II)
Forward Pricing and Risk Transfer
Cash market participants are price takers.
Futures markets allow the possibility of forward pricing. Forward pricing or hedging
allows decision makers pricing flexibility.
A futures market transaction is a temporary substitute for a cash market transaction.
(So does trading futures change the nature of the eminent cash market transaction?)
Pricing becomes a decision.
Hedgers need to learn how to make good pricing decisions and need to recognize
good decisions can result in bad outcomes.
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There are two facts about cash and futures markets which make hedging effective.
1) Cash and futures prices respond to the forces of supply and demand such that
the two markets move together.
Cash commodities and futures contracts are assets the value of which moves in the
same direction. Therefore, an opposite position in the futures market will offset
changes in cash asset values.
2) As the futures contract approaches the expiration date, the cash and futures
prices will converge to a predictable difference. The difference is called:
basis = cash – futures.
This means that any futures prices can be converted to something that look like
cash market prices using: futures + basis = cash.
After working the examples, make sure you understand what is meant by “effective.”
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Perfect Conservative Hedge Example – Corn producer
ex) Falling prices
Date
6/1
Cash
Forward Price =
Futures + Basis
Futures
Basis
DEC Corn @ $4.25/bu.
+0.10
(expected)
DEC Corn @ $3.25/bu.
+0.10
(actual)
BE Price = $3.50/bu.
11/1
Sell cash corn @ $
Gain/Loss = $
Net Price = Cash Price + Gain or Loss in Futures
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ex) Falling prices (& this is the good 2016 outcome)
Date
6/1
Cash
Forward Price =
Futures + Basis
Futures
DEC Corn @ $4.25/bu.
Sell.
Basis
+0.10
(expected)
$4.35 = 4.25 + 0.10
BE Price = $3.50/bu.
11/1
Sell cash corn @ $3.35/bu. DEC Corn @ $3.25/bu.
Buy.
+0.10
(actual)
Gain/Loss = +$1.00/bu.
Net Price = Cash Price + Gain or Loss in Futures
$4.35/bu. = 3.35 + 1.00
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T-Account Schematic
Date
1)
Decision
period
2)
Outcome
period
Cash
Forward Price =
Futures + Basis
Futures
3) Futures price
4) Opportunity
5) Futures action –
temporary substitute for
cash action
6) Cash action
6) Futures outcome
Basis
3)
expected
basis in
outcome
period
6)
actual basis
in outcome
period
6) Gain/Loss
7) Net Price = Cash Price + Gain or Loss in Futures
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Perfect Conservative Hedge Example – Corn producer
ex) Rising prices
Date
6/1
Cash
Forward Price =
Futures + Basis
Futures
Basis
DEC Corn @ $4.25/bu.
Sell.
+0.10
(expected)
DEC Corn @ $6.25/bu.
Buy.
+0.10
(actual)
$4.35 = 4.25 + 0.10
BE Price = $3.50/bu.
11/1
Sell cash corn @ $
Gain/Loss =
Net Price = Cash Price + Gain or Loss in Futures
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ex) Rising prices (& this is the bad 2008-2013 outcome)
Date
6/1
Cash
Forward Price =
Futures + Basis
Futures
DEC Corn @ $4.25/bu.
Sell.
Basis
+0.10
(expected)
$4.35 = 4.25 + 0.10
BE Price = $3.50/bu.
11/1
Sell cash corn @ $6.35/bu. DEC Corn @ $6.25/bu.
Buy.
+0.10
(actual)
Gain/Loss = –$2.00/bu.
Net Price = Cash Price + Gain or Loss in Futures
$4.35/bu. = 6.35 –2.00
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Choosing and realizing a forward price is what is meant by effective forward pricing.
Not price enhancement, not the best price, not the highest price, not above
costs of production...
Hedging works because losses in one market are offset by gains in the other market.
The example also illustrates risk transfer. The risk of a price change is transferred to
(most likely) a speculator. The hedger is “protected” against all price changes.
