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INSTRUCTOR:        HESTON

International Investments (BUFN770)

Final Quiz, Fall 2015 Term A

Time:        Time available.

Instructions:        There are 2 questions.  Do all questions.    Answer directly on these pages and show your work.  In particular, show all formulas and reasoning used so I can grade it properly.  Good luck!

There are 3 pages to this exam including this title page.

Question 1

The country of Fruitopia has three currencies, called the Apple, the Pear, and the Plum.  All spot rates are currently 1.000, with no bid-ask spread.  However, interest rates differ.  Here are lending/borrowing rates in the three currencies.

Apple:        10% - 12%

Pear:         20% - 22%

Plum:        30% - 32%.

The current one-year forward rates are:

Apple/Pear:        1.10-1.11

Apple/Plum:        1.20-1.21

Pear/Plum:        0.99-1.01.

You are only allowed to borrow and lend Plums.  You may not borrow, lend or save the other currencies (because the other fruits will spoil).  You may transact spot and forward as much as desired.  Show an arbitrage that produces one free Plum today.  Be specific about trading amounts and prices.

Triangular arbitrage (forward):

Buy 14.12 Plums for 14.26 Pears,

Buy 14.26 Pears for 15.83 Apples,

Buy 16.94 Apples for 14.12 Plums.

Netting 1.12 Apples forward (round-off error).

Borrow 1 Apple against this profit.

Or sell 18.86 Plums for 22.63 Apples,

Sell 22.63 Apples for 20.34 Pears,

Sell 20.34 Pears for 20.18 Plums.

Netting 1.32 Plums forward.

Borrow 1 Pear against this profit.

Question 2

The U.S. risk-free interest rate is 4%.  A U.S. investor is currently 100% invested in the U.S. stock market, with an expected return of 14% and a standard deviation of 30%.  Measured in USD, the Chinese stock market return has a standard deviation of 40%.

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