Analysts often confront competing ideas about how financial markets work. Some of these ideas develop through personal research or experience with markets; others come from interactions with colleagues; and many others appear in the professional literature on finance and investments. In general, how can an analyst decide whether statements about the financial world are probably true or probably false?
When we can reduce an idea or assertion to a definite statement about the value of a quantity, such as an underlying or population mean, the idea becomes a statistically testable statement or hypothesis. The analyst may want to explore questions such as the following:
Is the underlying mean return on this mutual fund different from the underlying mean return on its benchmark?
Did the volatility of returns on this stock change after the stock was added to a stock market index?
Are a security’s bid-ask spreads related to the number of dealers making a market in the security?
Do data from a national bond market support a prediction of an economic theory about the term structure of interest rates (the relationship between yield and maturity)?
To address these questions, we use the concepts and tools of hypothesis testing. Hypothesis testing is part of statistical inference, the process of making judgments about a larger group (a population) on the basis of a smaller group actually observed (a sample). The concepts and tools of hypothesis testing provide an objective means to gauge whether the available evidence supports the hypothesis. After a statistical test of a hypothesis we should have a clearer idea of the probability that a hypothesis is true or not, although our conclusion always stops short of certainty. Hypothesis testing has been a powerful tool in the advancement of investment knowledge and science. As Robert L. Kahn of the Institute for Social Research (Ann Arbor, Michigan) has written, “The mill of science grinds only when hypothesis and data are in continuous and abrasive contact.”
The main emphases of this reading are the framework of hypothesis testing and tests concerning mean and variance, two quantities frequently used in investments. We give an overview of the procedure of hypothesis testing in the next section. We then address testing hypotheses about the mean and hypotheses about the differences between means. In the fourth section of this reading, we address testing hypotheses about a single variance and hypotheses about the differences between variances. We end the reading with an overview of some other important issues and techniques in statistical inference.