Irfan Ahmed, PhD

In many of the problems of interest in finance, the starting point is a time series of prices -- for example, the prices of shares in Ford, taken at 4p.m. each day for 200 days. For a number of statistical reasons, it is preferable not to work directly with the price series, so that raw price series are usually converted into series of returns. Additionally, returns have the added benefit that they are unit-free. So, for example, if an annualized return were 10%, then investors know that they would have got back ￡ 110 for a ￡ 100 investment, or ￡ 1,100 for a ￡ 1,000 investment, and so on. There are two methods used to calculate returns from a series of prices, and these involve the formation of simple returns, and continuously compounded returns, which are achieved as follows: Simple returns Continuously compounded returns Rt =     ( pt − pt − 1) / pt − 1   × 100%      (1.1) rt = 100% × ln( pt/ pt − 1 )          (1.2)   If the asset under considera