e., the firms were run by inde­pen­dent and knowl­edge­able boards.”

But with D & O (direc­tors’ and offi­cers’) insur­ance, the lim­ited down­side of losses severely decom­presses that so-​called “pres­sure of com­pe­ti­tion” for boards. More­over, share­hold­ers of bank hold­ing com­pa­nies (and other cor­po­ra­tions, too) implic­itly per­mit­ted man­agers to take greater risks. In fact, Mr. Blinder seems unwill­ing to blame share­hold­ers when almost every stock­holder was quite capa­ble of sell­ing their stakes. So, we have no sym­pa­thy for folks who wanted the oppor­tu­nity for large gains with­out bear­ing poten­tial lia­bil­i­ties if the firm.³

Incom­pe­tent Boards

While “Incom­pe­tent Boards,” may seem a bit harsh to some, we think that it is milder than many alter­na­tive and equally fair char­ac­ter­i­za­tions, and there is no short­age of evi­dence. See Direc­tors Are Faulted at Home Loan Banks for example.

Reg­u­lar read­ers will note that we often ask whether a party is igno­rant or cyn­i­cal, and in this case we’d pre­fer to believe that many direc­tors were unqual­i­fied to under­stand the uncer­tain­ties and risks asso­ci­ated with invest­ing and trad­ing, par­tic­u­larly with deriv­a­tives and other struc­tured prod­ucts. In some way, that seems more “decent” and eth­i­cal than the alter­na­tive: the cyn­i­cal and devi­ous behav­ior of under­stand­ing the poten­tial for loss but ignor­ing it due to one’s own lim­ited lia­bil­ity.⁴

For exam­ple, with the recent changes in the com­po­si­tion its board, Citi­corp has as much as admit­ted the lack of req­ui­site exper­tise of its past board. We’ve writ­ten about these top­ics in the past, par­tic­u­larly in: The Fail­ure of Boards to Direct, The Seventy-​Year-​Old Teenager, When the Going Gets Tough…Quit, and Idio­syn­cratic and Con­cen­tra­tion Risk, Again. (Update: within hours of pub­lish­ing this post, B of A announced that one of its direc­tors was resign­ing: see BofA Says Sloan Quits Board Seat. There was much spec­u­la­tion that it was due to gov­ern­ment pressure.)

Those (gen­er­ally weak and) incom­pe­tent boards per­mit­ted senior man­agers to main­tain the lax con­trols and poorly-​designed incen­tives about which we have often writ­ten, and here is a summary.

Lax Con­trols and Poorly-​designed Incentives

As Mr. Blinder notes, poorly-​designed incen­tives – pri­mar­ily via com­pen­sa­tion schemes – led to ex post “exces­sive” risk-​taking. We write ex post as in 20 – 20 hind­sight as in “there are mas­sive losses, so some­one must have done some­thing wrong,” but, in fact, we’re note using that logic. Instead, we note that there was no short­age of indi­vid­u­als warn­ing about the risk and uncer­tain­ties ex ante.

Unfor­tu­nately, many such folks were dis­missed either fig­u­ra­tively or lit­er­ally by senior man­age­ments. (It’s anal­o­gous to the SEC’s treat­ment of Harry Markopo­los. See Cas­san­dra, the SEC and Mr. Mad­off.) More­over, it is con­sis­tent with the per­spec­tive that risk man­agers gen­er­ate no rev­enue and are costs to be min­i­mized (and often voices to be ignored).

So, yes, traders (and their man­agers) took gam­bles because they bore (or thought they bore) lim­ited down­side risk but instead focused on the poten­tial for sub­stan­tial (enor­mous) com­pen­sa­tion rewards, but lax con­trols and igno­rance are big­ger issues than just poorly-​designed com­pen­sa­tion schemes because said traders were allowed to take those gam­bles with OPM.

That lack of con­trol has many facets, but can be sum­ma­rized in terms of as greed, igno­rance, and inse­cu­rity. Notice that, of course, those emotions/​human con­di­tions are always present, but pre­cisely the job of senior man­agers (and boards and own­ers) to design schemes and mech­a­nisms that take those as given and mit­i­gate them – rather than exac­er­bate them – while the orga­ni­za­tion attempts to achieve its objec­tive. (We’ll have more to say about that below.)

Igno­rance, and its rel­a­tive, inse­cu­rity, were cru­cial to the con­trol fail­ures. Few folks are will­ing to admit that some­thing is immea­sur­able or nearly impos­si­ble to quan­tify because that can be turned-​around and used against them as a per­sonal short-​coming:, e.g., “that’s just because he doesn’t know enough.” So, per­sonal inse­cu­rity and incen­tives often induce employ­ees to “take the easy way out” and endorse or embrace a sim­plis­tic and inap­plic­a­ble val­u­a­tion or risk model. 

For exam­ple, in early Novem­ber, we wrote The Under­state­ment of the Year! in response to an arti­cle in The Wall Street Jour­nal enti­tled, Behind AIG’s Fall, Risk Mod­els Failed to Pass Real-​World Test. While the entire post is rel­e­vant to this dis­cus­sion, we par­tic­u­larly like this extended excerpt:

The prob­lem, dear reader, is that few senior man­agers (and almost no board members) understand the val­u­a­tion and risk mod­els used for secu­ri­ti­za­tions, and many of the traders, con­sul­tants, and ana­lysts who wield such tools often suf­fer from, what one may call, “fram­ing” issues; we don’t mean that aspect of home con­struc­tion despite its recent relevance.

We mean that if one’s only tool is a ham­mer, then lots of things look like nails. The metaphoric ham­mer may be an intan­gi­ble Visual Basic or “C” pro­gram­ming algo­rithm, but the point remains the same; it’s just harder for senior man­age­ment to see what one is pound­ing in their cubi­cle, office, or trading-​floor seat.

To be sure, if any­one within most of the larger firms would have com­plained of the sys­tem­atic risk — and how every­thing could go bad all at once — and the inap­plic­a­bil­ity of the stan­dard mod­els, which gen­er­ally don’t per­mit such events, then that per­son most cer­tainly would have been told that they don’t know what they’re talk­ing about. Pos­si­bly, that they are unso­phis­ti­cated or too negative.

Ear­lier this week in Uncer­tainty: In God We Trust, we noted “Too many senior man­agers neglected their respon­si­bil­i­ties and per­mit­ted the sub­sti­tu­tion of cal­cu­la­tions for thoughts.” That as been a pet peeve of ours for quite some time and is the antithe­sis of our motto: thought before cal­cu­la­tion. See The Dif­fer­ence Between Risk and Uncer­tainty for a rel­a­tively short expo­si­tion of the issues.

Those dys­func­tional behav­iors were not nec­es­sar­ily mali­cious or anti-​social by intent, but does that mat­ter, espe­cially since thought­ful design of con­trol mech­a­nisms could have inhib­ited them? See Prin­ci­ples Lost and More, in which we con­trast Saint Thomas More’s actions in the 16^th cen­tury with the more recent actions of many less holy indi­vid­u­als prior to and dur­ing the Finan­cial Cri­sis; there’s a rea­son he’s a Saint and we’re not.

We’ve writ­ten much, much more on this topic, but as we noted in The Prob­lem of Induc­tion, we’re not under­es­ti­mat­ing the dif­fi­culty of the prob­lems faced by traders, struc­tur­ers, and risk man­agers. In fact, if any­thing, we’re overly con­ser­v­a­tive by stat­ing that not all uncer­tain­ties and losses can be quan­ti­fied and the prob­lems are much more dif­fi­cult than some sup­pose and/​or communicate.

What To Do?

Unfor­tu­nately, Mr. Blinder notices that there has been little-​to-​no struc­tural change in cor­po­rate gov­er­nance. He attrib­utes the dif­fer­ences in mar­kets – the illiq­uid­ity or lack of trad­ing – to fear, rather than to newly designed or revised con­trols, and that seems about right to us. As we noted last month in Learn­ing the Dif­fer­ence Between Risk and Uncer­tainty, or not, job descrip­tions and hir­ing require­ments for many trad­ing and risk man­age­ment posi­tions don’t seem to have changed; so, it doesn’t seem the firms have “re-​engineered” or redesigned their oper­a­tions or controls.

In Octo­ber, we wrote a tongue-​in-​cheek post about The Role for Sur­vival­ists and Depres­sives in Uncer­tainty Man­age­ment, but in all seri­ous­ness, hir­ing such per­son­al­i­ties and lis­ten­ing to them is one way to com­pen­sate for flawed risk models.

