Think less about what to buy, and more about how much. 少考虑买什么，多考虑买多少。

image: satoshi kambayashi

2023 年 9 月 21 日

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If you ever hear a professional investor talk about a trade that taught them a lot, prick up your ears. Usually, this is code for “a time I lost an absolutely colossal amount of money”, and you are in for one of the better stories about how finance works at the coalface.
如果你听到一位专业投资者谈起一笔让他们受益匪浅的交易，请竖起你的耳朵。通常，这意味着 "有一次我亏损了一大笔钱"，你就会听到一个关于金融如何在关键时刻发挥作用的精彩故事。

On this front, Victor Haghani is a man to whom it is worth listening. He spent the mid-1990s as a partner and superstar bond trader at the hottest hedge fund on Wall Street. In its first four years, Long-Term Capital Management (ltcm) made its initial backers average returns of more than 30% a year and never lost money two months in a row. Moreover, its partners had been trading the capital of Salomon Brothers, an investment bank, for the preceding 20 years, with similar results. But in 1998 the wheels came off in spectacular fashion. ltcm lost 90% of its capital at a stroke. Despite a $3.6bn bail-out from a group of its trading counterparties, the fund was liquidated and its partners’ personal investments wiped out. Mr Haghani writes that he took “a nine-figure hit”.
在这方面，维克多-哈加尼是一个值得倾听的人。20 世纪 90 年代中期，他曾是华尔街最炙手可热的对冲基金的合伙人和超级债券交易员。在最初的四年里，长期资本管理公司（Long-Term Capital Management，ltcm）为其最初的支持者带来了每年超过 30% 的平均回报，而且从未连续两个月亏损。此外，在此前的 20 年里，其合伙人一直在从事投资银行所罗门兄弟公司（Salomon Brothers）的资本交易，并取得了类似的成果。但 1998 年，ltcm 以惊人的方式发生了巨变，一下子损失了 90% 的资本。尽管一批交易对手向基金提供了 36 亿美元的救助，但基金还是被清算，合伙人的个人投资也化为乌有。Haghani 先生写道，他遭受了 "九位数的损失"。

Now, along with his present-day colleague James White, he has written a book that aims to spare other investors his mistakes. Fortunately, “The Missing Billionaires” is not a discussion of the minutiae of ltcm’s bond-arbitrage trades. Instead, it examines what its authors argue is a much more important—and neglected—question than picking the right investments to buy or sell: not “what” but “how much”.
现在，他与现在的同事詹姆斯-怀特（James White）一起写了一本书，旨在让其他投资者避免重蹈覆辙。幸运的是，《失踪的亿万富翁》并不是讨论 ltcm 的债券套利交易的细枝末节。相反，它探讨的是作者认为比选择正确的投资买卖更重要--但却被忽视了--的问题：不是 "买什么"，而是 "买多少"。

People tend to answer this question badly. To show this, the book describes an experiment in which 61 youngsters (college students of finance and economics, plus some young professional financiers) were given $25 and asked to bet on a rigged coin at even odds. Each flip, they were told, had a 60% chance of coming up heads. They had time for about 300 tosses, could choose each bet’s size and would keep their winnings up to a cap of $250. This was an exceptionally good deal: simply betting 10% of the remaining pot on each toss had a 94% chance of yielding the maximum payout and none of going bust. Yet the players’ average payout was just $91, only a fifth of them hit the cap and 28% managed to lose everything.
人们对这个问题的回答往往很糟糕。为了说明这一点，书中描述了一个实验：给 61 个年轻人（金融和经济专业的大学生，还有一些年轻的职业金融家）25 美元，让他们在一个被操纵的硬币上下注，赔率是均等的。他们被告知，每次掷硬币都有 60% 的概率是正面。他们有时间抛掷大约 300 次，可以选择每次下注的金额，并且可以保留最多 250 美元的奖金。这是一笔非常划算的交易：只需在每次掷骰子时下注剩余赌金的 10%，就有 94% 的几率获得最高赔率，而且不会爆仓。然而，玩家的平均赔率仅为 91 美元，只有五分之一的玩家达到了上限，28%的玩家输得精光。

