Convenience Yield

Among the most important concepts of the “Theory of Storage” (see last week’s Weekly Commodities) is the “convenience yield”.

Kaldor (1939) and Working (1948,1949) define the notion of convenience yield as a benefit that “accrues to the owner of the physical commodity but not to the holder of a forward contract.” Note that in the same spirit, the dividend yield is paid to the owner of a stock but not the holder of a derivative contract written on the stock. Brennan (1958) and Telser (1958) view the convenience yield as an “embedded timing option attached to the commodity” since inventory (e.g., a sugar storage facility) allows us to put the commodity on the on the commodity on the market when prices are high and hold it when prices are low. It also avoids the cost of
manufacturing disruption or the nuisance of revisions of the production schedule.

A substantial amount of recent research on commodities has chosen to model the convenience yield as a random quantity, allowing explanation of the various shapes of forward curves observed over time. Some authors (e.g., Gibson and Schwartz, 1990) view the convenience yield as an exogenous random variable. In contrast, Routledge et al. (2000) propose an equilibrium model for storable commodities in which the convenience yield appears as an inventory-dependent endogenous variable and allows one to make predictions about the volatilities of forward prices at different horizons.

Given the importance of the inventory levels to determine the “convenience yield”, in the future we will analyse the relationship of inventory and commodity spot price volatility.


Spot Forward Relationship for a storable commodity
f T (t) = S(t)e(r− y)(T −t )
Spot Forward Relationship for a dividend-paying stock
FT (t) = S(t)e(r−g )(T −t )
where:
f T (t) = Commodity Forward price;
FT (t) = Stock Forward Price;
S(t) = Commodity Spot Price / Stock Price;
r = Interest Rate;
g = Dividend Yield;
y = Convenience Yield;
r = Maturity;
t = Today;