To be fair, we have read about a few firms, like UBS, that have changed their com­pen­sa­tion schemes to include fea­tures like claw­backs. See Claw­backs: the Good, the Bad, and the Ugly and Incen­tives at UBS and in Gen­eral. How­ever, it is not clear whether such changes have been thought­fully man­aged. As we men­tioned in Busi­ness Schools, Incen­tives, Uncer­tainty, and the Finan­cial Cri­sis, it seems that lit­tle has been done because: (1) such incen­tive prob­lems are very chal­leng­ing to solve, and (2) uni­ver­si­ties don’t do a par­tic­u­larly good job of train­ing busi­ness stu­dents to solve them. (Of course, for the right fee, we would be glad to help.)

So what to do?

Mr. Blinder calls for change, but doesn’t exactly explain how or what.

We’ve made sev­eral rec­om­men­da­tions in past, includ­ing this post from early Octo­ber: Elim­i­nate Pro­pri­etary Trad­ing at Insured Insti­tu­tions. Every­thing in it – and there’s a lot – holds up well, and we’ve not heard a com­pelling argu­ment against such a ban. As we wrote back then:

We’re com­pletely for the free-​market—more so than most bank man­agers — but until such insti­tu­tions for­sake their gov­ern­ment insur­ance, we’ll insist that they have an oblig­a­tion to the cit­i­zenry — through the gov­ern­ment — to behave in a respon­si­ble, low risk man­ner. If that gen­er­ates lower returns for them on aver­age, then so be it. That’s the nature of the risk-​return spec­trum and their legal and fiduciary responsibilities…

We think that such a ban is fea­si­ble and would sub­stan­tially mit­i­gate many of the risks that those banks by elim­i­nat­ing the (socially) unde­sir­able behavior.

Now, that (max­i­mum) risk-​seeking behav­ior is not uni­ver­sally unde­sir­able, but it is within sub­si­dized insti­tu­tions. We’re all for per­mit­ting “prop” struc­tur­ers and traders to oper­ate in unreg­u­lated part­ner­ships and hedge funds, and wish such orga­ni­za­tions the best of luck.

P.S. Although this post is rife with links, we’ve writ­ten much, much more about the top­ics of risk man­age­ment, incen­tives, and the cri­sis. Feel free to peruse the archives, and let us know if we’re wrong about any­thing – other than a few predictions.

P.P.S. As posted, this is rather long, and we’ll likely revise it in the near future as we dis­cover typos, etc.

Mary Anas­ta­sia O’Grady has a good inter­view with Richard Fisher, the pres­i­dent of the Dal­las Fed­eral Reserve, in this Saturday’s edi­tion of The Wall Street Jour­nal. It is called “Don’t Mon­e­tize the Debt”.

Reg­u­lar vis­i­tors of our site, who are sym­pa­thetic to our crit­i­cisms of the Fed; elected and appointed gov­ern­ment offi­cials; and finan­cial reg­u­la­tors, will find much with which to agree.

We’re writ­ing today to men­tion a few parts that are directly related to our site. First, per our motto in the header, Thought before Cal­cu­la­tion, Ms. O’Grady writes:

And finally, he says, there was the ‘math­ema­ti­za­tion’ of risk.” Insti­tu­tions were “build­ing risk mod­els” and rely­ing heav­ily on “quant jocks” when “in the end there can be no sub­sti­tute for good judgment.”

We’re not averse to math­e­mat­i­cal mod­els, and don’t mind get­ting paid to develop, ana­lyze, or val­i­date them, but we do agree with Mr. Fisher’s crit­i­cism. It must be done thought­fully. Too many senior man­agers neglected their respon­si­bil­i­ties and per­mit­ted the sub­sti­tu­tion of cal­cu­la­tions for thoughts. That being said,we think that it is nec­es­sary to add that even the best judg­ment doesn’t assure favor­able out­comes. That, unfor­tu­nately, is the nature of uncer­tainty, which we’ve writ­ten about any num­ber of times.

Sec­ondly, the penul­ti­mate para­graph describes a paint­ing by Anto­nio De Simone of a ship in a storm. Accord­ing to the arti­cle, Mr. Fisher has owned it for thirty years.

In the final para­graph, Mr. Fisher is quoted as say­ing “no math­e­mat­i­cal model can steer you through the kind of seas in that pic­ture there. In the end some­one has the wheel…On mon­e­tary pol­icy it’s the Fed­eral Reserve.”

As the reader can hope­fully see for him or her­self, we have an image of a sim­i­lar paint­ing in our header: Rembrandt’s Storm on the Sea of Galilee.

We pre­fer the helms­man on that boat to the quite fal­li­ble men and women at the Fed, who – as we see it – are try­ing too hard to “steer” the economy.

Per­haps oth­ers con­sid­ered sim­i­lar ana­logues when the nation’s offi­cial motto became “In God We Trust.” More­over, we hope that each time they notice it on our paper cur­rency and coins, our rep­re­sen­ta­tives and agents are reminded of the inher­ent uncer­tainty that they face – be it nat­ural or man-​made.

Recently, we’ve noticed a sub­stan­tial num­ber of vis­its referred by search engines from folks try­ing to under­stand the dif­fer­ence between risk and uncer­tainty. In fact, we have a post from April 20, with the tongue-​in-​cheek title of Learn­ing the Dif­fer­ence Between Risk and Uncer­tainty, or not.

In that post, we crit­i­cize finan­cial firms because they don’t seem to have changed their uncer­tainty man­age­ment tac­tics or method­olo­gies despite the mar­ket upheavals and shocks of the past few years. In fact, they still refer to the field as “risk management.”

How­ever, for those look­ing for some­thing a bit less ver­bose – but only a bit – we offer the fol­low­ing ital­i­cized dis­tinc­tion, which we’ve excerpted from that post.

The fol­low­ing para­graph is repet­i­tive, but read­ing dif­fer­ent phrases that have the same mean­ing is often the eas­i­est way to learn. That’s why many stu­dents learn bet­ter in lec­tures than by solely read­ing a text­book; the con­cepts are usu­ally men­tioned and pre­sented in a vari­ety of ways in class, whereas often the text­books strive for par­si­mony of expo­si­tion.¹

As usual, we point new read­ers to our essay, Uncer­tainty Man­age­ment, which details our per­spec­tive and phi­los­o­phy on these issues… The main point is that not all uncer­tainty is mea­sur­able, i.e., that mea­sur­able uncer­tainty, or risk, is a proper sub­set of uncer­tainty and unknow­ing. (In other words, spe­cific math­e­mat­i­cal con­di­tions must be met for uncer­tainty to be risk. So, uncer­tainty is a more gen­eral term, i.e., all risk involves uncer­tainty, but not every­thing that is uncer­tain is risky because not all uncer­tainty is mea­sur­able, which, again, has a spe­cific math­e­mat­i­cal def­i­n­i­tion that we don’t care to mention.)

The above def­i­n­i­tion of risk as quan­tifi­able uncer­tainty is due to Frank Knight, who devel­oped it in the early-​to-​mid 20^th century.

Uncer­tain phe­nom­ena are often mod­eled as risky events. While there are a host of other mis­takes that one can make in the mod­el­ing process, a huge spec­i­fi­ca­tion error is made when the phe­nom­e­non is uncer­tain and immea­sur­able, but it is treated as being mea­sur­able. That’s espe­cially bad in finan­cial and eco­nomic set­tings because such mod­el­ing errors tend to reduce or elim­i­nate the mod­eled – but not the real – chances of really bad things happening.

To be a bit more pre­cise, note that for some uncer­tain phe­nom­ena, a prob­a­bil­ity dis­tri­b­u­tion will not exist.

For oth­ers, a dis­tri­b­u­tion may exist, but its moments – which one may grossly think of as its com­mon sta­tis­tics – may not. For exam­ple, there are math­e­mat­i­cal func­tions that are prob­a­bil­ity dis­tri­b­u­tions, but which have no mean or vari­ance (so no stan­dard devi­a­tion, either). Many of them look a lot like Nor­mal dis­tri­b­u­tion and den­sity func­tions – i.e., they have a famil­iar bell shape like a Nor­mal den­sity – but their “tails” are “too fat,” and extreme events are hun­dreds or thou­sands or mil­lions of times more likely than with a Nor­mal dis­tri­b­u­tion. That dif­fer­ence in fre­quen­cies of out­ly­ing events is why para­me­ters like the expected value and stan­dard devi­a­tion don’t exist.²

The prob­lem in real life is that unless one is play­ing a struc­tured game of chance, one’s never quite cer­tain whether some­thing is uncer­tain but not risky, or whether it can indeed be quantified.

