establishing risk and reward within fx hedging strategies · pdf fileestablishing risk and...

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]

07-14_CBA_RISK_2012 16/12/11 15:15 Page 7

mailto:[email protected]


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

07-14_CBA_RISK_2012 16/12/11 15:15 Page 8


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


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

07-14_CBA_RISK_2012 16/12/11 15:15 Page 9


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

Mar

-200

6

Sep-

2006

Mar

-200

7

Sep-

2007

Mar

-200

8

Sep-

2008

Mar

-200

9

Sep-

2009

Mar

-201

0

Sep-

2010

Mar

-201

1

Sep-

2011

Mar

-201

2

Sep-

2012

Mar

-201

3

Sep-

2013

Historical AUD/USD FX rates with forward looking confidence levels Exhibit 3


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%

07-14_CBA_RISK_2012 16/12/11 15:15 Page 10


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


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)

07-14_CBA_RISK_2012 16/12/11 15:15 Page 11


12

Probability weighted payoff for FEC and unhedged Exhibit 5


Probability weighted payoff for AUD put and unhedged Exhibit 6


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)

07-14_CBA_RISK_2012 16/12/11 15:15 Page 12


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


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)

07-14_CBA_RISK_2012 16/12/11 15:15 Page 13


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

Contact us:

Commonwealth Bank of Australia

Senator House, 85 Queen Victoria Street,

London EC4V 4HA, UK

tel: +44 (0) 20 7329 6266 or +61 (2) 9117 0377

email: [email protected]

web: www.commbank.com.au/corporatefx

07-14_CBA_RISK_2012 16/12/11 15:15 Page 14


http://www.commbank.com.au/corporatefx

Important information: Commonwealth Bank of Australia ABN 48 123 123 124 is incorporated in Australia with limited liability.This advertisement is directed at persons who are wholesale clients as defined in the Corporations Act 2001 (Cwth). CLA1408

FX experts so insightful,it’s as if they see into the future.As the best FX provider in Australia, we deliver our clients exclusiveresearch and insights from some of the world’s top FX forecasters.No matter how complex your transaction, our team of FX experts willhelp manage your exposure and capitalise on volatile currency markets.Commonwealth Bank FX. Insight. Foresight.

To access our insights, visit commbank.com.au/corporateFXor contact us at [email protected]

OBC_RISK_2012 16/12/11 15:59 Page 1


http://www.commbank.com.au/corporateFX

http://www.commbank.com.au/corporatefx

establishing risk and reward within fx hedging strategies · pdf fileestablishing risk and...

Documents