Monetary and Nonmonetary Benefits Affecting the Value and Price of a Forward Contract

The value and price of forward contracts are affected by the benefits and costs of holding its underlying asset. Carrying costs and opportunity costs can affect the value of holding the asset, and it is sometimes beneficial to hold the physical asset underlying the contract rather than the forward contract itself.

Opportunity Cost

Opportunity cost is important to consider when investing in a forward contract. Opportunity cost is simply the loss or potential gain from other alternatives when one alternative is already chosen. Fortunately, this effect is most likely included in the present value calculation.

Carrying Cost

Carrying costs, or storage costs, is another cost to consider when investing in an asset. There are costs associated with physically holding the asset, insurance costs, etc.

If the storage costs are taken into account, the forward price must equal the spot price compounded over the life of the forward contract at the given risk-free rate, plus the future value of the storage costs over the life of the contract. The avoidance of the storage costs is essentially a benefit to transacting via a futures contract rather than purchasing the underlying asset upfront.

$$ F_0 (T)=S_0 (1+r)^T+FV(SC,0,T) $$

Where \(FV(SC, 0, T)\) is the value at time \(T\) (expiration) of the storage costs.

It is assumed that the costs associated with storage are known when the storage is initiated. Therefore, the final value of the contract is simply the price of the underlying today discount back to the present plus the costs associated with holding the asset.

Convenience Yield

The main non-monetary benefit of holding the underlying asset is referred to as the convenience yield. The convenience yield is defined as the benefit of holding the physical product, rather than a contract or derivative product. Sometimes, holding the physical underlying good rather than a contract is more beneficial. An example of this would be holding actual barrels of oil rather than a forward contract. Should there be a sudden oil shortage, the demand for oil increases, and the difference between the price you paid for the oil and the current price after the proclaimed shortage would be your convenience yield.

Question

What will the forward price be if a barrel of oil is currently priced at $50, has an interest rate of 3.5%, expires in 10 months, and has a future value cost of $1.72 for storage?

A. $42.17

B. $53.03

C. $53.17

Solution

The correct answer is C.

F₀ = S₀(1 + r)^T + FV(SC, 0, T)

F_o = $50(1 +.035)^(10/12) + $1.72 = $53.17