pr abl buffett’s puts: a o ctri what are the risks? · ren buffett’s berkshire hathaway during...

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In the las t CORPORATE FINANCE

REVIEW piece , I thoroughlydescribed the very famous andvery controversial short deriva-tives trade undertaken by War-

ren Buffett’s Berkshire Hathaway duringthe 2004–2008 period. Once more, theSage of Omaha chose to se l l s izableamounts of put options on the S&P 500,FTSE 100, Nikkei 225, and Eurostoxx 50as well as credit protection on corporateand state-municipal names. If that pieceprovided many details about the charac-ter is t ics and evolut ion of the t rades ,together with an analysis of the rationalebehind them (recall: Buffett thinks thatthe eventual payouts to be suffered will bemore than offset by the premium initiallycol lec ted, thus af fording lots of ver ycheap funding in the form of “posit ivefloat”), here I focus on the put portfolioand on the risks that Buffett undertookby selling these particular options. Sincethe puts are by far the most sizable com-ponent of Buffett’s derivative forays, thisis a topic of particular relevance, and Iintend to shed some light on quite criti-ca l points that seem somet imes over-looked by observers and commentators.

Let’s briefly remind ourselves about themain aspects of the put portfolio. Theseare long-dated contracts, written between2004 and Februar y 2008 and expir ingbetween 2019 and 2028. As of the end ofSeptember 2013, the weighted averagelife of the puts was 7.5 years. The optionscan only be exercised at expirat ion andwere struck at the money (same levels asspot index leve ls at the t ime, but wehaven’t been told which ones, and this i s an unknown) . Berksh i re col lec ted $4.9 bil l ion in total premiums. Buffettbelieved the puts to have been severelyoverpriced and is confident he’l l makea substantial underwrit ing profit in the

end. Berkshire facesver y l imited col lat-eral requirements onthese contracts andhas so far had to postvery limited amountsthroughout the trade.

Exhibit 1 describes the evolution ofthe put portfolio’s notional amount andliabilit ies. The notional amount refers tothe size of the bet and thus the exposureand maximum potential loss facing Berk-shire. It changes if contracts are addedto or eliminated from the portfolio (thisgives you the equity exposure) and if thedol lar var ies w ith respect to the yen,euro, or Brit ish pound (this g ives youthe currency exposure; a lower dol lartranslates into a larger notional value).The liabilit ies figure refers to the mark-to-market value of the puts at any givent ime, or their l iquidat ion va lue (howmuch would it cost to buy them back).It represents Berkshire’s expected losson the contracts based on the outputfrom the Black–Scholes option pricingmodel, and it changes as the inputs intosuch a model experience a change (andagain as the relevant foreign exchangerates fluctuate).

In writing those puts, Buffett took twomajor types of r isks: accounting (evo-lut ion of the mark-to-market va lues)and settlement (final payouts at expira-t ion, if any). Since the market value ofthese derivat ives is accounted for in theincome statement on a continuous basis,higher liabilit ies translate into quarterlylosses on the posit ion and lower l iabil-it ies into quarterly gains. If those lossesor gains are significant, they could sub-stantial ly alter Berkshire’s overal l P&L(in fact, they have done so on occasion).Settlement r isks wil l materialize if theequity index levels are below the presetstr ikes come contract maturity date.

In this piece, we talk about both typesof risks. We’ll describe the main factorsthat can produce changes in the account-ing value of the puts sold by Berkshire.Buffett seems not to care too much (ifanything) about the accounting risk andbelieves settlement risk to be negligible.That’s not the case with everyone, sincemost financial players watch closely and

PABLO TRIANA is a professor at ESADE Business School andthe author of The Number That Killed Us: A Story of ModernBanking, Flawed Mathematics, and a Big Financial Crisis.

PABLO TRIANA

PRACTICAL MATTERS

BUFFETT’S PUTS: WHAT ARE THE RISKS?

CORPORATE FINANCE REVIEW JANUARY/FEBRUARY 2014

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35PRACTICAL MATTERS JANUARY/FEBRUARY 2014 CORPORATE FINANCE REVIEW

anxiously the evolution of a trade’s mar-ket value, given how setbacks in this areahave historically sunk many an operator.

We’l l also give ascer taining possiblesettlement date setbacks for the firm atr y. The focus is on possible negat ivebad news — taking into account that, asBuffett has said, it would seem reason-able to argue that the more likely scenariois one where equit ies don’t fal l as hardas they would need to fal l to harm Berk-shire. In that sense, here we tackle the lessstandard/orthodox argument and thus pos-s ibly the most interest ing to contem-plate . We go about i t by doing threethings: First , we assume that the yen,euro, and pound can, by put expirat iondates, strengthen to the high levels seenjust a few years ago (this would be thecurrency rates hypothesis). Second, weassume that index levels can, by put expi-rat ion dates, decline to the pretty lowlevels also experienced just a few yearsago (equity markets hypothesis); finally,we estimate possible strike prices for theputs in a somehow gregarious (yet per-haps not i r rat iona l ) manner ( s t r ikeshypothesis) . Once we have our hypo-thet ical currency, equit ies , and str ikelevels in place, we can est imate possibleloss payout figures for Berkshire.

The analysis concludes that Berkshireundertook very significant accountingexposures by writ ing such a large, long-dated multiple put portfolio; such a port-folio can incur very substantial and verysudden liabilit ies for many varied and

unpredictable reasons — a true mark-to-market massacre if al l those forces con-spire to act against the put sel ler at thesame t ime with intensity. And it may notbe unreasonable to argue that Berkshirealso took on significant settlement expo-sures : I f ex t reme but ce r t a in ly notunprecedented or unfathomable eventswere to take place in the equit ies andcurrency markets, payout loss amountscould be in something l ike a $14 bi l-lion–$20 bil l ion range. The main pointis not that those unfavorable things wil lunfa i l ing ly happen, and we cer ta in lydon’t even try to assign any specific prob-ability to their occurrence. The point,rather, is to illustrate the myriad of expo-sures Berkshire got itself entangled withby deciding to sel l the puts and how thefirm could hurt badly both accounting-wise and cash-wise just if some thingsthat have already happened (and not thatlong ago, actually) were to happen again.

