数字金字塔：公司规模、增长率与估值
2003 年 9 月 23 日 第 2 卷 第 17 期
September 23, 2003 Volume 2, Issue 17
数字金字塔：企业规模、增长率与估值
增长之所以重要，是因为公司通过盈利增长为股东创造价值。然而，有力的证据表明，一旦公司的核心业务走向成熟，寻求新的增长平台便会带来巨大的风险。大约每十家公司中只有一家能够持续实现那种能在多年间转化为高于平均水平的股东回报的增长……
The Pyramid of Numbers Firm Size, Growth Rates, and Valuation Growth is important because companies create shareholder value through profitable growth. Yet there is powerful evidence that once a company’s core business has matured, the pursuit of new platforms for growth entails daunting risk. Roughly one company in ten is able to sustain the kind of growth that translates into an above-average increase in shareholder returns over more than a few years. . . .
因此，大多数高管都陷入了两难境地：股市要求他们增长，但如何增长却难以把握。
Consequently, most executives are in a no-win situation: equity markets demand that they grow, but it’s hard to know how to grow.
克莱顿·M·克里斯坦森与迈克尔·E·雷纳，《创新者的解答》。
Clayton M. Christensen and Michael E. Raynor The Innovator’s Solution 1
分析师和投资者似乎相信，许多公司的利润能在相当长一段时间里持续高速增长。但证据表明，这种情况出现的次数，与纯凭运气所预期的数量相差无几。
Analysts and investors seem to believe that many firms’ earnings can consistently grow at high rates for quite a few years. The evidence suggests instead that the number of such occurrences is not much different from what might be expected from sheer chance.
路易·K·C·陈、杰森·卡尔塞斯基与约瑟夫·拉科尼肖克《增长率的水平与持续性》2
Louis K. C. Chan, Jason Karceski, and Josef Lakonishok The Level and Persistence of Growth Rates 2
为什么凶猛的巨型动物很罕见
表面上看，物种、城市和公司的规模与频次分布似乎没有太多共同之处。然而，每一种都遵循幂律分布，在对数-对数坐标系上绘出来是一条直线。幂律分布表明，小的个体数量庞大，大的个体则极为稀少。在自然界中，蚂蚁数量极多——蚂蚁的总重量超过人类的总重量——但大象却寥寥无几。与此类似，我们也有很多小公司和数量不多的大型公司。图 1 并列展示了这些分布的实例。
Why Big Fierce Animals are Rare On the surface, the size and frequency distribution for species, cities, and company sizes may not seem like they would have a lot in common. Yet each follows a power law, which looks like a straight line when plotted on a log-log scale. Power laws 3 indicate that there are lots of small occurrences and very few large ones. In nature, there are lots of ants—the combined weight of ants is larger than the combined weight of humans—but very few elephants. Similarly, we have many small companies and a Michael J. Mauboussin modest number of huge ones. Exhibit 1 shows examples of these distributions side- 212-325-3108 by-side.
克里斯汀·巴索尔德森 展品 1：按物种、城市和公司规模的分布
Kristen Bartholdson Exhibit 1: Distribution for Species, City, and Company Sizes
212-325-2788 16.0 15.5 1.00000 15.0 0.10000 14.5
212-325-2788 16.0 15.5 1.00000 15.0 0.10000 14.5
Log (population)
Log (population)
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。
0.01000 Probability 14.0 13.5 0.00100 13.0 12.5 0.00010 12.0 0.00001 11.5 11.0 0.00000 0.0 1.0 2.0 3.0 4.0 5.0 6.0 104 10 6 108 1010
0.01000 Probability 14.0 13.5 0.00100 13.0 12.5 0.00010 12.0 0.00001 11.5 11.0 0.00000 0.0 1.0 2.0 3.0 4.0 5.0 6.0 104 10 6 108 1010
对数（排名）收入（1997 年美元）
Log (rank) Receipts (1997 $)
来源：Juan Camacho 和 Ricard V. Sole，“生态规模谱中的缩放与齐普夫定律”，圣塔菲研究所工作论文，1999 年；http://www.few.eur.nl/few/people/vanmarrewijk/international/zipf.htm，Robert L. Axtell，“美国公司规模的齐普夫分布”，《科学》杂志，2001 年 9 月 7 日，第 1819 页。
Sources: Juan Camacho and Ricard V. Sole, “Scaling and Zipf’s Law in Ecological Size Spectra,” Santa Fe Institute Working Paper, 1999; http://www.few.eur.nl/few/people/vanmarrewijk/international/zipf.htm, Robert L. Axtell, “Zipf Distributions of U.S. Firm Sizes,” Science, September 7, 2001, 1819.
