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CHAPTER 2 I EUROMONEY HANDBOOKS
7
Establishing risk and reward withinFX hedging strategiesby Stephen McCabe, Commonwealth Bank of Australia
So how does a company choose the best hedging strategy?
The most important consideration is the risk tolerance of
the organisation; but, often other factors such as required
upfront payments will also impact the organisation’s
decision. There are a number of technical aspects to
consider when choosing the hedge. Factors such as
forward points, option implied volatilities and put/call
skew will all have a material impact on the attractiveness
of different hedging strategies, but ultimately the starting
point is the strategy that best supports the risk and reward
profile of the company. Even with a clear risk tolerance
profile, companies cannot rely solely on the traditional
‘payoff’ diagram to decide which strategy best fits their
individual risk and reward profile.
In this chapter we present a probability weighted approach
that modifies the traditional ‘payoff’ diagram to allow easy
estimation of risk and reward in conjunction with
probabilities of outcomes.
Setting the scene
In order to demonstrate the representation of risk and
reward we will use a case study. Company X is a US
domiciled company and is looking to convert AUD100m of
sales revenue it will receive in Q1 2012, into USD. Clearly
the key objective is to maximise the amount the company
receives in USD. To achieve this, four hedging strategies
are considered.
Almost all Australian corporate entities have exposure to ForeignExchange (FX) markets. Typically this will either be a direct or indirectexposure. Importers and exporters are the most obvious examples ofentities that can see large fluctuations in income or revenue if this FX riskis not hedged. There exists many strategies to hedge this FX risk rangingfrom vanilla Forward Exchange Contracts (FECs) to exotic Barrier OptionStrategies and choosing the right strategy is not always simple.
Stephen McCabe
Head of Analytical Risk Management
Commonwealth Bank of Australia
tel: +44 (0) 20 7329 6266; +61 (2) 9118 1040
email: [email protected]
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The FX hedging strategies
Strategy 1: forward exchange contract (FEC)This is the simplest strategy and also acts as a bench-mark
to the other strategies. Under this strategy a fixed rate is
agreed for exchange at a future time. In this example the
FEC rate is 1.01 with the underlying spot rate of 1.0250.
Strategy 2: vanilla AUD putA bought vanilla AUD put is an option that effectively floors
the FX rate to a known downside. The downside is worse
than the FEC because the purchaser of the option is
required to pay a premium. For this example we have
selected an option that is approximately 400 points out of
the money and has a strike of 0.97. The premium is $2.7m
or 2.8%. It is obviously possible to buy different AUD puts
with tailored strikes and premiums.
Strategy 3: zero premium collarThe premium paid by purchasing a vanilla AUD put can be
offset by selling a vanilla AUD call. This creates a collar in
FX rates than can be structured so that the cost is zero
(i.e., cost of the AUD put is exactly offset by the AUD call).
This gives limited exposure to unfavourable movements by
restricting the exposure to favourable movements hence
forming an upper and lower bound (or collar) on possible
outcomes. Therefore if the spot rate is above (below) the
upper (lower) strike, then the rate is capped (floored) at
the strike rate. In this example the lower limit is 0.97 and
the upper limit is 1.03. It is possible to increase the
participation to favourable movements by decreasing the
strike level of the AUD call resulting in an upfront payment
to enter the hedge strategy. These paid collars are a
simple extension of the zero premium collar.
Strategy 4: FX seagullAgain this strategy is aimed at offering upside benefit but
at a reduced premium to the vanilla AUD put. The strategy
consists of a vanilla AUD put spread (bought and sold AUD
puts at different strikes) and a sold AUD call. Similar to the
collar it has a capped upside and downside, however if the
FX rate falls to a certain level, the downside is no longer
capped. In this example the upper limit is 1.07 and the
lower limit is 0.97 to a rate of 0.85. The premium paid
upfront is $0.56m, significantly cheaper than the AUD put.
Cash flows at maturity
The first step in establishing the risk reward profile of any
financial instrument is to analyse its potential cashflows for
different scenarios – commonly called the ‘payoff’ diagram.
