The Capital Asset Pricing Model

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Changes in technology and the markets were not the only factors that brought more attention to MPT. In 1960 a student named William Sharpe began work under Markowitz's direction to simplify the MPT calculations. This research led to a number of developments in addition to simplified calculations, culminating in what is known as the Capital Asset Pricing Model or mean-variance analysis and is widely used today.

Sharpe's first step was to sidestep the need to make calculations for each potential security to be considered for a portfolio. Instead, for each security there is a factor that is very influential in the security's performance. For stocks and bonds, the primary factor determining price changes is the appropriate market index. The primary factor for large company stocks, for example, usually is the Standard & Poor's 500 Index, though there are alternatives, such as the Russell 1000 Index. A small company stock index, such as the Russell 2000 or S&P 600, is the primary factor determining the performance of the stocks of smaller companies. The Lehman Brothers Aggregate Bond Index is the primary influence on bond prices.

Substituting an index for individual securities means that far fewer calculations are required to determine the efficient portfolio. Instead of performing calculations for dozens or hundreds of securities, the investor needs to make calculations only for the indexes of the asset classes that are being considered for the portfolio. The results might not be as precise as making the calculations for each security, but the results would be close enough that the greater efficiency of using indexes instead of individual securities justifies the substitution.

I ndexes can be used instead of securities because the markets are fairly efficient, Sharpe argued. The direct relationship between an individual stock and an index varies. The performance of some stocks is closely tied to the index, but in general about one third of the performance of an individual stock is determined by the movements of the index. The rest of the performance is attributed to the movements of stocks in that company's industry and to characteristics of the individual company and its stock. But as more stocks are added to a portfolio, the differences of the individual stocks are diluted. The movement of all the stocks in the portfolio as a whole will closely match the performance of the index, especially if the investor attempts to construct a diversified portfolio.

Portfolio construction under CAPM focuses on asset classes: U.S. large company stocks, U.S. small company stocks, developed market international stocks, emerging market international stocks, and the like. Determining an efficient portfolio requires calculations for only a relatively small number of indexes instead of for all the securities in those indexes.

The development of personal computers made implementing CAPM even easier, because speed and sizeable memory were needed to perform even the simplified calculations under CAPM. PCs became affordable, widely available, and more robust. Software was developed so that anyone who could operate a PC could perform the calculations. The software is known generically as the portfolio optimizer. Today many individuals and institutions use optimizers to implement CAPM and guide their investment decisions. The software produces "the efficient frontier," showing the portfolio that returns the highest return for a given level of risk or the lowest risk for a desired level of return. The investor can select the portfolio with the risk and return profile that comes closest to meeting the investor's goals, which is the efficient portfolio for that investor.

The CAPM Revolution

The simplification of the calculations and increase in computer power were but two factors in making CAPM more widely accepted than MPT was. At least equally important as we discussed were the turbulence in the economy and markets in the 1960s and 1970s. Traditional investment strategies were not producing the results that were expected, and investment professionals searched for alternative ways to build portfolios. Further, the additional attention from investment professionals and increased computer power spurred more academic research. In a short time, a rather rich body of research developed from the foundations of MPT and CAPM.

CAPM today is much more than substituting indexes for individual securities while searching for an efficient portfolio. The notions of index efficiency and market efficiency led to several other principles that are part of CAPM.

First, investors and money managers cannot reliably or consistently earn higher returns than a market index. This is known as the Efficient Market Hypothesis (EMH).

Research consistently shows that a minority of mutual funds and money managers outperform the index in any year, and very few consistently earn higher returns than the index or for periods longer than one year.

There are several possible reasons for this result. Active money management that seeks to earn a higher return than an index incurs costs. There are brokerage commissions from buying and selling securities. The money manager charges a fee. In taxable accounts, taxes must be paid on dividends and when a security is sold at a gain, something that occurs more frequently in managed portfolios than in index funds. In addition, the free flow of information and general efficiency of the markets makes it difficult for an investor to achieve an information edge to identify a portfolio of stocks that will outperform the index.

