confusing q on valuing forward rate contracts in the derivatives practice.

CFA Level II
#1

Parisi proceeds to review an equity forward contract held by Quantum. The contract was initiated thirty days ago when the fund expected a large inflow of cash in 60 days. In order to hedge against a potential rise in equity values over this period, Quantum entered into a long forward contract on the UAX 300 Index expiring in 60 days. Sheroda tells Parisi that she estimates the current price of this contract to be USD 1457.38. Parisi collects the information in Exhibit 1 for his review.

Exhibit 1

Selected Financial Information for UAX 300 Forward Contract

Price of a 60-day UAX 300 forward contract 30 days ago USD1403.22 UAX 300 Index level today USD1450.82 Annualized continuously compounded risk-free rate 3.92% Annualized continuously compounded dividend yield for UAX 300 2.50%

q: Based on the data in Exhibit 1, and given Sheroda’s value of the UAX 300 forward contract, the arbitrage profit is most likely to be:

  1. greater than zero.
  2. less than zero.
  3. zero.

answer is 1 which is fine. I dont understand the explanation though.

" The forward contract on the UAX 300 was entered into 30 days ago at a price of 1,403.22. Currently, with 30 days remaining on the contract the value is

F0(T) = S0e(rc−g)T = 1450.82_e_(0.0392 − 0.025)(30/360) = 1,452.54. An arbitrageur would sell the futures contract, buy the underlying, and earn a risk-free profit of 4.84." why are we using the current price of the forward contract of 1457? what happened to the 1403 that we entered into at inception? that’s what we will need to base our arbitrage profits on right? usually the questions say the spot price has changed and the compute the value to long/short. here its the forward price. can someone pls clarify whats going on here?

#2

The problem with the question is that the position the “we” already entered into has zero relevance. You can rephrase the question to “Given the price of the futures contract today, the spot price of UAX 300, and the interest rates in Ex. 1 the arbitrage profit is: …”.

Aside: Doing arbitrage with past prices would be a nice ability to have :slight_smile: