Analysis of Financial Time Series, Third Edition

1.1 Asset Returns

Most financial studies involve returns, instead of prices, of assets. Campbell, Lo, and MacKinlay (1997) give two main reasons for using returns. First, for average investors, return of an asset is a complete and scale-free summary of the investment opportunity. Second, return series are easier to handle than price series because the former have more attractive statistical properties. There are, however, several definitions of an asset return.

Let Pt be the price of an asset at time index t. We discuss some definitions of returns that are used throughout the book. Assume for the moment that the asset pays no dividends.

One-Period Simple Return

Holding the asset for one period from date t − 1 to date t would result in a simple gross return:

1.1

The corresponding one-period simple net return or simple return is

1.2

Multiperiod Simple Return

Holding the asset for k periods between dates t − k and t gives a k-period simple gross return:

Thus, the k-period simple gross return is just the product of the k one-period simple gross returns involved. This is called a compound return. The k-period simple net return is Rt[k] = (Pt − Pt−k)/Pt−k.

In practice, the actual time interval ...