Asked by Keyla Ortiz on Jul 14, 2024
Verified
Suppose that the risk-free rates in the United States and in Canada are 5% and 3%, respectively. The spot exchange rate between the dollar and the Canadian dollar (C$) is $0.80/C$. What should the futures price of the C$ for a one-year contract be to prevent arbitrage opportunities, ignoring transactions costs.
A) $1.00/C$
B) $0.82/C$
C) $0.88/C$
D) $0.78/C$
E) $1.22/C$
Risk-free Rates
The theoretical return on an investment with no risk of financial loss, often represented by the yield on government securities like U.S. Treasury bonds.
Spot Exchange Rate
The ongoing market rate for the prompt conversion of one currency into another.
Futures Price
The agreed price for the underlying asset in a futures contract to be paid on the contract's settlement date.
- Determine and compute the correct future prices to eliminate arbitrage possibilities utilizing interest rate differences and currency exchange values.
Verified Answer
SW
stephanie wigginsJul 21, 2024
Final Answer :
B
Explanation :
The futures price can be calculated using the Interest Rate Parity (IRP) formula, which prevents arbitrage opportunities. According to IRP, the future exchange rate is determined by the formula: F=S×(1+id)(1+if)F = S \times \frac{(1 + i_d)}{(1 + i_f)}F=S×(1+if)(1+id) , where FFF is the future exchange rate, SSS is the spot exchange rate, idi_did is the domestic interest rate, and ifi_fif is the foreign interest rate. Plugging in the given values: F=0.80×(1+0.05)(1+0.03)=0.80×1.051.03=0.80×1.019417=0.8155336F = 0.80 \times \frac{(1 + 0.05)}{(1 + 0.03)} = 0.80 \times \frac{1.05}{1.03} = 0.80 \times 1.019417 = 0.8155336F=0.80×(1+0.03)(1+0.05)=0.80×1.031.05=0.80×1.019417=0.8155336 , which rounds to $0.82/C$, thus preventing arbitrage opportunities.
Learning Objectives
- Determine and compute the correct future prices to eliminate arbitrage possibilities utilizing interest rate differences and currency exchange values.