The Capital Asset Price Model (CAPM) is a financial model thatattempts to predict the rate of return on a financial instrument,such as a common stock, in such a way that it is linearly relatedto the rate of return on the overal market. Specifically,
RStockA,i = β0 + β1RMarket,i + ei
You are to study the relationship between the two variables andestimate the above model:
iRStockA,i - rate of return on Stock A for month i,i=1,2,⋯59.
iRMarket,i - market rate of return for month ii, i=1,2,⋯,59
β1 represent's the stocks 'beta' value, or its systematic risk. Itmeasure's the stocks volatility related to the market volatility.β0 represents the risk-free interest rate.
The data in the  file contains the data on the rate ofreturn of a large energy company which will be referred to as AcmeOil and Gas and the corresponding rate of return on the TorontoComposite Index (TSE) for 59 randomly selected months.
| TSERofReturn | AcmeRofReturn |
| 2.29651 | -0.34793 |
| -1.61176 | -1.75424 |
| 0.8957 | 0.24095 |
| -0.46309 | -0.52434 |
| 1.17586 | -1.39147 |
| 0.36339 | -0.89941 |
| -0.09888 | 0.62191 |
| 1.54007 | 0.21203 |
| 1.20388 | 0.89063 |
| 0.40541 | -0.31979 |
| -0.50512 | -0.26566 |
| -2.94253 | -0.48511 |
| 0.39141 | -1.22745 |
| 2.9549 | 2.35981 |
| -2.39621 | -0.02795 |
| -0.16892 | -0.63943 |
| -0.09888 | -0.69269 |
| -0.60317 | -0.57024 |
| -1.8639 | -1.26911 |
| 1.79222 | -0.16832 |
| -0.16892 | -0.73469 |
| 2.08639 | 0.33578 |
| -1.31759 | -0.99294 |
| 1.17586 | 0.06602 |
| -0.1409 | -0.02439 |
| -1.56973 | 1.75941 |
| 5.16818 | 3.23171 |
| -0.00082 | 1.19321 |
| -1.24755 | 0.74471 |
| -0.4771 | -0.28887 |
| -0.86933 | 0.4171 |
| -0.46309 | -1.21974 |
| 0.5595 | 1.06245 |
| -0.32301 | -0.14503 |
| -0.50512 | 1.69671 |
| -0.00082 | 0.58354 |
| 0.34938 | -2.45484 |
| -0.68722 | 0.452 |
| 4.08955 | 0.93878 |
| -3.01257 | -1.62261 |
| -3.71298 | 0.25316 |
| -0.29499 | -0.51118 |
| 0.93772 | 1.53503 |
| 1.63813 | 0.82144 |
| 0.71359 | 0.61567 |
| -3.22269 | -0.22444 |
| 0.5455 | 1.42175 |
| -0.60317 | -1.03702 |
| 1.91829 | 0.51314 |
| -0.15491 | 0.07771 |
| -1.91994 | 0.10144 |
| -0.23896 | 0.22354 |
| -1.59775 | 1.36347 |
| 0.23732 | -0.61873 |
| -1.19151 | -0.96878 |
| -1.30358 | 0.00046 |
| 2.87085 | 1.67688 |
| 2.05837 | -2.55599 |
| -1.10747 | -0.01911 |
Therefore RAcme,i represents the monthly rate of return for acommon share of Acme Oil and Gas stock; RTSE,i represents themonthly rate of return (increase or decrease) of the TSE Index forthe same month, month ii. The first column in this data filecontains the monthly rate of return on Acme Oil and gas stock; thesecond column contains the monthly rate of return on the TSE indexfor the same month.
(a) Use software to estimate this model. Use four-decimals in eachof your least-squares estimates your answer.
RAcme,i^ = ____+____RTSE,i
(b) Find the coefficient of determination. Expresses as apercentage, and use two decimal places in your answer.
r2=
(c) In the context of the data, interpret the meaning of thecoefficient of determination.
A. There is a strong, positive linear relationshipbetween the monthly rate of return of Acme stock and the monthlyrate of return of the TSE Index.
B. There is a weak, positive linear relationshipbetween the monthly rate of return of Acme stock and the monthlyrate of return of the TSE Index.
C. The percentage found above is the percentage ofvariation in the monthly rate of return of the TSE Index that canbe explained by its linear dependency with the monthly rate ofreturn of Acme stock.
D. The percentage found above is the percentage ofvariation in the monthly rate of return of Acme stock that can beexplained by its linear dependency with the monthly rate of returnof the TSE Index.
(d) Find the standard deviation of the prediction/regression, usingtwo decimals in your answer.
Se =
(e, i) You wish to test if the data collected supports thestatistical model listed above. That is, can the monthly rate ofreturn on Acme stock be expressed as a linear function of themonthly rate of return on the TSE Index? Select the correctstatistical hypotheses which you are to test.
A. H0:β0=0HA:β0≠0H0:β0=0HA:β0≠0
B. H0:β1=0HA:β1≠0H0:β1=0HA:β1≠0
C. H0:β1=0HA:β1>0H0:β1=0HA:β1>0
D. H0:β1=0HA:β1<0H0:β1=0HA:β1<0
E. H0:β0=0HA:β0>0H0:β0=0HA:β0>0
F. H0:β1≠0HA:β1≠0H0:β1≠0HA:β1≠0
G. H0:β0=0HA:β0<0H0:β0=0HA:β0<0
H. H0:β0≠0HA:β0≠0H0:β0≠0HA:β0≠0
(e, ii) Use the FF-test, test the statistical hypotheses determinedin (e, i). Find the value of the test statistic, using threedecimals in your answer.
Fcalc =
(e, iii) Find the P-value of your result in (e, ii). Use threedecimals in your answer.
P-value =
(f) Find a 95% confidence interval for the slope term of the model,β1.
Lower Bound =
(use three decimals in your answer)
Upper Bound =
(use three decimals in your answer)
(h) Find a 95% confidence interval for the β0 term of themodel.
Lower Bound =
(use three decimals in your answer)
Upper Bound =
(use three decimals in your answer)
(k) Last month, the TSE Index's monthly rate of return was 1.5%.This is, at the end of last month the value of the TSE Index was1.5% higher than at the beginning of last month. With 95%confidence, find the last month's rate of return on Acme Oil andGas stock.
Lower Bound =
(use three decimals in your answer)
Upper Bound =
(use three decimals in your answer)
