贝比·鲁斯效应：频率与幅度
2002 年 1 月 29 日 第 1 卷，第 2 期
January 29, 2002 Volume 1, Issue 2
贝比·鲁斯效应：
The Babe Ruth Effect:
频率与幅度 “在现实世界中，不存在确保财务利润的‘捷径’。至少，理性地告诉自己‘我们宁愿聪明地亏钱，也不愿无知地赚钱’，这让人感到欣慰。”
Frequency versus Magnitude “In the real world there is no ‘easy way’ to assure a financial profit. At least, it is gratifying to rationalize that we would rather lose intelligently than win ignorantly.”
理查德·A·爱泼斯坦 《博弈论与统计逻辑》
Richard A. Epstein The Theory of Gambling and Statistical Logic
与贝比一起挥棒
一位知名且业绩非常出色的投资组合经理，最近给我们讲了一个乍听起来有些矛盾的故事。他解释说，他是一家公司旗下约 20 位管理资金的组合经理之一。这家公司的财务主管对自己麾下主动型经理的总体表现感到失望，决定逐一评估每位经理的决策过程，试图剔除表现差劲的人。这位财务主管断定，哪怕是一种完全随机的选股过程，最终构建出的股票组合里，大约也有一半能跑赢基准（此处基准是标普 500 指数），另一半则跑输基准。于是，他根据每个组合中跑赢市场的股票所占的百分比，来衡量各组合的表现。
Batting with the Babe A well-known and very successful portfolio manager recently told us a story that initially sounded incongruous. He explained that he was one of roughly 20 portfolio managers running money for a company. The company’s treasurer, dismayed with the aggregate performance of his active managers, decided to evaluate each manager’s decision process in an effort to weed out the poor performers. The treasurer figured that even a random process would result in a portfolio of stocks with roughly one-half outperforming the benchmark (in this case the S&P 500) and the other half underperforming it. So he measured each portfolio based on what percentage of its stocks beat the market.
这位投资组合经理发现自己处境奇特。尽管他的整体投资组合业绩在同行中名列前茅，但若按“打击率”来算，他却是垫底之一。在解雇了所有其他“表现不佳”的经理后，财务主管召集这位投资组合经理开会，想厘清业绩良好却“打击率糟糕”这一矛盾。
The portfolio manager found himself in an unusual position. While his total portfolio performance was among the best in the group, he was among the worst based on this batting average. After having fired all of the other “poor” performing managers, the treasurer called a meeting with this portfolio manager to sort out the divergence between the good performance and the “bad” batting average.
投资组合经理对业绩差异的解释，揭示了一个贯穿任何概率性操作的根本教训：正确的频次并不重要，重要的是正确时的幅度。假设你持有四只股票，其中三只小幅下跌，但第四只大幅上涨。那么，即便多数股票都在下跌，整个投资组合的表现依然会很好。
The portfolio manager’s explanation for the discrepancy underscores a lesson inherent in any probabilistic exercise: the frequency of correctness does not matter; it is the magnitude of correctness that matters. Say that you own four stocks, and that three of the stocks go down a bit but the fourth rises substantially. The portfolio will perform well even as the majority of the stocks Michael J. Mauboussin decline.
212-325-3108 要构建一个能带来卓越表现的组合，你需要在评估每项投资时使用期望值分析。令人瞩目的是，不同领域的顶尖思想家——包括赛马博彩、赌场赌博和投资——都强调同一个要点。我们称之为贝比·鲁斯效应：尽管鲁斯经常被三振出局，他仍是棒球史上最伟大的击球手之一。
212-325-3108 Building a portfolio that can deliver superior performance requires that you evaluate each Kristen Bartholdson investment using expected value analysis. What is striking is that the leading thinkers across 212-325-2788 varied fields—including horse betting, casino gambling, and investing—all emphasize the same 1 point. We call it the Babe Ruth effect: even though Ruth struck out a lot, he was one of baseball’s greatest hitters.
