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)