The recommendation in CAPM is that an investor should invest in an asset class only through an index fund. While this was difficult in the early years of CAPM's development, it is easy today. Numerous index funds exist in both traditional open-end mutual funds and in the recently developed exchange-traded funds. An investor can purchase broad-based U.S. stock index funds as well as funds tracking various sectors and subsets of the U.S. stock market. An investor also can invest in international stocks by purchasing a fund that tracks a broad international stock index or through different funds that track the indexes of separate countries or regions. Index funds also have been developed for other assets such as bonds and commodities.

Under CAPM, an investor should decide which investment asset classes should be in the portfolio and purchase index funds to invest in those asset classes. Individual security selection is not considered a fruitful activity. Next, once established, the efficient portfolio should not be changed unless the risk or return targets change. In other words, the efficient portfolio is a buy-and-hold portfolio. The exception to this is periodic rebalancing of the portfolio. After the portfolio is created, market activity will change the allocation. For example, a portfolio might be 60 percent invested in stocks and 40 percent in bonds. After one year, stocks might increase 10 percent while bonds decline 3 percent. That would change the allocation to 63 percent stocks and 37 percent bonds. This might seem like a small difference from the original allocation, but it is not the efficient portfolio so it will not produce the expected results. In addition, if the portfolio is not rebalanced to its original allocation, the portfolio will drift further from the efficient portfolio each year. To avoid this and achieve the expected results, periodically the investor should buy and sell assets to return the portfolio to its target allocation.

Other than rebalancing, changes in the portfolio are not advisable. Just as an efficient stock market makes it difficult for an investor to select securities that will earn higher returns than the index, it also makes it difficult for an investor to rotate a portfolio among different asset classes at opportune times to earn higher returns. Altering the asset allocation of the portfolio often is called market timing by advocates of CAPM. Advocates of the process refer to it as tactical asset allocation.

A properly constructed efficient portfolio produces the best risk-and-return combination. If investors are unable to identify those factors that make an individual stock or a collection of individual stocks generate higher returns than the market index, they also are unlikely to be able to identify factors that will earn returns exceeding those of the efficient portfolio by periodically increasing and decreasing the allocations of the different asset classes in the portfolio.

Asset performance is divided between beta and alpha. Beta is the performance of an asset relative to an index. For example, a stock with a beta of 1.0 to the S&P 500 rises and falls exactly as much as that index. A stock with a beta of 0.50 fluctuates half as much as the index. If the index rises 10 percent, the stock is likely to rise 5 percent. If the index declines 10 percent, the stock will decline only 5 percent. Another expression for beta is the volatility of the portfolio relative to a benchmark.

Alpha is a measure of an investment manager's skill or, when applying it to a stock, it is a measure of how much better it performs than the benchmark. To determine alpha, start with excess return. That is the difference between the investment's return and a benchmark's return. In some discussions of investment results, alpha is considered synonymous with excess return. In the development of CAPM, however, alpha is the risk-adjusted excess return. If a mutual fund manager earns a higher return than the index by taking more risk, alpha could be negative. But if the manager earns a higher return after making a mathematical adjustment for the risk taken, alpha is positive and the manager is considered to have used skill to beat the benchmark.

Alpha is the return earned independent of an index's return and by taking the same level of risk. Determining alpha is especially useful when evaluating an investment manager or mutual fund. Alpha is a measure of the skill a manager demonstrates to add returns beyond the index's returns. A mutual fund with an alpha of 0.2 has earned a return 20 percent greater than an index return. If the index returns 10 percent, the manager earns 12 percent.

Investors should be careful not to confuse alpha and beta. A stock or a mutual fund might have a high beta, say 1.5. That means when the index is up 10 percent, the stock or fund is up 15 percent.

Investors during a bull market often confuse such beta with alpha. The problem is that during market downturns, a high-beta asset will lose more than the index. If the index is down 10 percent, the stock or fund will lose 15 percent. Only then will the investor realize he or she purchased beta instead of alpha.

Most investors take this information to mean that they should seek stocks or managers with high alphas. CAPM, however, asserts that the markets are efficient. Stocks with high alphas are more desirable and therefore will trade at higher prices. Stocks with low alphas will trade at lower prices. The price differences will offset the differences in alphas, so there is no advantage over time in owning a high-alpha stock. In addition, money managers with positive alphas are rare, difficult to identify in advance, and aren't likely to repeat their positive alpha performance over time. The advice from CAPM is to own the entire market instead of searching for attractively valued parts of the market or for managers who try to beat the benchmark.

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