Asked if he’s offended when people trash his investment ideas, Harry Markowitz chuckles like a kindly uncle. The founder of Modern Portfolio Theory replies that he’s in the videoconferencing business. From his San Diego office, he delivers lectures around the globe for $15,000 a pop. Markowitz lets audiences choose from a handful of nontechnical topics — among them, whether his influential blueprint for portfolio construction stopped working during the crash of 2008.
“我的生意一直在积极解释为什么现代投资组合理论仍然正确，”他说。
At 82, Markowitz is still dining out on the slim 1952 paper that changed finance forever — and won him a Nobel Memorial Prize in Economic Sciences. Written when Markowitz was a graduate student at the University of Chicago, this document contains a formula for building a diversified portfolio that delivers the best return for a certain amount of risk. A mathematical expression of the old adage “Don’t put all your eggs in one basket,” Modern Portfolio Theory, or MPT, is still widely used almost 60 years later because the logic behind it makes so much sense.
As Markowitz admits, though, MPT has taken plenty of knocks along the way: “For years — maybe almost from the beginning of [Modern] Portfolio Theory — there have been people who’ve been saying, ‘Well, that’s obsolete. We’re going to do something new and better.’”
这位合唱团自2008年以来一直很大程度。根据批评者，多样化，多样化对洛克斯特普普通的市场提供了很少的保护。他们说，在正常情况下可能是正确的事情，但它在危机时期最多的情况下，它无法完全失败。
Institutions ostensibly using MPT in 2008 got omelet on their faces. According to the Commonfund Institute of Wilton, Connecticut, and the Washington-based National Association of College and University Business Officers, U.S. college and university endowments lost, on average, 18.7 percent for the year ended June 30, 2009. Many of these funds followed the so-called Yale model of portfolio construction, which advocates diversification through significant exposure to alternative asset classes like hedge funds and private equity. When these illiquid investments stopped throwing off cash — alternatives plummeted, on average, 17.8 percent between July 2008 and June 2009 — endowments had trouble meeting their commitments.
最终，这个问题比投资组合理论更有关流动性。基于纽约的J.P.Morgan资产管理的美国的美国全球Multiagset集团的Cio，Cio表示，每个熊市的相关性朝向每个熊市。但三件事相结合，使2008年不同的动物：信贷市场一切却冻结，有广阔的拆迁，流动性迅速下降。
“People underestimated the risk they had in their portfolio vis-à-vis their demands and requirements for liquidity,” Geller says. “It was felt across all institutional portfolios, but perhaps most across endowments that typically hold larger allocations to alternatives.”
毫无疑问，市场比1952年的市场更复杂和挥发。在这种改变的世界中，这呈现出更多挑战和更多机会，MPT可以使用改造只是为了搁置工作。最近的崩溃是一个强大的提醒，以盲目遵守B学校公理，包括Markowitz和他的智力后代的型号。由于它可能是学者，但MPT很容易受到大市场动作和滥用成熟的影响。作为回应，从业者建立了他们希望更好地反映市场实际表现的施工工具。这些努力包括新的优化，一种生成投资组合的计算机辅助方法。他们还涉及通过建立一些识别，使企业更加适应湍流，以至于风险与返回随时间变化之间的关系。
像许多理论,MPT simplifying assumptions. One of them is that the market is perfectly liquid. MPT also assumes that there are no transaction costs, that investors can take a position of any size in any security they want and that there’s no herd mentality at work. “Last year all of those assumptions probably got violated at the same time,” says Geller’s colleague Rumi Masih, head of J.P. Morgan Asset Management’s strategic investment advisory group.
That’s reason to be more circumspect about MPT, but not to toss it aside like a quaint relic. With understanding of market dynamics still in its infancy, testing is part of the theory’s growing up. So says Lisa Goldberg, executive director of analytic initiatives and talent at New York–based MSCI Barra, which provides indexes, risk models and portfolio analytics to asset managers and other clients.
