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You have been asked by your client to recommend which of two available stocks will perform better
over time, relative to risk. You will need to compare risk and return relationship of the two stocks
over time, and present your findings as both a written report (detailing your calculations and
findings), and a short video presentation to your client, elaborating on one aspect of your
investigation.
The goal of this assignment is to
1. give you practice in performing the different types of quantitative analysis tasks often
undertaken by Busines...
Question Preview:
You have been asked by your client to recommend which of two available stocks will perform better
over time, relative to risk. You will need to compare risk and return relationship of the two stocks
over time, and present your findings as both a written report (detailing your calculations and
findings), and a short video presentation to your client, elaborating on one aspect of your
investigation.
The goal of this assignment is to
1. give you practice in performing the different types of quantitative analysis tasks often
undertaken by Business graduates
2. provide you with feedback on your ability to carry out such tasks
3. learn how and when to use different quantitative techniques covered in the second half of the
course
This is an individual assignment, worth 30% of the total assessment in this subject. This
assignment is based on topics including; Sampling and Estimation, Hypothesis Testing, and
Regression Analysis.
• Use the marking rubric as a guide when working on your assignment.
Comparison of Stock Returns
Variables and Data Sources
• PS&P = S&P 500 Price Index
This is Standard and Poor index of 500 companies and will be used as market portfolio.
http://finance.yahoo.com/quote/%5egspc/history?p=^gspc
• PG = Google Stock Price
A particular stock we are interested in to determine how it behaves in response to market changes.
http://finance.yahoo.com/quote/GOOGL/
• PY = Yahoo Stock Price
A particular stock we are interested in to determine how it behaves in response to market changes.
http://finance.yahoo.com/quote/YHOO/
• rf =Interest rate on 10 year US-Treasury Note
This variable is given in percentage (with % sign omitted) and will serve as a risk-free interest
rate. We will use this variable to compute excess returns on our preferred stock (either Google or
Yahoo) and Market excess returns.
http://finance.yahoo.com/quote/%5ETNX/
Now perform the following tasks.
Task A: Downloading the data
Download the data for S&P 500 index, Google Stock Price, Yahoo Stock Price, and US TN (10 year),
using the links provided above and choosing Monthly Historical Data for all variables covering the
period related to a group your Student ID belongs to. Please use Close as the final series as sample
for this assignment.
Data Group Example: Suppose my student ID is 19178800. This ID falls in last group and I would
download monthly data covering the period Oct 2010 - May 2015.
Task B: Questions
1
Create the line charts for each of S&P, Yahoo and Google series using Close prices against time in Excel and
comment on your observations (focusing time series features).
2
a. Calculate returns for these three series in Excel using the transformation: rt = 100 ln[Pt/Pt-1]
Hints:
• We performed a similar task in Tutorial 01.
• These numbers would represent percentages after multiplication with 100 in the formula above. However,
you would not put a percentage sign in your data. For example, returns for two periods are 0.35% and
0.41% but we omit % sign in our excel worksheet and use 0.35 and
0.41.
b. Obtain the summary statistics for your sample and briefly discuss the risk and average return relationship in
each stock. Which stock (Google or Yahoo) is relatively riskier than the other?
c. Perform the Jarque-Berra test of normally distributed returns for each of Yahoo, Google and S&P.
3
Now, assume the following information about population distribution of returns on Google and Yahoo stocks.
Stock µ σ
Google 1.85 6.90
Yahoo: 1.30 8.02
a. Write down the sampling distribution of sample means for both stocks when a sample of 36 months is taken.
Use the sampling distributions of part (a) above to answer the following parts.
b. What is the probability of observing average return of at least 4% in both stocks?
c. What is the likelihood of loss in a sample of 36 periods for both stocks?
4
Before investing in one of the two stocks based on higher risk-return relationship, you further want to determine
whether both stocks have same population average return. Perform an appropriate hypothesis test using
information in your actual sample of 56 observations and report your findings. Also, which stock will you prefer
and why?
5
Create two new columns in Excel for excess return on your preferred stock (yt) and excess market return (xt) by
subtracting the 10-year T-Bill rate from both series as follows.
