My question regarding the answer of the below problem, should not the short experience loss when the value of the contract increase (i.e interest decrease) because the contract will be exercised?
Troubadour next considers an equity forward contract for Texas Steel, Inc. (TSI). Information regarding TSI common shares and a TSI equity forward contract is presented in Exhibit 2.
Exhibit 2. Selected Information for TSI
The price per share of TSI’s common shares is $250.
The forward price per share for a nine-month TSI equity forward contract is $250.562289.
Assume annual compounding.
Troubadour takes a short position in the TSI equity forward contract. His supervisor asks, “Under which scenario would our position experience a loss?”
Three months after contract initiation, Troubadour gathers information on TSI and the risk-free rate, which is presented in Exhibit 3.
Exhibit 3. Selected Data on TSI and the Risk-Free Rate
The price per share of TSI’s common shares is $245.
The risk-free rate is 0.325% (quoted on an annual compounding basis).
TSI recently announced its regular semiannual dividend of $1.50 per share that will be paid exactly three months before contract expiration.
The market price of the TSI equity forward contract is equal to the no-arbitrage forward price.
The most appropriate response to Troubadour’s supervisor’s question regarding the TSI forward contract is:
a decrease in TSI’s share price, all else equal.
an increase in the risk-free rate, all else equal
a decrease in the market price of the forward contract, all else equal.
B is correct. From the perspective of the long position, the forward value is equal to the present value of the difference in forward prices:
Vt(T) = PVt,T[Ft(T) – F0(T)],
where Ft(T) = FVt,T(St + θt – γt).
All else equal, an increase in the risk-free rate before contract expiration would cause the forward price, Ft(T), to increase. This increase in the forward price would cause the value of the TSI forward contract, from the perspective of the short, to decrease. Therefore, an increase in the risk-free rate would lead to a loss on the short position in the TSI forward contract.