A Course on Statistics for Finance

Chapter 3

Several Stocks and Their Rates of Return

3.1 Introduction

This chapter introduces price series and rates of return of several assets, that is, sets of assets. The price series from a single stock is a single time series; prices from several stocks constitute a multiple time series. That is, at time t, the prices P1t , P2t , . . . , Pmt of m assets are observed.

Stock closing prices are recorded at the end of successive time periods. The time period could be days, weeks, months, quarters, or years.

The RORs are, for i = 1, 2, . . . , m assets and t = 1, 2, . . . , n time periods, the ordinary ROR,

$R_{it}=\left(P_{it}-P_{i,t-1}\right)/P_{i,t-1}=P_{it}/P_{i,t-1}-1,$

and the continuous ROR,

$r_{it}=\text{In}\left(P_{it}/P_{i,t-1}\right)$