Question

A swap is initiated between Microsoft and Intel in which Microsoft receives a 6-month LIBOR and pays a fixed rate for every 6 months for 1 year on a notional principal of $100 million. Assuming that 6-month, 12-month, 18-month spot rates (zero rates) are 4.3%, 4.7%, 4.9% with continuous compounding, respectively, the swap rate under this swap should be closest to

Select one:

a. 4.95%

b. 4.55%

c. 4.35%

d. 4.75%

The two-month interest rates with continuous compounding in Australia and the United States are 4.2% and 3.5% per annum, respectively. The spot exchange rate is currently priced at USD 0.780 per AUD. Given the two-month forward contract on the Australian dollars in the market is currently priced at USD 0.782 per AUD, which transactions should an investor take today in order to take advantages of this arbitrage opportunity?

Select one:

a. The forward is underpriced; the investor should buy the forward contract, borrow USD and lend AUD

b. The forward is underpriced; the investor should buy the forward contract, borrow AUD, and lend USD

c. The forward is overpriced; the investor should sell the forward contract, borrow AUD and lend USD

d. The forward is overpriced; the investor should sell the forward contract, borrow USD and lend AUD

Answer 1

Q1.

Period	LIBOR p.a	Periodic Libor	d = 1 / e^r
6 month	4.3	2.15	0.978729
12 month	4.7	4.7	0.954087
18 month	4.9	7.35	0.929136
Total	2.861952

Swap rate = (1 - last discounting factor ) / sum of discounting factor * 100

= ( 1 - 0.929136 ) / 2.861952 * 100

= 2.48% for 6 months

Annual swap price = 2.48 * 2 = 4.95%

The answer is a ) 4.95%

Q2 :

As per the International fisher effect futures exchange rate ans the spot rate is in proportion to the interest rate of the two currencies.

Future exchange rate = Current exchange rate * ( 1+ interest rate of price currency ) / ( 1 + interest rate of domestic currency

= 0.780 * ( 1.005850377) / 1.007024557

= 0.779 usd / aud

Current price = 0.782 usd / aud

Theorital forward price is lower than the actual forward price hence :

d) d. The forward is overpriced; the investor should sell the forward contract, borrow USD and lend AUD