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书摘:Fischer Black and the Revolutionary Idea of Finance

Perry Mehrling这书前言写的太好了。金融学教授这么会写书,文字工作者很沮丧。传主Fisher Black,学以致用,知行合一,这个不容易但也不罕见,罕见的是Black用以指导人生(不是投资,Black几乎不投资)的指南,是CAPM模型。市场如人生。
 
Black是期权定价公式主要发明者,可惜去世早。没拿到诺奖。要说学术与现实的距离,Black, Scholes, Merton三人求出期权定价公式后,开心地依据公式交易权证,然后,就亏了钱……
 
 
 
书摘
01/17/1536
Although a deeply introverted and shy man by nature,Fischer foundthat he needed interaction with other people as a stimulus to the high-variance thinking he wanted to do,and also as a regulator of that think-ing.All his life, he gravitated to people he could learn from, even as heusually drifted away from them after having learned what they had toteach. Almost all of these interactions were one-on-one, face-to-facewith immediate colleagues and then increasingly by phone and e-mailas his intellectual range (and communication technology) expanded.There was never any chitchat,and each interaction focused on the spe-cific problem that he was working on at the moment. As a result, al-though he interacted with literally hundreds of people, none saw anymore of Fischer than the sliver where his interests overlapped with theirown, and maybe not even that because he typically would not explainthe larger issue behind his specific questions.
 

01/17/1536

More important than the transformation of financial institutions wasthe way that a changed understanding of risk and time would allowpeople to live different lives, by freeing them from the superstition thatguides action wherever science has yet to penetrate.And even more im-portant was the way that a changed understanding of risk and timewould allow people to live different collective lives, by understandingbetter the larger society of which they are a part, and their place in it.Fischer chose to be a pioneer in both respects,organizing both his per-sonal life and his conception of the society in which he lived along linessuggested by the theory of modern finance.He was like a man from theCAPM future sent back in time to plant the seeds that would producethat future.
 

01/17/1536

His use of other people to regulate his thinking was also largely one-on-one, but with a much smaller set of trusted longtime colleagues.
 

01/17/1537

Here is where his craziest ideas got left behind. But if his colleaguescould not convince him to drop an idea,sooner or later he would try itout on a wider group, typically an academic seminar and later maybe aclass he was teaching. Unlike standard practice in academia, there wasvery little back-and-forth in one of Fischer’s seminars,since he was notreally trying to persuade his audience, but only to catalog their re-sponses for later reflection. He would lay some outrageous notion onthe table and then sit quietly while people reacted to it.Whether asking questions directly or provoking responses in a largerforum, Fischer got people to talk, and then took notes on what theysaid. He always carried with him a package of note cards, and wouldpull them out to make a note the very moment the thought occurred,while you were talking, or even in the middle of his classroom lecture.You always wondered what it was that he was writing,but you just hadto wonder, and wait until he was done. It made for a strangely synco-pated style of interaction,which some people tolerated better than oth-ers.But if you couldn’t tolerate it,too bad,because Fischer wasn’t aboutto change.What happened to all the notes? They all got taken back to his officewhere he would review them and decide what to save and what tothrow out. Everything that got saved then got placed into an elaboratefiling system where Fischer could put his hand on it within secondsshould he ever need it again. Each note had its own sturdy manila filefolder, with straight-cut tabs across the top to provide room for a de-tailed label, usually indicating the problem that the note addressed.Ascomputer technology improved, Fischer augmented this paper filingsystem with an equally elaborate electronic filing system. People whoworked closely with Fischer at Goldman Sachs joked that Fischer wasbecoming such an appendage to his filing system that one day they ex-pected to arrive at work to find that the bodily Fischer had completelydisappeared!In effect, Fischer surrendered himself to the problem he was work-ing on, and allowed it to take control of his interactions with otherpeople.When possessed by a problem,Fischer tended to treat the peo-ple around him as little more than data banks for his central processingunit (CPU) to query. It was as though he shut down that part of thebrain that looks after the give-and-take of human intercourse in orderto provide maximal resources to the problem-solving module.
 

