26. April 2018
Which market parameters have an impact on the attractiveness of the TARF?
The EUR-USD market environment is characterized by two mutually amplifying developments. On the one hand, the EUR-USD spot rates have been rising substantially since the beginning of 2017 (see figure 1). On the other hand, the widening of the EUR-USD interest rate differential (see figure 2) leads to increasing EUR-USD forward rates. From the perspective of an importer being located in the Eurozone who has to buy USD against EUR in the future, the hedging levels today compared to three years ago are much more attractive. In contrast, an exporter who has to sell USD against EUR in the future faces the challenge of less feasible and much more expensive exchange rate plans.
The Target Redemption Forward (TARF) is an opportunity for both importers and exporters to optimize exchange rates. The TARF is a very popular FX product and is used in various forms including different maturities and currency pairs. In its simplest form, the TARF is a series of forwards with a client benefit that is limited by a predefined target sum. The target is calculated based on the sum of all benefits received from the bonus rate compared to the spot rate at each fixing date. As soon as the target sum is exceeded, the transaction ends prematurely without any further payments (redemption). But what about the attractiveness of TARFs ex ante and ex post in different market phases? Can exporters benefit more from TARFs than importers and what are the relevant determinants for such a difference? With the help of LPACalc, which was developed in-house for pricing and structuring of securities, these questions are analyzed in detail.
An importer, who enters into a TARF today, can for example realize a price level of 1.3150 USD/EUR. This has not been achieved at spot since the third quarter of 2014. Additionally, the results of the ex post analysis below show that entering into a EUR-USD TARF has on average lead to noticeable price improvements in the last six years.
In order to analyze the attractiveness of TARFs in more depth, four different TARF-variants between 2012 and 2018 have been examined with the help of LPACalc : TARF with target sum and discrete TARF with and without a safety range, respectively. 
From an ex ante perspective (meaning upon entering into a TARF), both exporters and importers benefit directly from a TARF due to the more favorable bonus rate compared to the forward rate. Because of the option structure of this product, one can assume that this benefit depends considerably on the predominant volatility levels. Figure 3 confirms the close connection between the benefit of the TARF and the ATM 6M volatilities for the average of the relevant TARF variants (“Average-TARF”).
However, which customer groups benefit in which market phases most from the TARF? In order to answer this question, the benefits for exporters and importers will subsequently be put into relation.
In figure 4 a clear trend of the exporter-/importer-advantage is apparent. As it turns out, importers enjoyed a greater ex ante benefit from the TARF than exporters until mid 2016. Afterwards the opposite can be observed.
This development poses the question which market parameters can be identified that have an impact on the attractiveness of TARFs for exporters and importers in the respective market environment. As stated earlier, the widening of the interest rate differential has lead to substantial increases in forward rates. Thus, the benefit (as expected value) measured as the difference between bonus rates and fixing rate is higher for importers than for exporters on the earlier fixing dates. Therefore, importers can realize the benefit earlier. By potentially reaching the target amount earlier the termination probability also increases. Consequently, the probability of realizing a positive overall result increases. Thus, the bonus rate should, in the event of widening interest rate differentials, be less attractive for the importer compared to the exporter. Hence, the ex ante exporter-/importer-advantage increases. As shown in figure 5, the accumulated termination probability significantly differs for exporters and importers for an example TARF with target sum.
The empirical correlation between both parameters is also shown in figure 4. By widening of the interest rate differential the TARF turns out to be more attractive for exporters compared to importers, because compared to the forward rate a larger benefit can be realized.