Reg­u­lar read­ers know that we often cite (1) St. James’ admo­ni­tion in his only epis­tle that one is like a “puff of smoke,” in the sense that they and their wel­fare are tem­po­rary, ephemeral, and uncer­tain; and (2) the Prob­lem of Induc­tion, which notes that regard­less of the time series of obser­va­tions, one can never be quite sure of the under­ly­ing ran­dom process.

That’s why we gave two sub­ti­tles to our essay Uncer­tainty Man­age­ment: (1) igno­ra­mus et ignor­a­bimus , which means “we do not know and will not know,” and (2) How Trad­ing is Like Play­ing in a Cul­vert on a Hot, Sunny, Sum­mer Day, although “trad­ing” can be gen­er­al­ized to any num­ber of activ­i­ties, includ­ing many social ones where, obvi­ously, behav­ior and some­times panic come into play.

Copy­right © 2009 Spero Consulting.

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Foot­notes:

When we crit­i­cize risk man­age­ment and dis­cuss our take on Uncer­tainty Man­age­ment (our essay is sub­ti­tled, “How Trad­ing is Like Play­ing in a Cul­vert on a Hot, Sunny, Summer Day”) we often cite our favorite quote from St. James’ only Epistle:

Come now, you who say, “Today or tomor­row we shall go into such and such a town, spend a year there doing busi­ness, and make a profit”—
you have no idea what your life will be like tomor­row. You are a puff of smoke that appears briefly and then dis­ap­pears.
Instead you should say, “If the Lord wills it, we shall live to do this or that”

It cap­tures the notion that not all ran­dom­ness is measurable.

That quote came imme­di­ately to mind when we heard of the cir­cum­stances of actress Natasha Richardson’s tragic and untimely death.

How many times in sports and in cars – and even cross­ing the street, especially in front of Port Author­ity buses – have we taken chances greater than those found in a begin­ners’ ski lesson?

“There but by the grace of God go I.” We don’t think that thought is incon­sis­tent with our ear­lier post on freewill.

May God rest her soul and bring peace to her fam­ily, her hus­band, her chil­dren and her friends as they try to under­stand the tragedy and accept their per­sonal loss, espe­cially its unfore­seen and unimag­in­able suddenness.

If you missed it on Mon­day (Jan­u­ary 26), L. Gor­don Crovitz had an inter­est­ing arti­cle in The Wall Street Jour­nal enti­tled Bad News Is Bet­ter Than No News. In our zeal to com­plete a project, we missed it when it was pub­lished, but now men­tion to the reader that it is worth their time.

We like it because it is con­sis­tent with much that we’ve writ­ten on these pages since the blog’s incep­tion, and espe­cially since last Sep­tem­ber. For exam­ple: no one knows what the mort­gage thin­gies are worth, the banks can’t lend because they don’t know how unsound THEY are, and the government’s actions have exac­er­bated the prob­lem by not pro­vid­ing any res­o­lu­tion to the uncer­tainty. Our solu­tions: nation­al­ize the worst banks and pro­vide gen­er­ous tax incen­tives to buy­ers of the thin­gies to resolve the uncertainty.

Mr. Crovitz men­tions: “Bankers now recall the fine print of VaR analy­sis, which is that it always includes low but real risk that some new ele­ment could make the his­tor­i­cal data a poor mea­sure of the future.”

This, of course, is the Prob­lem of Induc­tion, but unlike Mr. Crovitz, we don’t think that there is nec­es­sar­ily a low risk that past is not pre­dic­tive of the future. (We could pro­vide many cita­tions to our old posts, but point new read­ers to our essay, Uncer­tainty Management, Or, Ignoramus et ignorabimus, Or How Trad­ing is Like Play­ing in a Cul­vert on a Hot, Sunny, Summer Day. You can still drown from a flash flood on a sunny day. Actu­ally, you could do it even with­out a flood.)

Feel free to search other posts for com­plaints about boards and senior man­agers, but here’s a brief recap of what we think hap­pened: many expe­ri­enced traders left the big banks for more lucra­tive options, and they were replaced dur­ing times of unusual placid­ity by junior traders with­out much of a his­tor­i­cal per­spec­tive. Through lax con­trol, e.g., greed com­bined with poorly-​designed incen­tives, and because the folks who gen­er­ate (short-​term) rev­enue tend to win inter­nal argu­ments with risk man­agers – if those argu­ments even occur – the orga­ni­za­tions were over-​confident and unpre­pared for adversity.

More­over, the over-​reliance on math­e­mat­i­cal mod­els, which were per­fectly fine when noth­ing was hap­pen­ing, allowed the banks to avoid the con­sid­er­a­tion of tail-​events. Those event are so unpleas­ant to comtem­plate, any­way, so why bother?

To even hypoth­e­size that really bad things could hap­pen could be taken as a sign of weak­ness or incom­pe­tence by undis­ci­plined man­age­ments, and prob­a­bly were. (We think that is a silly per­spec­tive in the finan­cial mar­kets and in life in gen­eral, and it is one of the rea­sons that although we don’t hunt, we’re a huge pro­po­nent of sec­ond amend­ment rights. As we men­tioned pre­vi­ous posts, we view guns as the equiv­a­lent of deep, out-​of-​the-​money puts: they’re gen­er­ally an incon­ve­nience, but they do help man­age tail risk.)

Back to our story: bad stuff starts to hap­pen, and no one admits they’re wrong – prices will bounce back, right – or knows how to react (until every­one pan­ics at the same time). 

Mr. Crovitz quotes a late J.P. Mor­gan exec­u­tive as say­ing that traders should earn their big money for man­ag­ing the tail-​risk, not the typ­i­cal, daily volatil­ity, but that advice seemed to have been ignored in hopes of prof­its and con­tin­ued stability.

We think that another water anal­ogy is appro­pri­ate. Placid times are like slow mov­ing streams: it’s easy to wade out into the deep parts with­out too much con­cern. That’s despite the fact that algae thrives in such envi­ron­ments (and makes the bot­tom quite slip­pery). It doesn’t take much of a change in cur­rent – or even a mis­step – to turn that con­fi­dence into panic. More­over, it doesn’t even have to be your mis­step when there are other folks nearby grasp­ing at any­thing when they start to fall – espe­cially ones who over­es­ti­mated their own abil­ity or the stream’s con­stancy and over­stepped the bound.

Implied Under the Assump­tion of Risk Neutrality

We have sev­eral posts related to the cal­cu­la­tion of price-​implied default rates under the assump­tion of risk neu­tral­ity and sev­eral posts related to sim­ple CDS calculations.

Those posts have involved dis­crete, single-​period prob­lems, where there are only two dates of inter­est: today and a future date where an uncer­tain claim or cash flow will be real­ized, i.e., when bank­ruptcy would occur.

We’ve focused on binary mod­els and will con­tinue to do so here. In fact, to ana­lyze a two-​period prob­lem, we’ll just build upon our lat­est post from Decem­ber 2: Price Implied Default Rates.

We think that need­less detail obfus­cates the cen­tral points while pro­vid­ing no mar­ginal explana­tory power: either in a sta­tis­ti­cal or ped­a­gog­i­cal sense. So, we like to keep things simple.

Note that we’re pro­vid­ing exam­ples of sim­ple, reduced-​form mod­els à la Jar­row and Turn­bull (1995) or Hull and White (2000), not a struc­tural Mer­ton model like KMV. We’ll do that when we have the time.

In our Decem­ber 2^nd post, we con­sid­ered a risky, one-​year, zero-​coupon bond. We assumed a face value of $1,000, a risk-​free rate of 5%, and the risky bond’s yield to be 8%. We could have stated that last assump­tion as the bond has a price of $925.93.

From those assump­tions, and the addi­tional assump­tion that the owner of the bond would recover 60% of the face value, we cal­cu­lated the risk-​neutral-​model-​implied default rate of 6.94%.

Now the cal­cu­la­tion of that default rate depends upon all of the assump­tions, and obvi­ously the answer will vary with changes in any of the assumed vari­ables: the bond’s price or yield, the risk-​free rate, and the loss given default rate.

