Spatial Aggregation and Weather Risk Management

misspecifying weather hedges that involve multiple underlying indexes. The current
work simplifies the analysis by investigating seasonal (June, July, and August)
temperature WDs.

Conceptual Model

Idiosyncratic effects may self-diversify when aggregated, leaving a greater proportion of
the total risk in the form of weather risk. Thus, WD hedging may be more effective for
aggregate rather than disaggregate yield exposures. The magnitude of the spatial
aggregation effect depends on the relative correlations of weather and idiosyncratic yield
effects across locations. To illustrate, assume yields can be decomposed into two effects,
weather effects, W, and all other effects,ε , which may be correlated. Consider a simple
model of crop yields which allows for non-linear terms

(1)                             Y_tk=α_k+f_k(W_tk)+ε_tk

t,k        k k       t,k         t,k

where t is the time index, k is the location index, W_t,k is a vector of weather variables,
f_k(W_t,k) represents the systemic weather component of yields, ε_t,k represents the
idiosyncratic risk component, and E[ε_t,k]= 0. Summing across k locations, gives
(2)                     E[∑Yt,k]=∑αk+E[∑fk(Wt,k)]+E[∑εt,k]

kk   k     k

and

(3)           Var[∑Yt,k]=Var[∑ fk(Wt,k)]+Var[∑εt,k]+Cov[∑ fk(Wt,k),∑εt,k].

kk  kkk

If the ε_t,k's are relatively less positively correlated than the f_k(W_t,k)'s across locations
then, as the individual yields are summed, more variation in yields may be able to be
attributed to the weather effects at larger levels of spatial aggregation. Thus, WD

<<   5   6   7   8   9   10   11   >>

More intriguing information