Spero Consulting

‘Credit’ Category

We occa­sion­ally write about CMBS or Com­mer­cial Mortgage-​backed Secu­ri­ties and the CMBX index. For exam­ple, last Novem­ber, we wrote CMBS Is Like Lumpy MBS and That’s Not Good. We tend to get more hits on our tongue-​in-​cheek post, How to Trade CMBS? and find that a bit scary.

What should truly frighten both CMBS hold­ers and banks with large commercial-​mortgage loan port­fo­lios more than our dis­cus­sion of our page rank­ings is this arti­cle in Saturday’s edi­tion of The Wall Street Jour­nal: Hotels Deliver Some ‘Jin­gle Mail.’ The arti­cle details how hotel own­ers are walk­ing away from highly-​mortgaged prop­er­ties and how delin­quency rates for secu­ri­tized hotel loans are almost ten times higher than they were one year ago – about 4.75%.

We sus­pect that banks that were erst­while struc­tur­ers and had accu­mu­lated an inven­tory of such loans (for later bundling that has not yet mate­ri­al­ized) may face even larger problems.

Using the logic that the last loans made before the bub­ble burst are likely to be less cred­it­wor­thy than ear­lier ones, we sus­pect that the delin­quency rates for those loans that didn’t make it into a CMBS pool before the mar­ket col­lapsed could be even higher than the nearly five-​percent rate men­tioned above.

More­over, while we’d argue that any claimed diver­si­fi­ca­tion ben­e­fit of CMBS was grossly over­stated, there is absolutely no diver­si­fi­ca­tion ben­e­fit from hold­ing the entire loan. Those banks and struc­tur­ers that are stuck hold­ing those loans bear the entire risk of default. In some ways, it reminds us of a very expen­sive adap­ta­tion of the game, musi­cal chairs. (CDOs and CDOs squared, etc., are rem­i­nis­cent of “hot potato” or blind folks toss­ing raw eggs back-​and-​forth.)

Finally, we would be sur­prised if for­mer struc­tur­ers and banks with clogged pipelines didn’t report higher credit losses in the sec­ond half of this year. If they don’t, we will won­der whether reg­u­la­tors are being par­tic­u­larly loose in super­vis­ing how those banks cal­cu­late their loan reserves.(At this point, we sus­pect those loans are no longer “held-​for-​sale,” but have been reclas­si­fied into the reg­u­lar loan portfolio.)

We hope that the finan­cial cri­sis, which seems to have sub­sided, has actu­ally sub­sided. How­ever, we have a sneak­ing sus­pi­cion that it may be per­son­i­fied by Mark Twain’s famous quote about how the report of his death was greatly exag­ger­ated. This is one indi­ca­tion that it’s not over.

How Much Have They “Gained” From Becom­ing Worth Less?

Since the begin­ning of April, when many large banks reported unex­pected (or unex­pect­edly large) first-​quarter prof­its, we’ve won­dered what per­cent­age of those prof­its could be attrib­uted to the account­ing rule that lets them rec­og­nize a gain because their own lia­bil­i­ties have become worth less. (We think “worth less” is the cor­rect form, but for the extreme cases, it should indeed be “worthless.”)

We wrote about this issue of rec­og­niz­ing gains from losses in mid-​December in our post Mark­ing Debt to “Mar­ket” or Addi­tion Through Sub­trac­tion. Basi­cally, if cred­i­tors don’t want your bonds, the value of the secu­ri­ties decrease, and yields (and credit spreads) increase. Firms are allowed to rec­og­nize the fact that oth­ers view them as worth less as an unre­al­ized gain to share­hold­ers. (“Unre­al­ized” means that no trans­ac­tion occurred between the firm and its cred­i­tors.) It doesn’t seem to be a very com­pelling argu­ment because as cred­it­wor­thi­ness declines, equity val­ues tend to do so, also. (Ask Citigroup.)

We wish we had more time, or at least more patience, to scan the banks’ first-​quarter finan­cial state­ments on their web sites, but based upon the sites we vis­ited, it doesn’t seem that those gains (from becom­ing riskier and worth less) are some­thing that banks want to pub­li­cize, sep­a­rately iden­tify, or explain. (You can’t blame them for that.)

In our brief on-​line search this morn­ing, we found this blog post, Mark-to-market’s strange account­ing ben­e­fits for Citi and BofA, which notes that Citigroup’s gain – or at least part of the gain – was $2.5 bil­lion but its over­all net profit was only $1.6 bil­lion, and Bank of America’s net gain because it was worth less was about half of its net profit of $4.2 bil­lion. In the pre­vi­ous sen­tence, we wrote the qual­i­fier – between the dashes – to empha­size that it’s pos­si­ble that such gains were actu­ally big­ger but may have been split among dif­fer­ent seg­ments or cat­e­gories. We looked at another bank’s first-​quarter income state­ment, and it showed the com­bined, net, unre­al­ized, gain on assets and lia­bil­i­ties of about $1.5 bil­lion; so, it’s con­ceiv­able that it actu­ally rec­og­nized a loss on assets of sev­eral bil­lion and a gain on re-​valuing/​devaluing lia­bil­i­ties of a larger amount, which nets to the $1.5 bil­lion or so. We ask: if that were the case, would the dear reader think bet­ter or worse of that par­tic­u­lar bank?

Our hunch, based upon these few obser­va­tions, is that bank stock prices would have decreased if these unre­al­ized gains would have been reported explic­itly for what they were/​are. Gen­er­ally, we’re agnos­tic about the ben­e­fits of trans­parency; how­ever, this is one time when we wish that there was a bit more of it. (See our post, Gos­samery Argu­ments for Trans­parency and Our Reply, from last Novem­ber for why more trans­parency isn’t nec­es­sar­ily better.)

The Irrel­e­vance of Book Equity and Cap­i­tal Ratios

Last month we wrote March Mad­ness: New Bank Cap­i­tal Require­ments. In that, we stated: “We’ve always thought that such require­ments were stu­pid and pro­vided a false sense of secu­rity: kind of like duck­ing and cov­er­ing under one’s school desk as prac­tice and prepa­ra­tion for a nuclear explosion.”

We also pro­vided an exam­ple from an old merger of two rust belt firms. At the time of the merger, the firms had com­bined book val­ues of $2.0 bil­lion ($2,000 mil­lion) but com­bined mar­ket val­ues of about $300 mil­lion. At its the­o­ret­i­cal best, book value rep­re­sents net expected future ben­e­fits from past trans­ac­tions or events, whereas mar­ket value rep­re­sents net expected future ben­e­fits from all trans­ac­tions and events – both past and antic­i­pated. In the rust-​belt merger exam­ple, at the time, equity investors had con­cluded that the future would be bleak, and it turned out to be, but also at the time, no loan covenants were breached.

We think that’s worth restat­ing because on Mon­day, Bank of Amer­ica reported com­mon share­hold­ers’ equity of $166 bil­lion, yet finance​.google​.com reports that the mar­ket value of com­mon stock was about $50 bil­lion. Now, exactly how rel­e­vant is the book value of $166 bil­lion when investors value the firm at less than one-​third of it? We’d say, “not very.”

Think about it. Do you care if your house has a net book value of $166,000 if its net mar­ket value is $50,000. Or, ignor­ing tax-​planning impli­ca­tions, do you care if your lever­aged port­fo­lio has a book value of $166,000 if it can be liq­ui­dated for $50,000? Would you make deci­sions based upon the actual net equity of $50,000 or the reported net equity of $166,000? What do you think that, say, poten­tial cred­i­tors would con­sider when offer­ing financ­ing? More­over, what would you want them to con­sider if those cred­i­tors were act­ing as agents for you? There may be reg­u­la­tory impli­ca­tions to the book val­ues, but it seems that investors have con­cluded that those reg­u­la­tions (and all of the sub­si­dies) haven’t pro­vided enough sta­bil­ity or value to secure their resid­ual interests.