关于期望值的教训之所以具有普遍性，是因为所有概率类问题都有相似的特征。然而，真正内化这个教训却很难，因为它在根本上与人性相悖。尽管揭示财务主管的逻辑缺陷并不难，但理解他的思维方式却很容易。
The reason that the lesson about expected value is universal is that all probabilistic exercises have similar features. Internalizing this lesson, on the other hand, is difficult because it runs against human nature in a very fundamental way. While it’s not hard to show the flaw in the treasurer’s logic, it’s easy to sympathize with his thinking.
硬接线之弊 1979 年，丹尼尔·卡尼曼与阿莫斯·特沃斯基提出了前景理论，该理论识别出两种与理性决策相悖的经济行为。该理论最重要的洞见之一在于：在风险抉择中，无论赌注多么微小，人们都会表现出强烈的损失厌恶。事实上，卡尼曼和特沃斯基发现，同等金额的损失对人的影响大约是收益的 2.5 倍。换言之，人们对特定数额损失的痛苦感受，远超过对相同幅度收益的喜悦感受。
The Downside of Hard Wiring In 1979, Daniel Kahneman and Amos Tversky outlined prospect theory, which identifies economic 2 behaviors that are inconsistent with rational decision-making. One of the most significant insights from the theory is that people exhibit significant aversion to losses when making choices between risky outcomes, no matter how small the stakes. In fact, Kahneman and Tversky found that a loss has about two and a half times the impact of a gain of the same size. In other words, people feel a lot worse about losses of a given size than they feel good about a gain of a similar magnitude.
这一行为事实意味着，当人们频繁正确时，他们会快乐得多。有趣的是，频繁正确并不一定与跑赢基准的投资组合相一致（如上文故事所示）。投资组合中上涨股票的百分比并不决定其表现，起决定作用的是投资组合的美元变动额。少数股票的剧烈涨跌对投资组合表现的影响，往往比命中率大得多。
This behavioral fact means that people are a lot happier when they are right frequently. What’s interesting is that being right frequently is not necessarily consistent with an investment portfolio that outperforms its benchmark (as the story above illustrates). The percentage of stocks that go up in a portfolio does not determine its performance, it is the dollar change in the portfolio. A few stocks going up or down dramatically will often have a much greater impact on portfolio performance than the batting average.
多头、空头与概率
在纳西姆·塔勒布的精彩著作《随机致富的傻瓜》中，他讲了一个趣闻，精妙地阐明了预期价值的含义。在一次与交易员同行的会议上，一位同事问塔勒布对市场的看法。他回答说，他认为未来一周市场小幅上涨的概率很高。在追问下，他给出了 70% 的上涨概率。这时，会上有人指出，塔勒布当时做空了大量标普 500 指数期货——这是一种押注市场下跌的赌注——表面上看，这与他的“看涨”观点相矛盾。塔勒布随后用预期价值术语解释了他的头寸。他用下面这张表格阐述了自己的思考过程：
Bulls, Bears and Odds In his wonderful book, Fooled by Randomness, Nassim Taleb relates an anecdote that beautifully drives home the 3 expected value message. In a meeting with his fellow traders, a colleague asked Taleb about his view of the market. He responded that he thought there was a high probability that the market would go up slightly over the next week. Pressed further, he assigned a 70% probability to the up move. Someone in the meeting then noted that Taleb was short a large quantity of S&P 500 futures—a bet that the market would go down—seemingly in contrast to his “bullish” outlook. Taleb then explained his position in expected value terms. He clarified his thought process with the following table:
| 事件 | 概率 | 结果 | 期望值 |
|---|---|---|---|
| 市场上涨 | 70% | +1% | +0.7% |
| 市场下跌 | 30% | -10% | -3.0% |
| 总计 | 100% | -2.3% |
Event Probability Outcome Expected value Market goes up 70% +1% +0.7% Market goes down 30% -10% -3.0% Total 100% -2.3%
在这种情况下，最可能发生的结果是市场上涨。但预期价值为负，因为 4 种结局呈不对称分布。现在用股票来想这件事。股票有时被以完美定价。即便公司大部分时间（频率）都能达到或略超预期数字，股价也不会涨多少。可一旦公司不及预期数字，股票的下跌空间则非常剧烈。令人满意的结果频率虽高，预期价值却是负的。
In this case, the most probable outcome is that the market goes up. But the expected value is negative, because the 4 outcomes are asymmetric. Now think about it in terms of stocks. Stocks are sometimes priced for perfection. Even if the company makes or slightly exceeds its numbers the majority of the time (frequency), the price doesn’t rise much. But if the company misses its numbers, the downside to the shares is dramatic. The satisfactory result has a high frequency, but the expected value is negative.
