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The recent expiration of the Oct NG contract provided an opportunity to revisit analysis of the Oct-Jan spread.
Background
This spread is calculated (as all NG spreads are) based on the nearer price minus the further price.  For example on the last day the October contract traded this year (September 28), the prices were $3.837 and$4.342, so the spread settled at -\$0.505.
Winter NG trades at a premium to summer due to the scarcity value of gas during the peak space heating season.  Gas is accumulated during the summer in seasonal storage which is depleted during winter.  This pattern is fairly predictable for a given weather forecast; a cold vs. warm winter has a significant impact on end of season inventory.  More about gas storage can be found here:
http://www.eia.doe.gov/pub/oil_gas/natural_gas/analysis_publications/storagebasics/storagebasics.html
What is interesting about Oct-Jan is that it provides a metric for this economic “scarcity rent” earned by storage in anticipation of the winter to come.  As winter approaches it provides a way of comparing gas here and now with gas at the time of peak usage (and presumably maximum rate of withdrawal from inventory).
As such it would seem intuitive that this premium was higher in years when storage was running below average and lower in years when storage is running above average.  For example if storage is filling earlier than usual, or at least is above the same level as this time last year, one might expect that winter gas will trade at less of a premium.
One problem with looking at this analysis across several years is that the outright level of gas prices has varied widely.  One approach this problem is to consider the spread in terms of its percentage premium to the October price itself.  Continuing the numerical example above, the spread settled at -.505/3.837 or 13%.  (For simplicity of discussion consider the negative of the premium.) In this way we can normalize the premium to the outright price level.

Premium vs storage level across time
If we consider the current level of storage compared with the same time last year, we get a rough metric for seasonally adjusted storage, and presumably market sentiment as to the scarcity rent that should be earned by gas supplied at times of peak demand.

Although it is difficult to see much of a pattern there is one clear message.  Greater levels of positive storage seem to be associated with greater premiums rather than the reverse as expected.  The correlation here is 0.51, so reasonably significant.
However it is possible that this is a “within year” effect.   Maybe with each year the spread moves in a way that is negatively correlated with storage, but from one year to the next we observe a positive relationship.
Although it is of questionable academic accuracy the following chart shows the average storage deviation from the prior year with the average spread premium.

This correlation is 0.60.  Even ignoring 2005/06 winter due to post Hurricane Katrina market turbulence and 2008/09 due to the credit meltdown / financial crisis, a fitted line still has a significant positive slope.  Every 100 bcf of incremental storage leads to a 1% increase in the premium of the spread over the October price.
Hypotheses
What are some hypotheses that explain this unexpected result?  Why would traders place more of a percentage premium on winter gas in years when storage is at a higher level?
·         Anchoring: winter prices are a constant level; therefore storage excess must show up in a depressed spot / current price.
·         Seasonal elasticity of demand: buyers in winter know their options are limited, whereas at other times of the year buyers can use the inventory level to drive a harder bargain
·         Regional storage / national price: when regional storage has filled early, basis markets become offered as there is less capacity in regional markets to store.  This basis softening flows “upstream” to Henry Hub depressing spot & prompt markets while leaving winter prices unchanged.
Whatever the reason, this counter intuitive phenomenon does help explain why calendar spread trading can be a “Bermuda Triangle” for natural gas traders.