Also, real­ize that B of A’s net book value is greater because its lia­bil­i­ties are worth less than they were, which is not quite com­pletely worth­less. The prices for claims on the gross assets have declined. These are the silly, unre­al­ized account­ing gains are shown as result­ing from increases in credit spreads. In B of A’s case, they rec­og­nized at least $2.2 bil­lion of them in the first quar­ter although it was prob­a­bly more. (We wrote about this topic in Decem­ber in Mark­ing Debt to “Mar­ket” or Addi­tion Through Sub­trac­tion. 

By the way, and of course, B of A is not alone with its imbal­ance between its lower net mar­ket value and its much higher net account­ing value. In fact, Citi’s ratio of market-​to-​book equity ratio is sub­stan­tially smaller. And remem­ber, that’s despite the hun­dreds of bil­lions of dol­lars of guar­an­tees made by the U.S. gov­ern­ment on Citigroup’s behalf.

Implied Risk Neu­tral Default Rates Ver­sus His­tor­i­cal Default Rates

For some prob­lems, there is no good or true solu­tion, but some­thing must be done or esti­mated. Such is the case with cal­cu­lat­ing credit reserves because real default rates can never be known, but risk-​neutral implied or his­tor­i­cal default rates can be cal­cu­lated and used, but both are flawed.

Gen­er­ally, when we dis­cuss this topic, we have reduced-​form mod­els in mind (as opposed to struc­tural ones, but there’s no short­age of assump­tions in struc­tural mod­els, either).

We’ve writ­ten about implied default rates on sev­eral occa­sions, and we recently had a con­ver­sa­tion with some­one who men­tioned that for trad­ing credit reserve cal­cu­la­tions, reg­u­la­tors are requir­ing firms to use implied default rates from risk-​neutral pric­ing mod­els rather than his­tor­i­cal default rates. To be pre­cise, these implied default rates would be derived/​inferred from CDS (credit default swap) prices using risk-​neutral mod­els and any num­ber of quite arbi­trary assumptions.

Pre­sum­ably, given recent high prices for pro­tec­tion – the credit default swaps – implied defaults rates are sub­stan­tially higher than his­tor­i­cal rates, and the reg­u­la­tors are just try­ing to be “con­ser­v­a­tive.” Oh well, so much for our motto of thought before cal­cu­la­tion.

Now, it’s true that for all else equal, if investors are risk-​averse, implied, risk neu­tral default rates will always be greater than actual default rates, and the “more” risk-​averse investors are, the higher the implied, risk-​neutral, prob­a­bil­ity of default. There’s a vari­ety of ways it can be stated, but using CDS prices, we can roughly say that for a fixed gam­ble with a fixed prob­a­bil­ity of default, the more risk-​averse the insurer, the higher the price required to com­pen­sate him for bear­ing that risk, the higher the price of guar­an­tee­ing default, the higher the risk-​neutral prob­a­bil­ity of default.

As we men­tioned above, in the real-​world, actual (future) rates are never known, but some­times, his­tor­i­cal default rates can be used as prox­ies for actual rates, espe­cially if the ana­lyst believes that the envi­ron­ment is unchanged. Below, we’ll briefly explain why we think that is prefer­able to use implied, risk-​neutral default rates.¹

Esti­mat­ing a Credit Reserve

Like a loan-​loss reserve, which is a bank’s esti­mate of the expected loss of default by its bor­row­ers, a trad­ing orga­ni­za­tion must also cal­cu­late a credit reserve for its trades. For trad­ing, that means mak­ing a guess or esti­mate of the expected loss asso­ci­ated with default (by the coun­ter­party) when the trade is in one’s favor.²

Con­di­tional Expected Values

Roughly, that means to cal­cu­late a credit reserve, it’s nec­es­sary to deter­mine when the trade is in one’s favor and then assume or esti­mate the prob­a­bil­i­ties of that occur­ring over the life of the trade.³

By know­ing that range of win­ning val­ues and using esti­mates of the prob­a­bil­i­ties of those val­ues, one can then cal­cu­late the con­di­tional expected gain from the trade – the aver­age trad­ing gain given that one has gained (and not lost). (We’re think­ing of a a discrete-​time, single-​period prob­lem here.)

Ignor­ing col­lat­eral agree­ments for the moment, which would reduce the poten­tial credit expo­sure when one is ahead, the con­di­tional expected value rep­re­sents the aver­age amount that the other party will owe at the end of the trade (if it owes anything).

So, that con­di­tional expected value is a rea­son­able esti­mate of the credit expo­sure at, say, the end of the account­ing period. It’s very sim­i­lar to the esti­mated uti­liza­tion of a credit line at a future date, which is needed to cal­cu­late a loan-​loss pro­vi­sion and reserve. Whether for loans or trades, one needs to esti­mate the expo­sure at default, which those in the indus­try abbre­vi­ate as EAD.

EADs, LGDs, and PDs

Once that expected expo­sure at default is esti­mated, one needs two more esti­mated val­ues to cal­cu­late the coun­ter­party credit reserve (for a sin­gle trade): the prob­a­bil­ity of default (PD) and the loss given default (LGD) rate.

The prod­uct of the three – the (EAD × LGD rate) × PD – is the reserve for that trade.⁴ Also, note that the prod­uct of the first two terms is the (expected) lost given default.

For com­pletely col­lat­er­al­ized trades, the loss given default is nearly zero. There are some tim­ing issues, so sharp changes in val­ues and the lags in post­ing col­lat­eral could cre­ate a small chance of loss, but that’s a rel­a­tively small level of expo­sure com­pared to a sim­i­lar but uncol­lat­er­al­ized trade.⁵

In the past, insti­tu­tional LGD rates were par­tic­u­larly dif­fi­cult to esti­mate because there were so few obser­va­tions of bank­rupt­cies of firms within par­tic­u­lar indus­tries and of par­tic­u­lar sizes. (By the way, it’s worth not­ing that there is some evi­dence that banks recover more than bond-​holders – banks are bet­ter orga­nized for the con­tin­gency – so they have lower LGD rates.)

Now, because LGD rates are dif­fi­cult to esti­mate, they’re usu­ally assumed. With an assump­tion about the LGD rate, one can then solve for the default rate in most risk-​neutral mod­els. For more on this topic, please see our post from last sum­mer: Implied Default Prob­a­bil­i­ties and Risk Neu­tral Mod­els, par­tic­u­larly the graph that shows a sim­ple rela­tion­ship between the LGD rate and the implied default rate (in a sim­ple model).

Now we have enough to com­pare two options for prox­ies of default rates that firms can use to cal­cu­late credit reserves.

Of course, and to reit­er­ate, we’d like to know the actual, true default rate dur­ing some future period for a firm, but we can never know that for sure. (Actu­ally, we’d like to know if the trade is a win­ner and whether the coun­ter­party will default.) In fact, for a sin­gle firm, after that future period, we’ll know if the firm defaulted or not, but we won’t know the true prob­a­bil­ity of default, and even with a cross-​section of firms, we’ll be able to cal­cu­late a real­ized aver­age rate, but that will be only one pos­si­ble aver­age rate, not the true aver­age rate so-​to-​speak. So, we can esti­mate (1) a his­tor­i­cal aver­age default rate across firms, which may or may not be sta­tion­ary and/​or mean­ing­ful, or (2) an implied default rate, which depends upon any num­ber of assump­tions, includ­ing an assump­tion about the LGD rate, and which–by def­i­n­i­tion–is hypo­thet­i­cal and does not reflect reality.

Which One is Better?

Of the two, we’d pre­fer to use actual observed rates rather than implied, risk-​neutral rates. Why? For a few rea­sons. First, there are set­tings in which the observed his­tor­i­cal default rate is a rea­son­ably proxy of the unknown, “true” default rates. That’s never the case with risk-​neutral, implied default rates, which could only equal “true” rates if investors were risk-​neutral, which they are not. (Some of our related posts pro­vide exam­ples of this dif­fer­ence. They are stark and easy to follow.)

