Suppose a forward contract that expires in one year is available on an asset that is currently worth $100 and the risk-free rate is 4%, the forward price is 100x1.04 = 104. It is now nine months later, and the asset is worth $101.50. The value to the long and amount of the credit risk is_______

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BlackTom AI · Accepted Answer

We start by restating the given setup and the current situation to ensure clarity. The original forward contract is for one year with a delivery price K = 104, based on the asset's value at t = 0 of 100 and a risk-free rate r = 4% per year. Now, nine months have passed (T = 0.75 years elapsed, so T_remaining = 0.25 years). The current spot price is S_t = 101.50. The forward contract will mature in 0.25 years, so we need the value of the forward to the long at this moment.

Key formula: the value of a long forward with delivery price K at time t with remaining maturity T_r is
V_t = S_t − K × (1 + r)^{-T_r}  (using a simple discounting convention consistent with the problem’s prior 104 = 100 × 1.04)
This mirrors the idea that the present value of paying K at maturity is K discounted back to time t, and the current value of the asset is S_t.

Step through each option:
- Option 1: D. -$2.5000. This would imply a much larger discount factor effect or a different discounting regime. If we plug numbers into the formula, the discrepancy is substantial: the actual present value of paying 104 at maturity is only mildly less than 104, given T_r = 0.25 and r ≈ 4%, so a value around −2.5 is not supported by the math here.
- Option 2: A. -$1.4852. This is a negative value close to zero, which aligns with the intuition that the long is underwater because the current spot (101.50) is below the present value of paying 104 at maturity, discounted over 0.25 years at around 4%. Calculating precisely with the given discounting convention: discount factor = (1 + r)^{−T_r} = (1.04)^{−0.25} ≈ 0.99023; present value of the strike = 104 × 0.99023 ≈ 102.98; thus V_t ≈ 101.50 − 102.98 ≈ −1.48, matching this option’s magnitude.
- Option 3: C. $2.5000. A positive value of this magnitude would require the strike to be worth less in present value terms than the current price by a margin that is not supported by the computed discounting, given the 0.25-year horizon and 4% rate. Hence this option misrepresents the sign and the magnitude.
- Option 4: B. $1.4852. This is the positive counterpart of the correct magnitude. Since the actual value computed is negative (the long would incur a loss given the current S_t and the discounted strike), this option incorrectly flips the sign.

A key point in this scenario is recognizing that the value of the forward to the long is the current spot minus the present value of the forward price (strike) at the remaining horizon. Because 101.50 is less than the discounted strike (approximately 102.98), the result is a negative value for the long position, on the order of around −1.48. The small difference between continuous vs. discrete compounding changes the third or fourth decimal place, but the overall sign and approximate magnitude remain consistent with option A.

Putting it together, the reasoning shows that the long position is underwater by roughly one and a half dollars, not a gain, and among the listed choices the one with the negative sign and magnitude near 1.4852 best matches the calculation. The other options either exaggerate the loss, produce a positive (incorrect) value, or differ in sign due to an incorrect interpretation of the discounting or payoff structure.

BU.232.750.81.FA25 Final Exam Fall 2025- Requires Respondus LockDown Browser

Suppose a forward contract that expires in one year is available on an asset that is currently worth $100 and the risk-free rate is 4%, the forward price is 100x1.04 = 104. It is now nine months later, and the asset is worth $101.50. The value to the long and amount of the credit risk is_______

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