“这所谓的失败理论有很多辉煌的元素以及需要修改或重新思考的材料，”加利福尼亚州的加利福尼亚伯克利·戈德伯格争论。“绝不应该被丢弃。”
围绕MPT的许多争论都与优化有关。传统上，这意味着马科维茨均值-方差优化，即投资者从一篮子资产中产生最有效的投资组合。首先，他们使用统计方法来估计预期收益率、波动率和协方差（也就是说，在一定时期内，资产将如何相对移动）。
所有这些信息都被插入到一个叫做优化器的软件中。然后，优化器筛选所有可能的资产组合，并生成一个图表，显示一条称为有效边界的曲线。沿着它排列的是一系列最佳的投资组合，从最低的风险和最高的回报。
虽然多样化的好处很难被忽视，但均值-方差优化并不那么有效，原因有两个。它可能会产生可疑的投资组合，而且它不考虑厚尾收益——这远远超出了历史标准。也被称为“黑天鹅”，这些意想不到的和戏剧性的价格变化可以波及整个系统，因为他们在2008年。
For some practitioners, relying on MPT is simply too dangerous. Svetlozar (Zari) Rachev — chief scientist at FinAnalytica, a risk management and portfolio construction consulting firm based in New York, London and Sofia, Bulgaria — compares it to living beneath an avalanche-prone mountain. “The correlations that are embedded as the main assumption — the normality of returns — are telling you the chance of an avalanche affecting everybody in the village below is zero,” he says.
此外，根据Rachev的说法，Markowitz从未打算为任何投资组合创建适用的通用模型。“他为一种问题进行了MPT：安静的市场，恒定波动，持续相关，”Rachev说。“现在世界不是这样的。我们需要不同的解决方案。“
再说一次，人们应该知道不要天真地应用MPT。在2008年之前，他们承担了太多的风险，愚蠢地打赌雪崩永远不会发生。马科维茨说，MPT“没有失败”一些金融顾问，当然也有一些卖方的人，在没有正确分析它们如何影响整个投资组合的情况下，就卖出了一些东西。”
Markowitz通过长时间斯坦福大学财务教授William Sharpe在1964年制定的理论的简化版本上遵守了他的辩护，他在华盛顿大学教学（见时间表，第68页）。现在被称为资本资产定价模型，或CAPM，Sharpe的“单因素”理论假设投资组合中的所有资产均份额系统，或市场，风险。Beta回归的来源，这种共同的危险因素是不可能的多样化。然而，每次安全性也都有一个不系统的，或特殊的风险，它产生alpha。由于不同资产的回报不会完全排列，因此您可以通过多样化缩小风险。
但在危机中，市场风险淹没了特殊风险。因此，马科维茨解释说，每个人都向下移动——但距离不同。正如MPT所说，你的beta值越高，你跌得越远。
此外，多元化实际工作于2008年。耶鲁管理学院的金融教授Roger Ibbotson指出，高质量的债券在股票市场总体上涨40％。虽然Beta或波动性，风险是股票回报的关键驱动因素，但Ibbotson增加了，流动性的作用往往被忽略了。“这种影响返回的流动性组成部分是每一位与风险成分一样重要，”Ibbotson表示，康涅狄格州扎贝拉资本管理席位和米尔福德的董事长和Cio。
马科维茨说,投资者应该知道他们的beta puts them on the efficient frontier. But he admits that MPT doesn’t make sophisticated assumptions about probability distributions — a big problem for highly leveraged investments that get marked to market daily. “There are ways of acting where you’re exposing yourself to model risk in a very major way,” says Markowitz.
解决办法是作出反映未来不确定性的估计。马科维茨是加州大学圣地亚哥拉迪管理学院（University of California，San Diego's Rady School of Management）金融学的兼职教授，同时也是GuidedChoice的联合创始人和首席架构师，GuidedChoice是一家总部位于加州洛斯加托斯（Los Gatos）的401（k）咨询公司。他表示，GuidedChoice倾向于波动率和回报率估计值，这两个估计值分别至少与历史平均值一样高，略低于历史平均值。这种谨慎的前景鼓励客户选择60%的股票和40%的债券组合，而不是在可疑的假设上进行高度杠杆化。
You could also build a better optimizer. One firm that claims to have done so is Cambridge, Massachusetts–based Windham Capital Management, which developed full-scale optimization with a division of Boston’s State Street Global Markets. According to its creators, this technique is much more sensitive to extreme events than mean-variance optimization.