The bonus rate, which is more favorable for the customer, is facilitated by the option structure (leverage and premature termination) of the product. Therefore, the volatility is a central price-influencing factor. However, the ATM volatility has a symmetrical effect on the bonus rates of exporters and importers. The price of the TARF, on the other hand, is sensitive to the entire volatility smile. Therefore, one can conclude that the risk reversal is essential for analyzing the exporter/ importer advantage. Because the risk reversal is quoted as “calls over puts”, a risk reversal greater than zero means that the implied volatility of the call is higher than that of the put. This facilitates much better conditions for importers than for exporters because for importers the risk side of the TARF is on the upper side (higher compensation for the short option). Due to the path dependency of the product an exact determination of the relevant risk reversal is not possible. When using the six-month risk reversal with a delta of 25% as proxy, its fluctuation range of the past 5 years moves at around 3.5 percentage points. Compared to the current EUR-USD ATM-level (~7% for 6 months) this is a significant scale.
Whereas the above analysis in this article are limited to the ex ante benefit of the TARF, most customers are particularly interested in the ex post benefit: Was the customer able to realize a benefit by entering into a TARF compared to entering into a forward from an ex post point of view? In order to analyze this question, the ex post exchange rate (meaning after the termination of the product) of the four respective TARF-variants has been compared to a series of forwards. This implies that the customer will in the event of an early termination trade the remaining amounts at corresponding spot rates according to his needs.
The results in figure 6 show that between 2012 and 2018 the ex post benefit especially for exporters has been extraordinarily large with a median of approximately 500 USD-pips. During this period customers were able to realize much more attractive exchange rates by entering into TARFs compared to normal forwards. However, one should not forget that the realized benefit can vary substantially from the median and has also been considerably negative in the past. The success probability, meaning that a customer benefited more from a TARF than from a normal forward, was ~75% for exporters and ~50% for importers in the investigated period. This heterogeneous result can be explained by EUR-USD developments during the investigated period. The EUR-USD exchange rate has significantly dropped since 2012.
Over the last six years the TARF-variants reviewed in this article have on average lead exporters to benefits regarding their exchange rate optimization. So one can conclude that the development of the interest rate differential has a non-intuitive impact on the ex ante benefit of a TARF. Because of the path dependency of the product, exporters (compared to importers) can realize better bonus rates compared to the average forward rate during the term. Thus, with growing interest rate differential between USD and EUR the incentives for exporters to enter into TARFs increase.
The pricing tool LPACalc, which has been developed by LPA cannot only help you price and value TARFs but allows you to also analyze different market scenarios and compare the performance of different TARF-variants ex ante and ex post.
LPA combines unique quantitative and regulatory expertise with deep knowledge of capital markets. Our quantitative models and tools enable fast results and contribute to the success of our consulting services. If you have questions concerning TARFs or other analysis options with LPACalc, we are happy to assist you with our profound knowledge on capital markets. That way you can offer the best possible customer service while simultaneously securing your earning capacity.
We are looking forward to discussing this and other capital market related issues in-depth with you.
 6 months have been chosen as the lead-time for 13 monthly fixings with a leverage factor of 2 for the USD-nominal. The chosen target sum is 0.25 USD/EUR or 4 favorable fixings for the discrete TARF with the early termination variant “overpay”. For the variant „overpay“ the USD-nominal will be exchanged the last time on the fixing date where the target sum is either reached or exceeded and the contract will terminate. The protection corridor is 500 USD-Pips. The historical TARF conditions have been taken into account including a common bank margin.
 To compare the TARF with a forward rate, an average was calculated based on forward rates for each of the 13 fixing dates.
 Because of 13 maximal possible fixing dates an expected maturity of 6 months can be assumed, so that the ATM 6M Vola may be viewed as a suitable benchmark.
 For this purpose the differences between the benefit for an exporter (USD-seller) and the benefit for an importer (USD-buyer) were calculated. The respective benefit is calculated based on the difference between bonus rate and corresponding forward rate. In order to isolate the impact of the interest rate differential the exporter-/importer-benefit was calculated based on ATM volatilities.
Christian Behm, CFA, is with LPA since 2004. He has broad experience in advising banks and has got a distinct capital markets focus. As Partner he is responsible for LPA’s Risk & Quant Consulting Practice and he covers large consulting mandates.