CFAI EOC Reading 39 (Pricing and Valuation of Forward Commitments) Question 7: The question is based on these two exhibits:
Exhibit 1 (selected information for TSI):
- The price per share of TSI’s common shares is $250.
- The forward price per share for a nine-month TSI equity forward contract is $250.562289.
- Assume annual compounding.
Exhibit 2 (3 month after contract initiation):
- The price per share of TSI’s common shares is $245.
- The risk-free rate is 0.325% (quoted on an annual compounding basis).
- TSI recently announced its regular semiannual dividend of $1.50 per share that will be paid exactly three months before contract expiration.
- The market price of the TSI equity forward contract is equal to the no-arbitrage forward price
The question is asking for the value of the short position 3 months after contract initiation. The answer should be pretty straight forward (no pun intended) but I’m getting tripped up in the last part. To make it simple, let’s say the contract was initially entered into on Jan 1. We have to find its value to the short holder on April 1 for the contract expiring on Oct 1. The dividend is payable on July 1 so discounting that for 3 months @ 0.325% gives us a div value of 1.4987 on April 1st. That means the no-arbitrage price of this “new” forward is 243.89 (245+1.4987 looking ahead 6 months on Oct 1 at 0.325%). The value to the short holder (since the price has fallen) = 250.56 – 243.89 = 6.67. This really should be the answer and it is but in the solution explanation, they take this number forward another six months at the 0.325% rate. It makes very little difference to the final answer but I’m scratching my head why they did this.