第4页 The Most Important Single Influence

William Sharpe， “A Simplified Model for Portfolio Analysis.” ，1961
The procedure Sharpe recommends eliminates the tedious chore of calculating the covariances between each pair of securities. The analyst need only calculate the relationship of each of the securities to the dominant factor. If the price of a security is more volatile than the movements of the dominant factor, that security will make the portfolio more variable, and therefore more risky, than it would have been otherwise; if the price of the security is less volatile, it will make the portfolio less risky. In well-diversified portfolios, the simple average of these relationships will then serve as an estimate of the volatility of the portfolio as a whole.
What is the “basic underlying factor” to which Sharpe refers? There is no doubt that individual stocks respond most directly to the stock market as a whole. About one-third of the variability of the average stock is simply a reflection of moves in the “index”—or “the most important single influence.” The rest of its variability is split about evenly between the influence of other stocks to which it has a family resemblance, such as the auto stock group or the public utility group, and the unique characteristics of the stock itself. Even those influences disappear when as few as a dozen individual stocks are combined into a portfolio. Then the power of diversification obliterates the individual attributes of the stocks, and more than 90 percent of the portfolio’s variability is explained by the index.
夏普的简化模型是不计算不同资产之间的协方差，而只是计算每项资产相对于“主导因素”的协方差，以此减少计算量。这样的简化比Markowitz的方法更加接近现实。 
The big attraction of the single-index model was the computing time it saved. Sharpe disclosed in his article that the time needed to solve a 100-security example on a  state-of-the-art mainframe IBM computer was reduced from 33 minutes with the full Markowitz program to 30 seconds with the simplified model.
 Moreover the old model used so much of the computer’s memory that it could handle a maximum of 249 securities; the new model could handle up to 2,000. Sharpe pointed out to me that today’s IBM personal computer, equipped with an 80386 chip and math-coprocessor, would take less than a minute to perform the full Markowitz run that took 33 minutes. The 30-second run with Sharpe’s simplified model would take only an instant.
在计算机上，夏普的简化模型计算更快、更节省内存。
Sharpe’s major breakthrough came in 1964, with what is known as the Capital Asset Pricing Model, which the cognoscenti call CAPM, pronounced “CAP-EM.” CAPM starts out from the basic idea of the single-index model that returns are related “only through common relationships with some basic underlying factor.”
The model concludes with the startling but inescapable conclusion that Tobin’s super-efficient portfolio is the stock market itself. No other portfolio with equal risk can offer a higher expected return; no other portfolio with equal expected return will be less risky. This controversial view was what had prompted Sharpe’s disturbing interrogation of me at that lunch meeting in New York. If the market itself is the super-efficient portfolio, no one can beat it without taking on an unwarranted amount of risk.
资本资产定价模型 CAMP， 如果股市本身就是一个超级有效资产组合，那么就没有人能够在不承受比它更多的风险的情况下击败市场。