以物种为例。为什么像老虎这样的大型食肉动物相对罕见，而像白蚁这样的小动物却如此繁多？生态学家的解释是：所有动物都有其生态位——这不仅是物理上的栖息地，更是万物宏大格局中的实际位置。一个物种不仅要在自己的家园里生存下去，还必须成功地与共享家园的其他动植物互动。
Take species for a moment. Why are large carnivorous animals, like tigers, relatively rare, while small animals, like termites, are so abundant? Ecologists answer by pointing out that all animals have a niche—not just a physical location, but a real place in the grand scheme of things. A species must not only survive in its home, it must successfully interact with the other plant and animal species that share that home.
然而，生态位理论依然无法解释物种分布为何呈现目前的样子。牛津大学的查尔斯·埃尔顿带来了这一洞见：他指出，体型较大的动物需要依靠体型较小的动物来维持生存。（动物很少捕食比自己体型更大的猎物。）因此，埃尔顿推断，随着体型每增一级，其数量必然相应减少。他将这一生命事实称为“数量金字塔”。大型猛禽之所以稀少，是因为它们可获取的能量来源少于小型动物。物种的幂律分布，正是动物之间相互制约、受物理定律束缚的自然结果。
The niche idea, though, still doesn’t explain why the distribution of species looks the way it does. That insight came from Oxford’s Charles Elton, who noted that larger animals need smaller animals to sustain them. (Animals rarely prey on animals larger than they are.) So, Elton reasoned, with every increment in body size, there should be an associated loss in numbers. He called this fact of life “The Pyramid of Numbers.” Big fierce animals are rare because they have less sources of energy than 4 smaller animals. The species power law distribution is a natural outcome of interacting animals 5 constrained by the laws of physics.
这与股票市场有什么关系？投资者应该关注这些分配，原因有三。第一，公司和物种一样，各有其生态位。思考这些生态位以及它们如何变化，可以让人对公司的增长潜力有所洞察。
What does this have to do with the stock market? Investors should pay attention to these distributions for three reasons. First, companies, like species, fit into niches. Thinking about these niches and how they change can provide some insight into a company’s growth potential.
第二，大量证据表明，大型企业的增长率波动小于小型企业（尽管从整体来看，增长率的中位数相当稳定）。
Second, a strong body of evidence shows that the variance of growth rates is smaller for large firms than for small firms (even though the median growth rate is fairly stable across the population).
此外，大型企业的增长常常陷入停滞，当投资者重新调整预期时，股价表现便会显著落后。
Further, growth for large companies often stalls, leading to marked share price underperformance as investors recalibrate their expectations.
最后，投资者常常将过去的增长率外推到未来，这使得那些无法达到这些预期的公司给股东带来令人失望的回报。意识到增长模式的投资者或许能够避开不利的预期落差。
Finally, investors often extrapolate past growth rates into the future, leading to disappointing shareholder returns for those companies that cannot meet those expectations. Investors who are aware of patterns of growth may be able to avoid unfavorable expectations gaps.