Obvi­ously, it also depends upon the applic­a­bil­ity of risk-​neutral val­u­a­tion, which allows us to impose two very impor­tant con­sid­er­a­tions (ver­sus real­ity). It allows us to (1) treat the bond’s price as the expected value of its cash flows, which is only valid if the cred­i­tor (in the model, not in real life) is risk-​neutral, and (2) use the risk-​free rate as the proper dis­count rate for a risk-​neutral per­son. Those assump­tions allow us to work with expected cash flows, rather than curvy pref­er­ences. We’ll focus on cal­cu­la­tions in this post and not on applicability.

Finally, the answer also depends upon our choice of prob­a­bil­ity func­tions. Here, the only uncer­tainty involves full pay­ment or not; so, that credit risk is eas­ily mod­eled as a binary func­tion, but it is impor­tant to note that risk-​neutrality does not imply a par­tic­u­lar prob­a­bil­ity func­tion. Once the ana­lyst has cho­sen from a fam­ily of dis­tri­b­u­tion func­tions, the assump­tion of risk neu­tral­ity will deter­mine (imply) par­tic­u­lar para­me­ter val­ues, but that is all. For the more math­e­mat­i­cally inclined, that is the change-​of-​measure that is referred to in the texts. (Prob­a­bil­i­ties are weights. Dif­fer­ent para­me­ter val­ues within a dis­tri­b­u­tion cause pos­si­ble events to be weighed dif­fer­ently; ergo, the mea­sure is changed.)

In this prob­lem, we’ll keep the same assump­tions as in our pre­vi­ous post for the first of our two peri­ods. So, here is the set­ting: We have two zero-​coupon, risky bonds issued by the same firm and each with a face value of $1,000: one matures in one-​year and the other matures in two years. Imag­ine that there are two risk-​free bonds, too.

The one-​year risky bond is described as above; so, it will have a price of $925.93. If that bond were risk-​free, it would have a price of $952.93. In a risk-​neutral model, the dif­fer­ence in prices is the present value of the expected loss (of the risky bond, of course).

The risk-​free rate in the sec­ond period is 7%. Note that there is no mar­ket risk – that is, no inter­est rate risk – so there is no evo­lu­tion of inter­est rates or any type of rate process in our hum­ble, lit­tle exam­ple. (We’re just mak­ing up num­bers to illus­trate a few basic ideas.)

The bond that matures in two years has a yield-​to-​maturity of 9.982%, which for all intents and pur­poses – and for every­one except the truly anal – is 10%.¹

As an aside, with our two sets of inter­est rates, we can cal­cu­late an over­all yield-​to-​maturity from our term struc­ture of for­ward, risk-​free rates, and for risky rates, we can deter­mine the struc­ture of for­ward rates from our risky yield curve.

Risk-​free yield-​to-​maturity: we don’t really need to cal­cu­late this, so you can skip it is you want, but if the risk-​free bonds are priced to earn 5% in the first year, and a two-​year bond is priced to earn 7% in the sec­ond year, then the geo­met­ric aver­age return for the zero-​coupon, risk-​free bond bet­ter be close to the arith­metic mean of 6%. That yield-​to-​maturity is simply:

[(1 + r₁)·(1 + r₂)]^1⁄₂ — 1 = [1.05·1.07]^1⁄₂ — 1 = 5.995%

So, the yield on a two-​year, zero-​coupon, risk­less bond is about 6%: just like we knew before we did the calculation.

Risky for­ward rate: now, given the risky yield-​to-​maturity is about 10% on the two-​year, zero coupon, bond, and given a first-​year risky rate of 8%, then the implied for­ward rate for the sec­ond period must be:

[(1 + 0.08)·(1 + r₂)]^1⁄₂ — 1 ≈ 10% implies r₂ = 1.1² /1.08 - 1 = 12%

So, if (and only if) the two-​year, risky bond yields (about) 10%, then its price is:

$1,000 ÷ 1.1² = $826.45 ≈ $826.72.

By the way, we’re off by 26¢ by using the easy 10% instead of the more pre­cise 9.982%, but the les­son is free; so, the reader really shouldn’t complain.

Notice that credit spread increased from 3% (8% — 5%) in the first year to 5% (12% — 7%) in the sec­ond. All things equal, we should expect that the risk-​neutral, price-​implied, default rate will increase, too. Let’s see if that happens.

Three Prob­a­bil­i­ties of Default (or default rates): when we move to a multi-​period prob­lem, we have to be care­ful to spec­ify the default rate to which we’re refer­ring. There are con­di­tional, mar­ginal, and cumu­la­tive prob­a­bil­i­ties of default, and that is true whether we’re dis­cussing actual (but unknown) prob­a­bil­i­ties of default or risk-​neutral-​implied prob­a­bil­i­ties of default like we’re doing here.

The con­di­tional prob­a­bil­ity of default for a period, t, is the eas­i­est notion to under­stand: given that the firm has sur­vived until the begin­ning of that period, it is the prob­a­bil­ity that the firm can’t pay its bills dur­ing the next inter­val of time; here, we’re using one year as the time inter­val. We’ll denote con­di­tional prob­a­bil­i­ties as p_t for every period t.

The mar­ginal prob­a­bil­ity of default is the prob­a­bil­ity that the firm will default in period t. Now, the firm only has the oppor­tu­nity to default in period t, if it hasn’t already defaulted; so, the mar­ginal prob­a­bil­ity con­sid­ers the prob­a­bil­ity of sur­viv­ing until that point and the con­di­tional prob­a­bil­ity of default. If p₁ is the (mar­ginal) prob­a­bil­ity of default in the first period, the (1 — p₁), then the mar­ginal prob­a­bil­ity of default is:

(1 — p₁)·p₂,

For our lit­tle prob­lem, we won’t intro­duce any spe­cial nota­tion for the mar­ginal prob­a­bil­i­ties of default.

Finally, the cumu­la­tive prob­a­bil­ity of default is the sum of all the mar­gin­als: p₁ + (1 — p₁)·p₂ in a two-​period prob­lem. We wrote about longer term cumu­la­tive prob­a­bil­i­ties of events in this post, Good Col­umn, Bad Math, where we talk about 100-​year floods.

So, let’s find the con­di­tional prob­a­bil­ity of default in the sec­ond period. Given that there was no default at the end of the first period, what is the prob­a­bil­ity of default in the sec­ond period implied by the bond’s price?

Well, with one period remain­ing, the price of the only remain­ing bond is:

$1,000 ÷ 1.12 = $892.86.

So, we can find the con­di­tional prob­a­bil­ity of default in the second-​period, p₂, the same way that we found the prob­a­bil­ity in our one-​period prob­lem.²

price = $892.86= (1 — p₂) × ($1,000 ÷ (1 + 0.07)) + p₂ × (600 ÷ (1 + 0.07))

$892.86= (1 — p₂) × $934.58 + p₂ × 560.75.

So, if the firm sur­vives the first period, there is an 11.16% con­di­tional prob­a­bil­ity of default in the sec­ond period. That means that the mar­ginal prob­a­bil­ity of default for the sec­ond period is the prob­a­bil­ity that the firm sur­vives the first period mul­ti­plied by the con­di­tional prob­a­bil­ity of default in the second:

(1 — p₁) ·p₂ = (1 — 0.0694) · 0.1116 = 10.385%

The cumu­la­tive prob­a­bil­ity of default is the sum of the two mar­gin­als: 6.94% + 10.39 = 17.33%.

Note that at the end of the first period the dif­fer­ence between the risk-​free bond’s price of $934.58 and the risky bond’s price of $892.86 is $41.72. The $41.72 rep­re­sents the risk-​neutral, “present value” at the start of the sec­ond period of the con­di­tional expected loss in the sec­ond period of the two-​period bond. So, the $41.72 is related to the con­di­tional prob­a­bil­ity of loss and the poten­tial loss of $400:

($400 × 11.16%) ÷ 1.07.

But the sec­ond period will be expe­ri­enced only if there was no default in the first period! So, in a risk-​neutral world, a cred­i­tor will only expe­ri­ence the oppor­tu­nity to lose (a dis­counted aver­age) of $41.72 if there is no default in the first period: with prob­a­bil­ity (1 — 6.944%).

And the value of that today – at the start of it all – must be dis­counted by the first period’s risk-​free rate of 5%. So, the present value of that expected loss that

$41.72 × (1 — 0.06944) ÷ 1.05 = $36.97.

Is our analy­sis cor­rect? Let’s see. A two-​year, risk-​free, zero-​coupon bond would have a price of $890.08. Our risky bond has a price of $826.45. That means that in a risk-​neutral world – given all of our assump­tions – the present value of the sum of the expected losses is the dif­fer­ence: $890.08 — $826.45 = $63.63.

