Answer:
Greetings, your inquiry seems to lack detail; below is the full question along with the missing table
Your investment bank has allocated $100 million in stocks of the Swiss Roll Corporation while holding a short position in Frankfurter Sausage Company. The recent stock price history for both companies is as follows: based on the last six months, how much should your short position in Frankfurter Sausage be to adequately hedge against fluctuations in the Swiss Roll stock price?
response: $42003667
Clarification:
$100 million invested in stocks
Utilizing the data presented in the attached table below, the calculation to short Frankfurter in order to hedge the investment in Rolls is as follows
we must determine the total returns for both the Roll corporation and Frankfurter Sausage
for f-sausage
∑ (1 + monthly returns ) / 100
= ( 1 - 0.1 + 1 - 0.1.... + 1 + 0.1 ) = -0.0297 = -2.97%
for Roll corporation
∑ (1 + monthly returns ) / 100
= ( 1 - 0.1 + 1 - 0.05.... + 1 + 0.1 ) = -0.012475 = - 1.24%
next we will compute the total loss incurred from investing in Roll corporation
Total loss = percentage loss * total investment
= 0.012475 * $100 million = - $ 1247500
we will need to compensate for the loss by shorting investments in F sausage
thus: $1247500 = investment in sausage * total return
1247500 = investment in sausage * 0.0297 ( The total return of F sausage is positive because it was a short position )
therefore, to cover the loss from the ROLLS INVESTMENT by shorting F sausage
= 1247500 / 0.0297 = $42003667