Windham总裁兼首席执行官Mark Kritzman将常用的优化方法与一套基于波士顿的平均气温进行比较。“我喜欢调整人 - 我说，”多元化的唯一错误是它从未被尝试过。“
In his 2006 book, The Poker Face of Wall Street, Aaron Brown makes a strong case that gambling is intrinsic to financial markets. Brown should know — the veteran quant played poker semiprofessionally as a student in the 1970s and ’80s. Today he’s a risk manager at Greenwich, Connecticut–based hedge fund and asset management firm AQR Capital Management. Brown doesn’t think poker players make particularly good portfolio managers, but he says there are mathematical similarities between his favorite game and portfolio construction.
在扑克中，只玩你的强手可能是灾难性的，棕色解释。但是玩太多弱手意味着把钱扔掉。“Similarly, as a portfolio manager, if you go only with the best ideas, you’re not diversified enough,” says Brown, who was an executive director in risk methodology at Morgan Stanley in New York before he joined AQR in 2007. “But if you strive for maximum diversification, you get a lot of bad ideas in there.”
Academically speaking, Brown says, the basic idea of MPT is unassailable: You identify asset classes and try to estimate what return you can expect for a certain amount of risk. Then, rather than consider each asset class individually, you build a diversified portfolio with an acceptable risk-return trade-off. “That’s never been challenged, and I don’t think it ever will be,” says Brown, who has an MBA in finance and statistics from Markowitz’s alma mater, the University of Chicago.
但在实践中，MPT设置了几个可以引导投资者误入歧途的陷阱，棕色增加。首先，它可能会使他们盲目地通过给予印象，即资产在其历史新高的历史和其历史低价上同样危险。它还推动了不已的用户朝着未来在偏离正常回报方面的过去时的想法。此外，MPT在价格流动方面定义了风险，这是一项隐含的假设，只要投资者选择，即可以特定的价格购买和销售一切。
布朗说：“如果你不能从一项投资中获得资金，那么你的投资目标是什么并不重要。”这不是一个真正的标记，因为你不能以这个价格买卖。”
Besides creating products that reflect its views on what makes an optimal portfolio, Brown’s firm helps institutional and individual clients build their own. David Kabiller, a founding principal and head of client strategies at AQR, which has $24.5 billion under management, says the discussion is different every time. Still, most large institutions have a limited appetite for illiquid private equity, Kabiller asserts. “And there are only so many hedge funds and so much skill out there,” he says. “If institutions are going to meet their investment objectives, it’s going to be more heavily influenced by how they structure and allocate to core betas.”
考虑到这一点，AQR提供了25亿美元的全球风险溢价产品，该产品完全由流动性证券组成。布朗说，Global Risk Premium旗下的两只基金投资于多种资产类别，包括股票和债券指数、大宗商品和美国国债通胀保值证券（TIPS），因为这样做为给定的预期回报水平提供了更低、更可预测的风险。但如此广泛的投资有两大潜在隐患。一是使用过度杠杆的诱惑；另一种是在猜测波动性和相关性时建立风险模型。
AQR通过杠杆上限、提款和风险控制来防范这些潜在风险。”“这些投资组合需要更仔细的风险管理，”布朗说但我们认为，在降低风险方面的回报——尤其是降低尾部风险——是值得的。”
AQR starts by assuming that each asset class has its own independent risk. Mindful that assets tend to correlate, especially during crises, it seeks the broadest possible exposure. Right now, Brown says, there are very high correlations between equities and commodities, equities and credit, and interest rates and foreign exchange. Although those assets don’t yield much diversification today, he says, you’re better off buying them because they may diverge. And even if they end up being 100 percent correlated, it doesn’t hurt to split your money.
但如果相关性极高，坚持长期目标配置风险太大。布朗说，如今的低波动率和高相关性的奇怪组合使许多投资看起来比现在更安全，但波动率可能会迅速飙升。
“It’s a very scary market environment, almost scarier than a volatile environment like the fall of ’08,” he explains. “It’s too quiet out there.”