现在再来看那些遭人冷落的股票。多数时间里它都令人失望，让股价一步步走低。但只要出现一个积极结果，就会带来急剧的上涨。在这种情况下，发生坏结果的概率更高，但预期值却是有利的。
Now consider the downtrodden stock. The majority of the time it disappoints, nudging the stock somewhat lower. But a positive result leads to a sharp upside move. Here, the probability favors a poor result, but the expected value is favorable.
投资者必须持续地透过频率看本质，去考量期望值。事实证明，在所有涉及概率的领域，最出色的从业者都是这么思考的。然而这在很多方面违背人的天性：投资者希望自己的股票上涨，而不是下跌。事实上，前景理论在实践中最主要的结果就是，投资者往往过早卖出盈利的股票（以满足“自己判断对了”的心理），却长期持有亏损的股票（寄希望于不必承认损失）。现在，我们把目光转向三个不同概率领域的顶尖实践者：投资、赛马彩池投注和二十一点。
Investors must constantly look past frequencies and consider expected value. As it turns out, this is how the best performers think in all probabilistic fields. Yet in many ways it is unnatural: investors want their stocks to go up, not down. Indeed, the main practical result of prospect theory is that investors tend to sell their winners too early (satisfying the desire to be right) and hold their losers too long (in the hope that they don’t have to take a loss). We now turn to three leading practitioners in separate probabilistic fields: investing, pari-mutuel betting, and black jack.
沃伦·巴菲特无疑是 20 世纪最优秀的投资者之一，他说智力和天赋好比发动机的马力，但发动机的产出取决于理性。“很多人起步时拥有 400 马力的发动机，却只得到 100 马力的输出，”他说，“拥有 200 马力的发动机，并让它全部发挥出来，这要好得多。”而其中一个关键，就是用预期价值来审视所有投资机会。正如巴菲特的合伙人查理·芒格所指出的，“像巴菲特这样的人，一个优势就是他本能地用决策树来思考。”巴菲特说：“用盈利概率乘以可能盈利的金额，再减去亏损概率乘以可能亏损的金额。这就是我们在做的事情。它并不完美，但投资的核心就是这个。”
From OTC to OTB th Warren Buffett, undoubtedly one of the 20 century’s best investors, says that smarts and talent are like a motor’s horsepower, but that the motor’s output depends on rationality. “A lot of people start out with a 400-horsepower motor but only get 100 horsepower of output,” he said. “It’s way better to have a 200-horsepower motor and get it all 5 into output.” And one of the keys is to consider all investment opportunities in terms of expected value. As Buffett’s partner Charlie Munger notes, “one of the advantages of a fellow like Buffett is that he automatically thinks in terms 6 of decision trees.” Says Buffett, “Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all 7 about.”
自然，得出各种可能的结果和相应的概率并不是一项轻松的任务。但这种分析过程迫使投资者去思考，价值驱动因素——销售收入、成本、投资——预期的各种变化会如何影响股东价值，以及不同结果出现的可能性。这样的练习还能帮助投资者克服风险厌恶这个陷阱。
Naturally, coming up with likely outcomes and appropriate probabilities is not an easy task. But the discipline of the process compels an investor to think through how various changes in expectations for value triggers—sales, costs, and investments—affect shareholder value, as well as the likelihood of various outcomes. Such an exercise also 8 helps overcome the risk aversion pitfall.
