Setting the scene. by Stephen McCabe, Commonwealth Bank of Australia

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1 Establishing risk and reward within FX hedging strategies by Stephen McCabe, Commonwealth Bank of Australia Almost all Australian corporate entities have exposure to Foreign Exchange (FX) markets. Typically this will either be a direct or indirect exposure. Importers and exporters are the most obvious examples of entities that can see large fluctuations in income or revenue if this FX risk is not hedged. There exists many strategies to hedge this FX risk ranging from vanilla Forward Exchange Contracts (FECs) to exotic Barrier Option Strategies and choosing the right strategy is not always simple. 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 AUDm 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. Stephen McCabe Head of Analytical Risk Management Commonwealth Bank of Australia tel: +44 (0) ; +61 (2) globalfxsales@cba.au 7

2 8 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 Strategy 2: vanilla AUD put A 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 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 collar The 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 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 seagull Again 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 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.

3 Total USD cashflows for notional of AUDm Exhibit FEC (USD) Put (USD) Collar (USD) Seagull (USD) AUD/USD FX rate at maturity 9 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 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 move upfront premium in a favourable way AUD put Best exposure to favourable movements lowest Largest upfront cost in the form of a premium exposure 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 significant reduced upfront premium opportunity cost as well as limited downside protection if floor rate is passed

4 07-14_CBA_RISK_ /12/11 15:15 Page 10 i. finance. The model will produce individual simulation what is the probability of one strategy being better paths (of AUD/USD rates over time) but the best way to than the other; and graphically show the output is to use confidence interval ii. what is the magnitude of over or underperformance cones as shown in Exhibit 3. The first metric gives the company an idea of the success Exhibit 3 shows the projected confidence levels for rate of a particular strategy and the second gives insight as AUD/USD rates over time. The confidence levels show the to the ratio of magnitude of win to lose. Different hedging fixed probability of spot rates, for instance the 95% strategies will offer protection at different levels and for confidence level shows the spot rate of which there is only differing amounts, so comparison of these key parameters a 5% chance of exceeding that rate (equivalent to a 1 in 20 is crucial in determining the most effective hedge strategy. chance). Similarly the 5% shows the same on the lower The simplest way of putting together the pay off of each rate side. These confidence levels allow future rate strategy with the probability of an FX rate at expiry is estimates to be bounded depending on the level of shown in Exhibit 4. This is combination of the payoff confidence. The vertical line in Exhibit 3 shows the range of diagram shown in Exhibit 1 with the probability distribution the simulation as at March 31, 2012 the maturity date of (cross section) at the maturity date as shown by the the case study. 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 Putting it all together probabilities. In fact there is less than a 1% chance of rates metrics that must be considered: being less than 0.84 or greater than 1.23 at maturity. Historical AUD/USD FX rates with forward looking confidence levels Exhibit % AUD/USD 75% % % 0.8 5% 0.7 Historical 0.6 Sep-2013 Mar-2013 Sep-2012 Mar-2012 Sep-2011 Mar-2011 Sep-2010 Mar-2010 Sep-2009 Mar-2009 Sep-2008 Mar-2008 Sep-2007 Mar-2007 Sep-2006 Mar Sep movements from the current spot have relatively high When considering two or more strategies there are two key

5 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. 11 Here are the key points: Pay off diagram and probability of AUD/USD spot rates Exhibit Real probability FEC (USD) Put (USD) Collar (USD) Seagull (USD) AUD/USD FX rate at maturity

6 Probability weighted payoff for FEC and unhedged Exhibit 5 Cumulative probability (%) Over performance of FEC compared to unhedged Area A Area B Underperformance of FEC compared to unhedged FEC (USD) Spot (USD) Probability weighted payoff for AUD put and unhedged Exhibit 6 80 Cumulative probability (%) Over performance of put compared to unhedged Underperformance of put compared to unhedged Put (USD) Spot (USD)

7 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 ii. FEC is approximately 50% and the probability of the seagull performing better than the FEC is marginally lower at 48%; 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 13 participation is up to 75%; and Probability weighted payoff for FEC, collar and seagull Exhibit 7 Cumulative probability (%) Underperformance compared to the FEC FEC (USD) Collar (USD) Seagull (USD) Over performance compared to the FEC

8 14 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. Contact us: Commonwealth Bank of Australia Senator House, 85 Queen Victoria Street, London EC4V 4HA, UK tel: +44 (0) or +61 (2) globalfxsales@cba.com.au web:

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