New Findings in Asset Pricing

Nilanjana Chakraborty

contact: dr.nila.chakraborty@gmail.com

 

 We have found that asset prices are linear polynomials of market returns and preceding asset prices. Hence, asset returns being ratios of these polynomials, are rational functions that should be averaged not directly from returns series but through ratios of consecutive average prices. This is the main reason behind the Capital Asset Pricing Model (CAPM) anomalies that were reported in the empirical studies in the past. The mathematical reasoning behind this is that for three consecutive asset prices xt-1, xt and xt+1, the direct average of the time series of the returns does not equal the actual average of the time series, i.e.

[(xt / xt-1) + (xt+1/ xt)] [(xt + xt+1)/ (xt-1 + xt)].

Similarly, for the cross-sectional returns, the direct average of two stock returns on a day ‘t’, do not equal their index return, i.e.

[(xt/xt-1) + (yt/yt-1)] [mt/mt-1], where mt = (xt + yt) and mt-1 = (xt-1 + yt-1).

But these are the flaws of the linear asset pricing models (like the CAPM and the Fama French 5 factor model - FF5F) when they equate the direct average return of a portfolio represented by the expected return E(Ri), with the direct average return of the market portfolio, represented by the expected return E(Rm), as can be seen from the CAPM equation:

E(Ri) = Rf + βi,m [E(Rm) – Rf ]                                                                                                 

Hence, average returns should be modeled based on stock prices. However, continuous returns may be treated as approximately linear across time and modeled directly. Our new Rational Function (RF) models, empirically outperform the traditional asset pricing models like the Capital Asset Pricing Model (CAPM) and the Fama-French three and five-factor models for both average and continuous returns. Moreover, the RF theory also provides a model to estimate the asset volumes. The average change in asset volumes together with average returns provide the estimates for average change in market values of assets. Thus, the RF model approach can be used to select assets that provide either highest returns for profit maximization or highest change in market values for wealth maximization for given levels of risk. Thus, the RF model indicates that both the price and the volume of a stock together express the total economic impact of any economic event, or a time period in general.

Similarly, we have also found that various risk factors like size, book to market ratio, investment and operating profit etc. cannot definitively identify assets with higher average returns though they may help identifying assets with lower risk.

 

  

Paper 1: Returns & Volumes (DOI:10.1080/00036846.2018.1540848)

 

Paper 2: Relevance of Risk Factors (Working Paper)

 

 Web presentation