Financial Risk Manager Part 1

Explanation

The correlation between the return on the stock and the return on the market is -0.90. The correlation coefficient, denoted as r, is a measure of the strength and direction of the linear relationship between two variables. In this case, the variables are the return on the stock (R) and the return on the market (MR). The correlation coefficient is calculated as:

$r = [\text{Sign of estimated slope coefficient}] \sqrt{R^2}$

Given that the estimated slope coefficient is -1.15 (a negative value), the sign of r will also be negative. The square root of $R^2$ (which is 0.81) is approximately 0.90. Therefore, the correlation coefficient r is -0.90, indicating a strong negative linear relationship between R and MR. This means that as MR increases, R tends to decrease, and vice versa.

Choice A is incorrect. The relationship between the return on the stock and the market return is not positive as suggested by this option. The coefficient of MR in the given equation is -1.15, which means that a 1% increase in MR results in a 1.15% decrease in R, not an increase.

Choice B is incorrect. This choice incorrectly interprets the constant term (2%) as the change in R for a 1% change in MR. In reality, this constant term represents the expected value of R when MR equals zero.

Choice C is incorrect. The coefficient of determination ($R^2$) measures how well our model explains variation in our dependent variable (in this case, R), but it does not directly give us correlation between variables. Correlation would be the square root of $R^2$, but since we have a negative relationship, it should be -0.9 and not +0.81.