01/18/15111

At first glance, the Mandelbrot hypothesis doesn’t sound like such aradical idea, just a generalization of the familiar Gaussian random walk.Paul Cootner,a professor at MIT,sounded the alarm at a meeting of theEconometric Society, December 29, 1962: “Mandelbrot, like PrimeMinister Churchill before him,promises us not utopia but blood,sweat,toil, and tears. If he is right, almost all of our statistical tools are obso-lete—least squares, spectral analysis, workable maximum likelihood so-lutions, all our established sample theory, closed distribution functions.Almost without exception, past econometric work is meaningless.Surely, before consigning centuries of work to the ash pile, we shouldlike to have some assurance that all our work is truly useless.”33 We seehere the instinct of the established professor to defend his intellectualcapital accumulation, but the instinct of the young student Fama wasjust the opposite. His only intellectual investment was in efficient mar-kets and, so far as he could see, the Mandelbrot hypothesis did not re-quire giving up efficient markets. Quite the contrary, efficient markets(in the sense of serial independence) plus the Mandelbrot hypothesis (inthe sense of fat tails) together seemed like a pretty good empirical char-acterization of the data.Mandelbrot himself,however,had a different view.For him,the arbi-trage trading that works to eliminate serial dependence is also responsi-ble for the price jumps that cause fat tails, as prices move to discountthe entire future consequences of any new piece of information. But ifthere is a limit to how far prices can jump, then there is also a limit tohow much serial dependence can be eliminated by arbitrage. 34 Serialdependence is therefore likely to be just as permanent a feature of thedata as fat tails.For Mandelbrot,inefficient markets and Paretian distrib-utions go together as a package, as a matter of theoretical logic, just asefficient markets and Gaussian distributions do.
 

01/18/15113

As a consequence, while everyone else was sorting out the differencesbetween Sharpe and Lintner, and the relationship of the theoreticalCAPM to the empirical market model,Fischer was already extending theCAPM he had learned from Treynor into a theory of the economy as awhole.Whereas Sharpe started from the problem faced by the individualinvestor, and Lintner started from the problem faced by the individualfirm, Fischer consistently took the perspective of the economy as awhole.Everyone else used the idea of equilibrium only to help solve theproblem. Only Fischer adopted the idea of equilibrium as the veryessence of the problem.As he himself would say:“I can’t help trying tolook at the big picture.”Twenty years later, speaking as a partner at Goldman Sachs to a sell-out audience in Japan,he would reflect on how he got started:I liked the beauty and symmetry in Mr. Treynor’s equilibriummodels so much that I started designing them myself.I worked onmodels in several areas:Monetary theoryBusiness cyclesOptions and warrantsFor 20 years I have been struggling to show people the beauty inthese models to pass on the knowledge I received from Mr.Treynor.
 

01/18/15114

In monetary theory—the theory of how money is related toeconomic activity—I am still struggling. In business cycle the-ory—the theory of fluctuations in the economy—I am still strug-gling.In options and warrants,though,people see the beauty. 41
 

01/19/15146

Fischer, however, took adifferent tack.He approached the problem as a matter of diversification.“The prin-ciple of time diversification is this: just as the investor should spread hisinvestments across different securities to minimize the risk associatedwith a given expected return, so also should the investor spread his in-vestments across different time intervals to minimize the risk associatedwith a given expected return.”3 Recall that the capital asset pricingmodel (CAPM) treats each stock as if it were a die and urges diversifica-tion across all the dice. Black’s idea was to treat the market portfolio ineach period of time as if it were a single die.Then the lifetime portfolioproblem is just a matter of deciding how much wealth to allocate toeach of the dice the individual will encounter over the course of his life.The diversification principle leads immediately to the answer that theindividual should bet exactly the same amount of money on each die.The logic is straightforward. If you load up on risk when you areyoung and then pull back when you are old,as many would advise,thenyou are adding to your risk without increasing your expected returnbecause there may be a run of bad dice rolls just when you are maxi-mally invested.Just as it is better to spread your wealth across many dif-ferent risky stocks rather than loading up on a single stock,so it is betterto spread your wealth across many different risky time periods ratherthan loading up on risk at a specific moment in time. In fact, if risk isthe same in each time period,then you might want to plan to have ex-actly the same risk exposure when you are young as when you are old.The “same amount of money” today and tomorrow means theamount of money tomorrow that would have the same value as theamount invested today.Suppose there is a rate of interest r at which wecan turn money today into money tomorrow. Then $1 today is thesame as $(1 + r) tomorrow,and the principle of time diversification saysthat if we plan to invest $x today we should also be planning to invest$(1 + r)x tomorrow. In the real world things are not so simple becauseof uncertainty,but the same basic logic applies.
 