Producers are still price takers but when they take price is flexible and forward
pricing decisions become an opportunity.
forward pricing window
(months)
price
taking
(day)
harvest
forward pricing window
(months)
price
taking
(day)
harvest
Example) What is JUL17 KC wheat trading for? What about DEC16 & DEC17 corn?
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Corn producer example,
decision to hedge: falling prices

good or bad?
decision to hedge: rising prices

good or bad?
Example) Former student with $650k of margin calls in 1994.
Example) Suppose the corn producer in our examples sold 10 contracts – 50,000 bu.
– and suppose the market rallied to where the producer was losing $2/bu. How
much financing would be needed? Where would that money come from?
Margin calls, margin calls, margin calls… What are you going to do when you get
margin calls?
What about using forward contracts? (And what about credit risk?)
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Corn producer example,
decision to hedge: falling prices

good or bad?
decision to hedge: rising prices

good or bad?
Are you thinking DECISION or OUTCOME?
Was the decision good or bad given the information available when the decision was
made?
What information and processes would it take for you to make good forward pricing
decisions?
Break-even Price & Costs of Production
Basis Information
Access to Credit
Capital Budgeting – Risk Assessment
& Target RoR or ROI
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Market Outlook?
Price Forecasts?
Probabilistic Forecasts?
(Crystal ball?)
10
Where does this information go on the Cash Flow Statement?
Jan
Feb
Mar
Apr
May
Jun
Jul
Aug
Sep
Oct
Nov
Dec
Total
Beginning Cash Balance
Operating Receipts
Grain
Livestock
Futures G/L
$
$
$
Capital Receipts
...
$
Total Cash Inflow
Operating Expenses
...
$
Debt Payments
...
$
Total Cash Outflow
Ending Cash Balance
What is the date when the decision was made and when is the outcome realized?
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Where does this information go on the Balance Sheet?
ASSETS
LIABILITIES
Current Assets
Current Liabilities
Cash assets
$
...
Futures assets
$
Futures liabilities
...
...
Capital Assets
Capital Debt
$
...
...
$
$
...
...
$
$
Total Assets
$$$
Total Liabilities
$$$
EQUITY
$$$
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Perfect Conservative Hedge with Options Example – Corn producer
ex) Falling prices
Date
6/1
Cash
Forward Price Floor =
Option Futures Price +
Basis - Premium
$4.00 = 4.25 + 0.10 – 0.35
Futures
DEC Corn @ $4.25/bu.
Basis
+0.10
(expected)
Right to sell DEC Corn @
$4.25/bu. is $0.35/bu.
Buy option (Put).
BE Price = $3.50/bu.
11/1
Sell cash corn @ $
DEC Corn @ $3.25/bu.
+0.10
(actual)
Right to sell DEC Corn @
$4.25/bu. is $?
Net Price = Cash Price + Gain or Loss in Options
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ex) Falling prices
Date
6/1
Cash
Forward Price Floor =
Option Futures Price +
Basis - Premium
$4.00 = 4.25 + 0.10 – 0.35
Futures
DEC Corn @ $4.25/bu.
Basis
+0.10
(expected)
Right to sell DEC Corn @
$4.25/bu. is $0.35/bu.
Buy option (Put).
BE Price = $3.50/bu.
11/1
Sell cash corn @ $3.35/bu. DEC Corn @ $3.25/bu.
+0.10
(actual)
Right to sell DEC Corn @
$4.25/bu. is $1.00/bu.
Sell option.
Net Price = Cash Price + Gain or Loss in Options
$4.00/bu. = 3.35 – 0.35 + 1.00
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Perfect Conservative Hedge with Options Example – Corn producer
ex) Rising prices
Date
6/1
Cash
Forward Price Floor =
Option Futures Price +
Basis - Premium
$4.00 = 4.25 + 0.10 – 0.35
Futures
DEC Corn @ $4.25/bu.
Basis
+0.10
(expected)
Right to sell DEC Corn @
$4.25/bu. is $0.35/bu.
Buy option (Put).
BE Price = $3.50/bu.
11/1
Sell cash corn @ $
DEC Corn @ $6.25/bu.
+0.10
(actual)
Right to sell DEC Corn @
$4.25/bu. is $?