Excess return on your preferred stock: yt = rt - rf,t
Excess return on market: xt = rM,t - rf,t
6
a. Estimate the CAPM using linear regression where the dependent variable is excess return on your preferred
stock while the independent variable is excess market return (computed as return on S&P 500 minus the risk fee
rate) and report your results.
b. Interpret the estimated coefficients in relation to the profitability of the Stock and its riskiness in comparison
with the market.
c. Interpret the value of R2
.
d. Interpret 95% confidence interval for the slope coefficient.
7
Using the confidence interval approach to hypothesis testing, perform the hypothesis test to determine whether
your preferred stock is a neutral stock. (You would not be given any marks if you do not use CI approach to
hypothesis testing)
The Capital Asset Pricing Model
The capital asset pricing model also known as CAPM is one of the fundamental models in the field of finance. The
model explains variations in the rate of return on a security (rt) as a function of the rate of return on a market
portfolio (rM,t) consisting of all publicly traded stocks. Generally, the rate of return on any investment is measured
relative to its opportunity cost, which is the return on a risk free asset (rf,t). The difference between the return and
risk free rate is called the risk premium, because it is the reward or punishment for making a risky investment.
According to CAPM, the risk premium on a security (rt - rf,t ) is proportional to the risk premium on the market
portfolio (rM,t - rf,t). Thus,
rt - rf,t = βM (rM,t - rf,t) (1)
where the coefficient βM provides security’s ‘‘beta’’ value.
Model in equation (1) is called economic model since it describes relationship between excess stock return and the
excess market return based on financial theory.
Why CAPM is important?
The CAPM beta is important to investors since it discloses the stock’s volatility. In particular, this beta measures
the sensitivity of given security’s return to variation in the whole stock market. Value of beta determines whether
the stock is a defensive, a neutral, or an aggressive stock.
Defensive stock: A stock is known as defensive stock if its beta value is less than 1. A defensive stock has its
variation less than the market’s and therefore is considered as less risky than the market is.
Neutral Stock: A stock with beta equal to 1 is called neutral stock because it is as volatile as the market is.
Aggressive stock: A beta with value greater than 1 is known as an aggressive stock since it has variation larger
than the market’s and therefore is considered as more risky/volatile than the market is.
Since beta is an unknown parameter, therefore, investors usually require an estimate of a stock’s beta before
purchasing it. However, the statistical model can be obtained by including an intercept (β0) and an error term (ut)
in the model, so that we have a simple linear regression model as
rt - rf,t = β0 + βM (rM,t - rf,t) +ut
By defining yt = rt -rf,t and xt = rM,t -rf,t , we can express CAPM model in above equation as
yt = β0 + β1 xt +ut (2)
Analyse Data & Submit Report
Prepare your written report in two Parts:
Part A: Calculations
• Set out all your calculations for each of the tasks (listed above) using Data Analysis Tool in Excel. Present
your results in graphs and charts as appropriate
Part B: Interpretation
• Explain what your results mean, in language that your client can understand. For example, what
conclusions can you draw from each of your findings?
• Your written report must be no more than TWELVE (12) pages in total, including all appendices, graphs,
tables and written answers. Answer the questions directly. Do not present unnecessary graphs or
numerical measures, undertake inappropriate tests or discuss irrelevant matters.
Marks Distribution
Description Total
Marks
Task A Downloading of correct data 6
Task B Statistical Analysis 84
1. Line charts 9
2. a Returns computation 6
2. b Summary statistics 8
2. c Jarque-Berra test of normality 10
3. a Sampling Distribution 6
3. b & c Probability or average returns 8
4. 0 Hypothesis Testing-Two Population Means 10
5. 0 Computing excess returns 5
6. a CAPM estimation 6
6. b Interpretation of Coefficients 6
6. c Interpretation of R2 3
6. d Interpretation of Confidence interval for beta 3
7. 0 Confidence Interval approach to Hypothesis test 4
Organisation of the report (Word Document)
This includes; charts/graphs, equations, tables, explanation
and interpretation of results
10
Grand Total 100
End of the assignment
Task A:
The snapshot for the stock price for Google, Yahoo, S&P 500 and interest rate on 10 year
Treasury Note is presented in Figure 1 below.
Figure 1: Stock price for Google, Yahoo, S&P 500 and interest rate on 10 year Treasury
Note
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