找到你的利基。公司寻找利基这一观点当然并不新鲜。例如，竞争战略文献中的许多内容——特别是博弈论——都探讨了公司应如何以及为何寻找盈利的利基。这里的主要信息是，环境——进而也包括利基——会随着技术发展、监管变化以及行业进入与退出而随时间发生改变。
Find Your Niche The idea that companies find niches is certainly not new. For example, many aspects of the competitive strategy literature in general, and game theory in particular, address how and why companies should seek profitable niches. The main message here is that the environment, and hence niches, change over time as the result of technological developments, regulatory shifts, and industry exit and entry.
拿小型钢厂对比综合钢铁公司，或者网络零售对比实体店竞争对手。新的利基市场不断涌现，新的公司则在其中大展身手。企业适应环境变化的能力至关重要——而能做到这一点的公司寥寥无几。
Think of mini-mills versus integrated steel companies, or Internet-based retailers compared to brick-and-mortar competitors. New niches open, and new companies exploit them. A company’s ability to adapt to a changing environment is critical—and the number of companies that can do so is small.
因此，一家公司的最优规模在特定行业里可能并非固定不变，而将采用不同经济模式的公司估值放在一起比较，也毫无意义。
As a result, optimal firm size may not be fixed for a particular industry, and comparing the valuations of companies with different economic models doesn’t make sense.
尊敬的 CEO——我们已跻身《财富》50 强！你被解雇了
关于企业规模分布与增长率的研究揭示了四个典型事实：
Dear CEO—We’ve Made It to the Fortune 50! You’re Fired Studies of firm size distributions and growth rates reveal four stylized facts:
6
6
企业规模分布遵循齐普夫定律（幂律分布的一个特定类别）。对投资者而言，关键在于这种分布在经历重大经济变革时依然极为稳健。这意味着，未来大型企业与小型企业的数量占比不太可能发生显著变化。
1. Firm size distributions follow Zipf’s Law (a specific class of power law). What is crucial for investors is that this distribution is very robust in the face of significant economic change. This means that the proportion of very large companies to smaller companies is unlikely to vary much in the future.
7
7
2. 公司增长率的方差随规模扩大而收窄。我们的分析表明，在涵盖美国上市公司的大样本中（销售额在 1 亿美元或以上），增长率的中位数保持稳定，但增长率的方差显著缩小。（见图表 2。）从某种程度上说，这一观察结果符合常识——大型公司占 GDP 的很大比例，因此它们不太可能以显著幅度超越 GDP 增长。（《财富》50 强公司占 GDP 的 25% 以上。）然而，跻身《财富》50 强的公司往往是那些过去实现了强劲增长的企业，这便可能造成投资者预期的错位。
2. Variances of firm growth rates decrease with size. Our analysis suggests that median growth rates are stable across a large sample of U.S. public companies (sales of $100 million or more), but that the variance in growth narrows substantially. (See Exhibit 2.) On one level, this observation is common sense—large companies represent a substantial percentage of GDP, so it’s unlikely that they will outstrip it to any meaningful degree. (The Fortune 50 represent over 25 percent of GDP.) Yet companies that launch into the Fortune 50 are often those that have realized strong past growth, setting up a potential investor expectations mismatch.
这一实证发现与吉布拉定律（Gibrat’s Law）类似的随机模型相吻合。该定律又称等比例效应定律，认为企业的增长率与其规模无关。经过一定修正后，将吉布拉定律应用于一组公司样本，会产生齐普夫分布（Zipf distribution）。经典微观经济学未能提出令人满意的模型来解释这 8 项发现。
This empirical finding is consistent with stochastic models similar to Gibrat’s Law. This law, also known as the law of proportionate effect, says that a firm’s growth rate is independent of its size. With some modifications, applying Gibrat’s Law to a sample of companies generates a Zipf distribution. Classical microeconomics has no satisfactory models to explain these 8 findings.