Richard Michaud，联合创始人，波士顿新的前沿顾问的总裁兼Cio，几乎四十四年前开始质疑意思 - 方差优化。收到他的博士后。在1971年波士顿大学的数学和统计中，Michaud担任波士顿有限公司的高级研究分析师。他的第一个作业之一：使用均值 - 方差优化来研究欧洲国家基金的发展。Michaud必须获取Markowitz优化计划的录像机，并在波士顿公司的大型计算机上运行它们。
Michaud向该公司的研究总监展示了没有被印象的公司的研究主任，为他制作的优化投资组合感到骄傲。“'这是什么，迪克？我们需要在奥地利投资34％？“Michaud记得他说。“当他理解时，这是一个疯狂的投资结果，但它也是优化的正确结果。”
很感兴趣，Michaud和他的quant朋友交谈，了解到他们在优化器方面也有类似的经验。1977年，他离开波士顿公司，到波士顿大学教授高级投资组合理论，因为学术界允许他研究这些问题，拓宽了他的金融知识。米肖后来调回金融业，在1999年创办机构研究和投资咨询公司newfrontier之前，他曾担任总部位于纽约的美林证券公司（merrilllynch&Co.）的股票分析主管。
Throughout his career Michaud kept thinking and writing about optimization. He began collaborating with his son, Robert, who is managing director of research and development at New Frontier. The pair developed and patented a portfolio optimization process called Resampled Efficiency.
The elder Michaud says the trouble with traditional optimizers is that they assume the information you feed them is perfect — to at least 16 decimal places. If you’re performing a scientific task like landing a rocket on the moon, that level of precision is the bare minimum. “But in finance it’s absolute nonsense,” Michaud says. “Sixteen decimal places of accuracy for whether stocks are going to beat bonds or not? Investors are more than happy just to get the sign right.”
此外，用户通常不喜欢他们的优化器提出的投资组合，因此他们会更改输入。”最终，你要做的就是所谓的“何必费心优化”，拥有波士顿大学数学硕士学位和加州大学洛杉矶分校金融学硕士学位的罗伯特·米肖说你已经折磨了优化器，让它给你你心里知道的一切都是对的。”
According to the younger Michaud, Resampled Efficiency builds on Markowitz’s good work. But rather than forecasting risk and return exactly, it allows some room for error. Using a statistical method called a Monte Carlo simulation, the optimizer generates thousands of possible market scenarios. It then recommends investing in the portfolio that performs the best across all of them. “That results in something a little more tolerant to markets not working out quite the way you were expecting them to,” Robert Michaud says.
有证据表明,重新取样工作效率。Besides selling its optimization software, New Frontier manages about $1 billion in 15 Global Strategic ETF model portfolio strategies offered through Pleasant Hill, California–based Genworth Financial Wealth Management. Designed to be fixed-risk core investments for long-term institutional investors, these products run from 20 to 100 percent in equities. Optimized, rebalanced and managed using Resampled Efficiency, they contain a mix of domestic equities, fixed income, real estate and international exchange-traded funds.
With 20 percent in equities, New Frontier’s most conservative fund is the $64 million Global Income Portfolio. Since its October 2004 inception, it has posted an annualized return of 4.1 percent. In 2008 the fund was the third-best performer among ETFs ranked by iShares, a division of New York–based BlackRock. Its –4.4 percent return far outstripped the Standard & Poor’s 500 index, which finished the year down more than 37 percent.
