Page 100 - Contributed Paper Session (CPS) - Volume 4

CPS2134 Yutaka Kuroki et al.
Capital Asset Pricing Model (CAPM, Sharpe; 1964 and Lintner; 1965) is the
most broadly applied asset pricing model in finance and among researchers
and practitioners. CAPM describes the relationship between systematic
market-portfolio risk and expected excess return of assets. The deficiency of
the use of CAPM models including the validity of its assumptions can be found
in, for example, Bank (1981), Basu (1983), Bhandari (1988) and Fama & French
(1995).
The market risk premium is the difference between the expected return of
the market and the risk-free rate. The Fama-French three-factor-model (Fama
& French, 1996) expands CAPM by adding size risk factor and value risk factor
to the market risk factor. The size risk called “SMB (Small Minus Big)” measures
excess return of small-cap companies over big-cap companies, and the value
risk called “HML (High Minus Low)” measures excess return of high book-to-
market ratio (value companies) over companies with a low book-to-market
ratio (growth companies). Then the three-factor models are defined as
− = + ( − ) + () + () + ,

2
3

1

where is risk free rate, is the expected return of -th stock, are factor

coefficients and ( − ) is the market risk premium. The size factor, is

the difference between average return on the Small-firm portfolios and the
average return on the Big-firm portfolios, that’s why the factor can be an
alternative variable for latent capitalization risk premium. As well as ,
is the difference between average return on the High value portfolios and Low
value portfolios.
We investigate similar characteristics in retail demand time-series
modelling by introducing fundamental factors constructed from the store-
specific information. In retail marketing, it is well-known that there are
apparent seasonal effects in daily demand time series: weekly and yearly cycles
and holiday effects. We consider this seasonal pattern as a market portfolio,
since weekly and yearly cycles and holiday effects seem to be “systematic risk”
that appears overall demand fluctuation in some retail business. Similarly, SMB
like factor is constructed from the portfolio of stores that has large or small
number of customers. From the viewpoint of prediction, many time series
models explicitly including these effects have been suggested (Harvey &
Shephard 1993, Hyndman et al. 2002, Taylor & Letham 2018), but there has
not discussed about the characteristics of the retail demand return and risk
structure anymore.
In this study, we investigate the risk and return structure of retail stores
using number of customers in restaurants in Japan. We introduce a factor
model for restaurants demand in a similar way of traditional financial factor
models. First, we show that daily demand for whole restaurants is almost
dominated by calendar effect like market portfolio. Second, we construct a
factor derived from sizes of restaurants, and estimate factor-model by The
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