附录 2：销售额增长的方差相对于市值的缩小
Exhibit 2: Shrinking Variance of Sales Growth in Relation to Market Cap
销售额增长与市场资本化之间的方差在缩小。
Shrinking Variance of Sales Grow th in R elation to Market C ap
150%
150%
100%
100%
50%
50%
| 销售增长率 | 0% | |||
|---|---|---|---|---|
| 100 | 1,000 | 10,000 | 100,000 | |
| -50% | ||||
| -100% | ||||
| -150% | ||||
| 基准年销售额 |
Sales Growth 0% 100 1,000 10,000 100,000 -50% -100% -150% Ba se Ye a r Sa le s
资料来源：Factset，瑞信第一波士顿分析。
Source: Factset, CSFB analysis.
3. 大公司的增长常常会停滞。这是企业战略委员会（Corporate Strategy Board）一项详细研究的结论。该研究认为，一旦公司销售额达到一定水平，其增长率就会停滞。几十年来，这个停滞门槛一直在上升，但在 1990 年代末，这个数字大概在 200 亿到 300 亿美元之间。
3. The growth for large companies often stalls. This was the conclusion of a detailed study by the 9 Corporate Strategy Board. The research argued that once companies reach a sufficient sales level, they see their growth rate stall. That stall level has risen over the decades, but looked to be in the $20-30 billion area in the late 1990s.
表 3 展示了进入《财富》50 强（以销售额排序的公司）的企业年均增长率。数据显示，企业通常在跻身前 50 强之前享有强劲的增长率，但一旦进入该集团后，增长往往相当乏力。第一年的高增长率表明，收购将许多公司推入了《财富》50 强。
Exhibit 3 shows the average annual growth rate for companies entering into the Fortune 50 (a ranking based on sales). The data show that companies often enjoy strong growth rates prior to making the top 50 but tend to have rather anemic growth once they attain that group. The high growth rate in the first year suggests that acquisitions catapult many companies into the Fortune 50.
展品 3：进入《财富》50 强企业的年均增长率 30.0% 28.6%
Exhibit 3: Average Annual Growth Rate for Companies Entering Fortune 50 30.0% 28.6%
25.0%
25.0%
| 年均增长率 |
|---|
| 20.0% |
| 20.0% |
| 15.0% |
| 15.0% |
| 13.5% |
| 9.5% |
| 9.0% |
| 10.0% |
Average Annual Growth Rate 20.0% 20.0% 15.0% 15.0% 13.5% 9.5% 9.0% 10.0%
(GNP-Deflated)
(GNP-Deflated)
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。
5.1% 4.5% 5.0% 2.1% 2.8% 2.0% 1.4% 0.7% 1.2% 0.1% -0.1% 0.0% -0.7% -0.7% -1.6% -5.0% -3.9% -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
5.1% 4.5% 5.0% 2.1% 2.8% 2.0% 1.4% 0.7% 1.2% 0.1% -0.1% 0.0% -0.7% -0.7% -1.6% -5.0% -3.9% -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
进入《财富》50 强以来的年数
Years from Entrance into Fortune 50
来源：企业战略委员会，《停滞点：大型企业增长面临的障碍》，1998 年，第 15 页。
Source: Corporate Strategy Board, Stall Points: Barriers to Growth for the Large Corporate Enterprise, 1998, page 15. 10
4. 大多数产业会经历一个清晰可辨的生命周期。早期阶段，产业往往呈现大幅增长和大量企业涌入，随后出现大规模退出和高经济回报（对幸存者而言），接着是增长逐渐放缓。到了成熟阶段，公司增长乏力，经济回报接近竞争均衡水平。大公司往往就是成熟公司。
4. Most industries follow an identifiable life cycle. Early on, an industry tends to see substantial growth and entry, then meaningful exit and high economic returns (for the survivors), followed by gradual growth deceleration. In mature stages, companies have muted growth and economic returns close to competitive equilibrium. Large companies tend to be mature companies.
为面临增长放缓的公司出谋划策，本身已经成为一门产业。确实，大公司由于种种原因，很难像小公司那样成功创新。我们热情推荐克莱顿·克里斯坦森和迈克尔·雷纳的新书《创新者的解答》，这本书为管理者提供了一套实用的创新框架。但现实是，并非所有公司都能永远保持高速增长。
Advising companies what to do in the face of slowing growth is an industry in and of itself. It is true that large companies have a difficult time innovating as successfully as smaller companies for a host of reasons. We enthusiastically recommend a new book by Clayton Christensen and Michael Raynor, The Innovator’s Solution, which provides managers with a useful innovation framework. But the reality is that not all companies can grow rapidly forever.
