Question

In an attempt to “time the market,” a financial analyst studies the quarterly returns of a stock. He uses the model y = β₀ + β₁d₁ + β₂d₂ + β₃d₃ + ɛ where y is the quarterly return of a stock, d₁ is a dummy variable that equals 1 if quarter 1 and 0 otherwise, d₂ is a dummy variable that equals 1 if quarter 2 and 0 otherwise, and d₃ is a dummy variable that equals 1 if quarter 3 and 0 otherwise. The following table shows a portion of the regression results.

	coefficients	error	t stat	p-value
intercept	10.50	7.78	1.35	0.19
d1	6.15	2.73	-2.25	0.03
d2	-1.10	0.44	-2.50	0.02
d3	-7.70	2.80	-2.75	0.01

a-1. Given that there are four quarters in a year, why doesn’t the analyst include a fourth dummy variable in his model?

• Inclusion of d₄ would cause perfect multicollinearity.

• Inclusion of d₄ would cause changing variance.

• Inclusion of d₄ would cause correlated residuals.

• Inclusion of d₄ would cause d₁ to be significant.

a-2. What is the reference category?

a. Quarter 1

b. Quarter 2

c. Quarter 3

d. Quarter 4

b-1. At the 5% significance level, are the dummy variables individually significant?

1. Yes, since the relevant p-value is less than 0.05.

2. Yes, since the relevant p-value is greater than 0.05.

3. No, since the relevant p-value is less than 0.05.

4. No, since the relevant p-value is greater than 0.05.

b-2. Is the analyst able to obtain higher returns depending on the quarter?

• No

• Yes

c. Reformulate the model to determine if the quarterly return is higher in quarter 1 than in quarter 2, still accounting for all quarters. (You may select more than one answer.)

1. y = β₀ + β₁d₁ + β₂d₂ + β₄d₄ + εunchecked

2. y = β₀ + β₁d₁ + β₃d₃ + β₄d₄ + εunchecked

3. y = β₀ + β₁d₁ + β₂d₂ + β₃d₃ + εunchecked

4. y = β₀ + β₂d₂ + β₃d₃ + β₄d₄ + ε

Answer 1