FX mattersBefore we delve into the accounting andsettlement risks, let’s first take care of aninitial pressing issue: How much do expo-sures to currency rates really matter? Or,in other words, how much of the total putsexposure comes from non-U.S. indexes?This is a very necessary and crucial firstquest ion to tackle, since both the mark-to-market and potential loss payouts fig-ures could be very different, contingenton the actual forex exposure facing Berk-

EXHIBIT 1 The Evolution of the Put Portfolio’s Notional Amount and Liabilities

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36 CORPORATE FINANCE REVIEW JANUARY/FEBRUARY 2014 PRACTICAL MATTERS

shire. Clearly, the higher the proportionof non-U.S. puts in the por t fol io, thehigher the forex r isk. If that proport ionis high, a lower dollar could now do realdamage l iabi l i t ies-w ise and payouts-wise; the dollar-denominated setbacks(Berkshire natural ly reports in dollars,and the internat ional contracts wouldpay out in their local currencies) frominternational index contracts that moveagainst the firm could be nightmarishlyenhanced. If , on the other hand, non-U.S. contracts made up just a modestshare of the portfolio, currency marketsdevelopments would be of minor, if notentirely irrelevant, importance.

So how much of the total puts expo-sure comes from non-U.S. indexes? Berk-shire doesn’t tell us directly, but it seemsthat i t’s quite a bit (as per Exhibit 2 ,which displays quarter-to-quarter per-centage changes in the put por tfol io’snotional value and in foreign exchangerates). During periods with no additionsor reductions in the number of contracts,changes in notional value is due entirelyto currency movements; Berkshire Hath-away reports in dollars, so the S&P 500puts can only impact the notional valueof the por t fol io i f new cont rac t s areadded or cancel led. The Nikkei/FTSE/Eurostoxx puts can lead to changes inthe not ional value — even i f no con-tracts are added or cancel led — simplydue to forex moves; eventual payouts onthose contracts wil l be denominated inthe respect ive domest ic currency, mak-ing the potent i a l max imum payoutamount higher if the dollar depreciatesversus those currencies. The 2004–Q12008 period is left out of the analysis, sinceal l the put-sel l ing act iv it y was takingplace then. Q3 2O10 and Q4 2010 com-parisons are also lef t out of the picture,since the size of the put portfolio suffereda significant modificat ion in the latter(significant unwinding of contracts).

As can be seen, the dimension of thechanges in currency rates is quite simi-lar to the dimension of the changes in theportfolio’s notional size — an indicationthat many of the contracts are linked tonon-U.S. indexes. If a portfolio made upof U.S. and non-U.S. indexes puts, thatcan only change in size due to currency-

rates-driven changes in the value of thenon-U.S. indexes contracts, goes up by, say,10 percent when exchange rates go up(the dollar goes down) by, say, 15 per-cent, then we can conclude that a signif-icant proportion of the total portfolio iscomposed of non-U.S. contracts. (If theportfolio was entirely comprised of non-U.S. contracts, the notional value wouldhave increased by that same 15 percent.)

For instance, in Q1 2009, the quarter-to-quarter change in portfolio notionalamount was -4.430 percent (that is, Berk-shire’s maximum equity puts exposurediminished; the portfolio became tem-porarily less r isky). During that period,the dol lar strengthened by 4.727 per-cent versus the euro, 2.182 percent ver-sus the pound, and 8.432 percent versusthe yen. As forex movements were theonly way for the portfolio’s size to suf-fer modificat ions (no new contracts, nobig contract unwind), it seems clear thata very significant share of the puts arereferenced to at least one or two of thenon-U.S. indexes. Q3 2010 was a simi-lar situat ion, with declines in the dollarof 10.658 percent , 5 .245 percent , and5.938 percent respect ively, leading to anotional value increase of 6.337 percent.

As equit ies recovered from mid-2009following financial crisis lows, the put port-folio nonetheless registered larger liabilitiesin many quarters due to the offsett ingdepreciat ion of the dol lar, especia l lyagainst the yen and the pound. In par-t icular, periods with some of the high-est put l iabilit ies, such as Q2–Q3 2010and Q2–Q3 2012, coincide w ith weakdollar levels (see Exhibits 3 and 4, againespecially true for the yen and the pound),although it is true that some of the inter-national equity indexes, not so much theS&P, recorded somewhat low levels atthose points. Also, notice the big jumpin notional amount and liabilit ies (evenas all equity indexes were edging higher)between Q2 2010 and Q3 2010 on accountof the sharp dollar decline. It seems obvi-ous that currency rates are an impor-tant contributor to Berkshire’s exposure.

Berkshire itself makes no secret of thefact that currency fluctuat ions can havea protagonist impact on the portfolio’sperformance (although, strangely enough,

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IT SEEMSOBVIOUS

THAT CURRENCYRATES ARE AN

IMPORTANTCONTRIBUTOR

TO BERKSHIRE’SEXPOSURE.