外推预期 对企业规模与增长率关系的研究证据表明，随着公司规模变大，投资者应调降其增长预期。但现实是，投资者倾向于将近期表现外推到未来，因此忽略了增长率的下降。据 Chan、Karceski 和 Lakonishok 的研究：
Extrapolative Expectations A review of the evidence on firm size and growth rates suggests investors should temper their growth expectations as companies get large. But the reality is that investors tend to extrapolate the recent past, and hence miss declining growth rates. According to Chan, Karceski, and Lakonishok:
市场估值比率在区分高增长企业与低增长企业方面几乎毫无用处。相反，与“外推预期假说”一致，投资者往往将目光锁定在过去的增长率上。过去实现高增长的企业获得高估值，而过去增长低迷的企业则受到低估值的惩罚。公司战略委员会（Corporate Strategy Board）的数据支持了这一观点。其长达数十年的研究显示，在触及增长瓶颈的公司中，大约三分之二会在十年内蒸发掉其市值（相对道琼斯工业平均指数）的 50% 或更多。百分之九十五的公司跑输道琼斯指数 25% 或更多。
Market valuation ratios have little ability to sort out firms with high future growth from firms with low growth. Instead, in line with the extrapolative expectations hypothesis, investors tend to key on past growth. Firms that have achieved high growth in the past fetch high valuations, while firms with low past growth are penalized with poor valuations. 11 Data from the Corporate Strategy Board support this point. Its multidecade study shows that roughly two-thirds of the companies that hit the stall point lose 50 percent or more of their market value (relative to the Dow Jones Industrial Average) within a decade. Ninety-five percent underperform the DJIA by 25 percent or more.
我们问了一个类似的简单问题：如果在每年年底买入一篮子等权重配置的《财富》50 强公司股票，在随后 1 年、3 年和 5 年的表现，与标普 500 指数相比会如何？我们统计了 1980 年到 2002 年的数据，发现在每个持有期，标普 500 指数的表现都优于《财富》50 强组合。（见图表 4。）同样，最大的公司很难显著跑赢市场，因为它们在市场中占的比重太大了。
We asked a similar, simple question: How would an equal-weighted portfolio of the Fortune 50, purchased at year-end, fare versus the S&P 500 in the subsequent 1-, 3-, and 5-year periods? We ran the numbers from 1980 through 2002 and found that for each holding period, the S&P 500 outperformed the Fortune 50 portfolio. (See Exhibit 4.) Again, it’s hard for the largest companies to meaningfully outperform the market because they are such a large percentage of the market.
附表 4：股东总回报——财富 50 强与标普 500 指数 1 年股东总回报 3 年股东总回报 5 年股东总回报
Exhibit 4: Total Shareholder Return—Fortune 50 Versus S&P 500 1-Year TSR 3-Year TSR 5-Year TSR
Fortune 50 13.8% 13.5% 14.3%
Fortune 50 13.8% 13.5% 14.3%
S&P 500 14.3% 15.0% 15.9%
S&P 500 14.3% 15.0% 15.9%
来源：Factset、Ibottson、瑞信（CSFB）分析。
Source: Factset, Ibottson, CSFB analysis.
我们还考察了一个非常简单的估值指标——市值与销售额之比，想看看那些最大的公司是否表现突出。事实确实如此。目前，前 50 大公司的平均市值与销售额之比为 0.9，是前 500 家公司中所有十分位组里最低的。销售额最大的 500 家公司的平均比值为 1.2。这些最大公司不仅拥有最低的市值与销售额比，而且这些比值的标准差也远低于其他十分位组。对最大公司而言，既不容易获得高溢价估值，也不容易实现高溢价增长。
We also looked at a very simple valuation measure, market capitalization-to-sales, to see if the largest companies stood out. And indeed they do. The current average market cap-to-sales ratio for the top 50 companies is 0.9, the lowest of any decile in the top 500. The average ratio for the 500 largest sales companies is 1.2. Not only did the largest companies have the lowest market-cap-to–sales ratios, the standard deviation of those ratios was much lower than those of other deciles. Neither premium valuations nor premium growth are easy to come by for the largest companies.