01/19/15153

From the point of view of options pricing, corporate bondholdersmay be viewed as owners of the firm’s assets who have issued a call op-tion (the stock),the exercise price of which is just the face value of thebonds.At any date in the future when the firm is liquidated,the bond-holders will get paid first up to the face value of their bonds,and stock-holders will get everything left over. The Black-Scholes formula cantherefore be used to value the stock,leaving the value of the bonds as aresidual from the total value of the firm.The difference between thiscalculated value and the face value of the bonds provides a measure ofthe discount due to the possibility of default.In this way,the Black-Scholessolution to the options pricing problem seemed to open up a new“contingent claims valuation”approach to traditional problems of valu-ation in corporate finance.
 

01/19/15156

In 1971, Merton was asked by his senior colleague Paul McAvoy ifhe might be willing to publish his own derivation of the options pric-ing result in a new journal he was editing.Merton agreed,but with theproviso that publication be delayed until the Black-Scholes paper ap-peared.Thus it was not until 1973 that Merton’s paper “Theory of Ra-tional Option Pricing” appeared in the Bell Journal of Economics andManagement Science. 21Meanwhile,excited by their results,all three men began buying war-rants, using the Black-Scholes formula to identify mispricing, but theylost money. (Black liked to say that he lost less money than Scholes orMerton.) It turned out that the warrant price was different from theformula for a very good reason that the formula did not take into ac-count, namely an imminent corporate takeover. Black drew the lessonthat sometimes the market knows more than the formula.
 

01/19/15160

Black missed out on Ibbotson’s arbitrage profits because he believedas much in the efficiency of actual market prices as he did in his ownCAPM-based model of what those efficient prices should be. Blacksummed up his position for Ibbotson: “Information is more valuablesold than used.”Rather than becoming a gambler himself,he went intothe business of selling information to the gamblers. Since the key un-known input into the option pricing formula is a measure of the stock’svolatility,he started an options service that sold his own proprietary es-timates of volatility.Every month he distributed printed tables showinghis own valuation of all the options listed on U.S. exchanges and help-fully indicating which options were overpriced and which were under-priced, always according to the Black-Scholes formula calculated usinghis own volatility estimates.
 

01/19/15257

After Merton’s introduction, Fischer stood up and the audience set-tled in for the usual 45 minutes to an hour. But after only 15 minutesFischer sat down. Was he finished? Yes, he was. The audience wasstunned,and not just by the unexpected hole now open in their sched-ule. Fischer’s words rang in their heads:“We might define an efficientmarket as one in which price is within a factor of 2 of value; i.e., theprice is more than half of value and less than twice value.By this defin-ition, I think almost all markets are efficient almost all of the time.‘Almost all’means at least 90 percent.”2It was Fischer’s way of getting people to talk,and talk they did.Whatstunned them was not the idea that price can deviate quite far fromvalue, but the fact that Fischer Black of all people should now be pro-moting the idea. Hadn’t he been arguing the other side for his entireacademic career? Had only two years on Wall Street been enough tochange his mind?
 