麦考维茨是米肖夫妇的朋友，他也对重采样效率进行了测试。在2003年发表在《投资管理杂志》上的一篇论文中，马科维茨和蒙特克莱尔州立大学金融学教授尼鲁弗·乌斯曼试图回答一个问题：一个更好的优化器是否胜过更好的信息。在两个模拟玩家之间建立一个裁判决斗，他们构造一些原始的历史返回数据，并将其插入传统的优化器，然后通过Michaud优化器运行相同的数据。
Markowitz和Usmen旨在击败重采样的效率。但要令他们惊讶的是，Michaud优化器赢得了所有30个测试。“我不确定为什么他的进程很好地工作，我不使用它，”Markowitz说。
在理查德·米肖看来，投资组合理论的重大创新将有数学证明。他对最近成为金融流行语的各种统计建模技术没有太多的评价。”他说：“有很多人提出了一些花哨的术语，比如‘copulas’和‘极端事件’，以及各种各样的看待统计数据的替代方法。”他们中的大多数人一点也不了解情况。”
正如AQR的Brown所指出的，优化器只和它的输入数据一样好。如果你知道未来五年回报的协方差，即使是基本的回报也足够了。如果你的估计是远远偏离，没有优化器会救你。
布朗表示，没有现成的解决方案的粉丝说，优化要求从个人资产课程的专家判断出良好的判断。他补充说，投资组合越优化了。布朗说这不是一件坏事，只要你密切监测投资组合并有一个应急计划。正如优化可以提高投资组合性能，足以证明模型风险，完全跳过过程是愚蠢的。“你需要一些优化，但你想小心你使用多少，”布朗说。“这是一件危险的事情。”
The same goes for too much accuracy. Although AQR strives for precise portfolio weights, it knows when to stop. “Any optimization that is telling you it really matters a lot whether you’re 4 or 5 percent in something is just not very useful,” Brown says. “A robust optimization program will give you weights that if you change them a little bit, it won’t change the result very much.”
就马克·克里兹曼而言，MPT没有错。如果投资者选择天真地应用这一理论，那就是他们的问题。”Windham的首席执行官说：“你从一个使用简化假设的模型开始，然后放松这些假设，构建复杂的模型。”有些人比其他人更复杂。”
克里兹曼解释说，与普遍的看法相反，MPT并不鼓励投资者推断历史回报率、波动率和相关性。相反，他们必须对选定的前景做出最好的未来估计，并相应地进行多样化。Kritzman认为，2008年这样做的投资者比其他投资者遭受的损失要小。
To illustrate his point, he offers this example. Imagine that before the crisis hit, you used historical data to estimate the value at risk (VaR) over a five-year horizon of a traditional portfolio invested 60 percent in equities and 40 percent in bonds. Paying attention only to the distribution of outcomes at the end of the period, you’d have pegged the portfolio’s worst year in a century at a 9 percent loss.
For a result that bears a much closer resemblance to reality, Kritzman says to ditch average correlations in favor of those that have prevailed during turbulent markets, when losses are more likely. This approach would have given you a worst-case number of –25 percent, the loss suffered by a typical 60-40 portfolio in 2008.
“你会对投资组合的损失敞口有一个完全不同的评估，这与发生的情况基本一致，”他说。
Kritzman还希望您考虑这一事实：当美国和非美国。股票享受返回一个标准偏差高于平均水平，这是一个强大的牛市的典型，其返回的相关性-17％。当那些返回的标准偏差低于平均水平时，相关性为76％。
That tells you two things, Kritzman says. First, the average correlation is almost meaningless. Second, investors are getting the opposite of what they want: diversification when their portfolio’s main growth engine does well and unification when it does poorly.
教授Massachusetts Technoloction Sloan管理学院的金融工程的Kritzman表示，通过思考来自多种风险制度的回报来估算损失暴露是重要的。他强调，这种建立耐受市场动荡的投资组合的方法是没有新的。
In many cases, Kritzman says, mean-variance optimization works just fine. But sometimes returns aren’t normally distributed because of regime shifts or fat tails. Also, on its own, mean variance is lousy at approximating investor preferences. For example, depending on whether returns are above or below a certain threshold, a hedge fund may dramatically change its attitude toward risk.
Kritzman，其公司提供投资，技术和咨询服务，表示全面优化是最好的替代品。他通过SébastienPage，State Streat Associates的投资组合和风险管理组负责人开发了这种方法，Kritzman是创始伙伴。Windham，州街全球市场和基于剑桥的FDO合作伙伴于1999年组建了联合拥有的公司。同时，Windham的大部分资产3000亿美元是与SSGM合作的货币运行。
Whereas mean-variance optimization looks at summaries of returns, Kritzman says, full-scale optimization considers all features of the data. It takes into account every single return in an asset’s history — and even in the theoretical distribution — and zeroes in on the portfolio that yields the best outcome. It also factors in any investor preferences that can be turned into equations.