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EXHIBIT 2 Quarter-to-Quarter Percentage Changes in the Put Portfolio’s Notional Value and in Foreign Exchange Rates

puts euro pound yenQ2 2008 –0.524% –0.361% 0.257% –5.953%Q3 2008 –7.112% –10.585% –10.560% 0.217%YE 2008 0.248% –1.150% –17.889% 16.687%Q1 2009 –4.430% –4.727% –2.182% –8.432%Q2 2009 5.610% 5.724% 15.049% 2.831%Q3 2009 2.967% 4.351% –2.723% 7.744%YE 2009 –1.560% –2.037% 1.018% –3.857%Q1 2010 –3.238% –5.624% –6.068% –0.343%Q2 2010 –2.247% –9.131% –1.574% 5.549%Q3 2010 6.337% 10.658% 5.245% 5.938%Q1 2011 1.764% 6.888% 4.262% –1.317%Q2 2011 1.740% 2.397% 0.118% 2.629%Q3 2011 –2.026% –7.395% –2.757% 4.673%YE 2011 –1.059% –3.539% –0.557% 0.078%Q1 2012 –0.612% 2.783% 2.883% –6.589%Q2 2012 –1.015% –4.995% –1.871% 3.258%Q3 2012 1.688% 1.484% 2.843% 2.426%YE 2012 –1.972% 2.567% 0.806% –10.065%Q1 2013 –4.701% –2.806% –6.574% –7.986%Q2 2013 –2.683% 1.514% 0.112% –5.090%Q3 2013 3.197% 4.035% 6.371% 0.936%

EXHIBIT 3 Forex Movements’ Effects on the Put Portfolio: Some Illustrations

End Q2 2010 End Q3 2010 End Q2 2012 End Q3 2012S&P 1020 1150 1360 1460FTSE 4840 5600 5570 5870Nikkei 9200 9400 9020 8860Eurostoxx 2520 2730 2260 2530Yen/$ 88.49 83.53 79.81 77.92$/Euro 1.23 1.36 1.27 1.29$/Pound 1.49 1.57 1.57 1.61Puts Liabilities (mn) $8,928 $9,628 $8,983 $9,517Puts Notional (mn) $35,934 $38,211 $33,463 $34,028

the many observers and commentatorsof this trade seem not to have focusedtheir attention on the forex r isk, ratherconfining their analysis to the equit iesside). For instance, in its Q1 2009 regu-latory fi l ing, the firm stated:

Losses from equity index puts reflected declinesin the equity indexes that were part ial ly off-set by the impact of a stronger dollar on non-U.S . cont r ac t s . In Q1 2008 , lo s se s wereprincipally attributable to changes in the est i-mated fair value of the contracts as a result ofdeclines in equity indexes and declines in thedollar versus the Euro and the Yen.1

Or take the Q3 2010 statement:

The values of our equity index put contractswere negatively impacted by lower interest rate

as sumpt ions and a weaker dol l a r, wh ichadversely impacted our non-U.S. contracts.These factors more than offset the favourableimpact of increases in the indexes. As a result,the est imated values of the liabilit ies associ-ated with these contracts increased althoughthe intrinsic values of the contracts decreased.2

Another reason to think that the port-folio has substantial forex exposure isthe quite h igh premium col lec ted byBerkshire. The put writ ing period was,almost in its ent irety, characterized bybooming equity index levels, lack of tur-bulence, and increasing interest rates(al l factors that, as wil l be explained inthe next sect ion, should lead to fairlylow values for a put option) — and yet

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Berksh i re co l l e c ted $4 .9 b i l l ion inexchange for the possibi l it y of losingaround $35–40 billion. That more-than-10-percent-of-notional premium appearsintriguingly juicy, particularly given thepreviously mentioned conditions. Maybethe fact that the dollar was, during thatper iod, trading at extremely low (andever lower) levels versus the euro (his-tor ica l lows) and the pound can helpexplain the otherwise surprisingly highpremium.

Touching on a theme that w i l l beexpanded upon later, it is somewhat puz-zling that the liabilities numbers in Exhibit3 did not reach beyond $10 billion, giventhe relatively low index levels (surely wellbelow the original strikes for many con-tracts) and the strong foreign currencies.This is especially true for Q2–Q3 2010,since by 2012 the put portfolio had beenreduced in size through some unwind-ing. It must also be clarified that in Q22009 Berkshire renegotiated six put con-tracts, lowering strikes by between 29–39percent so that it became harder for thoseputs to suffer big losses even amid decreas-ing indexes (anecdotal evidence suggeststhat the notional amounts involved wereabout $2 billion). Still, those liabilities num-bers fee l more modes t than may beexpected.

Accounting risksA put-sel l ing speculator is exposed tothe market value of the options. What isan asset for the put buyer is a l iabilityfor the sel ler. When the market value ofthe opt ion goes up, the buyer’s assetsincrease — and so do the sel ler’s l iabil-it ies. When the liabilit ies overcome theinit ial value of the option (the premiumreceived), the seller begins to incur mark-to-market losses on the trade. These areunrealized losses, as the option may even-tual ly expire out of the money or lessdeep in-the-money, but can prove both-ersome nonetheless: They may be so largeas to severely impact the sel ler’s overal learnings, and they may force taxing col-lateral post ings. (Buffett was lucky tonegotiate very friendly collateral require-ments, but most others could face mar-gin cal ls on a continuous basis; many a

financial firm has collapsed amid unbear-able mark-to-market-driven col lateraldemands.)

So what would cause changes in the mar-ket value of put options such as the onessold by Berkshire? Borrowing from theBlack–Scholes model (the tool used byBerkshire to value the portfolio), as wellas from obvious common sense, the fol-lowing factors matter.