In the first year, the present value of the expected loss on debt with a face value of $1,000 is $26.67. That means that the present value of the expected loss in the sec­ond period must be: $63.63 — $26.67 ≈ $36.97. Hey, where did we see that num­ber before? That’s right — a few inches above where we dis­counted the expected present value of the second-​period loss.

What about CDS?

To pro­tect against loss, the CDS should pro­vide $400 in case of default at the end of each period.

If the CDS pol­icy were sold period-​by-​period, i.e., one-​year terms, the first year’s pre­mium would have to be at least $26.67 and the sec­ond year’s if sold today would cost at least $36.97. The actual cost, like every­thing else in the real world, would depend upon how badly cred­i­tors want to pro­tect against loss, but those val­ues are actu­ar­i­ally fair in a risk-​neutral setting.

Also note that if the CDS pol­icy were sold at the start of the sec­ond period, the pre­mium would have be to at least $41.72 to be actu­ar­i­ally fair in a risk-​neutral world. So, if pur­chased con­sec­u­tively, the insur­ance pre­mi­ums would need to $26.67 today and $41.72 next year in our risk-​neutral world.

What if the insur­ance were pur­chased for two peri­ods? What would the con­stant pre­mium be? In that case, there is a chance that one or both pre­mi­ums will be received (or paid). If there is no bank­ruptcy in the first period, then the pre­mium will be paid twice; so, we need:

pre­mium + (1 — 0.06944) pre­mium ÷ 1.05 = $63.63

pre­mium (1.0 +0.93056 ÷ 1.05) = $63.63

pre­mium = $33.74

We assumed that the pre­mium was paid at the begin­ning of each period; so, it is like an “annu­ity due” and actu­ally is like a ran­dom, annu­ity due. It’s ran­dom because it is a con­stant stream of cash flows, but the end­ing date is unknown. In this sim­ple two-​period exam­ple, the “stream” could be one or two payments.

Also remem­ber that risk-​averse cred­i­tors should be will­ing to pay more than that, i.e., a risk pre­mium, too.

And remem­ber, we’ve said absolutely noth­ing about prob­a­bil­i­ties in the real world that our exam­ple rep­re­sents. Risk neu­tral prob­a­bil­i­ties and default rates are derived from a set of assump­tions that per­mits (rel­a­tively) easy cal­cu­la­tion, but those prob­a­bil­i­ties and rates only work in our model, and they do not rep­re­sent real fre­quen­cies. For more on that, please see our other posts on the topic.

As we hope that you can see, CDS is iden­ti­cal to term life insur­ance – except mil­lions and mil­lions of sim­i­lar firms don’t die each year; so, there is lit­tle empir­i­cal evi­dence of var­i­ous fac­tors, includ­ing loss given default rates.

By the way, we’ve ignored counter-​party risk and a host of other com­pli­cat­ing assumptions.

As with many of our longer posts, we’ll likely edit this one in the near future.

Copy­right © 2008 Spero Consulting.

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Foot­notes:

Update: Decem­ber 12, 2008. While none of our analy­sis or cal­cu­la­tions was incor­rect, we did have a minor error in the penul­ti­mate para­graph. We should of said “first” not “last.” To make amends, here is a multi-​period prob­lem, Multi-​period Bond Price Implied Default Rates and CDS, but it won’t make sense with­out read­ing this one first. We also added a few para­graphs below, which should help explain the multi-​period case.

Fur­ther update: April 14, 2008. We also have a new, related post on default rates. It is Cal­cu­lat­ing Coun­ter­party Credit Reserves from April 8, 2009. Much of that post involves default rates, too.

We see that we’re get­ting a num­ber of hits from search engines for folks look­ing for infor­ma­tion about price-​implied default rates – pos­si­bly col­lege stu­dents with home­work assign­ments or peo­ple try­ing to under­stand the var­i­ous types of default rates they may encounter in their jobs or readings.

We have a num­ber of posts on risk-​neutral default rates, includ­ing Implied Risk Neu­tral Prob­a­bil­i­ties (of Default) , implied RISK NEUTRAL prob­a­bil­ity of default, redux, Risk Neu­tral Val­u­a­tion: There Are at Least Two Expected Val­ues, but we doubt if those set­tings are the ones that all guests want to see, espe­cially those look­ing for help on their home­work. (Of course, we think they are all worth read­ing.) So, as a pub­lic ser­vice, we offer an exam­ple of a sim­ple, one-​period bond prob­lem. (It is single-​period because it is gratis, after all.)

Sup­pose that a zero-coupon, risky bond with a face value of $1,000 matures in exactly one year. (Yeah, we said it was sim­ple.) We’ll ignore com­pound­ing issues and assume that the annual risk-​free rate is 5%. We’ll also assume that this risky bond’s yield-​to-​maturity is 8%.

Let’s cal­cu­late and dis­cuss a few things before we pro­vide addi­tional assumptions.

We’ll cal­cu­late the bond’s price that cor­re­sponds to an 8% yield, and we’ll cal­cu­late the bond’s price if it were risk­less; of course, by risk­less we mean free of default risk or credit risk, only. Our sim­ple one-​period model doesn’t really per­mit inter­est rate risk, which is a type of mar­ket risk.

The bond’s price with a 8% annual yield is: $1,000 ÷ (1 + 0.08) = $925.93.

Now, if the bond were risk-​free, its price would be $1,000 ÷ (1 + 0.05) = $952.38,

which is $26.45 higher. So, the price drops and the yield increases (over their risk-​free equiv­a­lents) because the owner(s) of the bond is forced to bear some type of credit risk or prob­a­bil­ity of loss.

That $26.45 will appear again later, but at this point we can’t say much more than it is the dif­fer­ence in the prices of a one-​period risk-​free bond and our one-​period risky bond.

The prob­lem with sim­ple cal­cu­la­tions – whether in one or mul­ti­ple peri­ods – is that they ignore all of the fac­tors that actu­ally affect and deter­mine prices. In other words, we’ve com­pletely ignored the mar­ket dynam­ics and fac­tors that would cause the price to be $925.93.

The market-​clearing price would depend upon sup­ply and demand con­sid­er­a­tions.¹ Those con­sid­er­a­tions would depend upon the pref­er­ences, beliefs, and endow­ments of actual and poten­tial sell­ers and buy­ers. In our sim­ple set­ting, the impor­tant pref­er­ences would be risk and time pref­er­ences, which could pos­si­bly be expressed as util­ity func­tions; beliefs would involve the prob­a­bil­ity of default as well as other prob­a­bil­i­ties asso­ci­ated with each agent’s wealth in other assets if they exist – i.e., their endowments.

So, we can think of the price of $925.93 as a “func­tion” of pref­er­ences, U(·); beliefs, f(·); and endow­ments, w.² Unfor­tu­nately, in real life, we don’t know those fac­tors; so, we’ll never be able to solve the actual prob­lem, but we can solve a sub­sti­tute problem.

All we know is that the price is $925.93, and it can be expressed as a yield-​to-​maturity – or a yield curve for multi-​period prob­lems – of (our assumed) 8%. So, the yield could be viewed as a func­tion of the price if you want, but they’re really deter­mined simultaneously.

As we’ve writ­ten many times before in related posts, because of sev­eral clever researchers in eco­nom­ics and finance, we can actu­ally do more than just dis­cuss the tau­tolo­gies of price and yield.

In cer­tain cases, we can assume that mar­ket par­tic­i­pants are risk-​neutral – that takes care of U(·) and makes the w irrel­e­vant – and we can assume a par­tic­u­lar form of a den­sity or dis­tri­b­u­tion func­tion of out­comes, f(·). Very impor­tantly, with those assump­tions, if we don’t know one of the para­me­ters of f(·) we can solve for it if we know every­thing else. That would be like solv­ing for the mis­named implied vol or implied default rate, which is what we will do here.³

Here’s the key to all risk-​neutral pric­ing: under cer­tain assump­tions, if agents are (assumed to be) risk-​neutral, then we can treat prices as equal to the expected value of the asset’s cash flows accord­ing to an asso­ci­ated den­sity func­tion. That’s the only time we can treat prices as expected cash flows, rather than expected util­i­ties, but depend­ing upon the level of the course, some profs are pretty bad at explain­ing that fact.⁴

So, there are three things to consider. First, if agents are risk neu­tral, we can assume that they care only about expected values.

