# P1.T3.22.19 Value of a forward contract

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Learning objectives: Distinguish between the forward price and the value of a forward contract. Calculate the value of a forward contract on a financial asset that does or does not provide income or yield. Explain the relationship between forward and futures prices. Calculate the value of a stock index futures contract and explain the concept of index arbitrage.

Questions:

22.19.1. Three months ago Sally entered into a one-year forward contract to buy a non-dividend-paying stock when the stock price was $30.00 and the risk-free rate was 3.0% per annum with annual compounding. In the meantime, although the risk-free rate has not changed, the underlying stock price has increased to$35.00. Which of the following is nearest to the change in the value of her forward contract?

a. -$4.96 b. +$4.78
c. +\$5.00
d. No change

22.19.2. In regard to a popular underlying asset, Peter's firm has a choice to enter into either a futures or forward contract. The contract specifications are similar. Both are long-term contracts; i.e., the maturity is greater than one year. The first version of Peter's pricing model is basic: it assumes the short-term interest rate is constant and it omits several technical factors.

For a revision to his model, he considers adding each of the following features or factors to the model (based on realistic differences between the contracts):

I. The forward contract is less liquid than the futures contract
II. The forward contract has greater counterparty risk than the futures contract
III. The underlying asset price is negatively correlated with stochastic interest rates

Which of these revisions, ceteris paribus and relative to the futures contract price, is likely to INCREASE the model's price for the forward contract?

a. I. only (the forward contract is less liquid)
b. II. only (the forward contract has greater counterparty risk)
c. III. only (the asset is negatively correlated with interest rates)
d. All three have a tendency to increase the price of the forward contract

22.19.3. The current level of a stock index is 7,790 while the risk-free rate is 4.0% per annum with annual compounding. The dividend yield assumption is 1.50% with continuous compounding. We can observe that the nine-month futures contract is currently trading at a price of 8,000. If an index arbitrage is possible, what is the index arbitrage trade?

a. Buy the underlying stocks and short the futures contract
b. Sell the underlying stocks and buy the futures contract
c. Cannot figure because compound frequencies differ
d. The implied reverse cash-and-carry may not be possible if the ease lease rate on the borrowed stocks exceeds the risk-free rate