Question

You have been asked to assess the economic exposure of Rand Corp. using the following regression:

r_t = a + β * Δe_t + u_t

where r_t is the return on Rand’s stock at time t, Δet is the percentage change in the dollar value of the Japanese yen at time t (i.e., dollars per yen), and u_t is the regression error term at time t.

The regression output shows:

a=intercept= 0.30

β=slope coefficient= -1.20 p-value of slope coefficient = 0.002 (t-stat =-3.25)

R² = 0.55

1. Provide an interpretation of the regression output, explaining: the p-value, the slope coefficient, and the R-squared.

2. Assess the level of economic exposure of Rand Corp: non-existent, low, or high (choose one). Cite at least two statistics from the regression output to justify your position.

3. Does Rand Corp. stock respond negatively or positively to an appreciation of the U.S. dollar? Explain.

Answer 1

The regression equation is:
rt = 0.30 - 1.20*Δet

As the p-value < 0.05, we can say that there is a significant lienar relationship between return on Rand's stock at time t and the percentage cahnge in the dollar value of the Japanese Yen at time t.
The intercept 0.30 means that if the percentage change is 0, the return on Rand's stock is 0.30.
The slope tells us that if there is a one unit increase in the percentage change in the dollar value, the expected return on Rand's stock decreases by -1.20%

The R-squared value tells us that 55% of the variation is explained in the dependent variable return on Rand's stock by the independent variable Δet.

b) As the p-value is significant, we can say that there exists some level of economic exposure.
As the coefficient of determination which is R = SQRT(0.55) = 0.74, we can say that the level of economic exposure is high.

If there is an appreciation in the dollar, Δet is positive, hence this makes the return on Rand's stock less. Therefore, Rand Corp. stock responds negatively to the appreciation of dollar.