Topic 4: Incorporating attitudes to risk, Part B
Shauna Phillips
School of Economics
Copyright By PowCoder代写 加微信 powcoder
AREC3005 Agricultural Finance & Risk
, file photo: Reuters, file photo
Dr Shauna Phillips (Unit Coordinator) Phone: 93517892
R479 Merewether Building
COMMONWEALTH OF AUSTRALIA Copyright Regulations 1969 WARNING
This material has been reproduced and communicated to
you by or on behalf of the University of Sydney
pursuant to Part VB of the Copyright Act 1968 (the Act).
The material in this communication may be subject to copyright under the Act. Any further reproduction or communication of this material by you may be the subjectofcopyright protectionundertheAct.
Do not remove this notice.
Estimating the value of new information [HHA2004, pp.131]
› In earlier lectures, we discussed the method of Bayesian updating, where we calculated posterior probabilities
– In our example, we looked at the dairy farmer, who was given the option to purchase from some agency a forecast on the likelihood of a disease outbreak
Estimating the value of new information [HHA2004, pp.131]
› Now, let’s try to estimate the value of the agency forecast information to the farmer
– The agency provides the forecast at an annual cost of $3000
– The farmer will be willing to pay for the forecast if their expected utility with the
information is greater than the expected utility without the information – Recall: z1 (unlikely), z2 (possible), z3 (likely)
Farmer’s utility
› We will adopt the same utility function as earlier: U =1−e−0.003658w
› So, the section of the tree with the decision not to buy the forecast is the same as the one we calculated earlier:
Payoffs with the forecast
› For each forecast (z1, z2, z3), we have the same set of options: take out insurance, or not
– So, the branches will be the same as above, but we need to subtract the cost of having bought the forecast, which is $3000
Payoff (with forecast)
497.0 0.8377 489.8 0.8333 487.0 0.8316 297.0 0.6626
Payoff (no forecast)
500.0 0.8394 492.8 0.8351 490.0 0.8334 300.0 0.6663
Decision tree representation to ‘buy forecast’ under z1 prediction:
Payoff (with
497.0 0.8377 489.8 0.8333 487.0 0.8316
297.0 0.6626
Decision tree representation to ‘buy forecast’:
Whole decision tree representation:
Rationalising the decision tree
› Work backwards, branch-by-branch…big job
› Step 1: Let’s start with the ‘no-forecast’ branch, where we already know the solution from the previous lecture:
Rationalising the decision tree
› Step 2: ‘Buy forecast’, with prediction z1:
(3) Insure EU = 0.8333 vs. Don’t insure EU = 0.8367
(2) EU = 0.989(0.8377) + 0.011(0.7471) = 0.8367
(1) EU = 0.5(0.8316) + 0.5(0.6626) = 0.7471
Rationalising the decision tree
› Step 3: ‘Buy forecast’, with prediction z2:
(3) Insure EU = 0.8333 vs. Don’t insure EU = 0.8306
(2) EU = 0.922 (0.8377) + 0.078(0.7471) = 0.8306
(1) EU = 0.5(0.8316) + 0.5(0.6626) = 0.7471
Rationalising the decision tree
› Step 4: ‘Buy forecast’, with prediction z3:
(3) Insure EU = 0.8333 vs. Don’t insure EU = 0.8158
(2) EU = 0.758(0.8377) + 0.242(0.7471) = 0.8158
(1) EU = 0.5(0.8316) + 0.5(0.6626) = 0.7471
Rationalising the decision tree
Buy Forecast EU = 0.570(0.8367) + 0.306(0.8333) + 0.124(0.8333)
Buy Forecast EU = 0.8352
EU = 0.8333 EU = 0.8367
EU = 0.8333 EU = 0.8306
EU = 0.8333 EU = 0.8158
Rationalising the decision tree
EU = 0.8352
Buy forecast EU = 0.8352 vs. No forecast EU = 0.8351
EU = 0.8351
Value of forecast?