Delta or underlying asset risk: In this case,Berkshire’s position suffers when equityindexes go down and benefits when equityindexes go up; that is, while put buyersface negative delta, put sellers face pos-it ive delta (delta equals sensit iv it y tosmall changes in the underlying asset). Whiledelta can be very large for in-the-moneyoptions with short maturities, it can benegligible for long-dated maturities, evenif the option is in-the-money. (This makessense: When there’s a lot of t ime prior toany payout, any individual index level ata single point matters l itt le unless theoption is already very deep in-the-moneyand thus apparently “guaranteed” to makea payout.) Given that many of the optionsmust have spent quite a long of t ime out-of-the-money or only s l ight ly in-the-money (due to rising stock markets bothas the puts were being sold before thefinancial crisis and soon after the crisis),Berskhire’s delta exposure must have beensmallish. This low delta characteristic isan attractive feature for option sellers,who have to care less about day-to-daydevelopments in the underly ing asset. Asexamples, a 15-year, 100-strike, 20-per-cent-volat i lity, 3-percent-interest rate,100-spot put would have a Black–Scholesdelta of –0.166 (–0.471 if spot is at 50),whi le the one-year equivalents wouldbe –0.41 (–0.999).

Gamma or jump r isk: This refers to thesens it iv i t y of delta to changes in theunderly ing asset or the sensit ivity of theoption’s value to bigger changes in theunderly ing asset . Opt ion buyers lovegamma, while option sel lers suffer fromgamma. This can be an important risk onoccasions, but it’s negligible in the caseof long-dated options (if delta matterslitt le, changes in delta matter l itt le)—again, another good feature for optionsel lers à la Buffett.


A PUT-SELLINGSPECULATOR IS

EXPOSED TO THEMARKET VALUE

OF THE OPTIONS.WHAT IS AN

ASSET FOR THEPUT BUYER IS ALIABILITY FOR

THE SELLER.

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EXHIBIT 4 Equities and Currencies Data

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EXHIBIT 4 Equities and Currencies Data, cont’d

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Ve g a o r vo l at i l i t y r i s k : Opt ions a reassumed to love volat i l it y, g iven theirasymmetrical payout functions with tonsof potential upside and limited downside.Opt ion buyers are , in fac t , known asvolatility buyers. Option sellers thus suf-fer when the underly ing asset is goingthrough volat i le t imes; that is, they facenegative vega. Volatility is the only inputin the Black–Scholes model that is notdirectly observable and is thus part icu-larly amenable to differ ing assessmentsor “manipulations.” Vega, typically alwayssignificant, can be quite large for long-dated options. For example, the 15-year,100-strike, 20-percent-volatility, 3-per-cent-interest rate, 100-spot put wouldhave a Black–Scholes vega of 0.967 (0.770if spot is at 50), while the one-year equiv-alents would be 0.387 (0.001).

Theta or t ime r isk: Options are said tobe “wast ing assets” because they losevalue simply because time goes by (sincethere would be less opportunity for ben-eficial market variat ions). Thus, theta isgenera l ly assumed to be negat ive foropt ion buyers and posit ive for opt ionsel lers. If you sel l options, your liabili-t ies should decrease just because theclock is ticking. However, there is a caveatin the case of puts: When the option isin-the-money, theta would be positive forthe buyer and negative for the seller (theidea being that since spot prices have anatural bottom at zero, there’s less togain from extra t ime, while the passageof t ime helps preserve the gained intrin-sic value). In any case, theta, both pos-i t ive and negat ive , i s ex t remely low(essential ly zero) for a long-dated put.

Rho or interest rate r isk: Black–Scholesassumes that stock pr ices grow at ther isk-f ree rate of interest ; therefore, ahigher rate implies higher expected stockpr ices and a lower rate impl ies lowerexpected stock prices. Put buyers thus facenegat ive rho, put sel lers posit ive rho: Ifinterest rates go down, put sel lers sufferbecause put va lues go up. Rho, of tenneglected as less relevant than the otherrisks, can be extremely large for long-datedoptions. In fact, it becomes the biggestr isk by far ; rho can be as much as fivet imes or more higher than vega. Rho isabout the future (g row th rate of the

underly ing), and long maturit ies havemore future in them. A 15-year, 100-str ike, 20-percent-volat i lity, 3-percent-interest rate, 100-spot put would have aBlack–Scholes rho of –4.048 (–7.254 ifspot is at 50), while the one-year equiv-alents would be –0.466 (–0.970). The15-year opt ion is wor th 10.338 whenspot is at 100 — thus, the option wouldexperience a whopping 39 percent gainin value if interest rates go down by 1 per-cent. That would be a whopping 39 per-cent increase in liabilit ies for the optionsel ler. One wonders if the huge interestrate bet implied by long-dated optionswould deter t raders f rom sel l ing suchcontracts (which are in fact i l l iquid).

In sum, the market value of Berkshire’sputs posit ion would gain f rom higherequity prices, from no equity price jumps,from low volat i l ity, from the passage oft ime (if not in-the-money), and f romhigher interest rates. Exposure to equi-t ies is quite low as long as the expirationdate is far away, and exposure to t imemoving on is negligible. Thus, so far thebiggest r isks have come from volat i l ityand interest rates, the latter in part icu-lar. Selling those puts, in essence, equates,from a mark-to-market point of v iew,heavily long interest rates.

And that may be the main takeaway fromthe analysis: Berkshire’s fate was firmlyplaced in rho’s hands. The firm did suf-fer as rates col lapsed upon the financialcr isis. Given that official interest ratesare currently extremely low in the coun-tr ies that concern us here, there may beless space for rho to fur ther hurt Berk-shire accounting-wise. Rather, rho couldbe of great help if rates begin to go upas economies recover and monetary poli-cies are changed. Berkshire’s put l iabil-it ies could be significantly reduced asrates are lifted and the value of the optionstumbles . So, as rho becomes a le s sersource of negativity due to decreasing timesto expirat ion and the possibi l it y of adirectional switch in interest rates, Berk-shire’s exposure would increasingly be lesson the interest-rate side.

