II. Who Put the 'A' in the APT?
Consider a world where investors are broadly diversified, but there may be multiple sources of risk in the economy. Instead of everyone caring solely about the market portfolio, investors actually care about lots of things, including shifts in stock index levels, interest rates, inflation, changes in GNP or other broad macro-economic factors that are difficult to purge from your portfolio through diversification. For now, focus on one of these factors -- the S&P 500. There is no need to presume that this or any factor matches the world wealth portfolio -- it is just one source of risk that people care about.
II.1 An Aside on Short-selling
Short-selling is a procedure that allows you to profit when the price of a security declines. In effect, it allows you to take a negative position in the security -- just the opposite of a long position i.e. holding the security. To short a stock, you must borrow a share from someone who holds it (typically via your broker) and then promise to return the share of stock upon demand. Then you sell the share of stock. This activity has two effects. First, you get money from the sale of the share of stock. Second, you incur an obligation to return a share of the same stock in the future. If the stock price drops, you can fulfill your obligation by buying a share on the market for less that the price at which you shorted it. The more the price drops the more you profit. Of course, if the price rises, you lose.
III. Arbitrage in Expected Returns: An Example
Suppose you observed the following conditions:
|ACTION||POSITION||SYSTEMATIC RISK (ß)|
|1) Buy one share of asset A, costing money||-$100||1.3|
|2) Short 1.3 shares of market portfolio, generating cash proceeds||$130||-1.3|
|3) Buy .3 bonds, costing money||-$30||0|
IV. The Arbitrage Pricing Theory Argument
The APT argument is best understood from the arbitrage in expectations example presented above. To achieve "arbitrage" pricing, we must assume that:
V. The World of the APT
The APT gives up the notion that there is one right portfolio for everyone in the world, and it replaces it with an explanatory model of what drives asset returns. The world of the APT is not some ideal, knife-edge equilibrium in which all investors are stuck in the same portfolio. It is a world with many possible sources of risk and uncertainty.
More formally, it is based upon the assumption that there are a few major macro-economic factors that influence security returns. No matter how thoroughly you diversify, you can't avoid these factors, although you can tilt your portfolio away from them. The APT claims that investors will "price" these factors precisely because they are sources of risk that can't be diversified away. That is, they will demand compensation in terms of expected return for holding securities exposed to these risks. Just like the CAPM, this exposure is measured by a factor beta.
It is tempting to see the APT as a behavioral model. It describes a world in which investors behave intelligently by diversifying, but they may chose their own systematic profile of risk and return by selecting a portfolio with its own peculiar array of betas. While formal proofs of the APT rely upon static equilibrium arguments, the spirit of the APT is an active one. It allows a world where occasional mispricings occur. Investors constantly seek information about these mispricings and exploit them as they find them. It allows for an industry of information collectors, risk arbitrageurs and speculators. It allows for different types of investors as well as evolving types of risks. In other words it describes a world somewhat closer to the world in which we live.
VI. Applying the APT
Finding Factors How do we apply the APT? One difficulty with the model it is generality. We have left the simple world of the CAPM. We no longer know exactly what sources of systematic risk people truly care about. On the other hand, reading the financial section of the newspaper we can get idea. The Wall Street Journal for instance, regularly reports on surprises in interest rates, surprises in GNP, surprises in inflation and changes in the stock market indices. All of these are candidates for APT factors. Indeed, we may not actually need to identify the economy's risk factors. We only need to find a collection of things that together are good proxies for them. After the theoretical development of the APT, Chen, Roll and Ross set out on a quest for the factors. They found that a collection of four or five macro-economic series' that explained security returns fairly well. These factors turned out to be surprises in inflation, Surprises in GNP, surprises in investor confidence (measured by the corporate bond premium) and shifts in the yield curve. In general these do as good a job at explaining returns as the S&P index. Of course, no one really knows if these are the "true" factors. As the APT continues to be used in practice, other variables are likely to be used. Once factors are chosen, only the unanticipated portion of the factor is used for estimating the APT model. As with the CAPM, we usually regress historical security returns on the factor to estimate ß's. These ß's are used in a model of expected returns to estimate the discount rate.
Building portfolios The APT is a useful tool for building portfolios adapted to particular needs. For example, suppose a major oil company wanted to create a pension fund portfolio that was insulated against shock to oil prices. The APT allows the manager select a diversified portfolio of stocks that has low exposure to inflation shocks (oil prices are correlated to inflation). If the CAPM is a "one size fits all" model of investing, the APT is a "tailor-made suit." In the APT world, people can and do have different tastes and care more or less about specific factors.
Sensitivity analysis With the APT we can model the effects of different economic scenarios on the investment portfolio. Once factor betas are estimated, we can describe the expected change in security returns with respect to changes in that factor. How will my portfolio perform in a recession? Am I exposed to shifts in the yield curve? These are typical questions addressed by APT analysis.
VII. Conclusion: APT as a Model of Expected Returns
The APT has a number of benefits. First, it is not as a restrictive as the CAPM in its requirement about individual portfolios. It is also less restrictive with respect to the information structure it allows. The APT is a world of arbitrageurs and vendors of information. It also allows multiple sources of risk, indeed these provide an explanation of what moves stock returns. The benefits also come with drawbacks. The APT demands that investors perceive the risk sources, and that they can reasonably estimate factor sensitivities. In fact, even professionals and academics can't agree on the identity of the risk factors, and the more betas you have to estimate, the more statistical noise you must live with.