hard · FRM Part 1 Financial Markets and Products
A trader holds a long position in a 6-month gold forward contract entered at the old forward price F_0. Gold has a known continuously-compounded lease rate (convenience-like income) of y and storage costs are zero. Three months later, the spot price is unchanged but the risk-free rate r has fallen sharply while the lease rate y is unchanged, leaving r<y.
Ignoring counterparty effects, what has happened to the mark-to-market value of the trader's existing long forward, and why?
- It has decreased, because the new 3-month forward price has fallen below F_0 now that the cost-of-carry term r-y has turned negative, making the contracted price unfavorable.
- It has increased, because a lower r raises the present value of the favorable payoff locked in at the higher original forward price F_0.
- It is unchanged, because the spot price did not move and the forward value depends only on the spot relative to the contracted delivery price.
- It has decreased, because the lower discount rate raises the present value of the delivery price the long must pay at maturity, increasing the effective cost of the position.
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