这绝不是说，当前最大型公司的估值就不包含合理的预期。根据瑞信第一波士顿 HOLT 的汇总数据，市值排名前 50 的美国公司所体现的增长和投资回报预期，显著高于标普 500 指数的整体水平。
None of this is to say that current valuations for the largest companies does not still embed healthy expectations. Based on CSFB HOLT aggregated data, the 50 largest U.S. companies by market capitalization reflect growth and return on investment expectations that are substantially higher than 12 those for the S&P 500 in total.
另一种审视预期的方式，是将股东价值拆解为现有资产所贡献的比例与未来投资所贡献的比例。如今，美国 20 家最大公司中，有 13 家的一半价值尚未兑现。（见图表 5。）
Another way to look at expectations is to break down the percentage of shareholder value that comes from assets in place versus the value attributable to future investments. Today, one-half of the value of 13 the twenty largest U.S. companies is on the come. (See Exhibit 5.)
表 5：大公司：现有资产产生的现金流现值与未来投资的对比
Exhibit 5: Large Companies: PV of Cash Flow from Existing Assets Versus Future Investments
| 股票代码 | 公司名称 | 市值（百万美元） | 现有资产产生的现金流现值占比 | 未来投资产生的现金流净现值占比 |
|---|---|---|---|---|
| MSFT | 微软公司 | 322,699 | 38% | 62% |
| GE | 通用电气公司 | 319,902 | 44% | 56% |
| WMT | 沃尔玛百货 | 254,025 | 50% | 50% |
| XOM | 埃克森美孚公司 | 246,058 | 84% | 16% |
| PFE | 辉瑞公司 | 244,877 | 41% | 59% |
| C | 花旗集团 | 242,038 | 46% | 54% |
| INTC | 英特尔公司 | 189,897 | 47% | 53% |
| IBM | 国际商业机器公司 | 161,391 | 62% | 38% |
| AIG | 美国国际集团 | 157,446 | 48% | 52% |
| JNJ | 强生公司 | 149,365 | 25% | 75% |
| CSCO | 思科系统公司 | 147,098 | 47% | 53% |
| VODPF | 沃达丰集团 | 134,352 | 38% | 62% |
| GLAXF | 葛兰素史克公司 | 122,894 | 54% | 46% |
| PG | 宝洁公司 | 120,211 | 36% | 64% |
| BAC | 美国银行 | 118,538 | 47% | 53% |
| MRK | 默克公司 | 117,151 | 50% | 50% |
| BRK.A | 伯克希尔·哈撒韦-A | 116,660 | 70% | 30% |
| KO | 可口可乐公司 | 106,241 | 37% | 63% |
| VZ | 威瑞森通信 | 97,159 | 94% | 6% |
| MO | 奥驰亚集团 | 90,475 | 44% | 56% |
| 平均值 | 172,924 | 50% | 50% |
Company Market Cap PV of CF from NPV of CF from Symbol Company in $ millions Existing Assets Future Investment MSFT Microsoft Corp $ 322,699 38% 62% GE General Electric Co 319,902 44% 56% WMT Wal-Mart Stores 254,025 50% 50% XOM Exxon Mobil Corp 246,058 84% 16% PFE Pfizer Inc 244,877 41% 59% C Citigroup Inc 242,038 46% 54% INTC Intel Corp 189,897 47% 53% IBM IBM Corp 161,391 62% 38% AIG American International Group 157,446 48% 52% JNJ Johnson & Johnson 149,365 25% 75% CSCO Cisco Systems Inc 147,098 47% 53% VODPF Vodafone Group PLC 134,352 38% 62% GLAXF GlaxoSmithKline PLC 122,894 54% 46% PG Procter & Gamble Co 120,211 36% 64% BAC Bank of America Corp 118,538 47% 53% MRK Merck & Co 117,151 50% 50% BRK.A Berkshire Hathaway-CL A 116,660 70% 30% KO Coca-Cola Co 106,241 37% 63% VZ Verizon Communications 97,159 94% 6% MO Altria Group 90,475 44% 56% Average 172,924 50% 50%
来源：Factset、Ibbotson、瑞士信贷第一波士顿银行（CSFB）分析。
Source: Factset, Ibottson, CSFB analysis.