Sec­ond, the credit reserve is sup­posed to rep­re­sent the expected loss – or dis­counted expected loss in a multi-​period set­ting – not the price of the expected loss. (Risk neu­tral mod­els per­mit prices to be viewed as expected val­ues, rather than as expected util­i­ties (of unknown util­ity func­tions). That’s the ben­e­fit of risk-​neutral mod­els; they “sim­plify” the math.) By def­i­n­i­tion, the reserve is the bank’s best guess of its expected loss over some time hori­zon. It’s not the price the bank would pay to elim­i­nate default risk. Those are two clearly sep­a­rate notions, and the dif­fer­ence would be the risk premium.

Third, as we men­tioned two para­graphs above, using observed or his­tor­i­cal rates does require assump­tions about the valid­ity of the past rep­re­sent­ing the future. That’s a huge prob­lem – the Prob­lem of Induc­tion – but in our mind that’s cleaner – and more likely to remain in one’s mind – than are the many addi­tional, spe­cific, math­e­mat­i­cal assump­tions to derive/​infer risk-​neutral default rates, the LGD.

As we men­tioned at the begin­ning of the post, there’s no good solu­tion, but we think that using his­tor­i­cal rates is the bet­ter solu­tion. We think that when oth­ers dis­agree it’s because they think that implied, risk-​neutral rates are more than the really are, i.e., the “market’s” esti­mate of default rates – not the “market’s” esti­mate of default rates under a risk-​neutral mea­sure, which means that they’re hypo­thet­i­cal, not real.

We’ll likely edit this post dur­ing the next few days.

Copy­right © 2009 Spero Consulting.

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Foot­notes:

Respond­ing to our request for com­ments in yesterday’s post, Happy Anniver­sary to…Us!, a reader from Aus­tralia pointed us to an excel­lent and quite com­pre­hen­sive arti­cle in May’s edi­tion of The Atlantic Monthly. (Thanks Steven.)

The arti­cle is enti­tled “The Quiet Coup,” and was writ­ten by Simon John­son, an econ prof at MIT and the for­mer Chief Econ­o­mist at the Inter­na­tional Mon­e­tary Fund (IMF). For­tu­nately, as you can tell by the link, the arti­cle is freely avail­able from The Atlantic’s web site.¹

Mr. John­son seems to be a very smart man with vast and use­ful expe­ri­ence and knowl­edge, and he uses his back­ground and skills to frame the cur­rent eco­nomic cri­sis in a very inter­est­ing way.

In much of the arti­cle, he treats the US as a poten­tial IMF client, and ana­lyzes the sit­u­a­tion the same way he would (or has) viewed emerg­ing mar­ket coun­tries faced by sim­i­lar crises, par­tic­u­larly with respect to the inter­ac­tions of the country’s oli­garchy and the gov­ern­ment. How­ever, he does rec­og­nize that the US is different.

“Of course, the U.S. is unique. And just as we have the world’s most advanced econ­omy, mil­i­tary, and tech­nol­ogy, we also have its most advanced oligarchy.”

We’ve talked about crony cap­i­tal­ism on sev­eral occa­sions, and Mr. John­son brings sev­eral insights to light. (We define oth­ers’ insights as things we haven’t thought, yet, or things that took us a long time to fig­ure out.)

Need­less to say, if you like our analy­ses of and pre­scrip­tions for the mort­gage débâ­cle and liq­uid­ity cri­sis, then you’ll like his, too. (If your new to our site, sam­ple our cat­e­gories and archives for related con­tent. There are vast quan­ti­ties of it.) For exam­ple, he writes:

“…This is what Ben Bernanke, the man who suc­ceeded him, said in 2006: “The man­age­ment of mar­ket risk and credit risk has become increas­ingly sophis­ti­cated. … Bank­ing orga­ni­za­tions of all sizes have made sub­stan­tial strides over the past two decades in their abil­ity to mea­sure and man­age risks.”

Of course, this was mostly an illu­sion. Reg­u­la­tors, leg­is­la­tors, and aca­d­e­mics almost all assumed that the man­agers of these banks knew what they were doing. In ret­ro­spect, they didn’t…”

and,

“To break this cycle, the gov­ern­ment must force the banks to acknowl­edge the scale of their prob­lems. As the IMF under­stands (and as the U.S. gov­ern­ment itself has insisted to mul­ti­ple emerging-​market coun­tries in the past), the most direct way to do this is nationalization…”

The entire arti­cle is well worth read­ing, and view­ing the cri­sis through the prism of an IMF econ­o­mist pro­vides fresh insights that few can offer.

There are two related essays in the edi­to­r­ial sec­tion of today’s (March 30) edi­tion of The Wall Street Jour­nal regard­ing gov­ern­ment over­sight and reg­u­la­tion that are worth men­tion­ing: Wel­come, Busi­ness­men, to Gov­ern­ment Over­sight and Trans­parency Is More Pow­er­ful Than Reg­u­la­tion. We’ll men­tion the suf­fo­cat­ing nature of reg­u­la­tions and then dis­cuss the more inter­est­ing topic last, includ­ing our own work of using XML-​based sys­tems and tags for (inter­nal) man­age­ment infor­ma­tion sys­tems, which relates to the dis­cus­sion of XBRL sys­tems in the sec­ond column.

Suf­fo­cat­ing Reg­u­la­tions and Bureaucracy

Is there any other kind? Well, yes. As we see it, reg­u­la­tion is either suf­fo­cat­ing or inef­fec­tive, and the for­mer often has a crush­ing feel about it. Like mod­ern dig­i­tal tele­vi­sion sets, gov­ern­ment reg­u­la­tors seem to have no “fine-​tuning” dial; it’s gen­er­ally one extreme or the other: either there’s “NO EXCEPTIONS” or “it’s all good, do what you want.”

Vic­to­ria Toens­ing dis­cusses that over­bear­ing weight of the gov­ern­ment in Wel­come, Busi­ness­men, to Gov­ern­ment Over­sight in which she high­lights, among other indig­ni­ties, the silli­ness of gov­ern­ment offices unable to accept small gifts like cherry pies. Our guess is that she has spent most of her life in pub­lic ser­vice and doesn’t appre­ci­ate how sim­i­larly bureau­cratic large cor­po­ra­tions can be, but that’s besides the point because much – although not all – of that cor­po­rate bureau­cracy is induced by gov­ern­ment regulation.

We’ve dis­cussed both neg­a­tive aspects of reg­u­la­tion in numer­ous posts although we tend to high­light inef­fec­tive­ness because it has been very obvi­ous in the cur­rent finan­cial cri­sis and the mort­gage débâ­cle that pre­ceded (and which con­tin­ues to coin­cide with) it. For exam­ple, on Sat­ur­day we wrote The Cure is Worse than the Dis­ease, which crit­i­cizes Mr. Geithner’s pro­posed finan­cial sys­tem reg­u­la­tions.¹ We fear the suf­fo­ca­tion to come.

Gen­er­ally, we favor decen­tral­ized gov­ern­ment and much pre­fer decen­tral­ized work­ing envi­ron­ments, i.e, light reg­u­la­tion with the polic­ing authority’s option to crush, i.e., heav­ily penal­ize for indis­cre­tions. We take that from the Bible and the Para­ble of the Good (and Bad) Ser­vants, which cov­ers both moral haz­ard and igno­rance, and that’s why we’re strong pro­po­nents of nation­al­iz­ing the weak­est of the large banks. (Not because we think the gov­ern­ment will man­age them bet­ter but because we think share­hold­ers and cur­rent man­age­ments have for­saken the right to con­trol those assets.)

Suf­fo­cat­ing reg­u­la­tions and bureau­cracy usu­ally pro­vide no ben­e­fit to soci­ety and are inhu­mane and demean­ing. If “effec­tive,” they usu­ally end up killing the thing they are try­ing to pro­tect. (Nation­al­ized health-​care any­one?) In short, that’s why we’re against Mr. Geithner’s plan.

Trans­parency Anyone?