Second, if agents are risk neu­tral, then they won’t pay a pre­mium for tak­ing risk like risk-​lovers would, nor will they need to be paid a pre­mium for tak­ing risk like risk-​averse agents would need to be paid.

Third, that means we can assume that risk neu­tral agents are sat­is­fied earn­ing the risk-​free rate. ⁵ So, given all of our words above, that means that risk neu­tral agents would value assets at the dis­counted value of the expected cash flows – dis­counted at the risk-​free rate.

So, as we showed above, if the bond were actu­ally risk-​free, then price would have been $952.38, but the price is $925.93. That means that mar­ket par­tic­i­pants must expect to receive less than the face value of $1,000 at least some per­cent­age of the time, and that per­cent­age is the prob­a­bil­ity of default.

Let’s see exactly how much less than $1,000, but first note that we could write the price of a risk-​free bond in a slightly expanded way. Risk-​free means 100% chance of get­ting $1,000; so,

Equa­tion A:

$952.38 = 100% × ($1,000 ÷ (1 + 0.05)) + 0% × (value given default ÷ (1 + 0.05))

We did noth­ing but add zero to our pre­vi­ous cal­cu­la­tion of a risk-​free bond.

Let’s make it risky. Let p rep­re­sent the prob­a­bil­ity of default, then for a risk-​neutral per­son, we could write that same line as:

price = (1 — p) × ($1,000 ÷ (1 + 0.05)) + p × (value given default ÷ (1 + 0.05))

Thus, with a price of $925.93, we could write:

$925.93 = (1 — p) × ($1,000 ÷ (1 + 0.05)) + p × (value given default ÷ (1 + 0.05))

There are two unknowns: the prob­a­bil­ity of default, p, and the value of the bond given default, which has to be less than $1,000. In fact, we could put a deter­mine a upper bound that is less than $1,000 if we wanted to do so. (How?)

Now, look at the last equation. Once we know or assume the value given default, we could find the prob­a­bil­ity of default, p, or vice versa.

Usu­ally, one assumes the value given default and solves for p. There’s not really a good rea­son for doing it other than that’s what just about every­one does. (Don’t let any­one attempt to fool you with some lame jus­ti­fi­ca­tion. It’s tra­di­tion, cus­tom, con­ven­tion. Regard­less of the word, it is arbitrary.)

So, let’s make-​up – er, we mean assume – a value given default. This is often given in terms of a loss given default, a loss given default rate, or a recov­ery rate, but they’re all equiv­a­lent as one can see in the fol­low­ing relationships.

value given default = $1,000 — loss given default

value given default = $1,000 — loss given default rate × $1,000 = $1,000 × (1 — loss given default rate)

value given default = $1,000 × (1 — loss given default rate) = $1,000 × recovery rate

The loss given default is often abbre­vi­ated LGD. Unfor­tu­nately, the loss given default rate is some­times abbre­vi­ated as LGD. Don’t let the bad nota­tion fool you. Now, where were we?

That’s right. Let’s sup­pose that the loss given default rate is 40%. That means the recov­ery rate is 60%, which is its com­ple­ment. Regard­less, of how that assump­tion is stated, that means that the value given default is $600. So, now we have another num­ber to put into our equation:

$925.93 = (1 — p) × ($1,000 ÷ (1 + 0.05)) + p × (600 ÷ (1 + 0.05))

or,

Equa­tion B:

$925.93 = (1 — p) × $952.38 + p × 571.43.

If we did the arith­metic cor­rectly, then solv­ing for p gives a prob­a­bil­ity of default of almost 7%: 6.94%. Clearly, all things equal, which means hold­ing every­thing else con­stant, as the loss given default increases, the prob­a­bil­ity of default decreases. One can make a graph of that rela­tion­ship as we did in Implied Default Prob­a­bil­i­ties and Risk Neu­tral Mod­els in June, 2008.

Now, under the assump­tion of risk-​neutral agents, the dif­fer­ence between the two bond prices of $26.45 can be express as the dif­fer­ence in the present value of their expected cash flows. The dif­fer­ence in the present val­ues of the expected cash flows in Equa­tions A and B is the present value of the expected loss. The loss given default is $400. The undis­counted expected loss is: 0.0694 × $400 = $27.76. The present value of the expected loss is – not sur­pris­ingly – $27.76 ÷ 1.05 = $26.45.

That’s not the most some­one would spend for insur­ance. That insur­ance pre­mium depends upon the person’s risk-​aversion.

Multi-​period prob­lems aren’t that much dif­fer­ent, but they require bonds of mul­ti­ple matu­ri­ties if one is attempt­ing to derive a credit curve, and one works for from the last first period for­ward solv­ing maturity-​by-​maturity. Oth­er­wise, one can find an “aver­age” annual mar­ginal prob­a­bil­ity of default. (We talk about a sim­i­lar issue in Good Col­umn, Bad Math.) So, in our multi-​period exam­ple, we’ll explain the price of a two-​year bond as the dif­fer­ence in present val­ues between a risky and risk-​free two-​year bond. Then we’ll say much much of that can be attrib­uted to the first period and then the sec­ond period.

Note: WE“VE SAID ABSOLUTELY NOTHING ABOUT THE REAL PROBABILITY OF DEFAULT! If all of the agents are risk-​averse, then the unknown real prob­a­bil­ity of default will be less than the risk-​neutral rate, but that’s not too help­ful, is it? Some of our older posts do illus­trate this idea.

Good luck with the assignment.

Copy­right ©2008 Spero Consulting.

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Foot­notes:

If you haven’t read it, For the Vix, 40 Looks Like It’s the New 20 in today’s The Wall Street Jour­nal please know that is a decent column.

We par­tic­u­larly like the paragraph:

“Volatil­ity may not return to its highs, but it isn’t clear when it will get back to nor­mal, either. Volatil­ity breeds fear, which breeds more volatil­ity. There is still too much uncer­tainty about the losses lurk­ing on bank bal­ance sheets and about the depth and breadth of the cur­rent reces­sion to inspire much calm.”

Now, the first sen­tence is true but says absolutely noth­ing. We’re not try­ing to ridicule Mark Gon­gloff the writer of the Ahead of the Tape column; instead, we empathize with the dif­fi­culty he faces writ­ing about mar­kets and uncertainty.

The notion of uncer­tainty about uncer­tainty–and the inabil­ity to mea­sure it in a sim­ple man­ner – tends to make state­ments about the topic either sound overly-​complex and overly-​qualified (by all of the nec­es­sary descrip­tive qual­i­fi­ca­tions to the state­ment) or makes them sound trite. Some­times that’s the writer’s fault, but often it is the reader’s fault, too, espe­cially when the reader incor­rectly pos­sess no uncer­tainty about their own “knowledge.”)

Now, we espe­cially like Mr. Gongloff’s fol­low­ing sen­tences because that’s almost exactly what we’ve writ­ten dur­ing the past sev­eral months – almost three months now.

The mort­gage cri­sis that cre­ated the con­fi­dence and liq­uid­ity cri­sis and the result­ing equity mar­ket volatil­ity all con­tin­ued unabated. Last Wednes­day, in The Mort­gage Cri­sis: Why Not Incen­tivize the Pri­vate Sec­tor? we wrote: “By the way, folks who think this Thanks­giv­ing week’s mini-​rally sig­ni­fies that the worst is over are likely to be sadly mis­taken. We do hope that we’re wrong, but doubt it.” 

While we try not to make much of one-​day changes, even when they are as large as today’s drop of 680 points in the DJIA and the nearly 9% decreases in the S&P 500 and NASDAQ indices, we do believe both the con­tin­u­ing volatil­ity and losses pro­vide evi­dence that the government’s actions to date have not helped instill con­fi­dence. In all like­li­hood have hin­dered econ­omy and finan­cial activ­i­ties by not allow­ing any res­o­lu­tion of the uncer­tainty of the value and via­bil­ity of large finan­cial intermediaries.

We wrote about that in Could a “Bailout” Pro­long the Finan­cial Cri­sis? and The Uncer­tain Value of Mort­gage Secu­ri­ties (among other posts) in late Sep­tem­ber. How­ever, the government’s exe­cu­tion and lack of plan­ning has been even worse than we could have imag­ined, and we had extremely low expec­ta­tions to begin with. 

As we have been men­tion­ing since that time, we wish fed­eral gov­ern­ment would pro­vide tax incen­tives – say, mort­gage invest­ment tax cred­its – to moti­vate pri­vate pur­chases of trou­bled assets. 

