第2页 Fourteen Pages to Fame

 Harry Markowitz,  Modern portfolio theory, 1952
Despite its formidable appearance, the true meaning of Markowitz’s article is also homey. It boils down to nothing more than a formal confirmation of two old rules for investing: Nothing ventured, nothing gained. Don’t put all your eggs in one basket.
1. 风险和收益匹配原则：通常高风险高收益，低风险低收益。
2. 不要把所有鸡蛋放到一个篮子里 。
Williams’s model for valuing a security calls for the investor to make a long-run projection of a company’s future dividend payments and then to test that projection against his own confidence in its accuracy. Forecasting future dividends for a public utility, for example, is easier than forecasting dividends for General Motors, and forecasting the long-run outlook for General Motors is easier than forecasting the outlook for a start-up company in a highly competitive business. Williams then shows how to combine the long-run projection of dividends with the expected degree of accuracy of that forecast to estimate the intrinsic value of the stock. Williams called his model the Dividend Discount Model.
股息贴现模型(DDM), Markowitz意识到Williams的模型在现实中存在悖论：如果作为理性人，应该投资于通过DDM模型得到最高期望收益的股票。如果Apple的DDM期望收益最高，就不应该购买GE的股票？如果股票的DDM期望收益最高，就不应该购买债券和房地产。而现实中，人们同时持有Apple和GE、或者同时持有股票、债券和房地产的原因只有一个：不要将所有鸡蛋放在一个篮子里。
“If projects were riskless, there would be no problem. . . . Risk means that more things can happen than will happen.” —— Elroy Dimson
Diversification depends more on the way individual assets perform relative to one another than it does on how many assets the investor owns. In Markowitz’s terminology, “It is necessary to avoid investing in securities with high covariances among themselves.”
多元化投资的本质不在于投资品种的数量，而是投资品种之间的协方差。
As a result, the portfolio that conforms to Markowitz’s rule and that he “commends” to the investor is an efficient portfolio. It is a portfolio that offers the highest expected return for any given degree of risk, or that has the lowest degree of risk for any given expected return.
Mean-Variance Analysis
Moreover, computers at the time were both slow and expensive. One of Markowitz’s students, William Sharpe, who was to share the Nobel Prize with Markowitz in 1990, reported in 1961 that the best commercially available IBM computer required 33 minutes to solve a 100-security problem. The cost of that modest experiment in terms of today’s purchasing power would be over $300. Sharpe subsequently developed a method that greatly simplified the elaborate procedure.
MVA主要的问题在于，其需要输入的两个参数：某资产的期望收益、资产之间的协方差在当时都需要计算机进行大量计算（考虑到当时计算机的计算能力和价格）。其实，更重要的问题是，后来人们发现对MVA中输入参数非常微小的调整会导致计算结果非常大的改变。
Market prices, investor expectations, and the riskiness of assets do not stand still. They are dynamic, not static. Moreover, they constantly interact as new information arrives in the marketplace. The consequence is that the necessary conditions for an accurate calculation of risk may not prevail.
市场价格，投资者预期以及资产的风险显然不是静止的，而是每时每刻动态的。更加重要的是，市场是个互为依赖的系统，数学中c=a+b,只要给定a, b的值就能得到确定的c值，但是在互为反馈的系统中，c值的计算依赖a,b，而同时a,b的值又依赖c值，那么就无法得到一个确定的c值。
effective frontier