Net Price = Cash Price + Gain or Loss in Options
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ex) Rising prices
Date
6/1
Cash
Forward Price Floor =
Option Futures Price +
Basis - Premium
$4.00 = 4.25 + 0.10 – 0.35
Futures
DEC Corn @ $4.25/bu.
Basis
+0.10
(expected)
Right to sell DEC Corn @
$4.25/bu. is $0.35/bu.
Buy option (Put).
BE Price = $3.50/bu.
11/1
Sell cash corn @ $6.35
DEC Corn @ $6.25/bu.
+0.10
(actual)
Right to sell DEC Corn @
$4.25/bu. is $0.00.
Option expires worthless.
Net Price = Cash Price + Gain or Loss in Options
$6.00/bu. = 6.35 – 0.35 + 0.00
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Scenario
Cash
Futures
Options
Falling Prices
Rising Prices
Steady Prices
First, find the prices for the different strategies under the different scenarios.
Second, determine which is the best strategy?
For a given scenario – row – which strategy – column – has the highest price?
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Scenario
Cash
Futures
Options
Falling Prices
$3.35
$4.35
$4.00
Rising Prices
$6.35
$4.35
$6.00
Steady Prices
$4.35
$4.35
$4.00
Which is best?
Are you thinking Decision or Outcome?
Cash and Futures are always best or worst outcome.
With options, the price protection is not as good as with futures. However, you are
not locked into a futures position that loses money. But options are not a fix-all for
the problem with a futures hedge – more flexible but more costly. Options are never
the best outcome – are many times second best – and sometimes the worst.
Decision makers need a forward pricing strategy – a method and information to
make good pricing decisions.
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Reading Assignment
USDA ERS Publication. “Managing Risk in Farming: Concepts, Research, and
Analysis.” Ag Econ Report 774 (AER-774).
http://www.ers.usda.gov/epubs/pdf/aer774/
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How Do We Measure Risk?
First, we have to answer – How do we measure return?
Then risk is like “experience...”
frequency
Ex) Enterprises A, B, & C
μA = μB < μC
σA < σB < σC
Price or Revenue or RoR
Which enterprise is best? Which is worst?
(See spreadsheet figure.)
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0.14
0.12
Probability
0.1
0.08
A
B
C
0.06
0.04
0.02
0
Rate of Return (%)
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Returns are some expected value – e.g., mean price, profit, or rate of return.
Risk is some measure of deviation from expected value – e.g., standard dev.
The first batch of equations...
T
Return: E(x) = μ = ∑ xt / T
t=1
Risk:
T
σ = ∑ ( xt – μ )2 / (T-1)
t=1
2
or
ෝ࢚ = β0 + β1 x1t + ... + βk xkt
E( yt ) = ࢟
and σ = √σ2
Measures of central tendency are measures of what we can expect – means or
conditional means (i.e., regression predictions). Measures of dispersion are
measures of departures from what we expect – how spread out are the realizations.
Interpret: 1) mean and 2) standard deviation?
The mean is easy as it’s the…?
Standard deviations measure dispersion or how spread-out the individual xt’s are
around the mean. Using σ with a Normal distribution, 68% of time what? 95% of the
time what? And 99% of the time what?
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Some real-world numbers
Livestock
Return (μ)
Risk (σ)
Grains
Specialty
Stocks
Bonds
T-Bills
5-8%
8-12%
15-25%
8-10%
5-7%
1-3%
10-20%
15-30%
25-50%
15-20%
10-15%
2-4%
Which enterprise is best?
Which investment is best?
Evaluating Investment and Other Business Decisions – Using Efficient Frontier
% Return
A choice is efficient if
has the highest return
for a given risk or
lowest risk for a given
return. There are no
wrong choices among
risk-efficient choices.
% Risk
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Some Ideas About Measuring Risk
Deviation from what we expect...
Outcome = Expectation ± Departures from expectation (Risk)
Simple Expectations
Yield:
Yt = μ + et
Price:
Pt = μ + et
Alternative:
Pt = Pt-1 + et
(Where et is a random variable with zero mean and possibly distributed Normal.)