The other col­umn worth men­tion­ing is L. Gor­don Crovitz’s Trans­parency Is More Pow­er­ful Than Reg­u­la­tion in which he focuses his atten­tion on a sub­sti­tute for exten­sive reg­u­la­tory over­sight: more report­ing trans­parency. For sup­port of his posi­tion, he men­tions for­mer Supreme Court Jus­tice Louis Brandeis’s point that “sun­light is the best dis­in­fec­tant,” which we often cite, but is irrel­e­vant here.

While we tend to agree with many of his points, we think, that in the end, Mr. Crovitz draws the wrong con­clu­sions because (1) in gen­eral, in social set­tings more trans­parency isn’t nec­es­sar­ily bet­ter (doesn’t nec­es­sar­ily improve social wel­fare and can decrease it), and (2) in the spe­cial case of secu­ri­ti­za­tions of pooled assets, addi­tional trans­parency won’t solve the prob­lem of flawed pric­ing mod­els because the mod­els’ own­ers have lost con­fi­dence in them.

Is More Infor­ma­tion Always Better?

It depends. In sin­gle per­son games – i.e., nat­ural sci­ence exper­i­ments and games against nature, more infor­ma­tion is bet­ter. Roughly, that means it leads to higher expected sat­is­fac­tion for the par­tic­i­pant.² Clearly, record-​keeping is nec­es­sary for sev­eral rea­sons, but often those records don’t nec­es­sar­ily pro­vide mar­ginal ben­e­fit for decision-​makers in all deci­sions, i.e., the records might not iden­tify addi­tional rel­e­vant or dif­fer­en­tial costs or ben­e­fits among the pos­si­ble alter­na­tives for the deci­sion. Alter­na­tively, because they are not per­fectly ratio­nal, decision-​makers may not be able to cat­e­go­rize and syn­the­size or relate the new infor­ma­tion that is present, or they might mis­use it.

In a seem­ing con­tra­dic­tion to that view, last week, in Sep­a­rat­ing the Mort­gage Débâ­cle from the Liq­uid­ity Cri­sis, we agreed with Her­nando de Soto’s rec­om­men­da­tion that more details about con­tin­gent claims and secu­ri­ti­za­tion con­tracts should be made pub­lic, and Mr. Crovitz explains how this is tech­ni­cally fea­si­ble through the XBRL initiative.

As we see it, such details are infor­ma­tive about cer­tain aspects of the con­tracts, but not what Mr. Crovitz thinks. For exam­ple, it might help cred­i­tors bet­ter under­stand par­tic­u­larly low out­comes asso­ci­ated with cer­tain secu­ri­ties; so, we think that the details are worth report­ing, BUT the addi­tional details may not help with pric­ing claims on the pooled assets. Thus, we don’t see how trans­parency will induce liq­uid­ity. In fact, mar­kets often fail because there is “too much” trans­parency to sus­tain trans­ac­tions, i.e., no one wants the clearly-​identifiable crap – the lemons.

As we’ve writ­ten in the past, one of the prob­lems with these pric­ing mod­els for pooled assets is that their own­ers have lost con­fi­dence in them. They’ve lost con­fi­dence because they view the mod­els as no longer applic­a­ble, and they view them as no longer applic­a­ble because they have failed empirically.

They failed because they did not cap­ture the rela­tion­ships and inter-​relations among the assets, par­tic­u­larly among res­i­den­tial mort­gages. (In other words, the traders and ana­lysts vastly under-​estimated the joint depen­den­cies among cash flows and col­lat­eral val­ues, which those folks may express as hav­ing a poor esti­mate of the cor­re­la­tions, but which is likely more com­pli­cated and far less cal­cu­la­ble than that.) We’ve writ­ten about that on sev­eral occa­sions, includ­ing here: Trad­ing, Incen­tives, Orga­ni­za­tional Struc­ture and Risk Man­age­ment, where we explain it as a con­ta­gion. (We also dis­cuss it in Well, This Is a Fine Mess You’ve Got­ten Us into…. along with other still per­ti­nent issues.)

The prob­lem is that there are few math­e­mat­i­cally tractable ways to spec­ify how these assets are related; so, solv­able – but non­de­scrip­tive and mis­spec­i­fied – meth­ods were employed. In sta­ble times and with a bit of good luck, that mis­spec­i­fi­ca­tion didn’t seem to mat­ter. Unfor­tu­nately, luck changed, and did and it does now.

So, we don’t see how trans­parency will induce trad­ing, but that doesn’t mean that trad­ing can­not occur. (Mr. Crovitz has a good solu­tion, but to a dif­fer­ent prob­lem, i.e., Mr. de Soto’s problem.)

Our Solu­tion

Since Sep­tem­ber we’ve rec­om­mended changes in tax poli­cies – via mort­gage invest­ment tax cred­its or imme­di­ate write-​offs of pur­chase prices – as a way to induce trade and cre­ate liq­uid­ity in these secu­rity mar­kets. Pro­vid­ing a 30 – 40% cush­ion in the pur­chase price, will induce trad­ing even if buy­ers aren’t com­pletely con­fi­dent of their cal­cu­la­tions. Imag­ine if the same tax incen­tives were avail­able to new car buy­ers? (See “The Good Cop” sec­tion of Poor Mr. Gei­th­ner: No For­est, No Trees, Just Lost for a recent overview of our plan.)

What Does This Have to Do with MIS?

The same types of sys­tem that XBRL is based upon are avail­able very cheaply for inter­nal decision-​makers. We’re design­ing and imple­ment­ing sim­i­lar robust, tagged sys­tems for our clients. They are eas­ily search­able sys­tems – both infor­mally (ad hoc) and for­mally (rou­tine reports); they’re easy to update and edit; they’re secure; and they’re rel­a­tively inex­pen­sive. The ben­e­fits of tech­nol­ogy can now be real­ized by any size firm or orga­ni­za­tion. Con­tact us for more information.

As always, we might update this post after we re-​read it.

Copy­right © 2009 Spero Consulting.

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Foot­notes:

We think the cur­rent gov­ern­ment and indus­try strat­egy of attempt­ing to prop-​up the dead as a way to re-​energize the party and stay alive (or rel­e­vant) is bound to fail. In reminds us of the plot from the 1989 com­edy, Week­end at Bernie’s. Is TARP II noth­ing more than a remake of the 1993 sequel?

We read in The Wall Street Jour­nal today that Bank of Amer­ica to Get Bil­lions in U.S. Aid, and as usual we won­der whether it is necessary.

We doubted the neces­sity of TARP the first time our money was wasted, and con­tinue to do so now. Well, we did more than doubt the neces­sity, we pre­dicted that the government’s plan – and, again, plan is too strong, too “orga­nized,” of a word to describe the sequence of actions – would exac­er­bate and elon­gate the crisis. 

And three months later…well, here we are. The weather is colder, but lit­tle else has changed – much as we predicted.

Accord­ing to today’s arti­cle, last month Mr. Paul­son, in another – and hope­fully final – fit of panic, promised our tax dol­lars to B of A to com­plete its merger with Mer­rill Lynch. Per­haps, we should say “to sur­vive its merger with Mer­rill Lynch,” because sur­prise, sur­prise, the arti­cle men­tions that Mer­rill lost even more than it had pre­vi­ously guessed.

Now the reg­u­lar reader may ask: why do we con­tinue to crit­i­cize this cor­po­rate wel­fare and crony-​capitalism? For all of the same rea­sons we’ve used in the past, but also with a new one, too.

Despite the con­tin­u­ing volatil­ity and losses – as we write, the DJIA is near 8,000, again – the finan­cial world is a dif­fer­ent place today than it was a mere three months ago. Either out of sheer panic or self-​preservation, many orga­ni­za­tions have reigned in their trad­ing oper­a­tions and have attempted to limit or elim­i­nate their counter-​party credit risk. (Uh, that’s the nature of a liq­uid­ity cri­sis, which we’ve joked is the psy­cho­log­i­cal pro­jec­tion of finan­cial state­ments; see the top two posts.)