This process is more sensitive to downdrafts than mean-variance optimization, which doesn’t distinguish between upward and downward moves, says Kritzman, who holds an MBA from New York University. “Full-scale recognizes that investors are much more averse to downside deviations and don’t mind upside deviations,” he adds.
事实上，Markowitz在1959年出版的《投资组合选择：投资的有效多样化》一书中引入了均值-半方差的概念，用来衡量下行风险。但他说他使用了他原来的优化方法，因为它更简单。马科维茨解释说，均值半方差需要使用历史收益率或生成假设历史“如果你这么做，你必须选择概率分布，”他说均值-半方差的使用更复杂，需要更多的估计，所以我一直不是它的主要支持者。”
Kritzman notes that two causes of market turbulence are exogenous shocks and crowded trades. But regardless of the cause, turbulence always has two main features: The ratio of returns to risk is much lower, and the turbulence is very persistent. Kritzman compares it to in-flight turbulence, which lingers until an airplane finds a new altitude or passes through the weather system. “The turbulence may arise unexpectedly, but once it begins, it takes time for investors to digest and react to what’s going on,” he says. “So it’s pretty likely that it’s going to be around for a while.”
湍流不仅仅是关于波动性，州街的Page强调;这也是资产如何彼此互动。如果这种方式重新定义了湍流，他说，测量不同资产的不寻常的回报产生了非常不同的图片。“有时波动率会很低，但你开始看到以不寻常的方式移动的东西，这可能是未来波动性的预测因素。”
As a navigational aid, State Street Associates has created an index that quantifies turbulence for any given trading day. Page says the first step is to use this turbulence index to identify periods in history when risky strategies have underperformed. Then, because crises are unpredictable, investors must determine whether turbulence will be persistent enough that they can scale back their exposure to these strategies after it hits.
这种动态或战术性的资产配置对一些投资者来说是可行的，但其他投资者只会选择建立一个能够抵御动荡的投资组合。”当你想到动荡指数时，你可以想到动态和静态，这取决于投资者的目标，”佩奇说。
J.P. Morgan的Masih表示，他的小组正在研究根据不同的经济和金融制度返回转移的想法。对他来说，回答的第一个问题是触发点将允许从一个制度迁移到另一个政权。第二个是根据历史证据对每个制度相称的返回行为。“第3号问题是，鉴于这种行为，我可以用来帮助我的资产分配决定的资产类别是什么？”马苏斯说。
采用这种方法，对传统资产配置的重视程度较低，而对行为关系的重视程度较高。Masih说，与其试图预测两种资产的相关性，聪明的做法是问是什么导致了这种相关性：“我们可以探讨这些更有趣的问题，这将为投资者的问题集增加洞察力，而不是‘让我们找出另一个奇特的优化例程’。”
AQR的棕色也倾向于对MPT的改进计费的产品持怀疑态度。他说，他们经常在精心包装方面是简单的想法。“我的一般信念是，有简单的方法可以做这些事情，”布朗解释道。“你不需要全新的方法。”
Still, finance has changed considerably since Markowitz first floated his theory. Back then, information was hard to come by, and the only asset classes were stocks, bonds and cash. Brown says there’s much better data now, as well as the ability to cover far more of the market portfolio. He guesses that when Markowitz was writing in the early 1950s, 30 percent of risk was incorporated into the market. Today there are liquid investments that give access to upward of 80 percent of risk — a huge advantage.
但是，而投资者曾经建立的股票投资组合，这些股票在同一市场上交易，他们现在违反了外汇，互换，期货和证券，以巨大不同的时间表。“在实际水平上，它更加困难，但是一个重要的原因是机会如此好，”布朗说。
Markowitz agrees that the intervening years have transformed the world, but he points out that investors still must deal with uncertainty. “The details are different, but the principles are the same,” he says. “The laws of probability have not changed.”
As for MPT, Markowitz contends that each market meltdown has delivered new converts. “Maybe the effect of the crisis will be that thoughtful people — the people who will listen — will go back and understand the basic assumptions of portfolio theory, rather than just listening to sell-side salesmen telling them how it has to work.”
通过持久的想法改变了世界，Markowitz没有缺乏听众，等待听到他解释了为什么MPT仍然很重要。他的继任者是否会享受同样的回报是没有模型可以预测的。