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4. (i) A forward contract written on a bond has 10 months remaining until matur...

May 10, 2024

4(i) Solution

Calculation of the Present Value of the Bond: The present value of the bond is calculated by discounting the future cash flows, which include the coupon payments and the face value, back to the present using the riskless rate of interest

Calculation of the Forward Price: The forward price is determined by adding the present value of the bond to the present value of the cost of carry, which in this case is the foregone interest at the riskless rate

Calculation of the Initial Value of the Forward Contract: The initial value of a forward contract is zero when the forward price is set to make the value of the contract zero at initiation

4(i) Answer

The theoretical forward price of the bond is calculated by adding the present value of the bond to the present value of the cost of carry. The initial value of the forward contract is zero.

Key Concept

Forward Pricing Relationship

Explanation

The forward price ensures that the value of the forward contract at initiation is zero, reflecting the no-arbitrage condition in financial markets.

4(ii) Solution

Arbitrage Strategy for Price Above Theoretical Forward Price: If a broker offers a forward price above the theoretical forward price, an arbitrageur can sell the forward contract at the higher price and simultaneously buy the underlying bond, locking in a risk-free profit

Arbitrage Strategy for Price Below Theoretical Forward Price: If a broker offers a forward price below the theoretical forward price, an arbitrageur can buy the forward contract at the lower price and short sell the underlying bond, again locking in a risk-free profit

4(ii) Answer

Numerical examples of arbitrage strategies include selling the forward contract and buying the bond when the forward price is above the theoretical price, and buying the forward contract and short selling the bond when the forward price is below the theoretical price.

Key Concept

Arbitrage Strategies

Explanation

Arbitrage strategies exploit the price differences between the theoretical forward price and the price offered by the broker to generate risk-free profits.