### Journal Menu >> Theoretical Economics Letters, 2011, 1, 1-2 doi:10.4236/tel.2011.11001 Published Online May 2011 (http://www.SciRP.org/journal/tel) Copyright © 2011 SciRes. TEL A New Method of Estimating the Asset Rate of Return Moawia Alghalith, Tracy Polius Economics, University of the West Indies, St Augustine, USA E-mail: malghalith@gmail.com, tracy.polius@sta.uwi.edu Received April 19, 2011; revised April 21, 2011; accepted April 25, 2011 Abstract We present a new consumption-based method of estimating the asset rate of return. Keywords: Return, Investment, Portfolio, Asset, Stochastic, Consumption CAPM In this note, we present a new model that links the stock/portfolio rate of return to consumption. Our app- roach is more general than the existing models such as the consumption-CAPM models, that are based on very restrictive assumptions . In so doing, we utilize a more advanced and appropriate theoretical and empirical framework than the ones used by previous literature. It is worth noting that previous literature mainly used simple linear regressions without a rigorous theoretical basis. We use a stochastic factor model, which includes a risky asset (portfolio, a risk-free asset and a stochastic external economic factor [2,3]. Thus, we have a two- dimensional standard Brownian motion 12,,ssstsTWW  on the probability space ,,sP, where stsT is the augmentation of filtration. The risk-free asset price process is d0=e ,TrZsstS where 2sbrZC R, is the rate of return and sZ is the sto- chastic economic factor. The dynamics of the risky asset price is given by  1d=dd ,stss sSS ZtZW (1) where tZ and tZ are the rate of return and the volatility, respectively. The stochastic economic factor process is defined as 212d=dd1d ,=,ss sstZaztWW Zz (2) where <1 is the correlation factor between the two Brownian motions,  is a parameter, and 1saZC R has a bounded derivative. The wealth process is given by  π,,1=πd πd,TccTsssssstTss stXxrYXYrY csYW (3) where x is the initial wealth, π,tstsT is the portfolio process and ,tstsTc is the consumption process, with 2πd