On top of the r isks represented by thepreviously mentioned parameters (the“Greeks” of options), Berkshire’s mark-to-market is naturally exposed to devel-


VOLATILITY IS THE ONLY INPUT IN THEBLACK–SCHOLESMODEL THAT IS NOT DIRECTLYOBSERVABLE AND IS THUSPARTICULARLYAMENABLE TO DIFFERINGASSESSMENTS OR“MANIPULATIONS.”

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

opments in the foreign exchange markets.If the dol lar declines versus the euro,yen, and British pound, the dollar-denom-inated size of the previously mentionedrisks gets enlarged. These puts thus makeBerkshire’s earnings statement passion-ately long the dollar.

Final ly, it is clear that while each putis pr iced independent ly, Berkshire i sexposed to correlat ions among the dif-ferent r isk factors. If the S&P goes down(bad), the impact is worse i f concur-rently the Nikkei also goes down. If theeuro collapses (good), the impact is evenbetter i f concurrent ly the pound a lsocollapses. A decline in the FTSE (bad) canbe compensated by a paral lel decline inthe pound. A rise in the Eurostoxx (good)can be offset by a decrease in interestrates. An increase in interest rates (good)can be offset by an increase in stock mar-ket volatility. Equity/equity, equity/forex,forex/forex, equity/interest rates, forex/interest rates, forex/volat i l it y, interestrates/volatility — too many correlationsto worry about perhaps? Will the Nikkeiand the Eurostoxx go down along withthe yen? Will the euro and interest ratesgo up and S&P volat i lity go down? Hardto estimate reliably. Correlations are par-t icularly tr icky in financial markets —and part icularly treacherous (they canquickly dev iate w i ldly f rom histor icalpatterns).

The very long-dated, over-the-countercontracts sold by Berkshire are said tobe i l l iquid (exchange-traded contractsgo out just a ver y few years) and thushave to be marked to model (Black–Scholes in this case), leaving room foropinionated interpretation; in particu-lar, what volatility and interest rate num-bers do you input?

A final note on mark-to-market expo-sures: It seems odd that put l iabi lit ieswould be just $10 bi l l ion in Q4 2008 and Q1 2009. Contracts that had cost$4.9 bil l ion during 2004–Q1 2008 (veryca lm per iod genera l ly, low volat i l i t y,ever-r ising stock pr ices, ever-increas-ing interest rates , the “great modera-t ion”) were now wor th just a bit overtwice that amidst incredible, historicallyunprecedented volat i l ity and dramati-cally tanking markets (well below str ike

prices) — causing much lower interestrates . It is t rue that the dol lar was inthose quarters stronger against the pound,especial ly, and the euro than it had beenin 2004–Q1 2008 (while being weakeragainst the yen), but it st i l l seems puz-zling that the put portfolio’s l iquidationvalue would be only two t imes the pre-mium original ly col lected.

During late 2008 and early 2009, the putportfolio faced the triple threat of a mar-ket meltdown that would lead to explo-sively enhanced volatility and urgentlylower rates (as officials tried to fight thepanic). This should have spel led totalaccounting massacre for short put optionpositions, and yet it looks like Berkshiremay have suffered a lesser pain.

Settlement risksThis i s s impler than mark-to-marketexposures , as only two fac tors wouldnow matter :• Stocks: Wil l equity levels be below

the preset str ikes at expirat iontime?

• Forex: Wil l the dollar be weak ver-sus the other currencies at expira-t ion t ime?The size of Berkshire’s loss payouts at

maturity dates, if any, will be determinedby whether the puts are in-the-moneyand by the relat ive strength of the dol-lar. Can we estimate what may happen bythe fateful 2019–2027 per iod in somereasonable way?

We can try (humbly). As mentioned pre-viously, we focus on possible future lossesfor Berkshire by assuming prett y bad(yet neither unprecedented nor ancientor ludicrously improbable) market devel-opments. We wonder, what would hap-pen to Berkshire’s puts at matur it y i fequ i t i e s and cur rency marke t s wentagains t them in an ext reme but con-ceivable/viable/plausible/realizable/cred-ible fashion? Let’s look at recent historyand pick rare negative events and hypoth-es ize that they could re-emerge 5–15years from now.

At of the end of Q3 2013, the putsportfolio’s notional value was $33 billion.Let’s assume that by the t ime the putsexpire in 2019–2027 the dol lar would


CORRELATIONSARE

PARTICULARLYTRICKY INFINANCIAL

MARKETS — ANDPARTICULARLYTREACHEROUS

(THEY CANQUICKLY DEVIATE

WILDLY FROMHISTORICALPATTERNS).

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

have decl ined against the three othercurrencies . For instance, let’s assumethat the yen strengthens by 22 percentfrom the level prevailing on September30, 2013. This would lower the dol larfrom 98.29 yen to 76.66 yen. That wouldnot be an utterly unseemly or impossi-bly rare event, as that was the prevailingrate during, for example, September andOctober of 2011. In other words, thatapparently sharp 22 percent drop wouldy ield a level not only already seen in themarket, but actually seen quite recently.

Similarly, let’s assume that the eurogains 18 percent, going f rom $1.35 to$1.59. Impossible? Well, the $1.59 markwas reached in April of 2008 — not thatlong ago either.

Fina l ly, suppose the Br it i sh poundgoes up by 30 percent, taking it f rom$1.61 to $2.10, a level already witnessedin November of 2007.

In sum, if we made the hypothesis thatthe yen, the euro, and the pound expo-sure will rise on average by around 25 per-cent by the puts’ expirat ion dates 5–15years from now, we would be hypothe-sizing that those currencies will reach lev-els versus the dollar that have not onlyhad historical precedent, but actual ly aquite recent one. These are things thathave actually happened — and they hap-pened not in a distant long-forgottenpast but just a very few years ago. Whycouldn’t they then happen again come2019–2027?