Exhibit 1 shows the total USD cashflow at maturity for the
different strategies. Note upfront premiums (where
applicable) are subtracted from the USD proceeds.
The FEC provides maximum certainty of cashflow but
minimum flexibility. Although there is no upfront payment
for the FEC, if rates move unfavourably there is potentially
a large ‘opportunity’ cost associated with this strategy.
In certain circumstances it may also create a liability.
The seagull has a payoff similar to the collar in that it has
a capped upside and a limited floored downside. The
distinguishing feature of this strategy is that the floor
disappears if rates get to a certain level (AUD/USD FX rate
of 0.85). Clearly this introduces additional risk for
company X.
So can we determine by looking at the payoff which
strategy is the best and which is the worst? This question
is not straightforward to answer. Firstly, the best and worst
strategy will depend on the risk tolerance of Company X.
These factors can be summarised as follows: a tolerance to
the best and worst case rate, ability to pay premium and
tolerance to the ‘opportunity’ cost. Exhibit 2 summarises
the pros and cons of each strategy.
So the first step in choosing the appropriate strategy is
determination of the risk tolerance. Typically a company’s
strategy is a mixture of all of the factors listed above and
identification of risk and reward for each one is critical. As
an example, the largest USD cashflow is generated by the
AUD put strategy with a FX rate of 1.3, so this strategy will
generate the best cashflow for Company X, implying the
AUD put is the best strategy. At the other end of the
spectrum the worst cashflow is generated by the seagull
implying that this is the worst strategy.
8
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Assigning probabilities to future FX rates
So far we have looked at the payout structure given
different AUD/USD FX spot rates at maturity. To assess the
probability that FX spot rates will reach certain levels, the
next step is to use a simulation framework. The simulation
framework uses all available historical information on
AUD/USD FX rates, to construct a model that allows
sensitivity analysis to be carried out on different AUD/USD
related strategies. The model is based on lognormal mean
reversion – a statistical technique commonly used in
9
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
Total USD cashflows for notional of AUD100m Exhibit 1
Source: Commonwealth Bank of Australia
AUD/USD FX rate at maturity
130
125
120
115
110
105
100
95
90
USD
proc
eeds
(m)
— FEC (USD) — Put (USD)
— Collar (USD) — Seagull (USD)
Benefits and shortfalls of different hedging strategies Exhibit 2
Source: Commonwealth Bank of Australia
Strategy Pros Cons
FEC Known USD cashflow at maturity, zero Large exposure to ‘opportunity’ cost if rates moveupfront premium in a favourable way
AUD put Best exposure to favourable movements – lowest Largest upfront cost in the form of a premiumexposure to ‘opportunity’ cost
Collar Known best and worst case and no upfront premium Capped upside – reduced but still significant‘opportunity’ cost
Seagull Good exposure to favourable movements and Capped upside – reduced but significantreduced upfront premium ‘opportunity’ cost as well as limited downside
protection if floor rate is passed
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CHAPTER 2 I EUROMONEY HANDBOOKS
finance. The model will produce individual simulation
paths (of AUD/USD rates over time) but the best way to
graphically show the output is to use confidence interval
cones as shown in Exhibit 3.
Exhibit 3 shows the projected confidence levels for
AUD/USD rates over time. The confidence levels show the
fixed probability of spot rates, for instance the 95%
confidence level shows the spot rate of which there is only
a 5% chance of exceeding that rate (equivalent to a 1 in 20
chance). Similarly the 5% shows the same on the lower
rate side. These confidence levels allow future rate
estimates to be bounded depending on the level of
confidence. The vertical line in Exhibit 3 shows the range of
the simulation as at March 31, 2012 – the maturity date of
the case study.
Putting it all together
When considering two or more strategies there are two key
metrics that must be considered:
i. what is the probability of one strategy being better
than the other; and
ii. what is the magnitude of over or underperformance
The first metric gives the company an idea of the success
rate of a particular strategy and the second gives insight as
to the ratio of magnitude of win to lose. Different hedging
strategies will offer protection at different levels and for
differing amounts, so comparison of these key parameters
is crucial in determining the most effective hedge strategy.