期望值思维绝不仅限于投资领域。一本新近出版的《与最优者下注》（Bet with the Best）为赛马彩金投注者提供了多种策略。《每日赛马通讯》（Daily Racing Form）首席执行官、编辑兼出版商史蒂文·克里斯蒂展示了一场假设有四匹马参赛的赛马中，包含马场抽成的投资回报率。在总结这一经验时他写道：“这个练习的要义在于说明，即便一匹马获胜概率极高，它也可能是一笔极好或极差的赌注，而两者之间的区别只取决于一件事：赔率。”
The expected value mindset is by no means limited to investing. A recently published book, Bet with the Best, offers various strategies for pari-mutuel bettors. Steven Crist, CEO, editor and publisher of Daily Racing Form, shows the return on investment, including the track’s take, of a hypothetical race with four horses. To summarize the lesson, he writes, “The point of this exercise is to illustrate that even a horse with a very high likelihood of winning can be either a very good or a very bad bet, and that the difference between the two is determined by only one thing: the odds.”
第 2 页所以，一匹有 50% 获胜概率的马，究竟是好赌注还是坏赌注，完全取决于赔率，而同样的道理……
Page 2 So a horse with a 50% probability of winning can be either a good or bad bet based on the payoff, and the same
这也适用于十赔一的冷门。他说的意思，直白地讲，重要的不是获胜的频率，而是频率乘以赢钱的幅度。
holds true of a 10-1 shot. He is saying, in plain words, it is not the frequency of winning that matters, but the 9 frequency times the magnitude of the payoff.
克里斯托还向他的读者们索要一份坦白：“现在问问你自己：你在下注分析时真的会这么想吗？还是你会找一些你‘喜欢’的马，然后在价格上指望运气最好？多数老实的赌徒都会承认他们走的是后一条路。”把“下注分析”换成“投资”，“马”换成“股票”，克里斯托讲的简直就是股市。
Crist also solicits a confession from his readers, “Now ask yourself: Do you really think this way when you’re handicapping? Or do you find horses you ‘like’ and hope for the best on price? Most honest players admit they follow the latter path.” Replace the word “handicapping” with “investing” and “horses” with “stocks” and Crist could be talking about the stock market.
另一个适用期望值思维的领域是二十一点，正如爱德华·索普的畅销书《击败庄家》所展示的那样。在二十一点中，赔率是固定的，玩家最主要的任务在于评估抽到有利牌型的概率。索普展示了如何通过算牌来识别牌局概率何时偏向玩家。当概率对玩家有利时，理想的策略是加大赌注（这实质上是在提高回报金额）。索普指出，即便在最理想的情况下，有利局面在 10 次中仅会出现 9.8% 的回合；其余 90.2% 的时间里，庄家拥有优势。
Yet another domain where expected value thinking is pertinent is black jack, as Edward Thorp’s best-selling book, Beat the Dealer, shows. In black jack, the payoffs are set, and the player’s principal task is to assess the probability of drawing a favorable hand. Thorp showed how to count cards in order to identify when the probabilities of a winning hand tilt in player’s favor. When the odds favor the player, the ideal strategy is to increase the bet (effectively increasing the payout). Thorp notes that even under ideal circumstances, favorable situations only arise 9.8% of the 10 time; the house has the advantage the other 90.2%.
由此可见，在这三个领域——均属概率性实践——顶尖思考者们都殊途同归，采用了相同的方法。我们还知道，在这些活动中，绝大多数参与者并未像他们应该做的那样明确地思考期望值。我们对风险厌恶、回避损失的本能，进一步加剧了股票投资者面临的挑战，因为我们会避开那些上行概率虽低但期望值颇具吸引力的情形。
So we see that the leading thinkers in these three domains—all probabilistic exercises—converge on the same approach. We also know that in these activities, the vast majority of the participants don’t think through expected value as explicitly as they should. That we are risk adverse and avoid losses compounds the challenge for stock investors, because we shun situations where the probability of upside may be low but the expected value is attractive.