经济体与市场无疑充满活力。但在不断变化的表象之下，潜藏着稳健的增长模式和公司规模分布规律。审慎的投资者在评估公司——尤其是大型公司——的增长前景时，应当将这些规律纳入考量。
Economies and markets are certainly vibrant. But underneath the constant change lurk robust patterns of growth and firm size distributions. Mindful investors should take these patterns into account as they assess the growth prospects of companies—especially large ones.
Clayton M. Christensen 与 Michael E. Raynor，《创新者的解答：创造并维持成功增长》（马萨诸塞州波士顿：哈佛商学院出版社，2003 年），第 1 页。
Clayton M. Christensen and Michael E. Raynor, The Innovator’s Solution: Creating and Sustaining Successful Growth (Boston, MA: Harvard Business School Press, 2003), 1.
2 路易斯·陈（Louis K. C. Chan）、杰森·卡尔切斯基（Jason Karceski）和约瑟夫·拉科尼肖克（Josef Lakonishok），《增长率的水平与持续性》（The Level and Persistence of Growth Rates），《金融学刊》（The Journal of Finance），第 58 卷，第 2 期，2003 年 4 月，第 644-684 页。
2 Louis K. C. Chan, Jason Karceski, and Josef Lakonishok, “The Level and Persistence of Growth Rates,” The Journal of Finance, Vol. 58, 2, April 2003, 644-684.
3 Michael J. Mauboussin 和 Kristen Bartholdson 合著，The Consilient Observer: More Power to You，第 1 卷第 17 期，2002 年 9 月 24 日。
3 Michael J. Mauboussin and Kristen Bartholdson, The Consilient Observer: More Power to You, Volume 1, Issue 17, September 24, 2002.
保罗·科林沃，《为什么大型凶猛动物如此罕见》（普林斯顿，新泽西：普林斯顿大学出版社，1978 年），第 10–31 页。
4 Paul Colinvaux, Why Big Fierce Animals Are Rare (Princeton, NJ: Princeton University Press, 1978), 10-31.
5 James H. Brown 和 Geoffrey B. West 编，《生物学中的标度》（Scaling in Biology）（牛津：牛津大学出版社，2000 年）。
5 James H. Brown and Geoffrey B. West, eds., Scaling in Biology (Oxford: Oxford University Press, 2000).
6 Robert L. Axtell，“美国公司规模的齐普夫分布”，《科学》，2001 年 9 月 7 日，第 1818-1820 页。 7 斯坦利等，“经济学中的标度行为：I．公司增长的实证结果”，《物理学报》，1997 年 4 月，第 621-633 页。
6 Robert L. Axtell, “Zipf Distribution of US Firm Sizes,” Science, September 7, 2001, 1818-1820. 7 Stanley, et al., “Scaling Behavior in Economics: I. Empirical Results for Company Growth,” Journal de Physique, April 1997, 621-633.
