However, it may also be shown that, in some scenarios, should a user of seasonal forecasts be able to apply a partial hedge with weather drivatives, the forecasts only need to be MARGINALLY better than climatology if benefit is to be realised from them.
It is the purpose of the paper to demonstrate this concept, which is not intuitive.
Let us take the example of a three-category seasonal rainfall forecast - below normal, normal, above normal.
Suppose the strategy is to plant a drought resistant crop (sensitive to rain), should below normal be forecast, with the financial outcomes of +$300,000 (below observed), +$150,000 (normal observed), and -$150,000 (above observed).
Suppose the strategy is to plant a moderate yielding crop should normal be forecast, with the financial outcomes of +$80,000 (below observed), +$200,000 (normal observed), and +$80,000 (above observed).
Suppose the strategy is to plant a high yielding crop (sensitive to drought) should above normal be forecast, with the financial outcomes of -$150,000 (below observed), +$150,000 (normal observed), and +$300,000 (above observed).
This suggests an outcome of $120,000 under the assumption of climatology (normal):
(($80,000+$200,000+$80,000)/3).
Suppose the matrix table forecast/observed suggests marginal skill thus:
...Forecast..........Below..........Normal..........Above
Observed
Below.................12%............11%.............10%
Normal................11%............12%.............11%
Above.................10%............11%.............12%
This suggests a slightly reduced outcome of only $116,600:
($300,000x0.12)+($80,000x0.11)+(-$150,000x0.10)+($150,000x0.11)+($200,000x0.12)+($150,000x0.11)+(-$150,000x0.10)+($80,000x0.11)+($300,000x0.12).
Suppose the matrix table forecast/observed suggests substantial skill thus:
...Forecast..........Below..........Normal..........Above
Observed
Below.................18%............11%.............4%
Normal................8%.............18%.............8%
Above.................4%.............11%.............18%
This suggests a much increased outcome of $173,600:
($300,000x0.18)+($150,000x0.08)+(-$150,000x0.04)+($80,000x0.11)+($200,000x0.18)+($80,000x0.11)+(-$150,000x0.04)+($150,000x0.08)+($300,000x0.18).
The ACTUAL matrix table forecast/observed for the CENTRAL Victorian city of Melbourne suggests SUBSTANTIAL skill over the period forecasts have been provided (1988-2003) thus:
...Forecast..........Below..........Normal..........Above
Observed
Below.................15.8%.........17.7%............6.8%
Normal................6.8%..........25.9%............4.5%
Above.................1.5%..........17.7%............6.4%
Under the above scenario, once again an outcome of $120,000 is suggested under the assumption of climatology (normal):
(($80,000+$200,000+$80,000)/3).
Using the ACTUAL forecasts, a greatly increased outcome of $151,220 is suggested:
($300,000x0.158)+($150,000x0.068)+(-$150,000x0.015)+($80,000x0.177)+($200,000x0.259)+($80,000x0.177)+(-$150,000x0.068)+($150,000x0.045)+($300,000x0.064).
The ACTUAL matrix table forecast/observed for the NW Victorian town of Mildura suggests skill, albeit MARGINAL, over the period forecasts have been provided (1988-2003) thus:
...Forecast..........Below..........Normal..........Above
Observed
Below.................10.9%..........17.4%...........8.0%
Normal................6.2%...........17.8%...........9.4%
Above.................5.8%...........17.8%...........6.9%
Under the above scenario, once again an outcome of $120,000 is suggested under the assumption of climatology (normal):
(($80,000+$200,000+$80,000)/3).
However, using the ACTUAL forecasts, a very slightly reduced outcome of $119,860 is suggested:
($300,000x0.109)+($150,000x0.062)+(-$150,000x0.058)+($80,000x0.174)+($200,000x0.178)+($80,000x0.178)+(-$150,000x0.080)+($150,000x0.094)+($300,000x0.069).
Suppose now that a weather derivative is written that pays $60,000 every time above normal rainfall is observed ('fair value' price=$20,000), and that a weather derivative is purchased that pays $60,000 every time below normal rainfall is observed ('fair value' price=$20,000), and this combination is only entered into whenever below normal rainfall is forecast. The outcome is now adjusted upwards to $121,820 thus:
($340,000x0.109)+($130,000x0.062)+(-$170,000x0.058)+($80,000x0.174)+($200,000x0.178)+($80,000x0.178)+(-$150,000x0.080)+($150,000x0.094)+($300,000x0.069).
The component of forecast skill that is being realised here is that related to the prediction of below normal rainfall. When such a forecast is made (22.9% of all cases), nearly half of them, 10.9%, are correct. A randomly generated forecast would only have been correct on one-third of occasions.
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