› We can calculate the certainty equivalents from the expected utilities we have calculated:
ln(1−U*) − 0.003658
w = ln(1−0.8352)= 492.89
buy_ forecast
− 0.003658
wno_forecast =ln(1−0.8351)=492.73 − 0.003658
Value of forecast?
› We have already factored in the cost of the forecast, so, once we purchase the forecast, it adds:
$492.89K – $492.73K = 0.16K
› So, the value after costs is $160
› The implication is that the farmer would be willing to pay up to $160 for the
– Any price for the forecast less than $160 adds to the farmer’s expected value
Application: (Marshall et. al. (1996)
› Various task forces to review policy responses to drought for agriculture (Drought Policy Task Force 1990, Multi Peril Crop Insurance Task Force 2003, National Review of Drought Policy 2008, Agricultural Competitiveness White Paper)
› Over time responsibility has shifted from government towards farmers in terms of self-preparedness for drought events.
› 1992 National Drought Policy stressed the importance of seasonal forecasting as a tool to assist framers to mitigate the consequences of drought. Funds were allocated by the government in NDP to improve forecasts.
› (Marshall et. al. (1996) assess seasonal forecasts of the Southern Oscillation Index (SOI)
› Goondiwindi NE wheat belt
Northern grain belt eastern Australia
Prime hard wheat- price premium
Rainfall variable and summer dominant and limiting
Wheat cropping uses soil water store in Summer fallow prior to wheat crop
High coefficient of variation in wheat yield historically Cultivar choice (effects development) allows some control over flowering date choice of planting time, fertiliser strategy
Representative farm Goondiwindi 2083 ha case study
› SOI measures difference in atmospheric pressure between Tahiti and Darwin. Different phases of SOI are associated with different rainfall and temperature patterns- frequency distributions can be constructed using past history of rainfall and temperature data to generate frequency distributions, to be used as probability distributions for seasonal forecasts.
› “A strongly and consistently positive SOI pattern (e.g. consistently above about +6 over a two month period) is related to a high probability of above the long-term average (median) rainfall for many areas of Australia, especially areas of eastern Australia (including northern Tasmania) – La Niña.
› Conversely, a ‘deep’ and consistently negative SOI pattern (less than about minus 6 over a two month period, with little change over that period) is related to a high probability of below median rainfall for many areas of Australia at certain times of the year – ̃o”. (Farmonline)
Objectives
› EU approach using prior and Bayesian probabilities.
› Calculates the EU of Bayesian strategy (optimal strategy with forecast)
› Calculate the value of the forecast as the difference between the EU based on prior information and the EU of the optimal strategy with forecast.
› Historical climactic frequency distributions used for prior probability distributions.
› Adopt functional form for utility – that assumes constant relative risk aversion unaffected by wealth.
› Embedded risk: Past models assume that outcomes of climatic risk arise after all decisions have been made. But risks are embedded in the decision process, don’t just arise after all decisions are made-need to account for tactical choices as they arise during a growing season as outcomes are revealed. Link to real options (in lectures to come).
Decision problem
› Add marshall et al as an application
Assumed utility
π is measure of financial payoff Rr is constant coefficient of relative risk aversion.
3 mathematical programs (MPs) NB we do not cover this stage in AREC3005
Results for various planting decisions
SO- forecasts more valuable when planting conditions favourable And when risk aversion increases
Forecast values positive-
Values increase as planting opportunity becomes earlier
Values increase for higher soil moisture & N (with some exceptions)
› [HHA2004] Hardaker, Huirne and Anderson (2004) Coping with Risk in Agriculture, CAB International.
– Chapter 6
› Marshall,G.R, Parton, K.A. & G.L Hammer (1996) Risk Attitude, Planting Conditions and the value of seasonal forecasts to a dryland wheat grower. Australian Journal of Agricultural Economics, December 1996.
› NSW Department of Primary Industries (2018) Valuing seasonal climate forecasts in Australian agriculture: Cotton case study (Darbyshire R., . and . (2018)).
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com