BUSINESS STATISTICS AND REGRESSION

QUESTION

MAE 356 Analytical Methods in Economics and Finance, Trimester 1, 2012

ASSIGNMENT 1: Due date Friday 18th May 5 pm.
Word limit: Maximum 1500 words plus computer analysis
Weight: 15%

The capital asset pricing model (CAPM) is an important model in the field of finance/financial
economics. It explains variations in the rate of return on a security as a function of the rate of
return on a portfolio consisting of all publicly traded stocks, which is known as the market
portfolio. Generally, the rate of return on any investment is measured relative to its opportunity
cost, which is measured as the return on a risk-free asset. The resulting difference is called the
risk premium, since it is the reward or punishment for making a risky investment. The CAPM
says that the risk premium on security j is proportional to the risk premium on the market
portfolio. That is,
where r
j
and r
f
( )
rrrr −=β

fmjfj
are the returns to security j and the risk-free rate, respectively, r
is the return on the
market portfolio, and
j
m
β
is the j’th security’s “beta” value. A stock’s beta is important to investors
because it reveals the stock’s volatility. It measures the sensitivity of security j’s return to variation in
the whole stock market. As such, values of beta less than one (1) indicate that the stock is
‘defensive’, since its variation is less than the market’s. A beta greater than one (1) indicates an
‘aggressive stock.’ Investors usually want an estimate of a stock’s beta before purchasing it. The
CAPM model shown above is the ‘economic model’ in this case. The ‘econometric model’ is obtained
by including an intercept in the model (even though theory says it should be zero) and an error term,
( )
errrr
+−+=− βα

fmjjfj
Data:
Please download the required data kept in the file ‘Assignmentdata_T12012’ in excel format
from the D2L site. The file contains data on monthly returns of six firms, viz., Microsoft (MSFT),
General Electric (GE), General Motors (GM), IBM, Disney (DIS) and Mobil-Exxon (XOM) from
January 1998 to December 2008 and with 132 observations. In the data file, the first column is
named “OBS”, under which you will find the observation dates. The second column (column B)
till the seventh column (column G) is labelled “DIS”, “GE”, “GM”, “IBM”, “MSFT” and “XOM”,
respectively. The last two columns represent the rate of return on the market portfolio (MKT),
and the rate of return on the risk free asset (RISKFREE).

You should use MSExcel for your statistical analysis to answer the following questions.
Please make
sure you include all your regression output as an appendix to your submission.
(a) Using XOM and MKT data plot the returns for the entire period and comment on the
relative fluctuations of these two variables.        [1]

(b) Calculate and construct the series of the risk premium on Microsoft and the risk
premium on the market portfolio for the entire period, using the data for “MSFT”,
“MARKET” and “RKFREE”.        [1]

(c) Present the descriptive statistics of monthly returns of GE, GM, IBM and DIS data.
Interpret and compare the measures of central tendency and deviation of the variables.
[2]

(d) Estimate the CAPM model for Microsoft and GM, and comment on their estimated beta
values.            [2]
α
should be zero. Does this seem
correct given your estimates?        [2]
(e) Finance theory suggests that the intercept parameter
j
(f) Suppose a financial consultant believes that Microsoft’s beta value is equal to 1. Test the
consultant’s claim of Microsoft’s beta value at 1% level of significance against the alternative
that it is less than one. Interpret your result.      [2]
(g) Predict the risk premium for Microsoft given the risk premium for market portfolio of 2%
and 7%.          [1]

(h)  Divide the data series into two halves, one for January 1998 to September 2001 and the
other for October 2001 to December 2008. Using 5% significance, test the null hypothesis
that both alpha and beta for Microsoft are equal over the two sub-samples, i.e., test for
parameter stability over the two periods.       [2]
(i) Briefly summarize your findings about Microsoft’s stock and its relationship to the stock
market.          [2]

Notes:  This is an individual assignment. All Excel worksheets should be attached at the end
of your submitted assignment. These should clearly demonstrate the work undertaken
independently by you.  Submissions should be made both in hardcopy and online on DSO.
On-campus students must submit to the campus specific faculty office while the off campus
students submit the assignments as per the information provided in the unit guide and should
contact the Division of Student Affairs (DSA).

SOLUTION

L020

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