So, we doubt that the demise of Mer­rill in late Decem­ber or the demise of other firms today would have been as “harm­ful” as the demise of Lehman, AND we seri­ously doubt that the demise of Lehman was as harm­ful as our pan­icky policy-​makers and cor­po­rate pro­pa­gan­dists and blame-​shifters would like to have oth­ers believe. 

For exam­ple, in another arti­cle in today’s paper, Deutsche Bank Warns of Loss, Blam­ing Its Trad­ing Mis­fires, it is men­tioned three times that Lehman was the cause of much of Deutsche’s trou­bles. (That thrice-​repetition reminds us of ancient Greek lit­er­a­ture and Bible pas­sages. As we’ve been told by both edu­ca­tors and priest, when you see it in threes, then you should know that it must be impor­tant! Ha!)

We’re sure that Lehman’s demise caused sub­stan­tial pain to many firms and indi­vid­u­als. But all the pain? No, much of that pain should be attrib­uted to lax con­trols, includ­ing poorly designed incen­tive schemes, and lax risk man­age­ment. We view much of the blame cur­rently put upon Lehman to be a school of red her­rings (either of the top two def­i­n­i­tions will suffice).

How­ever, we’ll use those con­ve­nient excuses to turn the argu­ment against the call for fur­ther bailouts. If Lehman’s demise – whether alone or in con­cert with other events – did cause mar­kets to seize and did cause many orga­ni­za­tions to begin to avoid risk and limit the exten­sion of credit, then it would seem that the fail­ure of another large firm would have less impact today than in Sep­tem­ber. So, what’s the harm.

Of course, as we writ­ten about on numer­ous occa­sions, despite our near Lib­er­tar­ian stance on eco­nomic issues, we’d pre­fer to see the gov­ern­ment nation­al­ize the worst offend­ers as a way to moti­vate the remain­ing firms to ratio­nal­ize their oper­a­tions: wipe-​out exist­ing share­hold­ers, except non-​executive employ­ees; fire the boards and senior man­agers; take 100% own­er­ship; and resell it as soon as possible.

Also, we’d still like to see changes in tax pol­icy to moti­vate the exchange of the moun­tains of cur­rently illiq­uid and deval­ued mort­gage secu­ri­ties: either res­i­den­tial mort­gage invest­ment tax cred­its or the imme­di­ate write-​off of the pur­chase price would suf­fice to pro­vide pur­chasers with a cush­ion against overly-​optimistic val­u­a­tions. (You might as well include com­mer­cial mortgage-​backed secu­ri­ties, too.)

As we wrote in early Octo­ber, the government’s solu­tion will extend the cri­sis because no one knows how to value those secu­ri­ties, and by the government’s own admis­sion, that hasn’t changed.

We think that com­bi­na­tion of moti­vat­ing the sell­ers with sticks and the buy­ers with car­rots, so-​to-​speak, would work.

It Doesn’t Add Up.

Accord­ing to The Wall Street Jour­nal, today S&P Cut Rat­ings on 11 Banks.

Depend­ing upon each institution’s account­ing poli­cies, indi­vid­u­als at those firms may have cheered their firm’s respec­tive down­grade because that action may have reduce the value of the firm’s out­stand­ing debt thereby allow­ing the firm to rec­og­nize an unre­al­ized gain on its income state­ment. (Yeah, it is per­verse and stupid.)

For exam­ple, by com­bin­ing the con­tents of this arti­cle about Mor­gan Stanley’s fourth quar­ter earn­ings and page two of this report, it seems that Mor­gan Stan­ley equity-​holders “gained” about $3.6 bil­lion because the firm’s debt – its promise to meet future long-​term oblig­a­tion – has become worth sub­stan­tially less to cred­i­tors than it was at the end of August. (We cal­cu­late the $3.6 bil­lion as $5.9 bil­lion of com­bined real­ized gains – from the actual repur­chase of its long-​term debt – and unre­al­ized gains – from writ­ing down the book value of debt – which are men­tioned in the arti­cle, minus about $2.3 bil­lion of real­ized gains men­tioned on the income state­ment, but we could be wrong, and its kind of besides the point; so, we don’t mind being wrong.)

Reg­u­lar read­ers will note that for quite some time, we’ve promised a rather long post on the nature of mark-​to-​market account­ing, but we’ve been busy, and it’s not the most excit­ing topic.

Our view is that there is noth­ing inher­ently wrong with mark-​to-​market account­ing for assets when mar­kets exist. 

Unfor­tu­nately, for many asset classes, there aren’t robust, active mar­kets; so, the exer­cise become mark-​to-​model (by def­i­n­i­tion an abstract, sim­pli­fied view of real­ity) or mark-​to-​quote (by def­i­n­i­tion an unful­filled wish or hope if no exchange took place). But we’ll save those issues for a longer and more detailed post when time is less pre­cious, but today we must fin­ish deck­ing the halls.

In our view mark-​to-​market for lia­bil­i­ties makes far less sense and cre­ates a per­verse sit­u­a­tion where a weak­ened firm may the­o­ret­i­cally ben­e­fit from that weak­ness; it’s not the same as loss carry-​forwards.

We’ll try to be clear. Take our esti­mated real­ized gains and unre­al­ized gains for Mor­gan Stan­ley as given, i.e., $2.3 bil­lion real­ized on retired debt and $3.6 bil­lion unre­al­ized on out­stand­ing debt.

Rec­og­niz­ing a real­ized gain on the early pay-​off on debt makes com­plete sense. If Mor­gan Stan­ley was able to repay $2.3 bil­lion less than the book value of its debt, then good for the firm and its own­ers. Note that such a sit­u­a­tion could occur if either base inter­est rates increased sub­stan­tially or credit spreads widened sub­stan­tially. (Those are actu­ally arti­facts, not rea­sons, but that’s how folks talk.)

In our mind, rec­og­niz­ing an unre­al­ized gain of $3.6 bil­lion is prob­lem­atic. Hold­ing base rates con­stant – and they’ve actu­ally decreased this fall – the only way for debt to lose such value is if the firm’s (per­ceived) cred­it­wor­thi­ness has deteriorated.

In that case and at some point, it would seem that the firm would not have the cash bal­ances nor the cash flow to real­ize the reduc­tion in out­stand­ing, con­trac­tual claims against it. To us, that means that the claim against the firm remains at the face value, and the resid­ual claimants – the share­hold­ers – would have to sat­isfy that entire claim (or some nego­ti­ated amount) before they would receive any­thing.

More­over, if the firm is uncred­it­wor­thy and can­not refi­nance the debt, then by the def­i­n­i­tion of a lia­bil­ity – an item of expected future sac­ri­fice from a past trans­ac­tion or event – the firm should record the lia­bil­ity at (1) its approx­i­mate face value (plus or minus any pre­mium or dis­count) or (2) its liq­ui­da­tion value in case of bankruptcy. In that lat­ter case, it is not clear whether the firm remains a going-​concern or not.

There­fore, if it is a going con­cern but it can­not pay-​off – say with cash or via refi­nanc­ing – at the deval­ued mar­ket value of debt, then we say that the expected future sac­ri­fice is not the “mar­ket value,” it is the face value. So, where is the gain? Nowhere; it doesn’t exist.

It seems that knowl­edge and its rarer cousin, wisdom, have no role at the FASB or the SEC. We derived our argu­ment from basi­cally one def­i­n­i­tion – a lia­bil­ity – and one assump­tion: the firm’s a going con­cern. Does it seem that our policy-​makers have lost sight of the prover­bial for­est because of the trees? Or are we wrong? If so, how?

In their attempts to become rel­e­vant, they’ve achieved the opposite.

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:

We were search­ing our hard drive for a paper, and found a very inter­est­ing arti­cle that we had saved about the per­ils of exces­sive lever­age. It is As Funds Lever­age Up, Fears of Reck­on­ing Rise from the April 30, 2007, edi­tion of The Wall Street Jour­nal. It is sub­ti­tled: Fed and SEC Ques­tion Wall Street on Poli­cies; ‘A Mock­ery’ of Mar­gin.

We’re not sure if an arti­cle from the Spring of 2007 is truly an early warn­ing per our title, but “Warn­ings of Exces­sive Lever­age” doesn’t read as nicely.