Better (or Smarter) Expectations
Yield:
Yt = trend + et = β0 + β1 t + et
Price:
Pt = β0 + β1 Pt-1 + et
(See spreadsheet figures for yields and prices.)
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It might not be on exams but it will be on assignments…
Make sure you can do the following.
Calculate the yield forecast, or expected dry-land corn yield, for 2016:
Yt = β0 + β1 t + et
Yt = 34.6004 + 0.4961 t + et
where t = 42 for 2016 so E(Yield2016) = 34.6004 + 0.4961 (42) =
bu./ac.
Now the unexplained variation in yields is measured by σ from the model above.
Given σ = 14.9 (find that in the spreadsheet table) then calculate the probability that
the dry-land corn yield is below 25.6 bushels/acre in 2016.
NORMDIST(25.6, 55.4, 14.9, true) =
%.
Change 24.1 above to 40.5, calculate the new probability, and interpret.
The answers are on the table of corn yield and price data. Do the work above, find it
on the table, and invest time in understanding the NORMDIST function in MS Excel.
We are measuring risk and I think that’s important.
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Similarly, on the price side, make sure you can do the following.
Calculate the price forecast, or expected corn price, for 2016:
Pt = β0 + β1 Pt-1 + et
Pt = 0.4739 + 0.8460 Pt-1 + et
where P2015 = 3.70 (price for 2015) so
E(P2016) = 0.4739 + 0.8460 (3.70) = $
/bu.
Now the unexplained variation in price is measured by σ from the model above.
Given σ = 0.61 (find that in the spreadsheet table) then calculate the probability that
the corn price is below $2.99/bu. in 2016.
NORMDIST(2.99, 3.60, 0.61, true) =
%.
Change 2.99 above to 2.38 and then to 3.25, calculate both new probabilities, and
interpret.
The answers are on the table of corn yield and price data. Do the work above, find it
on the table, and make sure you understand the NORMDIST function in MS Excel.
We are measuring price risk and I think that’s yahoo-important.
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More on
NORMDIST( X, µ, σ, TRUE ) or
NORMDIST( X, ExpectedValue, StandardDeviation, TRUE)
X is the event for which we want the probability,
µ is the measure of central tendency or the mean or the expected value (or forecast)
of the distribution,
σ is the measure of dispersion or the standard deviation of or the risk in the
distribution,
TRUE tells the function to do the integration for us so that we get the probability of X
or less happening.
For example, what’s the probability of corn price being $3.25 or below in 2016? We
need the forecast or expected value for 2016 (think of that as µ). We need the error
associated with our forecast (think of that as σ).
So NORMDIST( 3.25, µ, σ, TRUE) and we are in the ballpark.
Similarly, what the probability of the corn price being above $4.50/bu?
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Back to Expectations – and the Smartest Yet – Using Economics…
Demand: Pt = a + b Qt + c It + e1t
Supply: Qt = d + f Pt-1 + g Xt-1 + e2t
Pt = a + b ( d + f Pt-1 + g Xt-1 ) + c It + et
Pt = (a + bd) + bf Pt-1 + bg Xt-1 + c It + et
Pt = β0 + β1 Pt-1 + β2 Xt-1 + β3 It + et
You can (build an econometric model – especially if you need to do a short research
paper – to) predict this year’s price with last year’s price and (predications of)
variables that shift the supply curve and (predictions of) variables that shift the
demand curve. This will work well.
The bottom line is – good agribusiness planners have a fact-based or experiencebased perception of what’s going to happen before they act. Some use data &
econometrics and some years of experience. Outcomes are less surprising for
those that are smart and plan. (But those that forward price are not surprised much.)
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Potential Forecasting Exercise:
We need an expectation for (your choice commodity) this coming (your choice time).
We’ll use past prices...
What are potential supply shifters?
What are potential demand shifters?
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Better yet, let’s work on that corn price forecasting econometric model. The simple
regression model has been quite wrong for the past few years. So can we change it
so that it sees the big price drop coming?
We used last year’s price to explain this year, which is a reasonable start but what
else might we use?
How about this year’s production – or forecasted production – combined with the
coming year’s forecasted use which results in a corn stocks forecast?
