Spatial Aggregation and Weather Risk Management

due to the presence of strong non-linear temperature effects. The superior performance
of options, which is illustrated in Figure 2, is consistent across risk measures. For
example, in Table 2 the “State (Aggregated)” portfolio reduction in RMSL (change in ES
6%) was 43.31% ($59.91) when hedging with options compared to 31.88% ($46.37)
when hedging with swaps.

Next, we turn attention to investigation of the spatial aggregation effect. The
unhedged portfolio results for the full-sample (Table 2) show that the RMSL (ES 6% and
9%) is (are) lower (higher) for the “State (Aggregated)” portfolio, $39.80 ($235.38 and
$255.18), than for the “Average of Districts” portfolio, $45.42 ($221.48 and $235.55).
This result implies that yield risk “self diversifies” to some extent in the aggregate
portfolio.

The comparison of unhedged portfolios, however, does not allow us to determine
whether WD hedging will be more effective at larger levels of aggregation. For this we
must turn attention to the hedged portfolios. We restrict attention to portfolios hedged
with options for the remainder of the discussion. The results from the swap hedging
analysis, however, lead to similar conclusions.

All estimates of hedging effectiveness support the aggregation argument.
Reduction in the RMSL for the “State (Aggregated)” portfolio for the full sample,
43.31%, was greater than for the average of the districts, 28.93%, an improvement in
hedging effectiveness of approximately 50% over what is implied by separate evaluation
of the individual districts on average. The intuition behind this result is that the weather
effects are strongly correlated across the districts while the other effects are relatively less
correlated. Thus, the aggregated exposure is highly systemic and a substantial portion of

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