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SUN YAT-SEN BUSINESS SCHOOL
Science of Decision Making
SCIENCE OF DECISION
MAKING
Group #2 Fall 2018：
Cai Ningxin（YJ201809）
陈郁方（18220015）
戴显盛（18211565）
Kim Jingyung（M94630566）
李忠健（18211574）
Sim Suyeon（M27242584）
王苏媛（18211583）
Woe Wailun（17AT94749）
1
Agenda:
1 Abstract ......................................................................................................................................... 1
2 Problem Description .................................................................................................................... 1
3 Data Source ................................................................................................................................. 2
4 Model Justification ..................................................................................................................... 3
5 Analysis ....................................................................................................................................... 5
5.1 SIMPLE LINEAR REGRESSION (3 HORIZONS: 10Y, 5Y, 1Y) .................................................... 5
5.1.1 Estimation of the regression .............................................................................................. 8
5.1.2 Error Term(𝜀) .................................................................................................................... 9
5.1.3 Testing for Significance ................................................................................................... 13
5.2 MULTIPLE LINEAR REGRESSION: MLR - THREE-FACTORS FF MODEL ............................. 13
5.2.1 MRL-Error Term(𝜀) ........................................................................................................ 13
5.2.2 MRL-Testing for Significance ......................................................................................... 15
5.2.3 MRL- Market risk premium (MRP) ................................................................................ 16
6 Critics and Conclusion ............................................................................................................. 16
1 Abstract
In this paper, the hypothesis of the broad market portfolio (𝑅𝑀− 𝑅𝑓), SMB (small minus big) and
HML (high minus low) as influential return factor are tested. The capital asset pricing model
(CAPM)
1
and the Fama and French Three-Factor Model
2
are necessary to be used.
Two steps are used to verify the correlation between stock price, index of S&P 500 and index of
Fama French in this paper. Three scenarios, last 10 years, last 5years and last year, are chosen in the
simple linear regression analysis of the first step and one scenario is chosen in the multiple linear
regression analysis of the second step.
1
𝑟𝑖= 𝛼 + 𝛽𝑖(𝑟
𝑚− 𝑟
𝑓) + 𝜀
𝐸𝑅𝑖= 𝑅𝑓+ 𝛽𝑖(𝐸𝑅𝑚− 𝑅𝑓)
2
𝑅𝑖− 𝑅𝑓= 𝛼𝑖+ 𝑏𝑖(𝑅𝑚− 𝑅𝑓) + 𝑠𝑖𝑆𝑀𝐵 + ℎ𝑖𝐻𝑀𝐿 + 𝜀𝑖
2
2 Problem Description
People usually take it for granted that stock prices are determined in the marketplace, where seller
supply meets buyer demand. Actually, there is no clean equation that tells us exactly how a stock
price will behave. That said, we do know a few things about the forces that move a stock up or
down. These forces fall into three categories: fundamental factors, technical factors and market
sentiment. However, no clear equation that tells exactly how a stock price will behave. Is the broad
stock market an influential factor? This paper uses the CAPM and the Fama and French
Three-Factor Model, and the stock price of Disney as an example to analyze, whether there is a
significant correlation between stock price and the broad stock market.
3 Data Source
We chose the stock price of Disney, index of S&P 500
3
, and index of Fama French 3 Factors
4
from
Jan. 2009 to Nov. 2018. The data sets are real data obtained from S&P and Data Library section of
the website of Kenneth French. The stock price data for holidays and weekend is not included, since
stock market will be closed on those days. Further, the S&P 500 index components and their
3
The Standard & Poor's 500, abbreviated as S&P 500:
a) an American stock market index based on the market capitalizations of 500 large companies having common
stock listed on the NYSE or NASDAQ.
b) The S&P 500 index components and their weightings are determined by S&P Dow Jones Indices.
4
The Fama and French Three-Factor Model:
a) asset pricing and portfolio management model
b) designed by Eugene Fama and Kenneth French to describe stock returns
c) considers the fact that value and small-cap stocks outperform markets on a regular basis
The three factors are:
a) the excess return on a broad market portfolio (𝑅𝑀− 𝑅𝑓);
b) the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks
(SMB, small minus big);
c) the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of
low-book-to-market stocks (HML, high minus low).
3
weighting are determined by S&P Dow Jones Indices.
Disney is a multinational company, which use umbrella strategy. Thus, they have lots of subsidiary
brand such as, Pixar, Marvel and amusement park etc. They are animation and movie producer,
world largest film maker measured by revenue and their corporation size.
As its branch’s largest movie and animation producer measured by revenue and size the
management and operations department are well organized. Further Disney have huge impact on
American stock market. We are considering three factors. First, the excess return on a broad market
portfolio. We are going to subtract from 𝑅𝑚 to R𝑓. Second, difference between the return on a
portfolio of small stocks and the returns on a portfolio of large stocks (SMB, small minus big).
Third, difference between the return on a portfolio of high-book-to market stocks and the return on
a portfolio (HML, high minus low).
Scenarios
S&P500: (𝑅𝑀− 𝑅𝑓)
FF: SMB
FF: HML
Unit
Scenario I 10ys (2009~2018)
119
119
119
Month
Scenario II 5ys (2014~2018)
59
59
59
Month
Scenario III 1ys (2017~2018)
49
49
49
Week
In total 504 observations were collected for this research, including 119×3 monthly data sets in last
ten years, 49×3 weekly data sets in last one year and the data sets of last five years were the second
half part of the data sets of last ten years.
4 Model Justification
1) Excess Returns
(i) investment returns from a security or portfolio that exceed the riskless rate on a security
generally perceived to be risk free, e.g. a certificate of deposit or a government-issued bond
(ii) the concept of excess returns may also be applied to returns that exceed a particular
benchmark, or index with a similar level of risk.
2) Alpha and Beta
(i) both metrics relating to the level of risk or volatility experienced in a particular security
(ii) the alpha provides a measurement in regards to the asset's performance
(iii) the beta specifies the level of risk present when compared to the capital asset pricing model
(CAPM)
(iv) the beta is a measure of the asset’s ability to respond to market fluctuations
some basics of the model Widely used as a measure of the value added by the portfolio or
investment manager, or the manager's ability to beat the market, excess returns may also be referred
to as the alpha after being adjusted by the risk assessed, known as the beta.
3) Capital Asset Pricing Model (CAPM)
(i) used to determine a theoretically appropriate required rate of return of an asset
(ii) to make decisions about adding assets to a well-diversified portfolio
(iii) to evaluate whether a stock is fairly valued when its risk and the time value of money are
compared to its expected return
𝑟𝑖= 𝛼 + 𝛽𝑖(𝑟
𝑚− 𝑟
𝑓) + 𝜀
