Returns on common stocks in the United States and overseas appear to be growing

Question

Returns on common stocks in the United States and overseas appear to be growing more closely correlated as economies become more interdependent. Suppose that the following population regression line connects the total annual returns (in percent) on two indexes of stock prices:

MEAN OVERSEAS RETURN = 4.4 + 0.66 × U.S. RETURN

(a) What is 0 in this line?

0 is the population intercept, 0.66.0 is the population slope, 4.4.     0 is the population intercept, 4.4.0 is the population slope, 0.66.

What does this number say about overseas returns when the U.S. market is flat (0% return)?

This says that the mean overseas return is  % when the U.S. return is 0%.

(b) What is 1 in this line?

1 is the population intercept, 4.4.1 is the population slope, 4.4.     1 is the population intercept, 0.66.1 is the population slope, 0.66

What does this number say about the relationship between U.S. and overseas returns?

This says that when the U.S. return changes by 1%, the mean overseas return changes by  %.

(c) We know that overseas returns will vary in years having the same return on U.S. common stocks. Write the regression model based on the population regression line given above.

yi =  +  xi + i,

where yi and xi are observed overseas and U.S. returns in a given year, and i are independent N(0, ) variables.

What part of this model allows overseas returns to vary when U.S. returns remain the same?

xi

yi

     ii

Explanation / Answer

(a) When x = 0, the corresponding y-value is the y-intercept. Thus 0 is the intercept and here 0=4.4.

This says that the mean overseas return is  4.4% when the U.S. return is 0%.

(b) 1 is the population slope, 0.66

This values tells me that, for every increase of 1 in input variable t , the value of my output variable y will increase by 0.66.

This says that when the U.S. return changes by 1%, the mean overseas return changes by 0.66%.

(c) i are independent N(0, ) variables.

It is said that the error term in a regression equation represents the effect of the variables that were omitted from the equation.

Thus, ii of this model allows overseas returns to vary when U.S. returns remain the same. C

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