The Capital Asset Price Model (CAPM) is a financial model that attempts to predict the rate of return on a financial instrument, such as a common stock, in such a way that it is linearly related to the rate of return on the overall market. Specifically:
R_(Sood )=eta _(0)+eta _(1)R_(seresu )+epsilon_(1)
You are to study the relationship between the two variables and estimate the above model:
R_(Sowit ) - rate of return on Stock A for month i, i=1,2,dots,59.
R_(Meilit ) - market rate of return for month i, f=1,2,dots,59.
eta _(1) represents the stock's beta value, or its systematic risk. It measures the stock's volatility related to the market volatility. eta _(0) represents the risk-free interest rate.
The data in the Download.csv file contains the data on the rate of return of a large energy company which will be referred to as Acme Oil and Gas and the corresponding rate of return on the Toronto Composite index (TSE) for 59 randomly selected months.
Therefore, R_(hew ) represents the monthly rate of return for a common share of Acme Oil and Gas stock. R_(rxj) represents the monthly rate of return increase or decrease of the TSE index for the same month, month i. The first column in this data file contains the monthly rate of return on Acme Oil and Gas stock. The second column contains the monthly rate of return on the TSE index for the same month.
(a) Using Minitab, create a scatter-plot of the data. What can you conclude from this scatter-plot?
1. There is a positive linear relationship between the monthly rate of return of Acme Oil and Gas stock and the monthly rate of return of the TSE index.
2. There is not a linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE index.
3. There is a negative linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index.
(b) Find the value of the correlation coefficient. Enter your answer using four decimals.
r=
(c) Use Minitab to find the least squares estimate of the linear model that expresses the monthly rate of return on Acme Oil and Gas stock as a linear function of the monthly rate of return on the Toronto Stock Exchange index. Use three decimals in each of your answers.
widehat(R_(k))=1=(1)=,R_(rsw )
(d) The rate of return on the TSE index for the month of October was -3.42%. Predict the monthly rate of return of Acme Oil and Gas stock for the month of October. Use four decimals in your answer.
(e) Interpret the meaning of the predicted value in (d) in the context of the data.
If the monthly rate of return of the TSE index is -3.42%, the ? of Acme Oil and Gas stock is
Find the coefficient of determination. Express as a percentage, and use two decimal places in your answer.
r^(2)=, # **
(y) In the context of the data, interpret the meaning of the coefficient of determination.
A. The percentage found above is the percentage of variation in the monthly rate of return of the TSE Index that can be explained by its linear dependency with the monthly rate of return of Acme stock.
B. There is a weak, positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index.
C. There is a strong, positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE index.
D. The percentage found above is the percentage of variation in the monthly rate of return of Acme stock that can be explained by its linear relationship with the monthly rate of return of the TSE index.
(a) Find the residual corresponding to the data point found in the 10th row of the data file. Use four decimals in your answer:
epsilon_(10)=
The Capital Asset Price Model (CAPM) is a financial model that attempts to predict the rate of return on a financial instrument.
You are to study the relationship between the two variables and estimate the above model:
Rw=o+PRMy+e
RMa-market rate of return for month i.=1.2.59
represents the stock's beta value, or its systematic risk. It measures the stock's volatility related to the market volatility. g represents the risk-free interest rate.
The data in the Download.csv file contains the data on the rate of return of a large energy company which will be referred to as Acme Oil and Gas and the corresponding rate of return on the Toronto Composite Index TSE for 59 randomly selected months.
Therefore Rm represents the monthly rate of return for a common share of Acme Oil and Gas stock. Rsg represents the monthly rate of return increase or decrease of the TSE Index for the same month, month i. The first column in this data file contains the monthly rate of return on Acme Oil and Gas stock. The second column contains the monthly rate of return on the TSE index for the same month.
A. There is a positive linear relationship between the monthly rate of return of Acme Oil and Gas stock and the monthly rate of return of the TSE index.
B. There is not a linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index
(b) Find the value of the correlation coefficient. Enter your answer using four decimals
(c) Use Minitab to find the least squares estimate of the linear model that expresses the monthly rate of return on Acme Oil and Gas stock as a linear function of the monthly rate of return on the Toronto Stock Exchange index. Use three decimals in each of your answers
(d) The rate of return on the TSE Index for the month of October was -3.42%. Predict the monthly rate of return of Acme Oil and Gas stock for the month of October. Use four decimals in your answer
(e) Interpret the meaning of the predicted value in (d) in the context of the data
Find the coefficient of determination. Express as a percentage, and use two decimal places in your answer
(u) In the context of the data, interpret the meaning of the coefficient of determination
A. The percentage found above is the percentage of variation in the monthly rate of return of the TSE Index that can be explained by s
B. There is a weak positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE Index
C. There is a strong positive linear relationship between the monthly rate of return of Acme stock and the monthly rate of return of the TSE index
D. The percentage found above is the percentage of variation in the monthly rate of return of Acme stock that can be explained by its linear relationship with the monthly rate of return of the TSE index
corresponding to the data point found in the 10th row of the data file. Use four decimals in your answer