01/19/15264

As the first Goldman quant, Fischer invented and then modeled thekind of contribution that quants could make to the firm.Traders whohad to face him in the postmortem conference after a losing tradelearned the advantage of facing him before putting on the trade in thefirst place. Deal makers who anticipated dropping the Fischer Blackname learned the advantage of soliciting his candid view before takinghim out on a sales call. In both dimensions, the analytical discipline of
 

01/19/15265

quantitative finance in the style of Fischer Black gradually seeped intothe general culture of the firm,just as Rubin had foreseen.
 

01/20/15267

Markets look a lot more efficient from the banks of the Charles thanfrom the banks of the Hudson.”
 

01/20/15275

Treynor always emphasized that the stock market game is zero-sum,like poker, in the sense that one trader’s profit is another trader’s loss.Value-based traders establish the bid price at which they are willing tobuy and the ask price at which they are willing to sell,setting the spreadwide enough to compensate for the risk of losing to an information-based trader with superior information. In Treynor’s world, this spreadcan be quite wide,as much as 30 to 40 percent of the price,so price candeviate rather far from value. Most of the time the price lies inside thespread, so value traders don’t trade.Whenever price reaches the spread,however, money flows from information traders to value traders.Thepoint is that the true cost of trading faced by the information trader (andby anyone else who wants to trade quickly) is not the visible spreadoffered by dealers,but the largely invisible and much wider spread offeredby the value trader.In this way of thinking, the value-based trader, not the dealer, is the ultimate source of liquidity in the market. “Although the securitiesmarket ostensibly involves the exchange of securities for cash,it actuallyinvolves the exchange of money for time, with securities serving as in-cidental vehicles.” Value-based traders choose the price of the trade,while information-based traders choose the time of the trade.In effect,the former are selling time while the latter are buying it, and the price of time is the value-based traders’spread.“On every trade,time is eitherworth more than it costs, or less.” What one side wins, the other sideloses. For Treynor, the key to success for an active investor is the deci-sion about which side to be on.He favored the value-based strategy onthe view that information-based traders tend systematically to underes-timate what they pay for time.Time tends to cost more than it is worth.
 

01/20/15276

As he thought about the problem, eventually Fischer concluded thatthere were at least two sources of trading profit that would survive evenin full equilibrium. One involved taking advantage of central bank in-tervention, either in currency markets or in credit markets. Centralbanks are willing to lose money in the cause of the presumably highergood of economic stabilization. Central banks attempt to lower theshort-term interest rate in order to stimulate the economy in a time ofbusiness downturn, but they can only succeed in doing so if they areprepared to lend to all comers at the new low rate.As a consequence,traders can make money by borrowing at that low rate and lending insome other market.“When a country like the U.S. makes its short rateartificially low,while a country like Germany makes its short rate artifi-cially high, traders can borrow at the U.S. short rate and lend at theGerman short rate.This combination of borrowing and lending is likebuying the deutsche mark against the dollar,so a trader can take this po-sition in the forward market without actually borrowing or lending.”32The other reliable source of trading profit is “flow”trading.Simply byparticipating in a market,traders obtain information about the sources ofsupply and demand,and that information allows them to anticipate pricemovements. For Fischer, this source of profit was potentially a very bigthing.He urged devoting more of the firm’s resources to it,and less to themore glamorous proprietary trading where he doubted that Goldmanhad any very dependable information advantage.“In general I think weunderestimate how much we earn from flow trading.”
 

01/20/15277

One constant throughout the evolution of Fischer’s thought was hisfocus on trading as a game played between active and passive traders,which is to say between the informed or “news”traders (such as Gold-man Sachs) and uninformed noise or “nice” traders (such as WellsFargo).Treynor’s conception of the trading game,by contrast,had pittedagainst one another the two different styles of active traders (information-based and value-based). (Treynor assumed that dealers capture all theprofit opportunities of trading with noise traders,which they use to off-set the losses involved in trading with information traders.) Fischer thusconceived of the problem more broadly than Treynor did, but eventu-ally he came to see that the central issue was the price of time, just asTreynor had said.Some traders are buyers of time,and others are sellers,and their interaction determines the price of time.
 