一个有用的类比：在这些充满概率的活动中取得长期成功，都具备一些共同特征。
A Useful Analogy Long-term success in any of these probabilistic exercises shares some common features.
我们总结了其中四项：
We summarize four of them:
• 专注。职业赌徒不会同时玩多种游戏——他们不会走进赌场，先玩几把二十一点，又掷几把骰子，再在老虎机上消磨一会儿时间。他们会专注于某一特定游戏，精通其里里外外。同样，大多数投资者必须划定自己的能力圈——即相对精通的领域。想在众多行业和公司中寻求竞争优势，至少可以说是极具挑战。大多数杰出投资者都坚守在自己的能力圈内。
• Focus. Professional gamblers do not play a multitude of games—they don’t stroll into a casino and play a little black jack, a little craps, a spend a little time on the slot machine. They focus on a specific game and learn the ins and outs. Similarly, most investors must define a circle of competence—areas of relative expertise. Seeking a competitive edge across a spectrum of industries and companies is a challenge, to say the least. Most great investors stick to their circle of competence.
• 涉及大量情境。概率游戏的玩家必须审视大量情境，因为“市场”价格通常相当准确。投资者同样需要评估大量情境、收集大量信息。例如，GEICO 资本业务那位极其成功的总裁兼首席执行官卢·辛普森，每天花 5 到 8 小时阅读，交易频率极低。
• Lots of situations. Players of probabilistic games must examine lots of situations, because the “market” price is usually pretty accurate. Investors, too, must evaluate lots of situations and gather lots of information. For example, the very successful president and CEO of Geico’s capital operations, Lou Simpson, tries to read 5-8 hours a day, and trades very infrequently.
• 机会有限。正如索普在《战胜庄家》中指出的，即便在理想条件下玩牌且你知道自己在做什么，你占优势的概率仍不到 10%。而且几乎没有人能在理想条件下玩牌。对投资者的启示是，即使你很有能力，有利的局势——即你对市场有明确的差异化看法——也不会频繁出现。
• Limited opportunities. As Thorp notes in Beat the Dealer, even when you know what you’re doing and play under ideal circumstances, the odds still favor you less than 10% of the time. And rarely does anyone play under ideal circumstances. The message for investors is even when you are competent, favorable situations—where you have a clear-cut variant perception vis-à-vis the market—don’t appear very often.
• 入场费。在赌场，你必须每次下注才能玩下去。理想情况下，在赔率差时可以下小注，赔率有利时下大注，但你得先有本钱才能参与游戏。而在投资中，当你觉得预期回报不吸引人时，可以不参与，当局势看起来有利时（当然是在投资政策的约束下），则可以大举下注。从这个角度看，投资比其他概率游戏要有利得多。
• Ante. In the casino, you must bet every time to play. Ideally, you can bet a small amount when the odds are poor and a large sum when the odds are favorable, but you must ante to play the game. In investing, on the other hand, you need not participate when you perceive the expected value as unattractive, and you can bet aggressively when a situation appears attractive (within the constraints of an investment policy, naturally). In this way, investing is much more favorable than other games of probability.
持续用预期价值来思考需要纪律，而且多少有些反直觉。但来自不同领域的顶尖思想家和实践者，都汇聚到同一个公式上：不要关注正确判断的频率，而要关注正确判断的幅度。
Constantly thinking in expected value terms requires discipline and is somewhat unnatural. But the leading thinkers and practitioners from somewhat varied fields have converged on the same formula: focus not on the frequency of correctness, but on the magnitude of correctness.
