Great confusion since the Great Crash
Seventy-five years ago this month, the music on Wall Street stopped. The Great Crash of 1929 brought an extraordinary decade of American prosperity to a shattering end, and toppled fortunes around the world. Today, after 75 years, you might think that economists fully understand what happened. Think again.
Great scholarship has gone into studying those fateful days at the close of the 1920s. In Britain and Germany, the decade had been one of post-war blight; but in the US and Canada it was a boom time. Speculative capital poured into New York from around the world. Calvin Coolidge, the president far from bursting the bubble declared stocks undervalued. When the end came, it was violent and confusing. The market jolted down on Black Thursday, October 24, and again on Black Tuesday, October 29. After three more years of turmoil, it bottomed out with half the country's banks shuttered and nearly one in four Americans out of work. Most scholarship has focused on the broad causes. There has been less study of what was the most important feature to anyone living through the crash: the juddering of prices up and down, the sheer confusion and risk of it all.
Mainstream economists are not much closer now to understanding volatility in markets than they were 75 years ago. That is a crime. A precise understanding of how violently prices move is critical to every investor. Now it is time to battle that ignorance.
The standard financial models make a few simplifying assumptions about the way prices move. These models can answer some very practical questions, such as how much Genentech stock should you add to a portfolio of General Motors and BP shares? At the heart of such questions is a riddle: how likely is it that the asset's value will drop? What are the precise odds of, say, a 5 per cent fall? If the odds are high, the models advise caution or suggest the investor demand a very high return as compensation for the risk. You might think calculating the odds would be simple: look at how prices behaved in the past and extrapolate into the future, the way a bookmaker calculates odds at the races. But the standard financial models do not bother much with the real data. They assume, based on faulty evidence, that prices typically vary by so much and not an iota more. In mathematical terms, they rely on a common tool, the bell curve the same curve that describes how IQs vary in a population, or how people vary in height.
In fact, financial prices behave much more wildly than the bell curve would imply. On Black Tuesday in 1929, the Dow Jones Industrial Average closed down 13 per cent. If the standard models were right, the odds of a one-day drop like that would have been one in about 10 virtually impossible. When, in 1998, Russia defaulted on some debt and markets temporarily swooned, the official odds were one in 20m. As for the worst crash of recent times on October 19 1987 the chances of it happening were less than one in 10. Either we live in an improbably improbable era, or the bell curve is an inappropriate yardstick for financial prices and the standard financial models built with it are faulty.
We believe the models are wrong. A new branch of mathematics called fractal geometry offers a more accurate, quantitative alternative. Fractals (from the Latin for “broken”) are tailor-made to study things that are uneven and rough, whether the shape of a steel fracture or the jagged outline of a stock chart. In fractal finance, sudden price movements, great leaps or profound dives and concentrated stretches of furious trading are all commonplace. But the point here is not to promote fractal theory; it is to highlight the fallacy behind mainstream financial theory. Many professionals know from their own experience that the standard models are flawed. Much effort has gone into “fixing” the practical problems. As a result, finance tools have grown ever more complex. But it would be better to go back to basics, and get the first answer right to the first right question: how do prices behave? This needs a global research effort. From the facts it establishes, simpler and more accurate models and tools can one day evolve. Let us understand the true odds of financial ruin, so we can enter the markets prepared.
