Price changes of two gold-mining stocks have shown strong positive correlation.

Their historical relationship is

Average percentage change in A = .001 + .75 (percentage change in B)

Changes in B explain 60% of the variation of the changes in A (R2 = .6).

a. Suppose you own $100,000 of A. How much of B should you sell to minimize the risk of your net position?

b. What is the hedge ratio?

c. Here is the historical relationship between stock A and gold prices:

Average percentage change in A = −.002 + 1.2 (percentage change in gold price)

If R2 = .5, can you lower the risk of your net position by hedging with gold (or gold futures) rather than with stock B? Explain.