If we then assume that 50 percent ofthe put portfolio is made up of contractslinked to non-U.S. indexes, then the (notentirely unreasonably) hypothesized 25percent dol lar drop would lead to anincrease in dollar-denominated portfo-l io not ional va lue, and thus a dol lar-

denominated maximum potential loss, of12.50 percent; that’s from $33 billion (asof the end of Q3 2013) to $36 bil l ion.Exhibit 5 exper iments w ith d i f ferentnot ional va lue scenar ios for dif ferentproport ions of non-U.S. contracts.

This keeps equity index levels con-stant (at end-Q3 2013 levels: 1,690 forthe S&P, 6,450 for the FTSE, 14,020 forthe Nikkei, 2,930 for the Eurostoxx). Butwhat if we assume that those wil l be dif-ferent come put expirat ion date? In par-t icular, le t’s assume that they w i l l bemuch lower. How much lower? Well, howabout down to 680 for the S&P 500, 3,530for the FTSE 100, 7,180 for the Nikkei 225,and 1,820 for the Eurostoxx 50. Those are,roughly, the lowest levels reached by theindexes in the last decade. In other words,they are quite low levels, but also quiterecent, and thus not insult ingly unfea-sible. These are not imaginary phantomequit y levels , but ac tua l ly ver y muchreal. They could, in other words, happenagain, r ight?

Some may argue that declines to thoselevels are even less likely nowadays, withbooming stock markets and a l l . Wel l ,not quite. Whi le the drop in the S&Pwould indeed have to be spec tacularfrom today’s levels (from 1,690 to 680 isa seemingly whopping 60 percent col-lapse) , the drop in the FTSE/Nikkei/Eurostoxx would actual ly be lower (andeven much lower) than was the case frompre-cr isis highs in 2007 to post-cr isislows in 2009. Contrast required dropsfrom today’s levels of 45 percent (FTSE),48 percent (Nikke i ) , and 37 percent(Eurostoxx) with the respect ive peak-to-through meltdowns actual ly experi-enced of 47 percent, 60 percent, and 60percent. Al l we are asking f rom these


EXHIBIT 5 Different Notional Value Scenarios for Different Proportions of Non-U.S. Contracts

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equity indexes, real ly, is that they fal l inthe next 5–15 years by quite less than bywhat they already fel l .

The key, of course, is to come up witha decent est imation of the str ike pricesat which the puts were sold. How couldthis be done semi-reliably? Well, we knowthat most of the exposure was under-taken in the 2005–2007 period, with par-ticularly intense activity in that last year.We a lso helpful ly know that the con-tracts were struck at the then-prevailingspot levels. If we calculate an averagespot price for the period, then we mayinfer an approximate “average” s t r ikepr ice (of course , th i s approximat ioncould be off by an immodest margin ifthe contracts happened to be sold withina very brief w indow of t ime in a part ic-ular year or in al l years).

Going down that path, we could inferapproximate weighted average s t r ikeprices of, for example, 1,350 for the S&P500 (1 ,190 at the beg inning of 2005,1,410 at the end of 2007; maximum of 1,560in October of 2007, minimum of 1,140in April of 2005), 6,000 for the FTSE 100(4,850 at the beginning of 2005, 6,350 atthe end of 2007; maximum of 6,730 inJune of 2007, minimum of 4,850 in Jan-uary of 2005), 16,000 for the Nikkei 225(11,430 at the beginning of 2005, 14,690at the end of 2007; maximum of 18,240in July of 2007, minimum of 11,000 inApr i l o f 2005) , and 3 ,800 for theEurostoxx 50 (2,980 at the beginning of2005, 4,270 at the end of 2007; maxi-mum of 4,560 on May 2007, minimum of2,940 in January of 2005).

Based on those strike prices, reachingthe lowest indices levels seen in the lastdecade would imply declines of roughly50 percent, 41 percent, 55 percent, and52 percent for, respec t ively, the S&P,

FTSE, Nikke i , and Euros toxx . Thosewould be the sizes of the payouts to bemade by Berkshire Hathaway were thoseindex levels to quote at expiration of thecont r ac t s — so l e t ’s s ay, 50 percentdeclines on average. Again, those wouldbe index levels that, far from never hav-ing been seen, have actual ly mater ial-ized in real l ife (and not that long agoeither). Added to the assumed average 25 percent drop in the dollar describedearlier, and assuming that non-U.S. con-t rac ts make up ha l f of the por t fol io,Berkshire’s est imated dol lar-denomi-nated loss payout on the puts wouldamount to some $18 bil l ion.

Exhibit 6 descr ibes several a lterna-t ive scenarios drawing on this analysis.

It’s worth pointing out that the per-centage decline from the str ike pr ices(and thus the payout loss, i .e . , corre-sponding not ional exposure decl ine),were those last-decade indexes lows toshow up around expirat ion t ime, wouldnaturally be greater had the actual strikeprices been set at a higher average levelthan our very imperfect est imates. Forinstance, assume that a lot of the S&P expo-sure ( in not ional terms, i f not neces-sa r i ly in te rms of ac tua l number ofcontracts written) was entered into dur-ing May–October 2007 with the indexhovering comfortably above 1,500. Orassume that much of the Nikkei exposurewas taken on during the first half of 2007,with the index consistently above 17,000and even 18,000.

Of course, the opposite could well betrue, with most of the put exposure beingwritten at a t ime of part icularly lowerindex levels — say June–July of 2006 forthe Nikkei (below 15,000 most of thetime). In that case, the proper weightedaverage strike prices could be quite lower


EXHIBIT 6 Alternative Scenarios — 50 Percent

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+*)%,*-$*'. /0!)/1!'2'()*+ 3*%$*3/-'&$4!'$35)!/&! 3!6'3*%$*3/-'0/-#!'78$--$*3&9 :;.

