Literally – or at least mathematically – there are two equations that tell the tale of interest rate impacts on commodities.

As my colleagues Fei Mei Chan and Craig Lazzara pointed out in a recent paper they authored, Much Ado About Interest Rates, “Since yields peaked in 1981, the three subsequent decades have witnessed a remarkable bull market for bonds. The yield of the 10-year Treasury bond fell from more than 15% in 1981 to its current level of less than 3%. *With interest rates at historically low levels, investors* might* reasonably assume that it’s not a matter of if but a question of when rates will increase.* ”

**10-Year Treasury Yield from 1953-2013 **

I’m not in the position to answer the question of when interest rates will rise but can explain how rising interest rates factor into the equations of commodity pricing and index returns.

The most direct and measurable impact of interest rates on commodities can be observed from the formal relationship between spot and futures prices, as defined by the theory of storage equation which can be written as:

*F _{0,T}* =

*S*exp[(

_{0 }*r+c-y*)

*T*]

Where:

* F0,T*= the futures price today for delivery at time T;*S0* = the spot price today;*r* = the riskless interest rate, expressed in continuous time;*c* = the cost of physical storage per unit time, expressed in continuous time;*y* = the convenience yield, expressed in continuous time.

This equation is often used to explain the futures price in terms of the spot price, the interest rate, the cost of storage and the convenience yield as discussed by Gunzberg and Kaplan (2007).

Although the interest rate and cost of storage are straightforward, the convenience yield is more complex. It’s defined by the flow of benefits to inventory holders from a marginal unit of inventory. Generally, inventory levels have an inverse relationship with convenience yield. This means that there is a low convenience yield when inventories are high. However, as inventory levels fall, the convenience yield increases at an accelerated pace as inventories are depleted.