The simplest way of putting together the pay off of each
strategy with the probability of an FX rate at expiry is
shown in Exhibit 4. This is combination of the payoff
diagram shown in Exhibit 1 with the probability distribution
(cross section) at the maturity date as shown by the
vertical line in Exhibit 3. This Exhibit shows that the
probability of the extreme pay offs (be it high FX rates >
1.20 or low FX rates < 0.84) is very small and small
movements from the current spot have relatively high
probabilities. In fact there is less than a 1% chance of rates
being less than 0.84 or greater than 1.23 at maturity.10
Sep-
2005
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-200
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Sep-
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-201
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Sep-
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Historical AUD/USD FX rates with forward looking confidence levels Exhibit 3
Source: Commonwealth Bank of Australia
1.4
1.3
1.2
1.1
1.0
0.9
0.8
0.7
0.6
0.5
— Historical
AU
D/U
SD
95%
75%
50%
25%
5%
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CHAPTER 2 I EUROMONEY HANDBOOKS
Although Exhibit 4 shows the probability weighted pay
offs, determination of the two key metrics (i.e., the success
rate and relative magnitudes of strategies) is not easy to
determine.
A better representation is to display the payoff as a function
of the cumulative probability. This is shown for each
strategy in Exhibits 5, 6 and 7. Note the colour convention
for each strategy is the same as used in Exhibit 1.
Exhibit 5 shows the USD cash flow generated as a function
of probability. There is a lot of information available on the
Exhibit and the following are some of the key points.
i. FEC cashflow has no variability hence is a straight line;
ii. unhedged cashflows are extremely variable;
iii. area to the left is where the FEC provides more USD
cashflow than the spot – it is the over performance of
the FEC compared to being unhedged;
iv. area to the right is where the FEC provides less USD
cashflow than the spot – it is the underperformance of
the FEC compared to being unhedged;
v. probability of over performance and underperformance
are both approximately 50%. This means there is an
equal chance of the FEC performing better or worse
than not hedging;
vi. the average level of over performance and
underperformance are both approximately equal; and
vii. both probability and magnitude can be summarised by
looking at the area bounded by the unhedged line and
the FEC to the left (over performance area labelled
Area A) which is approximately equal to the
underperformance area labelled Area B
Hence the FEC has approximately an equal chance in terms
of probability and magnitude of over or underperformance
compared to the unhedged position. This should be
expected but highlights the key areas of this type of chart.
Perhaps more interesting is Exhibit 7 that compares the
unhedged position to the AUD put.
Exhibit 6 shows a different story to the previous exhibit.
Here are the key points:11
0.80
0.82
0.84
0.86
0.88
0.90
0.92
0.94
0.96
0.98
1.00
1.02
1.04
1.06
1.08
1.10
1.12
1.14
1.16
1.18
1.20
1.22
1.24
1.26
1.28
1.30
Pay off diagram and probability of AUD/USD spot rates Exhibit 4
Source: Commonwealth Bank of Australia
AUD/USD FX rate at maturity
USD
proc
eeds
(m)
130
125
120
115
110
105
100
95
90
— Real probability— FEC (USD)— Put (USD)— Collar (USD)— Seagull (USD)
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CHAPTER 2 I EUROMONEY HANDBOOKS
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Probability weighted payoff for FEC and unhedged Exhibit 5
Source: Commonwealth Bank of Australia
Probability weighted payoff for AUD put and unhedged Exhibit 6
Source: Commonwealth Bank of Australia
85 90 95 100 105 110 115 120
USD proceeds (m)
100
90
80
70
60
50
40
30
20
10
0
Cum
ulat
ive
prob
abili
ty(%
)
Area B
Area A
Over performance of FECcompared to unhedged
Underperformance of FECcompared to unhedged
— FEC (USD)— Spot (USD)
85 90 95 100 105 110 115 120
USD proceeds (m)
100
90
80
70
60
50
40
30
20
10
0
Cum
ulat
ive
prob
abili
ty(%
)
Over performanceof put compared
to unhedged Underperformance of putcompared to unhedged
— Put (USD)— Spot (USD)
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CHAPTER 2 I EUROMONEY HANDBOOKS
i. the probability of the put performing better than the
unhedged position is approximately 20% (equivalent
to a one in five chance). Hence, 80% (or four times out
of five) the put is expected to perform worse than not
being hedged;
ii. however the average over performance is approximately
eight times that of the underperformance (as
underperformance is liked to premium and over
performance is a protection via the minimum level); and
iii. these are effectively summarised by the ratio of the
areas which is approximately three to one in favour of
underperformance.
