Question

Suppose It is the starting date of the current quarter now. There is a 6-month futures contract on copper. The copper’s spot price now is $2.90/pound. The storage cost for copper is 0.36/per pound annually. The storage cost is paid at end of each quarter. The copper does not provide income. However, the copper may provide some benefits to the owner if the copper is held as a consumption asset. The risk-free interest rate is 3% per annum with continuously compounding.

(a) What is the copper’s futures price if we assume the copper is an investment asset?

(b) What is the upper bound of the copper’s futures price if we assume the copper is a consumption asset.

Answer 1

Knowledge required:

Investment asset is an asset held primarily for investment by a significant number of investors, while a consumption asset is one held primarily for consumption.

Convenience yeild is th income that can be generated from asset by holding it for consumption.

Interest on continuous compunding = e^(r*t)

Case 1: Investment asset

Futures Price = Sport rate + Interest saved + storage cost saved

= 2.90 + 2.90*(e)^3*0.5 + 0.36

= 2.90 + 2.90*4.482 + 0.36

= 16.26 pound

Case 2: Consumption asset

Futures Price = Sport rate + Interest saved + storage cost saved - convenience yield

= 2.90 + 2.90*(e)^3*0.5 + 0.36 - Convenience yield

= 2.90 + 2.90*4.482 + 0.36 - Convenience yield

= 16.26 pound - Convenience yield

More the convenience yeild lesser will be futures price.