8 Axtell.
8 Axtell.
9 Corporate Strategy Board，《停滞点：大型企业增长障碍》，1998 年。10 Steven Klepper，“产品生命周期中的进入、退出、增长与创新”，《美国经济评论》，第 86 卷，第 3 期，1996 年，第 562–83 页。另见 Bartley J. Madden，《CFROI 估值：企业估值的全系统方法》（牛津：Butterworth-Heinemann，1999 年），第 18–21 页。
9 Corporate Strategy Board, Stall Points: Barriers to Growth for the Large Corporate Enterprise, 1998. 10 Steven Klepper, “Entry, exit, growth, and innovation over the product life cycle,” American Economic Review, Vol. 86, 3, 1996, 562-83. Also, Bartley J. Madden, CFROI Valuation: A Total System Approach to Valuing the Firm (Oxford: Butterworth-Heinemann, 1999), 18-21.
11 Chan、Karceski 和 Lakonishok，第 671 页。
11 Chan, Karceski, and Lakonishok, 671.
对于即将到来的一年（T+1），市值最大的 50 家公司的内含资产增长率为 8.8%，而标普 500 指数为 5.6%；CFROI 分别为 8.8% 和 7.6%。对于 2008 年（T+5），大公司的资产增长率和 CFROI 分别为 8.9% 和 10.9%。标普 500 指数的对应数字为 7.2% 和 9.0%。
12 For the upcoming year (T + 1), embedded asset growth is 8.8% for the 50 largest market capitalization companies versus 5.6% for the S&P 500, and CFROI is 8.8% against 7.6%. For 2008 (T + 5), the large companies reflect asset growth and CFROI of 8.9% and 10.9%, respectively. For the S&P 500, the corresponding numbers are 7.2% and 9.0%.
金融服务是一个突出的行业，其在标普 500 指数盈利中的占比（约 30%，不包括金融子公司）以及占 GDP 的比重（约 21%，而 1980 年为 15%）都显著增长。从历史上看，曾经达到如此高比例的行业（能源和科技）随后都经历了重要性的减弱。欲了解更多，请参阅 Paddy Jilek、Bradford Neuman 与 Arbin Sherchan 合著的《美国
13 Financial services stands out as a sector that has increased significantly as a percentage of S&P 500 earnings (about 30% excluding finance arms) and as a percentage of GDP (roughly 21% versus 15% in 1980). Historically, sectors that have risen to such levels (energy and technology) have seen their importance wane. For more on this, see Paddy Jilek, Bradford Neuman, and Arbin Sherchan, “U.S.
投资文摘：五则趣闻”，瑞士信贷第一波士顿股票研究，2003 年 9 月 5 日。
Investment Digest: Five Tidbits,” Credit Suisse First Boston Equity Research, September 5, 2003.
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结构化证券是复杂金融工具，通常涉及高风险，仅面向具备理解并承担相关风险能力的成熟投资者发售。任何结构化证券的市场价值都可能受到经济、金融和政治因素变化（包括但不限于即期与远期利率及汇率）、距到期日时间、市场状况与波动性，以及任何发行人或参考发行人的信用质量的影响。任何有意购买结构化产品的投资者，都应对该产品进行独立调查与分析，并就购买行为所涉风险咨询其专业顾问。
Structured securities are complex instruments, typically involve a high degree of risk and are intended for sale only to sophisticated investors who are capable of understanding and assuming the risks involved. The market value of any structured security may be affected by changes in economic, financial and political factors (including, but not limited to, spot and forward interest and exchange rates), time to maturity, market conditions and volatility, and the credit quality of any issuer or reference issuer. Any investor interested in purchasing a structured product should conduct their own investigation and analysis of the product and consult with their own professional advisers as to the risks involved in making such a purchase.
本报告讨论的部分投资具有高波动性特征。高波动性投资的价值可能在短期内大幅下跌，导致变现时出现亏损，且亏损金额可能等于您的初始投资。实际上，对于某些投资，潜在损失可能超过初始投资金额，在此情况下您可能需要追加资金来弥补亏损。
Some investments discussed in this report 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. Indeed, 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.
投资收益的回报率可能出现波动，因此，用于最初投资的本金可能会被用作这部分收益的一部分。部分投资可能不易变现，出售或变现这些投资或许存在困难，同样，您可能也难以获取有关此类投资价值或所面临风险的可靠信息。
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