3*3<=>?>'$3(!@!& A;. B:. C>:;. 2ADED;; 2FCEB;; -*&&'78$--$*3&9

D;. B:. F;>;;. 2A:EB;; 2FCEG;; -*&&'78$--$*3&9

:;. B:. FB>:;. 2AGE;;; 2FHE;;; -*&&'78$--$*3&9

G;. B:. F:>;;. 2AGEH;; 2FHED;; -*&&'78$--$*3&9

C;. B:. FC>:;. 2ACEG;; 2FHEH;; -*&&'78$--$*3&9

H;. B:. B;>;;. 2AHED;; 2FIEB;; -*&&'78$--$*3&9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

than our primitive approximations, andthus Berkshire’s potential setback wouldbe diminished. If the average S&P putsstrike turns out to be, say, 1,190 insteadof 1,350, then a decl ine to 680 wouldimply a 43 percent drop ( loss) ratherthan the aforementioned 50 percent. If theaverage FTSE puts strike turns out to be,say, 5,500 instead of 6,000, then a declineto 3,540 would imply a 35 percent droprather than the aforementioned 41 per-cent. If the average Nikkei puts str iketurns out to be, say, 13,000 instead of16,000, then a decl ine to 7,200 wouldimply a 44 percent drop rather than theaforementioned 55 percent. If the aver-age Eurostoxx puts str ike turns out tobe, say, 3,200 instead of 3,800, then adecline to 1,820 would imply a 43 per-cent drop rather than the aforementioned52 percent.

Exhibit 7 repeats the payout loss sce-nario analysis, but this t ime assumingthat the distance between the averagestrikes and the last-decade index lows is,on average, 40 percent. That is, we nowassume lower str ikes than in the earliernumerical exercise, a long the l ines ofthe analysis just presented.

We can infer some information aboutposs ible “t rue” s t r ike levels f rom theinformation on intrinsic values reportedby Berkshire. For instance, as of year-end2008, the total combined intr insic valueof the put portfolio was $10.80 bil l ion.All puts can be assumed to have beenin-the-money for Berkshire’s counter-parts at the t ime, since spot index lev-els were lower (and much lower) thanduring the 2004–Q1 2008 period whenthe puts had been written. The notionalvalue of the portfolio at that time was $37.1billion. Thus, the portfolio was 29.1 per-cent in-the-money (10.8 is 29.1 percent

of 37.1). Given the prevalent index lev-els (930 for the S&P, 8,860 for the Nikkei,2,530 for the Eurostoxx, and 4,560 for theFTSE), a 29.1 percent decline across theboard would y ield average str ike pricesof respectively 1,310, 12,480, 3,560, and6,420. Of course , the ac tua l numberscould be different, and different combi-nations of individual strikes and relativenotional sizes could al l lead to the over-all 29.1 percent intrinsic setback — evenwhen not a l l , i f any, of the indiv idualindexes actually fell by 29.1 percent ver-sus the respect ive str ike.

An interesting case appears in Q3 2013.Here only two of the underly ing assetscould be in-the-money and thus haveintrinsic value, namely the Nikkei and theEurostoxx with spot index levels as ofthe end of September of 2013 lower thanfor most of the 2004–Q1 2008 per iod(this is essential ly 100 percent for theEurostoxx and less so for the Nikkei ,with Q3 2013 levels above those regis-tered in 2004, most of 2005, and most ofQ1 2008). Spot levels for the S&P and theFTSE, in contrast, were above 2004–Q12008 levels. Total portfolio intrinsic valueas of the end of Q3 2013 was reportedas $2.3 billion. Given a portfolio notionalsize of $32 billion, it represented a 7 per-cent drop in value below the str ike (2.3is 7 percent of 32). Since this numbercou ld come on ly f rom Nikke i andEurostoxx puts (S&P and FTSE contractsbeing out-of-the-money at that point),and given then-prevailing spot levels of14,000 and 2 ,930 (and assuming thateach of the two underly ing categoriesmakes up 25 percent of the overall port-folio notional size and that an overal lportfolio setback of 7 percent implies a14 percent setback for each), we couldassume corresponding average str ikes


EXHIBIT 7 Payout Loss Scenario Analysis — 40 Percent

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3*3<=>?>'$3(!@!& A;. BC. D>C;. 2A:E:;; 2FAEDG; -*&&'78$--$*3&9

:;. BC. F;>;;. 2ACEB;; 2F:E;H; -*&&'78$--$*3&9

C;. BC. FB>C;. 2AGE;;; 2F:E:;; -*&&'78$--$*3&9

G;. BC. FC>;;. 2AGEH;; 2F:EDB; -*&&'78$--$*3&9

D;. BC. FD>C;. 2ADEG;; 2FCE;:; -*&&'78$--$*3&9

H;. BC. B;>;;. 2AHE:;; 2FCEAG; -*&&'78$--$*3&9

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

of 16,300 and 3,400. Str ikes est imateswould cer tainly differ for different rel-at ive not iona l s i z e s of Nikke i andEurostoxx exposures.

Going forwardBerkshire is in “put heaven” r ight now.Many of the puts are (must be) out-of-the-money, given recent sharp stock mar-ket r ises and the correspondingly verylow latest intrinsic value figures. Impliedvolat i l it ies are approaching histor icallows (although Nikkei vols have beenspiking up, FTSE, S&P, and Eurostoxxlevels have been pulling downward anddownward). Market condit ions are now,in fact, very similar to those prevalentduring the t imes the puts were written:booming equity index levels and dor-mant volat i l it y. See, for instance, howthings have been converging to pre-cri-sis levels for the FTSE, the Eurostoxx,and their respect ive volat i l ity indexes(Exhibit 8).

