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If we look from carry stand point, should we go long the Mar contract instead of shorting it to clip the backwardated yield?
Normally yes (backwardated futures curve so carry is positive) but in this case the Mar future also trades at a premium to spot. Normally Spot < Mar < May, if backwardated May < Mar < Spot, but here we have Spot < May < Mar
Ah I did miss out the spot. If I recall correctly, the front month contract is treated as "spot" in commodity carry factor, but with actual spot then the picture is different as you said.
Yes, commodity carry strategies generally use front month minus far month (in academia anyway -- in practice you need to do much more to make it useful -- e.g. at minimum account for seasonality in the futures curve)
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