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 = 4.1 + 0.62 × U.S. RETURN

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%.

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.

Explanation / Answer

When US return = 0%,

MEAN OVERSEAS RETURN = 4.1 + 0.62 × U.S. RETURN = 4.1 + 0.62*0 = 4.1%

This says that the mean overseas return is 4.1 % when the U.S. return is 0%.

When US return changes by 1%,

MEAN OVERSEAS RETURN changes by coefficient of US rate, which is 0.62%

This says that when the U.S. return changes by 1%, the mean overseas return changes by 0.62 %.

c. Population regression line:

yi = 4.1 + 0.62 xi + i

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