Pt = β0 + β1 Pt-1 + β2 Qt + et
Pt = 0.9040 + 0.8056 Pt-1 – 1.4385 Qt + et
Pt = 0.9040 + 0.8056 (3.70) – 1.4385 (0.167) = $
/bu.
with an standard error (σ) of $0.55/bu & R2 = 0.74.
What’s the forecast for 2016 and what’s the probability of $3.25/bu or lower corn?
(My most complicated but simple model has an R2 = 0.91, forecasts $3.35/bu and has
σ = $0.45/bu. Bottom line: we need forecasts but they will be wrong – they have
risk.)
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What can we do with measures of expectations and risk?
Determine efficient and inefficient choices. (Efficient frontier)
Risk preferences determine “best” choice among efficient choices.
Calculate probabilities of good and bad outcomes.
Might also need to assume a distribution – or we could use the histogram.
Illustrates downside risks – how much financing might be needed.
Simulate results of different strategies. (Stochastic simulation)
Dynamics or time is important.
Illustrates differences in mean and variability of returns.
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Risk and Return – Making Investment and Other Business Decisions
Return
Plan
Return
Std Dev
A
12%
10%
B
8%
2%
C
8%
10%
D
50%
2%
Risk
What are efficient Plans? What Plan can we rule out as inefficient? How to choose
among remaining Plans?
And forget about finding a Plan D – if you do then invest all your money and borrow
some and be quiet.
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Figuring out your risk preferences...
Choose a decision and flip coin for outcome. Monthly take-home pay...
Decision
Outcome
μ & (σ)
Heads
Tails
A
B
C
D
E
$1000 ($100) $1100 ($250) $1200 ($400) $1000 ($250)
$900 ($250)
$1100
$1350
$1600
$1250
$1150
$900
$850
$800
$750
$650
What decision letter do you want?
Are D and E efficient? Is there a best choice between A, B, and C?
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Simulation of Risky Decisions
In concept: Taking a random draw from a distribution (pdf). Outcomes are more
likely from the sample space of the pdf where the function is higher.
pdf
Return
(See spreadsheet figure.)
AREC 412 Lec D – Forward Pricing & Risk
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0.07
0.06
Probability
0.05
0.04
Bonds
Stocks
0.03
0.02
0.01
0
Rate of Return (%)
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In Practice: using, for example, a spreadsheet.
pdf
The probability is the area
under curve from point to
the left.
Return
cdf
The probability can be
found by reading the
number off the curve – the
integration is already
done.
Return
(See spreadsheet figures.)
AREC 412 Lec D – Forward Pricing & Risk
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1
0.9
0.8
0.7
Probability
0.6
Bonds PDF
Stocks PDF
0.5
Bonds CDF
0.4
Stocks CDF
0.3
0.2
0.1
0
Rate of Return (%)
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Simulate investment decision outcomes. Retirement after saving $1,200 per year for
45 years. (250 replications.) (Blend: 70-20-10.)
Decision
Outcome
Best
μ
Worst
Stocks
Bonds
T-Bills
Blend
$10.8 million
$1.4 million
$144 thou
$4.6 million
$1.9 million
$509 thou
$116 thou
$1.1 million
$323 thou
$190 thou
$94 thou
$256 thou
Average-Stocks are better than Best-Bonds.
Worst-Stocks are better than Best-T-Bills – Worst-Bonds are better than Best-T-Bills.
Best-Blend and Worst-Blend better than all but stocks.
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Observation and Commentary
The firms that succeed and grow in the commodity production and marketing
businesses are the firms that:
1) Aggressively manage risk
2) and are willing to live with the smallest rate of return (RoR).
Applies to cattle feeding, hog production, corn, wheat, oilseeds...
Thought Example – two cattle feeding firms
A – aggressively manages risk and willing to take $20/head profit.
B – wants $45/head profit and takes risk to get it.
Who’s still there after 10, 15, and 25 years? Who’s most likely to have experienced a
market event that has bankrupted, or serious setback, the firm?
Who is a better risk in the eyes of their lender? And can borrow more $?
Who has grown?
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