We also wish the gov­ern­ment would expro­pri­ate the worst offend­ers – the most poorly cap­i­tal­ized large banks. We know that the Trea­sury can’t run banks any bet­ter than the exist­ing man­age­ments, but that’s not one of our reasons. A main rea­son is to moti­vate other health­ier insti­tu­tions to act. Hav­ing ready buy­ers – moti­vated by such tax cred­its – would cer­tainly help those banks exchange assets for cash, and that lack of trade keeps the analy­ses of each bank’s finan­cial con­di­tional need­lessly opaque, and that’s (by def­i­n­i­tion) no way to resolve uncertainty.

We’re not sure when dur­ing the day, Mr. Paul­son spoke of new pro­grams (Paul­son Says Trea­sury Actively Mulling New Res­cue Pro­grams), but we doubt if that stemmed the (ebbing) tide of sharply decreas­ing equity val­ues. Unfor­tu­nately, there is no rea­son to expect any pos­i­tive news any time soon.

The Curi­ous Case of Robert Rubin

The week­end edi­tion of The Wall Street Jour­nal has a front page inter­view with Robert Rubin: Rubin, Under Fire, Defends His Role at Citi.

We’ve crit­i­cized Citi’s board in the (recent) past, and we’re still par­tic­u­larly fix­ated on the fact that few direc­tors had finan­cial indus­try expe­ri­ence. That seems nei­ther wise nor even pru­dent for a finan­cial insti­tu­tion with over $3,000,000,000,000 of assets. (That’s $3 tril­lion, but we like to write it out for effect, because it seems like a lot of money.)

As the arti­cle men­tions, Mr. Rubin was “the only board mem­ber with expe­ri­ence as a trader or risk manager.”

Since 1999, Mr. Rubin has made about $119 mil­lion from Cit­i­group while hav­ing no oper­at­ing respon­si­bil­i­ties. We have absolutely no prob­lem with that, and, in fact, are look­ing for sim­i­lar “work” our­selves. (Inter­ested par­ties may use our con­tact form.)

Where we do have a prob­lem is his insis­tence that none of Citi’s prob­lems is his respon­si­bil­ity. As the inside head­line reads: “Rubin Blames Citigroup’s Woes on the Broader Finan­cial Cri­sis.” He almost seems to imply that Cit­i­group is a hap­less, unwit­ting vic­tim of some­thing big­ger than itself – some­thing it couldn’t be expected to con­sider, man­age, of fathom: “Nobody was pre­pared for this…”

In that case, exactly what type of stew­ard­ship, guid­ance, and pro­fun­di­ties did he provide? 

Sup­pose it is true that Citi and its board were fault­less. Shouldn’t they have been able to con­sider how they might be dam­aged by a gen­eral down­turn or a finan­cial cri­sis that was no fault of its (their) own. Thus, our lit­tle proof-​by-​contradiction shows the silli­ness of the argument.

More­over, we doubt that even the gullible buys the story that Citi was sim­ple a vic­tim of exoge­nous fac­tors, which were unpre­dictable and beyond its control.

There is a cri­sis of con­fi­dence, but that cri­sis erupted and sur­vives because mar­kets and investors real­ized the large finan­cial insti­tu­tions, includ­ing Citigroup, were far less com­pe­tent invest­ing and trad­ing than they pre­vi­ously believed, i.e., that in ret­ro­spect, pre­vi­ous reported prof­its were unreal and unsustainable.

Citigroup’s share price of $8.29, which is about dou­ble where it was last week­end, has lost about 85% of its value in two years. (In the first three years of the Great Depres­sion – 1929 — 1932 – the Dow Jones Indus­trial Aver­age lost the same per­cent­age with­out a back­stop by gov­ern­ment.) That is an indict­ment against Citigroup’s way of doing busi­ness far beyond the gen­eral con­dem­na­tion of the finan­cial ser­vices indus­try in gen­eral and with all of the sub­si­dies pro­vided by tax pay­ers through the var­i­ous recent gov­ern­ment guar­an­tees and bailout measures. 

Clearly, investors find fault with Citi’s strate­gic and oper­at­ing deci­sions. So, if Mr. Rubin wasn’t mak­ing oper­at­ing deci­sions, what type was he mak­ing? If they weren’t strate­gic, what remains? As other crit­ics note, Mr. Rubin is “try­ing to have it both ways.”

Of course, his pos­tur­ing is silly, as it was he, him­self, who pushed senior man­age­ment to bear more risk in 2004 — 2005. If that’s not a strate­gic, board-level, decision, what is? From our read­ing, it seems that he may now be try­ing to blame a con­sul­tant for sug­gest­ing the board instruct man­agers to take addi­tional risk.

He also blames senior man­age­ment for not exe­cut­ing the strate­gic plans prop­erly and risk man­age­ment for, well, weak risk management. 

“I wouldn’t run a finan­cial insti­tu­tion based upon someone’s view about what mar­kets would do.”

Of course, as the arti­cle explains that is exactly what he did in 2004 — 2005. (We wouldn’t doubt that he did it at other times, too, but don’t have the time or energy to search for quotes or sto­ries.) Well, he didn’t do it based upon some­one else’s view; instead, Citi’s strat­egy seemed to be based upon his own views. (We could well imag­ine board­room dis­cus­sions where inex­pe­ri­enced direc­tors imme­di­ately defer to the for­mer Trea­sury Sec­re­tary and Gold­man Sachs Co-​Chair.

Now, Mr. Rubin should know that devel­op­ing and acknowl­edg­ing such a world-​view is exactly how finan­cial insti­tu­tions are run, whether that view is explic­itly stated or not. (If it is not explicit, then not pro­vid­ing such a view and or con­sid­er­ing its impli­ca­tions seems neg­li­gent at worst and imma­ture at best, ergo, our title.) What else could strate­gic and oper­at­ing plans be based upon? How else could risks be mea­sured, uncer­tain­ties be con­sid­ered, and con­tin­gen­cies be planned? Or are those con­sid­er­a­tions too much like work? If so, it is not dif­fi­cult to see why Citi is where it is at this Novem­ber, and that is com­pletely con­sis­tent with both a spe­cific and the more gen­eral cri­sis in confidence.

As we see it, Mr. Rubin is seventy-​years-​old. He should grow-​up and accept the respon­si­bil­i­ties that come with his posi­tion and rewards, and stop behav­ing like a petu­lant teenager.

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.

---

Foot­notes:

Behind AIG’s Fall, Risk Mod­els Failed to Pass Real-​World Test.

You Don’t Say! Our sub­ti­tle is the title of today’s Wall Street Jour­nal front-​page arti­cle about AIG (obviously).

As always we’ll point inter­ested read­ers to our essay, Uncer­tainty Man­age­ment, which empha­sizes the broader notion of unmea­sur­able uncer­tainty over the nar­rower notion of (mea­sur­able) risk, and there­fore per­mits really bad things to happen.

We mean bad things out­side the scope of someone’s purely math­e­mat­i­cal model, which, as an abstrac­tion of real­ity, may ignore imag­in­able and unimag­in­able bad things. (We’re all for math – when it is thought­fully and con­sci­en­tiously applied. In fact, we think such appli­ca­tion is one of the things that we do best.)

In that regard, we’ll once again note the sub­ti­tle of the above-​referenced essay, Or How Trad­ing is Like Play­ing in a Cul­vert on a Hot, Sunny, Summer Day. See dear reader, once one con­sid­ers that one could drown from a flash flood – even on a pre­sum­ably and locally Sunny day – the allure of such adven­ture dulls greatly – at least for the rea­son­able among us.

In other words, your mother may have been a scold, but there was prob­a­bly a good rea­son for her to warn you about play­ing in cul­verts and drainage ditches (pro­vided that she loved you, of course). She may not have dis­cussed it in prob­a­bilis­tic terms, but that doesn’t mean she can’t recall read­ing about such drown­ings, say, forty years ago, or even before you were born.

More­over, the fact that you didn’t read about any such cases in, say, the past ten years, doesn’t mean they don’t exist, and there, of course, lies the Prob­lem of Induc­tion, and the over-​reliance on infer­ences from rel­a­tively short-​duration, historical, data sets. (See our beau­ti­ful excerpt from St. James’ only Epis­tle on our Quotes page.)

The prob­lem, dear reader, is that few senior man­agers (and almost no board members) understand the val­u­a­tion and risk mod­els used for secu­ri­ti­za­tions, and many of the traders, con­sul­tants, and ana­lysts who wield such tools often suf­fer from, what one may call, “fram­ing” issues; we don’t mean that aspect of home con­struc­tion despite its recent relevance.