01/20/15292

For Fischer, trading congestion and its effects on market psychologywere sufficient to explain the mechanics of the crash,and so to counterother proposed explanations and their associated remedies.Some peoplesaid the market went down too quickly,while others said that it was toovolatile.Some blamed so-called program trades that triggered sell ordersafter an initial decline,or leverage that triggered margin calls on the waydown.Many people seemed to think that increased government regula-tion was the answer. The Brady Commission recommended “circuitbreakers” to halt trading after large downward price moves, and in-creased government control over margin requirements in the derivativesmarkets. 25 But Fischer had a different view.Fischer thought that the Brady proposals would probably not helpand might even hurt by making markets less liquid. Investors, dealers,and exchanges were already responding to what they learned on Octo-ber 19 by changing their investment strategies,computer programs,andbusiness practices.What was needed was less government regulatory in-terference, not more.“The only changes that make sense to me are tomove margin-setting authority away from the Federal Reserve Board tothe private sector, and to get rid of the uptick rule.”26 Fischer’s idea,apparently, was to focus on changes that would prevent a recurrence ofcongestion when prices drop sharply.Unlike most other commentators, Fischer was, by and large, com-pletely unconcerned about preventing the price drop that caused thecongestion in the first place. Everyone else took it more or less forgranted that such a large price drop could never be consistent withequilibrium, but Fischer had a different view.The underlying cause ofthe price drop, he said, was a change in investor taste for risk that hadbeen happening throughout the years preceding the crash, but withoutbeing fully recognized by market participants and so without being re-flected in market prices until the crash.This, in a nutshell, is Fischer’s“Equilibrium Model of the Crash”(1988a).
 

01/20/15293

The LOR business had grown out of Leland’s academic work,whichused the Black-Scholes option pricing formula to develop dynamictrading strategies that would produce a pattern of returns similar to aput option on a portfolio of stocks. 28 Leland’s idea was to provide an in-strument that would allow institutional investors such as pension fundsto ensure that the value of their portfolio would never fall below a spec-ified floor. If the value of the stocks fell, then the put option wouldcome into the money and so buffer the decline.The business opportunity came from the fact that in general therewas no traded put option available for investors to buy. Instead LORwould use its expertise to create a dynamic trading strategy,tailor-madefor each client’s portfolio, that would replicate as closely as possible thepayoff from the appropriate put option. The Black-Scholes formulashowed how, over any small interval of time, the return on a stockoption is like the return on a portfolio of stocks and bonds, wherethe proportion of stocks to bonds is called the delta hedge ratio. Blackand Scholes had used this idea to fix a rational price for an option giventhe observable prices of stocks and bonds. LOR simply reversed thelogic by using the delta to form the replicating portfolio dynamicallyover time.
 

01/20/15294

Constant proportion portfolio insurance is essentially theinvestment policy Fischer had proposed for individuals and tried toimplement at Wells Fargo two decades before. 29 Only the letters usedto signify the variables are changed: e = mc, or Exposure equals Multi-ple times Cushion. 30 The obvious reference is to Einstein’s relativityformula, E = mc 2 . It is meant to be a joke that helps you to rememberthe formula.The way it works is quite simple. First you specify a floor value be-low which you want to ensure that the portfolio never falls.That givesyou your Cushion as the difference between the current portfolio valueand the floor.Then you specify the Multiple in accordance with yourtolerance for risk,and the formula tells you how much of your portfolioto invest in the risky asset.Having chosen your risky portfolio,you thenhold the rest of your wealth in the safe asset.Over time,as the portfoliovalue changes, your cushion changes, and you continue using the for-mula to reallocate between the risky and safe assets. In order to reducetrading costs,you will want to specify the percentage move that triggersa trade,but that’s all there is to it.The beauty of the formula is in both its simplicity and its generality.Because it is simple,you can easily understand how it works,and so cus-tomize it for your own needs or preferences by specifying your ownfloor, your own multiple, and your own trigger percentage move.Andyou can change any of these over time as your needs or preferenceschange. Instead of producing something that was more elaborate ortechnically sophisticated than LOR, Fischer produced something thatwas simpler and also,as he proceeded to argue,better.
 