注意瑞士信贷第一波士顿银行在过去三年内，可能曾担任上述某家或全部公司证券公开募集的牵头或联合管理人，或为其证券做市。
N.B.CREDIT SUISSE FIRST BOSTON CORPORATION may have, within the last three years, served as a manager or co-manager of a public offering of securities for or makes a primary market in issues of any or all of the companies mentioned.
1 我们并非将投资等同于赌博。事实上，长期投资恰恰与赌博相反。赌博中，你玩的次数越多，输的概率就越高。投资中，你投资的时间越长，获得正回报的概率就越大。 2 丹尼尔·卡尼曼和阿莫斯·特沃斯基，《前景理论：风险决策分析》，《计量经济学》，第 47 卷，263-291 页（1979 年）。
1 We are not equating investing to gambling. In fact, long-term investing is really the opposite of gambling. In gambling, the more you play the greater the odds that you lose. In investing, the longer you invest, the greater the odds that you generate positive returns. 2 Daniel Kahneman and Amos Tversky, “Prospect Theory: An Analysis of Decision Under Risk” Econometrica, 47: 263-291 (1979).
3 纳西姆·尼古拉斯·塔勒布，《被随机性愚弄：市场与生活中偶然性的隐藏作用》（纽约：Texere 出版社，2001 年），第 87-88 页。 4 塔勒布指出，知名投资者吉姆·罗杰斯回避期权，因为“90% 的期权到期时都是亏损的”。罗杰斯混淆了亏损频率与平均盈利金额这两个概念。
3 Nassim Nicholas Taleb, Fooled By Randomness: The Hidden Role of Chance in Markets and in Life (New York: Texere, 2001), pp. 87-88. 4 Taleb points out that well-known investor Jim Rogers avoids options because “90 percent of all options expire as losses.” Rogers is confusing frequency with how much money is made on average.
5 布伦特·施伦德，《比尔与沃伦秀》，《财富》杂志，1998 年 7 月 20 日。
5 Brent Schlender, “The Bill & Warren Show,” Fortune (July 20, 1998).
6 查理·芒格，《关于投资管理与商业的基本世俗智慧一课》，《杰出投资者文摘》，1995 年 5 月 5 日，第 50 页。
6 Charlie Munger, “A Lesson on Elementary, Worldly Wisdom As It Relates to Investment Management & Business” Outstanding Investor Digest, May 5, 1995, p. 50.
7 伯克希尔·哈撒韦股东大会，1989 年。
7 Berkshire Hathaway Annual Meeting, 1989.
8 阿尔弗雷德·拉帕波特和迈克尔·J·莫布森，《预期投资》（波士顿：哈佛商学院出版社，2001 年），第 105-108 页。 9 《与最强者对决》（纽约：《每日赛马论坛》，2001 年），第 63-64 页。
8 Alfred Rappaport and Michael J. Mauboussin, Expectations Investing (Boston: Harvard Business School Press, 2001), pp. 105-108. 9 Bet With the Best (New York: Daily Racing Forum, 2001), pp. 63-64.
第 3 页 10 爱德华·O·索普，《战胜庄家》（纽约：Vintage 图书出版社，1966 年），第 56-57 页。
Page 3 10 Edward O. Thorp, Beat the Dealer (New York: Vintage Books, 1966), pp. 56-57.
