Question

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 overal market. Specifically,

RStockA,i = β0 + β1RMarket,i + ei

You are to study the relationship between the two variables and estimate 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. It measure'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 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.

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 a common share of Acme Oil and Gas stock; RTSE,i represents the monthly rate of return (increase or decrease) of the TSE Index for the same month, month ii. 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.

(e, ii) Use the FF-test, test the statistical hypotheses determined in (e, i). Find the value of the test statistic, using three decimals in your answer.

Fcalc =

(e, iii) Find the P-value of your result in (e, ii). Use three decimals 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 the model.

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 was 1.5% higher than at the beginning of last month. With 95% confidence, find the last month's rate of return on Acme Oil and Gas stock.

Lower Bound =

(use three decimals in your answer)

Upper Bound =

(use three decimals in your answer)

Answer 1

(e, ii) Use the FF-test, test the statistical hypotheses determined in (e, i). Find the value of the test statistic, using three decimals in your answer.

Fcalc = 8.433

(e, iii) Find the P-value of your result in (e, ii). Use three decimals in your answer.

P-value = 0.005

(f) Find a 95% confidence interval for the slope term of the model, β1.

Lower Bound = 0.072

(use three decimals in your answer)

Upper Bound = 0.394

(use three decimals in your answer)


(h) Find a 95% confidence interval for the β0 term of the model.

Lower Bound = -0.249

(use three decimals in your answer)

Upper Bound = 0.293

(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 was 1.5% higher than at the beginning of last month. With 95% confidence, find the last month's rate of return on Acme Oil and Gas stock.

Lower Bound = 0.010

(use three decimals in your answer)

Upper Bound = 0.733

(use three decimals in your answer)

	r²	0.129
	r	0.359
	Std. Error	1.038
	n	59
	k	1
	Dep. Var.	AcmeRofReturn
ANOVA table
Source	SS	df	MS	F	p-value
Regression	9.0942	1	9.0942	8.433	.005
Residual	61.4691	57	1.0784
Total	70.5633	58
Regression output				confidence interval
variables	coefficients	std. error	t (df=57)	p-value	95% lower	95% upper
Intercept	0.0220	0.135	0.162	0.871	-0.249	0.293
TSERofReturn	0.2331	0.080	2.904	0.005	0.072	0.394
Predicted values for: AcmeRofReturn
		95% Confidence Interval	95% Prediction Interval
TSERofReturn	Predicted	lower	upper	lower	upper	Leverage
1.5	0.3715781	0.010	0.733	-1.739	2.482	0.030