R51 Forward Markets

CFA Level II Derivatives
#1

Q1) When valuing currency forward contract prior to expiration, does anyone understand theoretically why the “Spot Rate” is divided by the rate of the foreign currency and the “forward rate” is divided by the rate of the domestic currency?

Not sure why the value of the forward contract at expiration is spot rate * e ^ (rate of domestic - rate of foreign) either. (basically don’t understand when to use foreign vs. domestic currency).

Q2) I thought that when the spot rate increases when in a long position, the value of the long position is always positive. However, this does not seem to be the case in the example below:

Q2 part I: You want to purchase a security in 9 months that is currenty worth $95. you enter into a long position on a forward contract on the security that expires in 9 months. the risk free rate is 4%. Given that 5 months into the term of the contract, the spot price is $96. The value of the long position is

V = $96 - PV of forward contract of $97.84 divided by 1.04 ^ (4/12) = -$0.57

How could the value of the long position be down when the spot price went up from 95 to 96?

Q2a) Now, if at contract maturity the spot price is $100, the overall gain or loss on the entire transaction (spot and forward combined is:

  • I thought it should be $100 - original forward price of 97.84. However, the answer subtract by 5 (as spot rate went from 95 to 100), and the actual answer is -2.84. The asset was never purchased, so how could it be a “loss position.”

Thank you for your help.

#2

Where is this question from?

on q2, just because the spot price went up doesn’t mean the long position makes money. As per the formula, the value of St must exceed the PV of the forward price for the long to have positive value. Without reading the question, I’m not sure what’s going on with the second part.

On q1, this is basically covered interest rate parity, which says the two risk free rates must provide the same return. So if you adjust that formula to bring 1+rf to one side you will see it equals the spot price times the domestic risk free rate divided by the forward rate. This is basically saying the foreign return must be equal to the domestic return (S times 1 + rd) converted back to the foreign currency (divided by F).