01/20/15312

As the twenty-first century approached,Fischer Black had a differentview. Like Keynes, he faced squarely the problem of a radically uncer-tain future. Like Keynes, he wanted to take maximal advantage of theopportunity offered by an open-ended future, while at the same timeimplementing methods of risk control to channel the realization of thatopportunity within manageable bounds. Also like Keynes, he recog-nized the inaccessibility of the unknown future to individual humanreason, and placed his faith instead in collective human reason. UnlikeKeynes, however, Fischer Black saw the best agent of collective humanreason as the market,not the government.Market equilibrium, as Fischer conceived it, is all about producingtwo numbers, the rate of interest and the price of risk, that summarizeour collective tolerance for risk as a guide for our individual choices.For Fischer, speculation and animal spirits are much the same thing,neither one good or bad, but just how people psychologically handlethe unknown future.The important thing is to offer them a better way.Given the collectively determined rate of interest and price of risk ateach moment in time, the capital asset pricing model (CAPM) showshow people can deliberately choose their risk exposure to match theirown risk tolerance, and how they can formulate plans for dynamicallyaltering that exposure over time.CAPM does not eliminate uncertainty,but it does show how to live with it.
 

01/20/15312

It is important to emphasize that Fischer’s conception of CAPMequilibrium is only an instantaneous balancing of forces at a single mo-ment in time, and a balance that is moreover constantly shifting frommoment to moment.The legendary speculator George Soros famouslycriticized the economists’ conception of equilibrium: “Equilibriumanalysis eliminates historical change by assuming away the cognitivefunction.”6 Possibly that criticism is apt for classical economists likeAdam Smith, but not for twenty-first-century thinkers like FischerBlack. Indeed, for Fischer, the cognitive function is at the very center
 

01/20/15313

of the conception of equilibrium. Market prices are as volatile as theyare mainly because people’s understanding of the situation they face,and will face in the future,is constantly changing.In Fischer’s world, the future is unknown, and it is probably noteven stationary, so knowledge of the past is not much help to us.Tomake matters worse,of the two prices that guide individual choices,weactually observe only the rate of interest, not the price of risk. As aconsequence, Fischer’s conception of equilibrium lacks any sense ofbalancing over time, a feature that is central to the concept of equilib-rium held by most economists, classical as well as modern. In Fischer’sworld, we can’t observe the price that links today with tomorrow, sowe can’t hope to optimize over time.What we observe is the marketprice of current wealth, and all we can choose is how to allocate thatwealth today.Simply put, radical uncertainty about the future means that humanreason is insufficient to determine behavior, and it is that indetermi-nacy that makes room for psychology and persuasion to make a differ-ence.The same indeterminacy is the source of what George Soros hascalled the alchemy of finance.Mere ideas about the future become re-alities in the present when enough people become persuaded. Fis-cher’s life was devoted to persuading people of one big idea, the bigidea embodied in the capital asset pricing model, and its manifoldramifications.To the extent he could persuade people to think aboutthe world in a CAPM way, he could make the CAPM ideal a reality.Ideas would change institutions, and institutions would change ideas,in a process of co-evolution toward CAPM.
 

01/20/15317

Are markets efficient as Eugene Fama insists,or excessively volatile asbehavioral economist Robert Shiller insists? 8 From Fischer’s point ofview, the question is ill-posed. Certainly he believed that the collectivewisdom embodied in market prices is usually much better than any in-dividual guess.But he also says,“Given the volatility of expectations,I’msurprised that markets are not more volatile.”9 At any moment in time,markets are about as efficient as they can be, given current conditions.But market prices are also not as a volatile as they should be,given idealconditions.As markets become more efficient, we should expect themalso to become more volatile. For Fischer, efficiency and volatility arenot alternatives but complements.
 
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