If the APT is to be a useful theory, the number of systematic factors in the economy must be small. Is this statement correct or not?

The statement is partially correct. The Arbitrage Pricing Theory (APT) does assume that there are a few factors that affect all securities' returns. However, it doesn't necessarily mean that the number of systematic factors in the economy must be small.

Here's a step-by-step explanation:

1. The APT is a general theory of asset pricing that holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors.

2. These factors, according to the APT, influence the returns of all securities in the market. Examples of such factors could be inflation rates, GDP growth rates, interest rates, etc.

3. The APT does not specify how many or which factors should be used for a particular model. It only assumes that there are a few factors that affect all securities' returns.

4. However, the practical application of the APT often involves using a small number of factors, simply because it's more manageable and less complex.

5. But theoretically, the APT does not limit the number of factors. In fact, the more factors included in the model, the more accurate it should be in explaining or predicting asset prices.

6. Therefore, while it's true that the APT often involves a small number of factors for practical reasons, it's not accurate to say that the number of systematic factors in the economy must be small for the APT to be useful.

In conclusion, the statement is partially correct in a practical sense but not entirely accurate in a theoretical sense.

The statement is correct. The Arbitrage Pricing Theory (APT) is a theory of asset pricing that holds that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk.

Here are the steps to understand why the number of systematic factors must be small:

1. The APT assumes that financial markets are perfect with no taxes, transaction costs, or restrictions on borrowing.

2. The theory suggests that the return of a financial asset can be modeled as a linear function of various macroeconomic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient.

3. The model-derived rate of return will then be used to price the asset correctly - the asset price should equal the expected end of period price discounted at the rate implied by the model. If the price diverges, arbitrage should bring it back into line.

4. If there are too many factors, the model becomes overly complex and difficult to use. It also becomes harder to identify and measure all the relevant factors.

5. Therefore, for the APT to be useful, the number of systematic factors in the economy must be small. This allows for a more manageable, efficient, and effective model.

So, the statement is correct. The APT is more useful when the number of systematic factors in the economy is small.