In summary, when this put strategy does perform well, it
performs very well but this does not happen often. Overall,
this implies that this put is not a good strategy as it will
likely underperform a non-hedged position.
The final analysis compares the FEC, collar and seagull.
This is shown in Exhibit 7.
This Exhibit again shows a different story to the previous
two Exhibits. The key points are:
i. the probability of the collar performing better than the
FEC is approximately 50% and the probability of the
seagull performing better than the FEC is marginally
lower at 48%;
ii. this technique easily allows identification of hitting
either the floor or the cap in each structure. For both
the collar and the seagull the floor is hit with a 30%
probability (approximately equivalent to a one in three
chance) and for the seagull the floor ceases to exist
about 1.6% of the time, a relatively extreme event. This
is in stark contrast to the original payoff diagram
where the risk appeared to be more significant. The
collar allows participation (i.e., does not hit the cap)
up to a 60% probability and for the seagull the
participation is up to 75%; and13
Probability weighted payoff for FEC, collar and seagull Exhibit 7
Source: Commonwealth Bank of Australia
85 90 95 100 105 110 115 120
USD proceeds (m)
100
90
80
70
60
50
40
30
20
10
0
Cum
ulat
ive
prob
abili
ty(%
) Underperformancecompared to the FEC
Over performancecompared to the FEC
— FEC (USD)
— Collar (USD)
— Seagull (USD)
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CHAPTER 2 I EUROMONEY HANDBOOKS
iii. analysis of the relevant areas of the chart shows that
underperformance of the collar is approximately two
times that of the over performance. However the
underperformance areas and over performance area
are approximately equal for the seagull
This clearly shows that this collar is not as good a strategy
as the seagull.
Summary
Any combination of strategies can be viewed and any of
the strategies can be used as a reference for comparison
purposes. Hence the conclusion for the case study is that
depending on the risk strategy of company X, either the
FEC or the seagull are the better strategies, this collar is
certainly inferior and this put is expensive.
In addition, this case study did not consider hedging
strategies based on Barrier Options. These products do not
simply have an ‘at maturity’ payoff but are dependent on
whether a particular trigger level is breached at any point
before maturity. Commonly called path dependant
structures, these are impossible to analyse using
traditional payoff technology and only by simulating the
potential future evolution of spot FX rates can the risk and
reward of these strategies be analysed.
Conclusion
When looking to address an FX exposure there are a
number of hedging strategies that can be employed.
Each strategy will have benefits and shortcomings and the
appropriate strategy to be used should be chosen to suit
the risk tolerance of the company and circumstances.
Factors such as FX rate achieved, ability to pay premium
and tolerance to the ‘opportunity’ cost are key
considerations in selecting an appropriate strategy.
Traditional payoff diagrams have uses in identifying
potential cashflow implications, but do nothing to address
the risk and reward implicit in a hedging strategy. It is only
by introducing a simulation framework and applying
probabilities to future FX rates that the true risk and reward
of a strategy can be established. Commonwealth Bank of
Australia (CBA) has developed a robust method of
displaying risk and reward using probability weighted payoff
diagrams and this allows comparison between hedging
strategies and thus better inform the user of hedging as to
the optimum strategy given the risk tolerance.
There are obviously other aspects to consider when
choosing the most appropriate hedge. Factors such as
forward points working for or against you, option implied
volatility at the time of execution and skew in put and call
option pricing all impact the relative attractiveness of
different hedging strategies. This probability based
approach (outlined here) implicitly takes all of these
factors into account and provides an informed base from
which to start the hedge selection.
14
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