MN20310 Finance Coursework: CAPM, Stock Returns, and Analysis

This document presents a finance coursework assignment analyzing stock returns using the Capital Asset Pricing Model (CAPM). The assignment involves calculating returns for a stock (Oracle Corp) and the market index, along with the Treasury Bill yield. It includes the calculation of average return, standard deviation, and correlation matrix. The core of the analysis is the estimation of the CAPM using STATA, involving regression analysis to determine alpha and beta coefficients, and interpreting their statistical significance. The analysis also includes the calculation of R-squared and hypothesis testing for the coefficients. The document provides the STATA code used for the analysis and interprets the results, discussing the volatility and relationship between the stock and the market index. The assignment demonstrates an understanding of financial modeling, statistical analysis, and the application of the CAPM in evaluating stock performance.

MN20310_Coursework
NAME:
REGISTRATION NUMBER:
1

PART 1 (40 marks)
The first thing you need to do is calculate the returns for the market index and your stock. Note: The
Treasury Bill yield is a rate of return so you do not need to calculate this (for example, the value of
0.0249% in December 2015 means that the monthly yield or rate of return on 3-month Treasury Bills
was 0.0249%). To calculate the returns for the stock and index you simply calculate the percentage
change in price month by month. Note: This ignores dividends but this is fine for our purposes. The
important thing is to calculate these returns on a consistent basis with the Treasury Bill yield which is
monthly. Since there are 33 months of price data you should have 32 months of returns. Calculate the
average return and standard deviation for the returns of your stock, the index, and the Treasury Bill
and insert the results in Table 1. Choose an appropriate number of decimal places in order to make
the results are easy on the eye.
Table 1
Market ORACLE CORP Treasury Bill yield
Average 98.7998 0.4628 0.0053
Standard deviation 3.1350 5.0391 0.0068
Complete the correlation matrix in Table 2. Present the correlations using two decimal places.
Table 2
Market ORACLE CORP
Market 1.00 0.75
ORACLE CORP 0.75 1.00
Looking at table 1 above, we can see that the standard deviation for Oracle Corp (SD = 5.05) is
way too large as compared to that of the Treasury Bills (SD = 0.01). These results shows that the
stock returns for Oracle Corp are very volatile (highly risky) as compared to the stocks returns for
the Treasury Bills. A high standard deviation is a clear indication of a more volatile stock. Therefore
the stock returns for the Treasury Bills are less volatile hence very little risk in investing in them.
The correlation coefficient between the S&P 500 index and Oracle Corp is 0.75. This shows that a
strong positive relationship exists between the S&P 500 index and Oracle Corp. That is, when the
stock prices of the S&P 500 index goes higher we would expect those of Oracle Corp to also rise.
I feel that the sensitivity of the security returns for my stock (Oracle Corp) is very high as compared
to those of the market. It is very insecure in terms of the returns.
2

PART 2 (70 marks)
Estimate the CAPM for your stock. The formula for the CAPM is:
r j=rrf +b j ( rm −rrf )
You will use STATA to estimate the CAPM. First you need to rearrange the equation by subtracting
the risk-free rate from both sides and allow for an intercept which we call alpha () giving the
empirical version of the CAPM:
r j−rrf =α j +b j ( rm−r rf )
In order to estimate this regression, you first need to construct the variables. You create the y-variable
(also known as the dependent variable) by subtracting the risk-free rate (the Treasury Bill yield) from
the returns of your stock and you create the x-variable (the independent variable) by subtracting the
risk-free rate from the return on the market (the S&P 500). The regression tool will enable you to
estimate the values of alpha (the intercept) and the beta (the slope coefficient).
Record the essential information from the regression in Table 3.
Table 3
ORACLE CORP
Intercept () coefficient -119.2048
Intercept standard error 19.0378
Slope (b) coefficient 1.2112
Slope standard error 0.1926
R2 0.5686
n (sample size) 32
The hypothesis that we sought to test for the intercept coefficient is;
Ho : β0=0
H A : β0 ≠ 0
Where We compute the test statistics as follows;
Steps;
 Obtain the coefficient and then divide by the standard error.
t= β0
S . E =−119.2048
19.03784 =−6.26
The t-critical value is given as −2.042 since the absolute value of the computed t statistic is greater
than the absolute value of the critical t we reject the null hypothesis and conclude that the intercept
coefficient is different from zero hence it is statistically.
The hypothesis that we sought to test for the slope coefficient is;
Ho : β1=1
H A : β1 ≠ 1
Where
We compute the test statistics as follows;
Steps;
 Obtain the coefficient and then divide by the standard error.
t= β1 −1
S . E =1.211223−1
0.1926066 =6.29
The t-critical value is given as 2.042 since the computed t-value is greater than the critical t-value
we reject the null hypothesis and conclude that the slope coefficient is different from one hence it is
statistically significant.
3

The intercept coefficient is given as -119.2048; this means that holding the independent variable
constant (zero value for x) we would expect the stock returns for Oracle Corp to be -119.2048.
On the other hand, the coefficient for the slope is given as 1.2112; this means that a unit increase
in the independent variable (market index) would result to an increase in the stock returns for the
Oracle Corp by 1.2112. Similarly, a unit decrease in the independent variable (market index) would
result to a decrease in the stock returns for the Oracle Corp by 1.2112.
The value of the R-Squared (R2) is given as 0.5686; this means that 56.86% of the variation in the
dependent variable (stock returns for the Oracle Corp) is explained by the independent variable
(stock returns for the market index) in the model. The remaining proportion (43.14%) of the
variation in the dependent variable is explained by other factors outside the model (error term).
4

Appendix
Stata Codes
gen datevar = date(date,"MDY", 2012)
tsset datevar, monthly
gen oraclereturns = 100*((oraclecorp[_n]- oraclecorp[_n-1])/oraclecorp[_n-1])
gen sp500indexreturns = 100*((sp500index[_n]- oraclecorp[_n-1])/sp500index[_n-1])
summarize oraclereturns sp500indexreturns monthtreasuybillyield
pwcorr oraclereturns sp500indexreturns
gen y= oraclereturns- monthtreasuybillyield
gen x = sp500indexreturns- monthtreasuybillyield
reg y x
estat hettest
estat imtest, white
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