In light of very recent events and mar­ket events since mid-​2007, it is quite inter­est­ing and dis­cusses or quotes many famil­iar names, includ­ing, John Paul­son (big win­ner); The Penn­syl­va­nia State Employ­ees’ Retire­ment Sys­tem (not a big win­ner); Tim­o­thy Gei­th­ner (next Trea­sury sec­re­tary); War­ren Buf­fett (not Jimmy Buf­fett); Ken­neth Grif­fin and Citadel Invest­ment Group (not big win­ners); Edward Lam­pert (not big win­ner, although we do like Lands End at Sears); and many more.

In the arti­cle, the reporters para­phrase Janet Tavakoli as follows: “the col­lat­eral pro­vided by hedge funds to secure swaps could be dif­fi­cult to trade… In a mar­ket down­turn, attempts to unwind such posi­tions could lead to a vicious cycle of sell­ing that would feed on itself…” Sounds reasonable.

We also par­tic­u­larly like this lit­tle box that doesn’t appear in the on-​line article:

RISK FACTOR

•  The Sit­u­a­tion: Reg­u­la­tors have grown wor­ried about ris­ing lever­age in the U.S. finan­cial sys­tem.
 
•  The Play­ers: Hedge funds and the Wall Street firms that pro­vide them with financ­ing are among the biggest con­trib­u­tors to the rise.
 
•  The Bot­tom Line: No one is sure what will hap­pen with this com­plex web of bor­row­ing and deriv­a­tives in the event of a seri­ous mar­ket downturn.

Wow, who would have thunk that there were peo­ple way back in 2007 warn­ing of such risks as well as the lax­ity of risk man­age­ment. Does this mean that the ongo­ing liq­uid­ity cri­sis need not have occurred? (By 2007, it was already too late to pre­vent the mort­gage cri­sis.) Does that mean the destruc­tion of tril­lions of dol­lars of wealth could have be pre­vented and avoided? So, this sug­gests that it wasn’t (and isn’t) a nat­ural dis­as­ter. Wow! And for what?

A Vari­ety of Risk & Incen­tive Ideas All in One Post!

There is an arti­cle in The Wall Street Jour­nal today enti­tled, Citadel’s Losses Add to Mr. Griffin’s Pain.

We’re rather indif­fer­ent to Mr. Griffin’s pain as we’re sure that he is to ours, but that’s not why we are writing.

We men­tion the arti­cle because it relates to ear­lier post­ings and pro­vides an idea for exec­u­tive com­pen­sa­tion that we haven’t seen dis­cussed before.

Mar­kets, Crises, Nedges and Sledges. It’s often the case that rel­a­tively the good per­form­ers or safer invest­ments suf­fer unjus­ti­fi­ably along with bad per­form­ers or losers in mar­ket down­turns, crises, and pan­ics. We ital­i­cized “unjustifiably” because we doubt that such a notion applies to mar­ket eco­nom­ics. However, such events can tran­spire for a num­ber of reasons. 

As we men­tioned on Tues­day in Tak­ing the Fun(ds) out of Hedge Funds, bet­ter per­form­ers may suf­fer – if there is such a notion in mar­kets – when poorly incen­tivized investors sell those secu­ri­ties at small gains or small losses rather than rec­og­nize large losses on ter­ri­ble performers.

Also, as Richard Book­staber nicely describes in the excel­lent A Demon of Our Own Design there may be runs on high qual­ity assets if mar­ket par­tic­i­pants know that dis­tressed sell­ers hold those assets. Mr. Book­staber pro­vides a few exam­ples, includ­ing the run on Brazil­ian bonds dur­ing the Asian Cri­sis (in 1997), and Long-​Term Cap­i­tal Management’s (LTCM’s) mas­sive prob­lems due to the fact that it was pub­licly announced that Trav­el­ers was end­ing pro­pri­etary, fixed-​income trad­ing at Salomon Smith Bar­ney in July, 1998.¹

In addi­tion, these mar­ket dynam­ics are why we often refer to hedges as nedges (near hedges) or sledges (some­what like hedges). Pedge or predge for “prob­a­bilis­tic hedge” also cap­tures this notion that things aren’t as secure, locked-​down, and pre­dictable as they might at times seem.

In stressed times, there are few proper – i.e., risk-​free – hedges. Instead, it becomes quite pos­si­ble to lose on both sides of trade. One of the main, exac­er­bat­ing prob­lems is the fact that dur­ing calm times, traders and ana­lysts receive evi­dence that allows them to over­es­ti­mate the valid­ity or pre­dictabil­ity of the inter­ac­tions of the var­i­ous parts. So, for those folks, “hedg­ing” day-​to-​day prof­its and activ­i­ties dur­ing calm times, espe­cially in “cost-​effective” ways, leaves them exposed to the rarer, but far more dam­ag­ing large events.²

High-​water Marks and Exec­u­tive Com­pen­sa­tion. The arti­cle on Citadel briefly men­tions high-​water marks that relate to asset val­ues and com­pen­sa­tion for fund man­agers. That means that if a (hedge) fund gen­er­ates loses, it must recoup those losses before the fund man­ager can earn a per­for­mance bonus – usu­ally 20% of gains.

We’d like to see cor­po­ra­tions imple­ment sim­i­lar, equity-​related com­pen­sa­tion schemes for their senior man­agers and boards.

A quick search of the web turns up oth­ers offer­ing the same rec­om­men­da­tion, but our brief search iden­ti­fied no firms that have incor­po­rated such a sched­ule into their exec­u­tive com­pen­sa­tion plans. 

We could see where it would be dif­fi­cult to show that such a pol­icy is opti­mal in a math­e­mat­i­cal agency model, but that’s due to com­pu­ta­tional con­straints that force such mod­els to be stark. The basic rea­son that such a pol­icy would be sub­op­ti­mal in a math­e­mat­i­cal model is that there would likely be a wide range of pre­lim­i­nary out­comes where it would be dif­fi­cult to moti­vate the per­son to con­tinue to work, and given that, the ini­tial risk pre­mium would have to be large to ensure that the agent would par­tic­i­pate.³

How­ever, in real life, such a pol­icy would seem very com­pelling and would likely be less demo­ti­vat­ing to other employ­ees, and that should be worth some­thing. In fact, maybe even more than the direct effect on man­age­ment, and that’s one of the ben­e­fits that would be dif­fi­cult to for­mally model with­out a sub­stan­tial loss of ele­gance or the elim­i­na­tion of solvability.

Now, per­haps we’re also drawn to the idea because we’ve seen any num­ber of man­age­ments paid for sub­stan­tial improve­ments in share prices that turn out to be noth­ing more than the right-​side of an upward fac­ing parabola. The same man­age­ment team was also in place dur­ing the left-​side decline, too. Of course, we’re will­ing to sar­cas­ti­cally admit that down times can’t be avoided as they’re always due to gen­eral eco­nomic con­di­tions, whereas the upsides are solely due management’s actions and prowess. Yeah, we doubt that you’re buy­ing it, either.

As always, we might update the post as we think about it a bit more.

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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.

This post greatly expands upon a com­ment we made about reg­u­la­tion in Even A Per­fect Bailout Will Fail and pos­si­bly elsewhere.

Reg­u­la­tors as wise monkeys.

Today’s The Wall Street Jour­nal has an arti­cle enti­tled, Bank Exam­in­ers Are Told to Step Up Sanc­tions on Lenders.

The first sen­tence of the arti­cle says it all: “The U.S. government’s armies of bank exam­in­ers have been ordered to be more aggres­sive in apply­ing for­mal sanc­tions to finan­cial insti­tu­tions when prob­lems are found.”

Unfor­tu­nately, order­ing does not make it so, and we doubt that it will work. We’re not mak­ing a blan­ket con­dem­na­tion here, but we’d be inter­ested in know­ing if and how the gov­ern­ment deals with the incen­tive prob­lems that we address below.

