What defines co-integrated stock prices?

• A. Stock prices that are volatile and unpredictable
• B. Stock prices whose linear combination is a stationary process
• C. Stock prices that follow a random walk
• D. Stock prices that are negatively correlated

Answer: (B)

Co-integrated stock prices refer to a statistical property of time series data, where two or more non-stationary series can be combined in such a way that the resulting linear combination is stationary. This concept is crucial in time series analysis, particularly in financial markets, because it helps identify long-term equilibrium relationships between stock prices, even when the individual series themselves may be trending or exhibiting volatility.

When stock prices are co-integrated, it implies that despite the potential for fluctuations and trends in the short term, there exists a consistent long-term relationship between them. This relationship can be leveraged in various investment strategies, such as pairs trading, where traders seek to exploit temporary deviations from this equilibrium.

By contrast, stock prices characterized as volatile and unpredictable do not exhibit reliable long-term relationships and thus, would not fall under the definition of co-integration. The notion of following a random walk also runs counter to the idea of co-integration, as random walks are typically non-stationary and do not imply any long-term relationship. Similarly, simply being negatively correlated does not establish the presence of a long-term equilibrium, as correlation does not imply co-integration.

Thus, the correct choice reveals the essential nature of co-integration in establishing a stationary linear relationship