Question

Suppose the futures price is $2.00, and spot price is $1.90. The interest rate is 3%, and cost of the storage is 1%. The future contract matures in 9 months. Calculate the convenience yield. Explain the possible reasons behind the calculated convenience yield.

Answer 1

The no-arbitrage condition of derivatives pricing links the current spot price, futures price, risk-free interest rate, storage cost and convenience yield through the following relationship:

Future Price = Spot Price x [1+Risk-Free Interest Rate + Storage Cost - Convenience Yield]^(T) where T is the time to maturity

Future Price = $ 2, Current Spot Price = $ 1.9, Storage Cost = 1 %. Risk-Free Interest Rate = 3 % and let the convenience yield be k. Tenure = 9 months or 0.75 years

Therefore, 2 = 1.9 x (1+0.03+0.01-k)^(0.75)

(1.04-k) = (2/1.9)^(1/0.75) = 1.070784

k = 1.04 - 1.070784 = - 0.03078 ~ - 0.031 or - 3.1 %

The convenience yield as the name suggests is the value of the benefit(s) accruing to the holders of the underlying asset, owing to the holder physically possessing the asset. This could be either due to the asset(s) possessing consumption quality or being highly coveted (such as gold). However, if the supply of the underlying asset is plentiful such that its physical possession adds no benefits and instead adds to the holder's costs, the convenience yield for the asset becomes negative which simply implies that holding the asset provided Negative benefits (a loss actually).