Unless the Fed, the OCC, and the OTS imme­di­ately trans­fer and reas­sign exam­in­ers, we doubt that many new issues will be found. Fur­ther­more, if such issues are dis­cov­ered, we doubt that those issues will be reported. (In this post, we’ll call such bank-​related prob­lems “issues,” and reserve the word “prob­lem” for the dys­func­tional incen­tives that may exist within the reg­u­la­tory agen­cies.) Of course, there are many obvi­ous issues that can be noticed with­out for­mal exam­i­na­tions and investigations.

Incen­tive Problems

There are, in fact, a cou­ple of related incen­tive prob­lems worth men­tion­ing. (1) Many exam­in­ers spend many years exam­in­ing only one firm. At large insti­tu­tions, the exam­iner is usu­ally located on the bank’s premises – pos­si­bly shar­ing office space, e-​mail sys­tems, and din­ing room priv­i­leges with bank employ­ees and managers. (2) Many exam­in­ers seek (and gain) employ­ment with the same finan­cial insti­tu­tion that they pre­vi­ously examined.

We’ll briefly address the sec­ond issue first by ask­ing: what incen­tive does an exam­iner have to take a “hard-​line” by ques­tion­ing the value of assets or cap­i­tal reserved if it may infu­ri­ate or alien­ate a poten­tial employer? (We’ll return to this issue at the end of the post, too.)

The elim­i­na­tion of the prospect of future employ­ment, however, does not elim­i­nate the incen­tive prob­lem for long-​time exam­in­ers. For rep­u­ta­tional rea­sons, they may still lack the moti­va­tion to closely scru­ti­nize and report issues.

Now, clearly some degree of famil­iar­ity is ben­e­fi­cial when exam­in­ing or audit­ing insti­tu­tions because that knowl­edge reduces the set-​up and oper­at­ing costs of per­form­ing the exam­i­na­tion: port­fo­lios, sys­tems, and key per­son­nel are all known by the repeat exam­iner. In addi­tion, it becomes quite expen­sive for the gov­ern­ment to move exam­in­ers and quite dis­rup­tive for exam­in­ers and their fam­i­lies to be peri­od­i­cally relo­cated to dif­fer­ent insti­tu­tions in pos­si­bly dif­fer­ent regions of the coun­try (or to travel extensively).

It is the case that cer­tain higher-​level man­agers are rotated, but that seems insuf­fi­cient to ensure that lower-​level work­ers will nec­es­sar­ily report issues of which they know. More­over, who is more likely to dis­cover (or be infor­mally informed of) such issues?

Sunk Cost Fallacy

Our long-​time exam­iner incen­tive prob­lem is sim­i­lar to the sunk cost fal­lacy that has been exten­sively stud­ied by econ­o­mists – includ­ing infor­ma­tion econ­o­mists – who address the question: why do man­agers keep invest­ing in (seem­ingly obvi­ous) los­ing projects?[1. There are other expla­na­tions, too. For exam­ple, we like this quote by Father Joseph Holzner, author of Paul of Tar­sus,: “When a man feels the bur­den of guilt on his soul, he tries hard to jus­tify him­self before his own con­science and before oth­ers by increas­ing his false zeal, and thus he sinks yet deeper into evil.”] 

There is an option-​value expla­na­tion that if (exoge­nous) cir­cum­stances change, the poorly-​performing project may become valu­able; so, it is worth the cost to main­tain that flex­i­bil­ity (and pay the equiv­a­lent of an option pre­mium). That expla­na­tion makes the deci­sion to invest to be very much like insurance.

The infor­ma­tion story is dif­fer­ent and involves adverse selec­tion and reputation. A man­ager who made or who sup­ported the ini­tial invest­ment may feel that his rep­u­ta­tion is at stake and his judg­ment may be ques­tioned by admit­ting that a project that they had picked as a win­ner was actu­ally a loser (and so oth­ers may infer that the said man­ager is a loser, too.)

How It Relates to Regulation

Most bank activ­i­ties are long-​lived – because they are or because they are like invest­ments. Thus, for dubi­ous ongo­ing ven­tures, the exam­iner must decide whether or not to crit­i­cize or men­tion them.

Imag­ine a multi-​year ven­ture, activ­ity, or invest­ment that the exam­iner has not men­tioned or crit­i­cized in pre­vi­ous years. Gen­er­ally, it would be highly unlikely that there were no warn­ing signs in prior peri­ods, espe­cially if the examiner’s supe­rior were gifted with per­fect, ²⁰⁄₂₀ hind­sight, which is quite easy to pos­sess (and requires much dis­ci­pline to control).

In that case, we could imag­ine the undis­ci­plined supe­rior ques­tion­ing the examiner’s past per­for­mance: “did you miss it because you are incom­pe­tent or did you catch it and fail to men­tion it because you are duplic­i­tous?” (Here is an essay on Strate­gic Con­sis­tency and Man­age­r­ial Dis­ci­pline.) It seems that any exam­iner with any bit of fore­sight could also make this inference.

Thus, it may be in the ratio­nal – though not con­sci­en­tious – examiner’s best inter­ests to act as a trin­ity of wise mon­keys and sup­press his pri­vate infor­ma­tion and discoveries.

Empir­i­cally and as a tax payer, we do believe it is fair to ask: how many exam­in­ers or final­ized exam­i­na­tion reports warned about any of the prob­lems that we are now expe­ri­enc­ing? How many of those unre­ported mortgage-​related issues arose only in 2008 or the lat­ter half of 2008? In that respect, the reg­u­la­tory agen­cies seem much like the government-​regulated credit agen­cies with their over-​optimistic scenarios.

We can’t hypoth­e­size all of the blame lower-​level work­ers. There are cer­tainly con­sci­en­tious exam­in­ers who may or may have men­tioned issues. Given our quite skep­ti­cal view of the (fallen) nature of man, it is quite easy to believe that in some cases their warn­ings were sup­pressed by their supe­ri­ors, who despite rota­tion, may be have attempted to main­tain good feel­ings with their sub­ject banks in their desire for a well-​paying cor­po­rate job.

Reg­u­la­tion as a Crutch (Causes Atrophy)

We’ll have more to say about the dele­te­ri­ous effects of reg­u­la­tion. We’re for­mu­lat­ing a post about the false sense of secu­rity that risk man­agers may pos­sess after they sat­isfy the ques­tions of (seem­ingly simian, albeit intel­li­gent simian) reg­u­la­tors. In other words, there is no rea­son to believe that pass­ing reg­u­la­tory hur­dles alone is equiv­a­lent to effec­tive risk or uncer­tainty management.

In today’s (Novem­ber 26) edi­tion of The Wall Street Jour­nal, there is a Deal Jour­nal arti­cle enti­tled, “Paul­son Plan: ‘Truly Idiotic.’”

Although we’ve not gone that far in describ­ing TARP et al, we’ve been harshly crit­i­cal of Mr. Paul­son. In fact, we’ve men­tioned that his series of actions don’t seem to con­sti­tute an actual plan, because the word “plan” implies a cer­tain degree of, well, plan­ning or fore­sight and forethought, and those pre­req­ui­sites seemed absent in his Panic of ’08.

The quoted accuser in the Deal Jour­nal arti­cle is Charles Calomiris, a prof at Colum­bia, and he make sev­eral good points, includ­ing “we’re using half-​measures designed in an inap­pro­pri­ate way,” and “The prob­lem is the com­pletely opaque dis­tri­b­u­tion of losses because no one knows how to value these mort­gage losses.”

We’ve made sim­i­lar remarks any num­ber of times, and it is exactly those opaque joint dis­tri­b­u­tions of cash flows (and there­fore losses) that cause all the trou­ble and makes the pools impos­si­ble to value with any degree of precision.

While we do agree with his crit­i­cism, we don’t agree with his rec­om­men­da­tions. Pri­mar­ily his sug­ges­tion that “the gov­ern­ment offer to buy any mort­gage for 40 cents on the dollar.”