Benoit B. Mandelbrot is professor of mathematical sciences at Yale University. Richard L. Hudson, former managing editor of the Wall Street Journal Europe, is chief executive and editor of Science/Business magazine. They are authors of The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward (Basic Books/Profile Books) 难解股市大崩溃之谜
75 年前的这个月，华尔街的音乐停止了。 1929 年的股市大崩溃将美国为期十年的极度繁荣时期打得粉碎，也使全球各地许多财富一笔勾销。 75 年后的今天，你或许认为经济学家已洞明当时所发生的一切。事实真是这样吗？
杰出的学者们投入了对上世纪 20 年代末那段灾难性日子的研究。对于英国和德国，那十年是战争所带来的打击之一；但对于美国和加拿大来说，这却是经济繁荣时期。投机资本从全球涌入纽约。美国总统卡尔文?柯立芝（ Calvin Coolidge ）不仅不去消除经济泡沫，反而宣布股价被低估了。到市场崩溃时，它是如此猛烈和令人费解。市场在 10 月 24 日黑色星期四发生震荡，并在 10 月 29 日黑色星期二再度下挫。直到经历了 3 年多的动荡之后，市况终于见底：结果是全国一半的银行倒闭，几乎每 4 个美国人中就有一人失业。大部分学者将研究焦点投向宏观的原因，而鲜有对经历过大崩市的人而言最重要的特点进行研究：股价震荡、人们的严重困惑以及其中的风险。
当今的主流经济学家与 75 年前的同行相比，对于市场波动性的认知不见得有何进步。这简直是犯罪。准确把握价格如何剧烈波动，对每个投资者来说都至关重要。现在是时候扫除这种无知了。
标准的金融市场模型对价格走势做了一些简单化的假设。这些模型能够解答一些非常实际的问题，比如你对通用汽车（ General Motors ）和英国石油公司（ BP ）的投资组合应追加多少 Genentech 股票？而这类问题的核心仍然存在一个谜：资产价值下跌的几率是多少？比如，下跌 5% 的准确几率有多大？如果几率比较高，这种模型就会告诫人们谨慎行事，或建议投资者要求很高的回报率作为对风险的补偿。你或许认为计算几率十分简单：观察过去的股价走势，然后再推断未来走势，这是赌马投注点在赌赛马时计算几率的办法。但是标准的金融市场模型根本不管现实数据，它们基于有缺陷的证据，假定价格的变化通常是某个量，而且一点也不会偏离。在数学上来说，这些模型依赖了一个常用的工具――钟形曲线（ Bell Curve ），也就是用来描述人群智商或身高分布状况的曲线。
而实际上，金融价格的变化比钟形曲线所描述的要更加离散。在 1929 年的黑色星期二，道琼斯工业平均指数收盘下跌 13 个百分点。如果上述标准模型正确的话，出现这么大日跌幅的几率只有十分之一，实际上几乎不可能。 1998 年俄罗斯因拖欠部分债务而造成市场暂时瘫痪，官方统计的几率只有二千万分之一。最近的一次严重金融风暴发生在 1987 年 10 月 19 日，而发生的可能性小于十分之一。如果不是我们生活在一个极端罕见的时代，那就只能是钟形曲线并非能准确衡量金融价格的标尺，而根据这条曲线建立起来的标准金融市场模型也存在着缺陷。
我们认为，是这些模型出了错。数学界一个新的分支――分形几何提供了一种更加准确和量化的方法。“分形”（ fractal ，源自拉丁文“破碎”之意）是专门用来研究不规则、粗糙的物体，它可以是钢的断裂形状，也可以是股价图中锯齿形的轮廓。在分形金融中，价格的骤变、飞涨或暴跌以及短期内的大量交易都属平常现象。我们在这里并非宣传分形理论，而是要着重指出主流金融理论背后存在的谬误。很多专业人士通过自身的经验得知，标准的金融市场模型存在着纰漏，并已做了大量努力去“纠正”其中的实际问题，但结果却使得金融工具变得越来越复杂。因此最好还是回归基本，针对第一个正确的问题给出第一个正确的答案：价格是如何变化的？这个问题需要全球参与研究。将基本事实弄清楚之后，终有一天会研究出更加简单而准确的模型和工具。让我们准确掌握金融风暴发生的可能性，这样就能胸有成竹地进入市场。
贝努瓦?曼德尔布罗特为耶鲁大学数学教授。理察德?赫德森曾任《欧洲华尔街日报》执行编辑，现为《科学 / 商业》（ Science/Business ）杂志首席执行官及主编。二人合著有《市场（不规范）行为：对风险、风暴和回报的分形研究》（ The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward ），（ Basic Books/Profile Books 公司出版）