It seems quite l ikely that the l iquida-t ion cost of the put portfolio wil l soonreach below the $4.9 billion originally col-lected in premiums (recal l that the lat-est liability figure is just above $5 billion).The trade wil l l ikely soon stop record-ing a mark- to-marke t lo s s and s t a r trecording a gain. In other words, Berk-shire could buy back its put exposure in

full. Wil l it do so? It would have enjoyedthe substantial free float for 6–10 yearsand gotten r id of al l the r isks describedin this piece, at zero net cost. Of course,this may not make sense if the expecta-tion is that the eventual loss payouts willbe lower than $4.9 bi l l ion, or that thereturn generated on investments w i l lamply compensate for any big setbackat expirat ion dates.

Buy ing back the exposure may in anycase be an indisputably clear case whenit comes to the S&P 500 puts: Given thedepth of out-of-the-moneyness of thesecontracts (the index having truly sky-rocketed after the financial crisis, and thestr ikes of at least some of the puts hav-ing in 2009 been substantial ly reducedfrom around 1,500 to around 990), theirrelat ively lower longevity (also in 2009the matur it ies of at least some of theputs were cut from 18 to 10 years), andthe incredibly reduced current volat i l-ity levels, the liabilities that Berkshire faceshere would be so low as to make it almostcostless to get r id of.

Using Black–Scholes, a 990-strike, 15-percent-volat i l i t y, 2-percent- interes trate, six-year, 1,800-spot put option isworth just 4,367, or 0.44 percent of strike.By deploy ing just a t iny bit of the orig-inally collected premium, Berkshire couldkiss goodbye to the entire American sideof its equit ies r isk.


EXHIBIT 8 FTSE and Eurostoxx: Index Levels and Volatility

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A paradoxThe Berkshire Hathaway put-selling strat-egy could be por t rayed as the posterchild for the merits of both put sel lingand put buy ing. Berkshire would arguethat the trade was — and continues tobe — a wonderful thing: Lots of moneywas raised (“these contracts were wayoverpriced”), the mark-to-market setbackswere arguably l imited , and expec tedfuture lo s s payout s appear now so modes t that the whole r i sk cou ld be economica l ly erased. But Berkshire’scounterparties could also be found amplysmiling, as they would have already (andlong before any at-expirat ion payment)enjoyed tremendous returns. The explo-sion in volatility witnessed in 2008–2009multiplied the value of their investmentsseveral-fold; had they then flipped theputs into the market, they would haveconsolidated amazing cash gains. A 1,500-str ike, 15-percent-volat i lity, 4-percent-interest rates, 15-year, 1,500-spot putbought in 2007 for $49,124 (3.3 percentof str ike), was suddenly worth $832,240(55.5 percent of s t r ike) in early 2009with spot at 800, rates at 2 percent, andvolatility at (say) 50 percent. That wouldbe a return of 1,500 percent.

This points to a cr it ical issue regard-ing option buy ing. You can make hugereturns long before the expirat ion date— in fact the play need not be an expi-rat ion play at al l . Even if you considerthe chances of at-expiration in-the-mon-eyness as null, buying the options can makegreat sense i f you expect w i ld marketswings in the interim. And another biglesson from the Berkshire case is thatbuy ing puts can be better than buy ingcal ls — as in the case of the former, theunleashing of a favorable market forcecan direct ly lead to the unleashing ofother favorable market forces. If equitiescol lapse, then volat i l i t y w i l l go crazyand interest rates wil l then be lowered(as an economic recess ion becomes aforegone conclusion). This glorious triadwill, of course, lead to glorious gains forput buyers — and to correspondinglyun-glor ious losses for those who soldthem the puts . When it comes to ca l loptions, upswings in equity prices, evenif sharp, need not drive up volatility with

the same intens it y ( in fac t , volat i l i t ytends to be massaged down during bullmarkets, such as today).

If Berkshire’s puts at expirat ion areout-of-the-money (or not too much in-the-money), this case wil l thus be ableto allow both sides of the trade to declarethemselves winners.

Conclusions• Berkshire exposed itself to a myriadof potential ly very volat i le factors;in part icular, its put portfolio canbe highly exposed to changes ininterest rates and currency rates.

• Given the low delta of long-datedcontracts, the mark-to-marketexposure would have come not somuch from equit ies as from interestrates and currency rates; on top ofposit ioning itself as long equit ies,Berkshire became massively longinterest rates and long the dollar.

• While Berkshire has endured someperiods of high puts-induced liabil-it ies, the numbers appear intuit ivelysomewhat modest, par t icularly dur-ing periods of stress.

• Assuming that by the puts expirationdates the dollar has experienceddeclines to levels seen as recently aswithin the last six years and thatequity indexes decline to levels seenas recently as within the last fiveyears, and even making conservativeassumptions about weighted averagestrike prices, Berkshire Hathawaywould face significant loss payoutsof $14–15 billion, depending on theproportion of the put portfolio madeup of non-U.S. contracts.

• If we made more aggressive strikelevel assumptions (if we assume thatmost of the notional exposure wassold during concentrated, high-index-level periods), then lossescould reach at least $17–19 billion. n

NOTES1Berkshire Hathaway Inc.’s First Quarter Report (2009):28. Available at: http://www.berkshirehathaway.com/qtr ly/1stqtr09.pdf.

2Berksh i re Hathaway Inc .’s Th i rd Quar ter Repor t(2010): 31. Available at: http://www.berkshirehathaway.com/qtr ly/3rdqtr10.pdf.


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