It is unclear how the 40% solu­tion is derived, and think­ing in terms of Akerlof’s Lemons Model, you can be sure that only one type of mort­gage would be offered: one with a value between zero and 40% of face value.¹ Thus, if the gov­ern­ment com­mits to pur­chase any mort­gage, it would cer­tain over-​pay, and thus sub­si­dize the worst cases, and if the gov­ern­ment does not com­mit, then it is likely the mech­a­nism would fail with few or any trans­ac­tions. (The dif­fi­culty of valu­ing the mort­gages does com­pli­cate mat­ters as does their cur­rent book value.)

Why not try a pri­vate solu­tion? Why not offer mort­gage invest­ment tax cred­its or per­mit imme­di­ate and accel­er­ated amor­ti­za­tion (depre­ci­a­tion) of the pur­chase price of those mort­gages and mortgage-​related secu­ri­ties for prospec­tive buy­ers? Then set low tax rates for prospec­tive real­ized cash flows.

We’re sure that many buy­ers have some val­u­a­tion model, but likely (and jus­ti­fi­ably) do not trust it. Giv­ing a 30% — 40% tax break should pro­vide them with an ample cush­ion to take a chance. How could such a plan be any worse than a government-​administered plan, or a government-​regulated, fixed-​price one? (Remem­ber the government’s suc­cess at other attempts at price con­trols: both sup­ports and ceilings.)

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.

Noth­ing has solved the over­whelm­ing prob­lem that the mar­kets do not trust the large finan­cial inter­me­di­aries, and those banks do not trust each other. The mort­gage cri­sis informed about the banks’ short­com­ings; so, solv­ing that mort­gage cri­sis won’t cause any­one to believe that the bank’s judg­ment has improved – at least for quite some time. In that respect, Mr. Calomiris is quite right. Mr. Paul­son has done noth­ing to help.

Thank god we live in a coun­try that can with­stand such epic mis­man­age­ment. What was the total $7.5 trillion?

(New read­ers can search the archives from the past sev­eral months to find many related articles.)

Note: We’ll likely expand and edit this post in the morn­ing, but wanted to cir­cu­late the idea before bedtime.

We’re rather dili­gent – but not obsessed– about keep­ing up with finan­cial new.¹ We’ve heard many finan­cial firms announce lay-​offs and have read how at a few, like Gold­man, senior man­agers have decided to forgo bonuses.

As we recall, most banks have announced with­drawals from sub­prime mort­gage orig­i­na­tion and loans, which seems like a wise move, but given the mag­ni­tude of their errors and mis­takes, we’re very sur­prised that we haven’t read more about banks tak­ing dra­matic and dras­tic actions to limit risks and exposures.

We don’t mean hoard­ing cash and the knee-​jerk reac­tions not to lend. We’re think­ing more about their invest­ing, trad­ing, and struc­tur­ing operations.

Maybe the banks are elim­i­nat­ing desks and floors, but they just aren’t talk­ing about it, or maybe they have men­tioned it, but we’ve missed it.

We’d cer­tainly encour­age finan­cial firms to change their ways. In fact, while we’re close to Lib­er­tar­ian on many eco­nomic issues, we wrote on Octo­ber 11, to Elim­i­nate Pro­pri­etary Trad­ing at Insured Insti­tu­tions as a way to mit­i­gate moral haz­ard and pro­tect tax-​payer interests. (Once they’re insured, it is no longer a free mar­ket, and there should be quid pro quo, not just subsidization.)

On Sep­tem­ber 24, in our post Could a “Bailout” Pro­long the Finan­cial Cri­sis?, we wrote:

So, if the government’s pur­chase of these thin­gies is approved, we would expect to see a con­tin­u­a­tion of the pan­icky behav­ior until the secu­ri­ties are actu­ally trans­ferred to the gov­ern­ment because it is unlikely that any­one will know who has the worse ones so (means that) all remain sus­pect. (Also note that the most pan­icky firms might be ones who are pro­ject­ing their port­fo­lios onto oth­ers, and so might be the ones that other firms would like to avoid.)

Now that the TA is out of TARP, it seems that this week’s equity mar­ket per­for­mance, par­tic­u­larly among finan­cial firms, sup­ports our Sep­tem­ber 24^th pre­dic­tion above, i.e., the con­tin­u­a­tion of pan­icky behav­ior until actual trans­fers occur. We dis­cussed related issues on Octo­ber 7, in Even A Per­fect Bailout Will Fail.

Or maybe they’re just tak­ing a wait-​and-​see approach. That’s what we pre­dicted in early Octo­ber when we described the very high prob­a­bil­ity of fail­ure of TARP.

Today’s Wall Street Jour­nal reports that Citi Weighs Its Options, Includ­ing Firm’s Sale, and we won­der if it will sur­vive the weekend.

As we argued in Big­ger Is Not Nec­es­sar­ily Bet­ter way back in Sep­tem­ber, we see no rea­son to encour­age mega-​mergers and we based that argu­ment on both moral haz­ard and sys­tem­ati­za­tion of idio­syn­cratic risk considerations.

So, as we argued in around Octo­ber 10, we believe that It’s Time! to nation­al­ize the worst offend­ers leav­ing no share­hold­ers, except non-​executive employ­ees, with any own­er­ship inter­ests. We reit­er­ated much of the same argu­ment in a very long post from Wednes­day: OMG, Mr. Paul­son Agreed with Us Twice in One Week! (Yeah, we have a teenager.)

It seems that given its size of around $2,000,000,000,000, we tax­pay­ers will be on the hook for Citi, any­ways, so why not elim­i­nate the mid­dle­man and pro­vide any upside ben­e­fit to the true resid­ual claimants?

In two recent posts, The Fail­ure of Boards to Direct and When the Going Gets Tough…Quit, we’ve crit­i­cized the com­po­si­tion of Citigroup’s board because of their gen­eral lack of finan­cial indus­try expe­ri­ence. (We’re sorry, but that seems uncon­scionable to us.)

We won’t repeat all of our argu­ments for nation­al­iza­tion, but the expro­pri­a­tion of Cit­i­group would cer­tainly moti­vate other banks to act quickly and largely to mit­i­gate risks and sta­bi­lize cash flows. (It would likely stop insur­ance com­pa­nies and oth­ers from buy­ing small banks or S&Ls in their beg­garly attempts to become bank hold­ing companies.)

By the way, for new read­ers, we’re not just for the nation­al­iza­tion of a few banks, we actu­ally have a pri­vate solu­tion for the mort­gage cri­sis that involves pro­vid­ing the right tax incen­tives – like invest­ment tax cred­its – to indi­vid­u­als, firms, and fund man­agers. (Read about it here: A Bet­ter Solu­tion (than a gov­ern­ment takeover).)

That solu­tion to the mort­gage cri­sis stills leaves the larger liq­uid­ity or con­fi­dence cri­sis for banks. That has arisen because the mort­gage cri­sis has informed us (and oth­ers) that despite their pseudo-​sophistication and the veneer of objec­tiv­ity and sci­ence (almost), there is a very good chance that they don’t under­stand their envi­ron­ment or have reli­able ways to value many of their prod­ucts – despite their mas­sive invest­ments and activ­i­ties for those pur­poses. In terms of an adverse selec­tion prob­lem, they’ve reveal them­selves to be low types. (See last week’s Global Warm­ing and the Mort­gage Cri­sis for a dis­cus­sion on that topic.)

So, as a nation, we should want (and attempt to moti­vate) the banks to act quickly and deci­sively (and with their pri­vate infor­ma­tion) to get their accounts in order.

The ben­e­fits of TARP don’t seem to have pro­vided the cor­rect moti­va­tion to the bank­ing firms to act to main­tain their own liq­uid­ity and cap­i­tal posi­tions. We’d argue that this is an incen­tive prob­lem and that if the ben­e­fit of the TARP “car­rots” have been insuf­fi­cient moti­vate socially-​optimal behavior. So, per­haps a “stick,” like the threat of expro­pri­a­tion, induce clean-​up. More­over, it is seems that Citi will be ours any­way, so, why not give it a try on tax­pay­ers’ terms rather than tax­pay­ers’ backs?