You work for a hedge fund that has made the following investments (at today's spot price):
(I) $100,000,000 (USD) in a private startup company in Australia
(II) $100,000,000 (USD) in a European company that is publicly traded
(a) If USD/AUD goes up by 10% over the next year and USD/EUR goes down by 20%, what is the overall return earned by the hedge fund if each investment goes up by 15%.
(b) Show exactly what you could do to hedge the investments in part (a) so that the hedge fund would earn an overall return of 15% regardless what happens to USD/AUD and USD/EUR over the next year. (Prove that the hedge works by showing examples!)