原件此处是表格，PDF 抽取时列结构已丢失，下面只剩按列读出的数字，行列对应关系无法还原。核对数据请打开来源正文。
| 城市 | 电话 | 城市 | 电话 | 城市 | 电话 |
|---|---|---|---|---|---|
| 阿姆斯特丹 | 31 20 5754 890 | 吉隆坡 | 603 2143 0366 | 旧金山 | 1 415 836 7600 |
| 亚特兰大 | 1 404 656 9500 | 伦敦 | 44 20 7888 8888 | 圣保罗 | 55 11 3841 6000 |
| 奥克兰 | 64 9 302 5500 | 马德里 | 34 91 423 16 00 | 首尔 | 82 2 3707 3700 |
| 巴尔的摩 | 1 410 223 3000 | 墨尔本 | 61 3 9280 1888 | 上海 | 86 21 6881 8418 |
| 曼谷 | 62 614 6000 | 墨西哥城 | 52 5 283 89 00 | 新加坡 | 65 212 2000 |
| 北京 | 86 10 6410 6611 | 米兰 | 39 02 7702 1 | 悉尼 | 61 2 8205 4433 |
| 波士顿 | 1 617 556 5500 | 莫斯科 | 7 501 967 8200 | 台北 | 886 2 2715 6388 |
| 布达佩斯 | 36 1 202 2188 | 孟买 | 91 22 230 6333 | 东京 | 81 3 5404 9000 |
| 布宜诺斯艾利斯 | 54 11 4394 3100 | 纽约 | 1 212 325 2000 | 多伦多 | 1 416 352 4500 |
| 芝加哥 | 1 312 750 3000 | 帕洛阿尔托 | 1 650 614 5000 | 华沙 | 48 22 695 0050 |
| 法兰克福 | 49 69 75 38 0 | 巴黎 | 33 1 53 75 85 00 | 华盛顿 | 1 202 354 2600 |
| 休斯顿 | 1 713 220 6700 | 帕萨迪纳 | 1 626 395 5100 | 惠灵顿 | 64 4 474 4400 |
| 香港 | 852 2101 6000 | 费城 | 1 215 851 1000 | 苏黎世 | 41 1 333 55 55 |
| 约翰内斯堡 | 27 11 343 2200 | 布拉格 | 420 2 210 83111 |
AMSTERDAM............... 31 20 5754 890 KUALA LUMPUR.........603 2143 0366 SAN FRANCISCO...... 1 415 836 7600 ATLANTA ......................1 404 656 9500 LONDON ...................44 20 7888 8888 SÃO PAULO ............ 55 11 3841 6000 AUCKLAND.....................64 9 302 5500 MADRID .....................34 91 423 16 00 SEOUL ....................... 82 2 3707 3700 BALTIMORE..................1 410 223 3000 MELBOURNE .............61 3 9280 1888 SHANGHAI............... 86 21 6881 8418 BANGKOK..........................62 614 6000 MEXICO CITY ..............52 5 283 89 00 SINGAPORE ................... 65 212 2000 BEIJING.......................86 10 6410 6611 MILAN .............................39 02 7702 1 SYDNEY ..................... 61 2 8205 4433 BOSTON........................1 617 556 5500 MOSCOW....................7 501 967 8200 TAIPEI ...................... 886 2 2715 6388 BUDAPEST .....................36 1 202 2188 MUMBAI......................91 22 230 6333 TOKYO ....................... 81 3 5404 9000 BUENOS AIRES..........54 11 4394 3100 NEW YORK.................1 212 325 2000 TORONTO.................. 1 416 352 4500 CHICAGO ......................1 312 750 3000 PALO ALTO................1 650 614 5000 WARSAW................... 48 22 695 0050 FRANKFURT ....................49 69 75 38 0 PARIS........................33 1 53 75 85 00 WASHINGTON........... 1 202 354 2600 HOUSTON .....................1 713 220 6700 PASADENA ................1 626 395 5100 WELLINGTON.............. 64 4 474 4400 HONG KONG..................852 2101 6000 PHILADELPHIA ..........1 215 851 1000 ZURICH ....................... 41 1 333 55 55 JOHANNESBURG..........27 11 343 2200 PRAGUE ...................420 2 210 83111
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Some investments discussed in the research may have a high level of volatility. High volatility investments may experience sudden and large falls in their value causing losses when that investment is realised. Those losses may equal your original investment. In the case of some investments the potential losses may exceed the amount of initial investment, in such circumstances you may be required to pay more money to support those losses. Income yields from investments may fluctuate and in consequence initial capital paid to make the investment may be used as part of that income yield.
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