A list of the coin-flippers’ mistakes reads like a parable of how not to invest in the stockmarket. Rather than picking a strategy and sticking to it, subjects bet erratically. Nearly a third wagered their entire pot on a single flip and, amazingly, some did so on the 40% chance of getting tails. Many doubled down on losses, even though doing so is a reliable way of making mild ones catastrophic. Others made small bets fixed in dollar amounts, avoiding ruin but also giving up the lion’s share of their potential returns. Few considered the optimal, lucrative strategy of betting a constant fraction of their wealth on an attractive opportunity.
炒币者的错误清单就像一则寓言，告诉我们如何避免投资股票市场。受试者并没有选择一种策略并坚持下去，而是反复下注。将近三分之一的人把全部赌注押在了一次抛硬币上，令人惊讶的是，有些人竟然押在了40%的反面概率上。许多人在亏损时加倍下注，尽管这样做有可能使轻微的亏损变成灾难性的。另一些人则以固定的美元金额进行小注，这样做虽然避免了损失，但也放弃了潜在收益的绝大部分。很少有人考虑过最佳的、有利可图的策略，即把自己财富的固定部分押在一个诱人的机会上。

The rest of the book offers a corrective to these wealth-sapping instincts. Most important is to devise rules for spending, saving and allocating investments, expressed as fractions of your total wealth. Then you must stick to them, avoiding the temptation to chase hot assets or spend too much in the face of losses.
本书的其余部分对这些掠夺财富的本能进行了纠正。最重要的是制定支出、储蓄和投资分配规则，以总财富的分数表示。然后，你必须坚持这些规则，避免追逐热门资产或在亏损时花费过多。

The authors’ great success is in offering a consistent and explicit framework within which to do all this. At its core is the concept of “expected utility”, or the pleasure derived from a given level of wealth. This accounts for the fact that most people are averse to risking large chunks of their capital. A happy consequence is that sizing investments to maximise expected utility, rather than wealth, can sharply reduce your chances of intolerable losses while keeping enough risk for a shot at decent returns.
作者的巨大成功在于提供了一个连贯而明确的框架来完成所有这些工作。其核心是 "预期效用 "的概念，即从给定的财富水平中获得的快乐。这说明了一个事实，即大多数人都不愿意拿自己的大笔资金去冒险。一个令人高兴的结果是，确定投资规模，使预期效用最大化，而不是使财富最大化，可以大大降低你遭受难以忍受的损失的几率，同时保留足够的风险，以获得不错的回报。

In practical terms, the book’s crowning achievement is its explanation of the “Merton share”. This is a simple rule of thumb for determining asset allocation, which says that allocations should rise in proportion to expected returns, fall in proportion to the investor’s risk aversion and fall a lot in proportion to volatility (specifically, to its square).
在实际操作方面，本书的最大成就是对 "默顿份额 "的解释。这是一条确定资产配置的简单经验法则，它指出，资产配置应与预期收益成正比上升，与投资者的风险规避成正比下降，与波动率（具体而言，与波动率的平方）成正比大幅下降。

This is not to suggest the book makes for light reading. The authors prescribe calculations that will appeal to only the most dogged investors, ideally with access to a Bloomberg terminal. Most will conclude that they need a wealth-management firm to help them; conveniently enough, Messrs Haghani and White run one. Yet for those investing in their own business—or, indeed, a hotshot hedge fund—it is worth reading simply for Mr Haghani’s reflection on how much he ought to have ploughed into ltcm all those years ago. Spoiler alert: it was rather less than he did. ■
这并不是说这本书是一本轻松的读物。作者提出的计算方法只对最执着的投资者有吸引力，他们最好能使用彭博终端。大多数人会得出这样的结论：他们需要一家财富管理公司来帮助他们；很方便，哈加尼和怀特先生就经营着这样一家公司。然而，对于那些投资自己企业的人来说，或者说，对于那些炙手可热的对冲基金来说，哈加尼先生对自己多年前应该向 ltcm 投入多少资金的反思就值得一读了。剧透：比他投入的要少得多。■