Question In the CAPM model, B0 is the risk free rate of return and its value is expected to be positive (usually the Treasury bill). The slope, B1,is the beta coefficient in CAPM model and measures the volatility of an asset’s return compared to that of the overall market. The benchmark value is 1.0 (perfect slope). The value can be more than 1.0 to show that a stock is more responsive to market changes or simply riskier than the market. The value can be less than 1.0 which indicates that the stock is less responsive to market changes (or is less risky).

Question 2

The plotted trajectories of x and y are shown in the chart below. As shown, a positive linear relationship between the two variables is expected.

Question 3

Obs

y

x

y2

χ2

yχ

=0+1χ

ɛ = y –

1

3.32

0.72

11.02

0.52

2.39

1.34

1.98

2

1.40

1.68

1.96

2.82

2.35

2.12

– 0.72

3

0.65

– 0.72

0.42

0.52

– 0.47

0.19

0.46

4

0.93

0.81

0.86

0.66

0.75

1.42

– 0.49

5

– 1.21

– 0.35

1.46

0.12

0.42

0.49

– 1.70

6

– 1.62

– 2.30

2.62

5.29

3.73

– 1.08

– 0.54

7

1.41

0.80

1.99

0.64

1.13

1.41

0.00

8

0.18

0.40

0.03

0.16

0.07

1.09

– 0.91

9

1.88

– 0.65

3.53

0.42

– 1.22

0.24

1.64

10

1.35

0.39

1.82

0.15

0.53

1.08

0.27

Total

8.29

0.78

25.74

11.30

9.68

8.29

–

Completed table

obs

Y

X

SQY

SQX

YX

Y_HAT

E

1

3.32

0.72

11.02240

0.518400

2.390400

1.355465

1.964535

2

1.40

1.68

1.960000

2.822400

2.352000

2.091122

-0.691122

3

0.65

-0.72

0.422500

0.518400

-0.468000

0.251979

0.398021

4

0.93

0.81

0.864900

0.656100

0.753300

1.424433

-0.494433

5

-1.21

-0.35

1.464100

0.122500

0.423500

0.535513

-1.745513

6

-1.62

-2.30

2.624400

5.290000

3.726000

-0.958791

-0.661209

7

1.41

0.80

1.988100

0.640000

1.128000

1.416770

-0.006770

8

0.18

0.40

0.032400

0.160000

0.072000

1.110246

-0.930246

9

1.88

-0.65

3.534400

0.422500

-1.222000

0.305620

1.574380

10

1.35

0.39

1.822500

0.152100

0.526500

1.102583

0.247417

Eviews Summary Descriptive Results

Y

X

SQX

SQY

YX

Y_HAT

E

nbsp.Mean

nbsp.0.829000

nbsp.0.078000

nbsp.1.130240

nbsp.2.573570

nbsp.0.968170

nbsp.0.863494

-0.034494

nbsp.Std. Dev.

nbsp.1.447730

nbsp.1.117615

nbsp.1.659833

nbsp.3.141602

nbsp.1.482091

nbsp.0.856439

nbsp.1.136141

nbsp.Sum

nbsp.8.290000

nbsp.0.780000

nbsp.11.30240

nbsp.25.73570

nbsp.9.681700

nbsp.8.634939

-0.344939

nbsp.Sum Sq. Dev.

nbsp.18.86329

nbsp.11.24156

nbsp.24.79541

nbsp.88.82698

nbsp.19.76935

nbsp.6.601388

nbsp.11.61734

nbsp.Observations

nbsp.10

nbsp.10

nbsp.10

nbsp.10

nbsp.10

nbsp.10

nbsp.10

Question 4

The slope (β0) = (0.620455)(1.45)/(1.12) = 0.804

The intercept (β1) = 0.83 – (1.01)(0.08) = 0.766.

Question 5

SSR = Sum of (Predicted y – population mean of y)^2 = 6.6132

SSR

nbsp.Mean

nbsp.0.661329

nbsp.Median

nbsp.0.305059

nbsp.Maximum

nbsp.3.196195

nbsp.Minimum

nbsp.0.074847

nbsp.Std. Dev.

nbsp.0.994800

nbsp.Skewness

nbsp.1.938750

nbsp.Kurtosis

nbsp.5.352234

nbsp.Jarque-Bera

nbsp.8.570002

nbsp.Probability

nbsp.0.013774

nbsp.Sum

nbsp.6.613286

nbsp.Sum Sq. Dev.

nbsp.8.906647

nbsp.Observations

nbsp.10

Question 6

Variance of returns, σ2 = 2.10

Standard deviation of returns, y, σ = 1.45

Standard deviation, x = 1.12

Question 7

The slope is 0.804 and the p-value is 0.056. At 5% level of significance, the slope is not significantly different from zero. The intercept is 0.766 and the p-value is 0.079. At 5% level, the intercept is not significantly different from zero.

Variable

Coefficient

Std. Error

t-Statistic

Prob.nbsp.nbsp.

C

0.766310

0.381844

2.006865

0.0797

X

0.803721

0.359171

2.237714

0.0556

R-squared

0.384964

nbsp.nbsp.nbsp.nbsp.Mean dependent var

0.829000

Adjusted R-squared

0.308084

nbsp.nbsp.nbsp.nbsp.S.D. dependent var

1.447730

S.E. of regression

1.204243

nbsp.nbsp.nbsp.nbsp.Akaike info criterion

3.386435

Sum squared resid

11.60160

nbsp.nbsp.nbsp.nbsp.Schwarz criterion

3.446952

Log likelihood

-14.93218

nbsp.nbsp.nbsp.nbsp.Hannan-Quinn criter.

3.320048

F-statistic

5.007366

nbsp.nbsp.nbsp.nbsp.Durbin-Watson stat

1.877887

Prob(F-statistic)

0.055623

Question 8

Testing whether the slope, 0.804, is bigger or lower than 1 is a one-tailed t-test. Since the calculated t-statistic is below the rejection level, we cannot reject the null hypothesis that the slope is significantly lower than 1. The stock is not more volatile than the market.

Wald Test:

Equation: EQ_CAPM_REG

Test Statistic

Value

df

Probability

t-statistic

-0.612004

nbsp.8

nbsp.0.5575

F-statistic

nbsp.0.374549

(1, 8)

nbsp.0.5575

Chi-square

nbsp.0.374549

nbsp.1

nbsp.0.5405

Null Hypothesis: C(1) = 1

Null Hypothesis Summary:

Normalized Restriction (= 0)

Value

Std. Err.

-1 + C(1)

-0.233690

nbsp.0.381844

Restrictions are linear in coefficients.

Question 9

SSE = 11.60

SST = SSE + SSR = 11.60 + 7.26 = 18.86

Question 10

Correlation coefficient = 0.62 (Excel I21)

Coefficient of determination, r2 = 0.622 = 0.38

Question 11

Done and tables pasted in the questions above.