兹维博迪金融学第二版试题库7TB(1)

3. Suppose you have $50,000 in a bank account earning an interest rate of 3.5% per year. At the

same time you have an unpaid balance on your credit card of $13,000 on which you are paying an interest rate of 21% per year. What is the arbitrage opportunity you face?

Answer: You could take $13,000 out of your bank account and pay down your credit card balance. You would give up 3.5% per year in interest earnings ($455) but you would save 21% per year in interest expenses ($2,730). So the arbitrage opportunity is worth $2,275 per year.

4. The quotes from Hubris Bank and Modesty Bank are given below:

Hubris Bank: 106 Yen/$ Modesty Bank: 104 Yen/$

Answer the following questions based on these figures.

a) If we assume no transaction costs, there is evidently an opportunity for arbitrage here.

If an arbitrageur started with $10,000, exactly how would (s)he make profits and how much profit would (s)he make?

b) As many traders engage in arbitrage who do you expect to see in the above quotes at

these two banks?

c) If there is a 1% transaction cost for transactions is there still an opportunity for

arbitrage?

Answer:

Hubris Bank: 106 Yen/$ Modesty Bank: 104 Yen/$ a) At Hubris Bank, buy Yen with dollars (Yen are cheaper).

At Modesty Bank, buy dollars with Yen (dollars are cheaper).

Start with $10,000: At Hubris Bank: $10,000 x 106 Yen/$ = 1,060,000 Yen At Modesty Bank: 1,060,000 Yen x 1$/104 Yen = $10,192.31 You make a profit of $192.31. b) The Yen will appreciate at Hubris Bank and it will depreciate at Modesty Bank.

Eventually the exchange rate will stabilize between 106 Yen/$ and 104 Yen/$.

c) Assume 1% transaction cost.

At Hubris Bank: $10,000 (0.99) x 106 Yen/$ = 1,049,400 Yen At Modesty Bank: 1,049,400 Yen x (0.99) x $1/104 Yen = $10,090.38

There is still an opportunity for arbitrage profit, but it has decreased from $192.31 to $90.38.

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5. In the United States, the real rate of return is expected to be 5% and in Switzerland it is

expected to be 4%.

a) If the inflation rate in the United States is expected to be 6% and the Swiss

inflation rate is expected to be 8%, what will the nominal interest rates be in the United States and Switzerland?

b) Are these markets in equilibrium? Where would you prefer to invest and why? c) What if the Swiss inflation rate were 6%? Are the markets in equilibrium? d) What are the respective nominal rates if the worldwide risk-free real rate of

return is 4% and inflation in the U.S. is 6% and in Switzerland it is 8%?

Answer: a) United States: Nominal interest rate = (1.05)(1.06) – 1 = 11.30% per year Switzerland: Nominal interest rate = (1.04)(1.08) – 1 = 12.32% per year

b) The markets are not in equilibrium. Investors will go where the real rate is highest.

That is, in the U.S.

c) United States: Nominal interest rate = (1.05)(1.06) – 1

= 11.30% per year

Switzerland: Nominal interest rate = (1.04)(1.06) – 1 = 10.24% per year Markets are still not in equilibrium.

d) United States: Nominal interest rate = (1.04)(1.06) – 1 = 10.24% per year

Switzerland: Nominal interest rate = (1.04)(1.08) – 1 = 12.32% per year

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