There are two ways to acquire an asset for use in the future.

• First, the asset could be purchased at the spot price today and stored until it is needed.
• Second, a long position in futures could be established today and funds could be set aside in an interest-bearing account to acquire the asset in the future.
• The two strategies must have the same costs.

F₀(T) = S₀(1 + r)T

The risk-free rate provides a fundamental link between spot and forward prices for underlying assets with no additional costs or benefits of ownership.

Few assets have interim cash flows like dividends and coupon payments. These benefits are called the monetary benefits. We can have non-monetary benefits with some assets as well especially with commodities. Those benefits are generally referred to as convenience yield. The non-monetary benefits are generally opaque and difficult to measure. Financial assets have nonexistent or extremely limited convenience yield. Commodities have convenience yield. If a commodity is in short supply or it is extremely difficult to short the commodity, then it is likely to have a higher convenience yield because by owning the asset, you have the flexibility to sell it when the price rises. Because of the convenience yield, the spot price of a commodity could be even higher than the expected future spot price.

The costs for holding the asset primarily include storage cost and the opportunity cost of the money invested. The commodities like gold, oil, and wheat incur storage cost. There are other costs as well such as insurance cost to protect commodities from theft and destruction.

When we include costs and benefits of holding an asset, then we need to include that in the pricing as well. We incorporate the effects of these costs and benefits by determining their value at the end of the holding period with the exception of the opportunity cost. We assume that these costs and benefits are certain unlike the price of the asset and discount these costs and benefits with the risk-free rate to get the present value. The costs reduce the current price, and the benefits increase the current price. The net of the costs and benefits is referred to as the term carry or cost of carry.

Denoting θ as the present value of the costs and γ as the present value of the benefits, we can calculate the spot price of an asset using the formula: S₀ = E(S_T)/(1 + r)^T - θ + γ.

Consider a forward contract on a 4-year bond with 1 year maturity. The current value of the bond is $1018.86. It has a face value of $1000 and a coupon rate of 10% per annum. A coupon has just been paid on the bond and further coupons will be paid after 6 months and after 1 year, just prior to delivery. Interest rates for 1 year out are flat at 8%. Compute the forward price of the bond.

F = 1018.86 x 1.04² - 50 x 1.04 - 50 = $1,000