讲解ACTL 2131/5101-Assignment 3

UNSW Business School
School of Risk and Actuarial Studies
ACTL 2131/5101 Mini - Assignment 3
Submission deadline:
Tuesday, 28th April 11 am sharp via Moodle
Instructions
This assignment is worth 5% of the course mark. To receive a full mark, you need to:
1. Upload your answer.
2. Respond to at least one of your peers’ answers.
Learning outcomes
This assessment activity aims to reinforce your learning by providing you with an opportunity
to apply the concepts you have learned in the course to practical problems. They will help you
solidify the relevance of the course to the real world. Therefore, what counts is that you make
a sincere attempt, reflect and learn as much as possible from the discussions.
Format of the report
• This is an individual assignment.
• You should perform your analysis in R.
• The assignment should be typed in.
• Maximum number of pages: at most 2. Be as concise as you can, while clearly addressing
each question.
• Assignment should be submitted via Moodle.
Background/Data preparation
Note: Use data for the single stock and SP 500 index prepared for Assignment 2. In addition,
you will have to download the following data:
1. From the Ken French’s website http://mba.tuck.dartmouth.edu/pages/faculty/ken.
french/index.html download daily observations for 3 Fama French Factors and the
Momentum Factor. Use the following links/titles on the website (under Data Library):
1
• Fama/French 3 Factors [Daily] Details:
The first column will include the date (yyyymmdd) followed by 3 Fama French
factors and the risk free rate:
– Mkt-RF (Market Return minus risk free rate)
– SMB (return on small market capitalization minus big market cap firms returns)
– HML (return on high book-to-market ratio minus low)
– RF (risk free rate)
2. Momentum Factor (Mom) [Daily] Details:
This is the average of the returns on two (big and small) high prior return portfolios
minus the average of the returns on two low prior return portfolios. Big means a firm is
above the median market cap on the New York Stock Exchange (NYSE) at the end of
the previous month whereas small firms are below the median NYSE market cap. Prior
return is measured from month -12 to -2. Firms in the low prior return portfolio are
below the 30th NYSE percentile. Those in the high portfolio are above the 70th NYSE
percentile.
For details on Fama French factors refer to Details on the website as well as references which
you can find on https://en.wikipedia.org/wiki/Fama?French_three-factor_model
Note: There should be no missing data after you merge data.
Assignment tasks
Note: Only these tasks are covered in the (max 2 pages) report.
Note: for all the tasks below, if you require to set a significance level for the tests, please use
5%.
It is reasonable to expect that stock returns have some degree of correlation with SP 500 index
returns, and potentially some other variables. In this task, you will analyse these relationships.
1. Perform a detailed statistical analysis on whether the simple linear regression model is
reasonable in describing the relationship between excess returns on the stock and excess
return on the SP 500 index. Excess return on the stock is defined as the difference
between the stock return Rt and risk free rate Rrf,t. Similarly, excess return on the SP
500 is defined as (RSP,t − Rrf,t). Perform the Capital Asset Pricing Model regression
(CAPM):
Rt −Rrf,t = α + β(RSP,t −Rrf,t) + εt. (1)
Estimate this model and comment on your findings. Your discussion should include,
but not limited to, the significance of these variables, model fit, residual statistics and
other findings you might find interesting. For references on the CAPM you can refer, for
example, to https://en.wikipedia.org/wiki/Capital_asset_pricing_model.
2. Your manager has told you that in addition to the SP 500 index returns, other variables
can explain fluctuations in the excess returns on the stock. He is suggesting that you
explore the following relationship:
Rt −Rrf,t = β0 + β1(RSP,t −Rrf,t) + β2SMBt + β3HMLt + β4MOMt + εt, (2)
2
the excess return on the stock is regressed on the three Fama-French factors MKT-RF,
SMB, HML and the momentum factor MOM. Estimate this model and comment on your
findings. Your discussion should include, but not limited to, the significance of these
variables, model fit, residual statistics and other findings you might find interesting.
What are the implications (in particular, with respect to the model fit) for the Capital
Asset Pricing Model (CAPM), which suggests estimating a simple linear regression in
equation (1), including only one factor, MKT-RF, rather than all four. For references
on the Fama/French model you can refer, for example, to https://en.wikipedia.org/
wiki/Fama-French_three-factor_model.
3. At recent conference, the manager heard about the so-called out-of-sample procedure
can be used to validate the predictive power of the model and want you to use it here.
The out-of-sample procedure assumes that the estimation of the model is performed in-
sample (i.e. using model fitted in point 2 for the first 750 out of 1000 observations), and
the remaining sub-sample (i.e. the last 250 observations) is treated as an out-of-sample
period, which is used to validate the quality of the predictive power of the model. Help
the manager validate the quality of the predictive power of the proposed Fama/French
regression model by using the out-of-sample procedure.