Assume that Patton Co. will receive 100,000 New Zealand dollars (NZ$) in 180 days. Today's spot rate of the NZ$ is $.50, and the 180-day forward rate is $.51. A call option on NZ$ exists, with an exercise price of $.52, a premium of $.02, and a 180-day expiration date. A put option on NZ$ exists with an exercise price of $.51, a premium of $.02, and a 180-day expiration date. Patton Co. has developed the following probability distribution for the spot rate in 180 days:
$$\begin{array}{l}
\text { Passible spot Fate }\
\begin{array} { c c }
\text { in 90 Days } & \text { Probraility } \
\$ 48 & 10 \% \
\$ 49 & 60 \% \
\$.55 & 30 \%
\end{array}
\end{array}$$
The probability that the forward hedge will result in more U.S. dollars received than the options hedge is ____ (deduct the amount paid for the premium when estimating the U.S. dollars received on the options hedge).

Question

Assume that Patton Co. will receive 100,000 New Zealand dollars (NZ$) in 180 days. Today's spot rate of the NZ$ is $.50, and the 180-day forward rate is $.51. A call option on NZ$ exists, with an exercise price of $.52, a premium of $.02, and a 180-day expiration date. A put option on NZ$ exists with an exercise price of $.51, a premium of $.02, and a 180-day expiration date. Patton Co. has developed the following probability distribution for the spot rate in 180 days:
$$\begin{array}{l}
\text { Passible spot Fate }\
\begin{array} { c c } 
\text { in 90 Days } & \text { Probraility } \
\$ 48 & 10 \% \
\$ 49 & 60 \% \
\$.55 & 30 \%
\end{array}
\end{array}$$
The probability that the forward hedge will result in more U.S. dollars received than the options hedge is ____ (deduct the amount paid for the premium when estimating the U.S. dollars received on the options hedge).

Quizplus · Accepted Answer

The forward hedge guarantees a rate of $.51, while the call option is only beneficial if the spot rate exceeds $.52. Given the probabilities, the spot rate is expected to be $.48 or $.49 (70% probability), both below the call option's exercise price, making the forward hedge more favorable in these scenarios.

Assume That Patton Co The Probability That the Forward Hedge Will Result in More