Question

Suppose the spot rate and the 90-days forward rate on the South African rand are 16.3958 and 16.5488 respectively, answer the following requirements. Is the rand at a forward discount or premium on the dollar? What is the annual percentage discount or premium on rand? The 1-year forward rate on the South African rand is 16.9753. Note: Enter your answer as a positive value. Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places. If you have no other information about the two currencies, what is your best guess about the spot rate on the rand three months hence?

Answer 1

The South African rand is at a forward premium against the US dollar, with the annual percentage premium calculated to be 3.79%. Without further information, one might guess the spot rate in three months to be close to the forward rate.

Step-by-step explanation:

The question pertains to whether the South African rand is at a forward discount or premium in relation to the US dollar, as well as how to calculate the annual percentage discount or premium on the rand. To determine this, one can compare the spot rate of 16.3958 and the 90-day forward rate of 16.5488. Since the forward rate is higher than the spot rate, the rand is trading at a forward premium against the dollar. To calculate the annualized premium:

1. Find the difference between the forward and spot rates (16.5488 - 16.3958 = 0.153).
2. Divide the difference by the spot rate to get the premium for the period (0.153 / 16.3958 = 0.009328).
3. Since it's for 90 days, multiply by the number of 90 day periods in a year to annualize (0.009328 * (365 / 90) = 0.03788).
4. Convert to percentage by multiplying by 100 (0.03788 * 100 = 3.79%).

Thereby, the annual percentage premium on the rand is 3.79%. Regarding the future spot rate, without additional information, it's challenging to forecast accurately, but one might speculate it could be near the forward rate given market expectations.