We mean that if one’s only tool is a ham­mer, then lots of things look like nails. The metaphoric ham­mer may be an intan­gi­ble Visual Basic or “C” pro­gram­ming algo­rithm, but the point remains the same; it’s just harder for senior man­age­ment to see what one is pound­ing in their cubi­cle, office, or trading-​floor seat.

To be sure, if any­one within most of the larger firms would have com­plained of the sys­tem­atic risk – and how every­thing could go bad all at once – and the inap­plic­a­bil­ity of the stan­dard mod­els, which gen­er­ally don’t per­mit such events, then that per­son most cer­tainly would have been told that they don’t know what they’re talk­ing about. Pos­si­bly, that they are unso­phis­ti­cated or too negative.

Per­haps we just don’t pay enough atten­tion to what hap­pens in all of the large firms, but if the reader dis­agrees with our pre­ced­ing para­graph, please note that there have been few recent suc­cess sto­ries within major firms like the gains enjoyed by Nas­sim Nicholas Taleb, John Paul­son, or Andrew Lahde–all inde­pen­dent fund man­agers. (If the new reader has read this far, then it is highly likely that they’ll like the link under Andrew Lahde’s name and his con­dem­na­tion of many things in one fell swoop.) We know that our exam­ples form a very small data set, but mostly what we’ve heard is how the more suc­cess­ful large firms haven’t lost as much as their brethren. We don’t recall any of them actu­ally do well this year.

Also, we’ll prob­a­bly have more to say about our boy, Taleb. We very much like his trad­ing style, as it reminds us of the value of the Sec­ond Amend­ment and laws that per­mit con­cealed carry. See, dear reader, carrying a pis­tol is very much like buy­ing deep-​out-​of-​the-​money puts. There’s a small, ongo­ing cost and a minor irri­ta­tion, but when cer­tain bad things hap­pen, there is an option to exer­cise to pro­tect ones self, and that value can­not be underestimated.

We haven’t said any­thing about CDS – the source of AIG’s prob­lems – in this post but plan to do so shortly.

We think that the cur­rent tur­moil in the mar­kets pro­vides an atmos­phere for inde­pen­dent thinkers and adviser such as our­selves to gain some atten­tion (and more clients) by com­ment­ing on cur­rent issues and by offer­ing free and use­ful advice, espe­cially if said advice is dif­fi­cult to imple­ment with­out us. For that rea­son, we’re in the mid­dle of writ­ing a few longer posts about a vari­ety of top­ics related to the ongo­ing finan­cial crisis.

One of those unfin­ished posts, “Hedging the Pen­ny­wise and Pound-​Foolish Way,” deals with myopia and tunnel-​vision, and it is the impe­tus for this post. 

Here, we con­tem­plate a few types of per­son­al­i­ties that would be ben­e­fi­cial hires for finan­cial firms, but read­ily admit that it is highly unlikely that most firms could or would ever know­ingly employ such folks. Their cor­po­rate cul­tures, par­tic­u­larly their empha­sis on hope and conformity, eliminate such indi­vid­u­als from employ­ment con­sid­er­a­tion. So much for diver­sity we guess!

Among the group of per­son­al­i­ties that we have in mind are the sur­vival­ist and the depressive.

First, as reg­u­lar (and by this time, possibly even occa­sional) read­ers may know, we pre­fer “uncer­tainty man­age­ment” to “risk man­age­ment,” because that is the true nature of the task. One needs pro­tec­tion from unknown and/​or immea­sur­able bad things, too. The task is about loss pre­ven­tion not just the nar­rower ex ante mea­sur­able loss prevention. 

Above we high­lighted our broader empha­sis on uncer­tainty, rather than merely risk, because such con­sid­er­a­tion of extremely bad events tends to be the nature of both sur­vival­ists and depressives.

Between the two groups – we’ll ignore the depressed sur­vival­ist inter­sec­tion for a few para­graphs – it seems that sur­vival­ists spend more time devel­op­ing strate­gies and tac­tics to cope with the bad out­comes than they do fix­at­ing on their causes (although we’re sure that many have their favorite con­spir­acy the­o­ries, too). 

Con­versely, depres­sives seem to spend much more time con­tem­plat­ing all of the bad things that could hap­pen and all the ways that those events could arise; many have suf­fi­cient imag­i­na­tions to con­struct the nec­es­sary chain of events to arrive at, say, Armaged­don – both lit­er­ally and fig­u­ra­tively. In fact, that’s what tends to make them so depress­ing to be around, and it is also what makes them unlikely to pass a day-​long sequence of inter­views at an invest­ment com­mer­cial bank.) 

Unfor­tu­nately, they often spend so much time wal­low­ing in the despair of such losses that they don’t pos­sess the nec­es­sary cop­ing skills or the determination/​drive to pro­vide use­ful solu­tions. That, of course, is what sur­vival­ists spe­cial­ize in: being pre­pared for the worst.

Now, we con­jec­ture that few sur­vival­ists would view most money cen­ter loca­tions as the opti­mal high ground on which to camp when West­ern Civ­i­liza­tion falls, espe­cially if said money cen­ter were, say, a small island of sev­eral mil­lion peo­ple with extremely-​limited, nat­ural, non-​cannibalistic food sources and very restric­tive gun con­trol to boot.

Of the cognoscenti, we’d view one of our favorites, Nas­sim Nicholas Taleb, the author of Fooled By Ran­dom­ness, as the per­son whose trad­ing strate­gies most closely embrace the the inter­sec­tion of the survivalist/​depressive men­tal­ity in markets. (He seems to have too much fun justly annoy­ing fools to be either depressed or overly-​fixated on survival.)

Based upon his reported trad­ing success, it would seem that at least on a small scale, analogs to our rec­om­men­da­tion can be prof­itable. As we under­stand it, Mr. Taleb would often buy deep-​out-​of-​the-​money puts fig­ur­ing that in the long run, he would gain out­sized returns because (1) oth­ers would under-​estimate the prob­a­bil­ity of bad out­comes, and (2) he had an exact strat­egy and tac­tics in place to ben­e­fit from such occurrences. Ergo, the suc­cess­ful, depressive-​survivalist trade.

However, as Mr. Taleb repeat­edly men­tions, such beliefs (and the strate­gies and actions that they induce) require a sub­stan­tial degree of dis­ci­pline to implement. Successful bets are few and far between, and it takes much sta­mina, patience, and deter­mi­na­tion to wait on the occa­sional win. Moreover, it is psy­cho­log­i­cally painful when friends, neigh­bors, and for­mer col­leagues are mak­ing imme­di­ate money on seem­ingly sense­less and ran­dom trades and you’re wait for that extreme event.) We’d imag­ine that the level of frus­tra­tion felt and the dis­ci­pline required to cope with it, aren’t much dif­fer­ent than what’s needed to seat next to a sur­vival­ist or depres­sive on the trad­ing floor.

Finally, we’d be remiss not to men­tion our other favorite author in the field, Richard Book­staber, author of A Demon of Our Own Design. In that excel­lent book, he admon­ishes traders and risk man­agers to keep their strate­gies sim­ple and robust. He points to the cock­roach as an exem­plary evo­lu­tion­ary sur­vivor with a very sim­ple phys­i­o­log­i­cal structure. 

We dis­agree with him slightly, because our tiny insec­toid brain is not con­cerned with the entire sur­vival of the species– but only with our own per­sonal via­bil­ity. So, Mr. Bookstaber’s long-​run is likely quite a bit longer than we (and most oth­ers) care about. How­ever, he does describe the prob­lems and costs of com­plex­ity; thus, the title of the book. We whole­heart­edly agree with him on those issues, e.g., no one under­stands the whole sys­tem; such things tend to be jerry-​rigged à la Rube Gold­berg; and the (initial) failure of a safety sys­tem can destroy the entire entity, etc. Some of those things are very scary when they hap­pen in air­planes and nuclear plants.

In that regard, our rec­om­men­da­tions to hire for per­son­al­ity might not seem that out­ra­geous: it is sim­ple and robust. Perhaps a few knowl­edge­able and imag­i­na­tive depres­sives and sur­vival­ists are worth an army of lemming-​like quants attempt­ing to “over-​calculate” the unknowable?

Look for our upcom­ing book series: Essen­tial Risk Man­age­ment I: Embrace Your Inner Sur­vival­ist and Essen­tial Risk Man­age­ment II: Embrace Your Inner Depres­sive. No, not really.