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  Dynamic Hedging of Currency Risk in InvestmentStrategies Qplum Investments ResearchNovember 2018 Abstract Often, investors fully hedge their portfolios for currency risk. This can leadto significant drag in performance for currencies with negative carry. However,not hedging the foreign currency exposure can lead to significant drawdowns, es-pecially for conservative investments. In this paper, we consider a conservative,global tactical asset allocation strategy implemented in US dollar denominated se-curities for a hypothetical, European investor and highlight the benefits of dynamiccurrency hedging over static hedging. Using a parsimonious model for hedge ratiobased on multiple features of merit and an explicit check for maximum allowedunder-hedging, we show that a cost aware, dynamic hedging strategy can reducethe hedging costs substantially while keeping the portfolio risk within mandatespecifications. * Gaurav Chakravorty (Qplum) and Ankit Awasthi (Qplum). Qplum is a globalinvestment management firm, which may or may not apply similar investment techniquesor methods of analysis as described herein. The views expressed here are those of theauthors and not necessarily those of Qplum. We would like to thank Dr Michael Steelefor his valuable comments and research assistance. Please refer to important disclosuresat the end of this document.1  1 Introduction Table 1 below shows what we are trying to achieve: Portfolio FX Risk Cost of FX Hedge Total Risk Original, Unhedged High None Higher than Investment Mandate100% Hedged None High Within Investment MandateDynamically Hedged Low Low Within Investment Mandate Table 1:  Our objective is to showcase a hedging strategy that lowers cost of currency hedging whilestaying within its mandate To summarize, we will describe a systematic approach to dynamically hedge currencyrisk in a manner that aims to maximize expected returns while still containing the riskto levels prescribed in the mandate. The work we have laid out in this paper ultimatelyshows that adjusting the hedging ratio over time to changing market conditions canpotentially yield significantly better performance than that from a constant hedge ratio.Table 3 illustrates our findings in this paper. For a European investor, investing in aUS Dollar based strategy, dynamic currency hedging achieves much of the reduction inrisk of full currency hedging while simultaneously avoiding much of the cost of currencyhedging. The remainder of the paper will explain how we accomplish this.In the following sections, first we highlight the need for currency hedging followedby a discussion on the determinants of currency hedging costs. Next we present ourmethodology for dynamic currency hedging and discuss results. 2 Survey of Related Work Optimal hedging strategies for the U.S. cattle feeder [NL98] is one of the earliest exam-ples that shows the effectiveness of hedging risks using futures contracts. It shows thathedging with futures can be an effective way of isolating the real source of income andremove sources of uncertainty that are tangential to the business model. In this work,we have chosen expected returns as the objective function. In Optimal hedging withhigher moments [BM13], the authors have looked at a general class of utility functions,HARA, and tried to optimize hedging rules to maximize that set of utility functions.The main contribution of that paper is to point out that if the strategy that is beinghedged has significant positive skew or if the securities we are hedging with have a skeweddistribution of returns, then we should look at higher moments in computing the hedgeratio. As opposed to traditional OLS hedge ratios, a hedge ratio computed by HARAutility functions would exhibit lower risks and better hedging in out of sample data.The methods we have outlined here can be extended to higher moments as well. Whileothers have highlighted that for global multi-asset portfolio, making currency-hedgingdecisions asset by asset rather than for the overall portfolio could be sub-optimal[GR17],the actual optimal hedging calculation is done under long-term capital market assump-tions considering strategic portfolios[SL16][GR17]. Our methodology is completely data driven and does not make any assumptions on long-term cost of currency hedging or therisk of the currency or asset allocation. And while we show results for a EUR portfolio,our method is agnostic to base currency and can be used across different base currencies. 3 Need for Currency Hedging If someone invests his assets in one currency into a strategy that is denominated inanother currency, he must take into consideration that he may lose out on returns after2  converting the assets back into his srcinal currency. For instance, say an investor withassets in EUR is invested in a USD denominated strategy. Then, they would be takingon a EUR/USD currency risk. Even if the strategy returns were flat but the US Dollardrops 10% against the Euro in that year, the overall net return for the investor wouldbe down 10%. In this scenario, by hedging currency risk, the investor would have beenable to avert most of this loss attributed to the EUR/USD exchange rate. Performance Statistics Fully-Hedged Strategy Unhedged Strategy Annualized returns 4.75% 6.55%Annualized volatility 4.9% 10.7%Worst Drawdown 10.4% 25.5% Table 2:  Backtested Return in EUR) and risk profile of a conservative global tactical asset allocationstrategy [See Appendix for details on the strategy] with and without hedging. Please note that theseare backtested gross return numbers and not net of fees. However, the conclusion would not change if this is measured net of fees Table 2 shows the returns of two Global Tactical Asset Allocation 1 strategies asmeasured in EUR. The underlying strategy is same in both cases. The only differencebetween the two is that in the “Fully Hedged Strategy”, the USD exposure has been fullyhedged by buying EUR/USD currency futures. The strategy has annualized volatility of 4.9% when fully hedged with EUR/USD currency futures. However, the same strategyhas annualized volatility of 10.7% without hedging, which is much higher than themandate of a typical conservative GTAA investment strategy. Moreover, it is importantto note the dramatic increase in the worst drawdown: a 10.4% in the fully-hedgedportfolio versus 25.5% in the unhedged portfolio. 4 Dynamic Currency Hedging We established that currency hedging is important specially for a low-risk investmentstrategy to remain low-risk. However, currency hedging can lead to significant per-formance deterioration as shown in table 2. The returns go down from 6.55% for theunhedged strategy to 4.75% for the fully hedged strategy. We propose a strategy fordynamic hedging that is cost aware. We use a number of previously researched featuresto model cost of hedging - these are discussed in the next section. Intuitively, the dy-namic hedging strategy reduces the hedge ratio when cost of hedging is high and triesto remain hedged when the cost of hedging is low. In other words, the strategy takeson currency exposure only when the cost of hedging could be substantially high or thegains from not hedging could make up for currency movements. In the next section, wediscuss details and implementation of the proposed dynamic hedging strategy. 5 Implementation of Dynamic Hedging Strategy Implementation of dynamic hedging could be quite different for different currency pairs.In this section, we will show the back-tested performance of a dynamic hedging strategyfor a European investor with stake in a US Dollar strategy. In future work, we willexpand the discussion to currency pairs which have shown significant skew in theirreturns.Since, our strategy involves reducing the hedge ratio, we will instead come up withunder-hedging in the portfolio. The dynamic hedging fraction is computed as follows 1 See Appendix for details 3  UHR ( t ) =  M  ( t )  ∗ C  ( t ) (1)UHR(t) denotes the under-hedging ratio at time tM(t) denotes the maximum allowed under-hedging as a fraction,  M  ( t )  ∈  (0 , 1)C(t) denotes the normalized cost of hedging,  C  ( t )  ∈  (0 , 1)Dropping the index t over time in the next set of equations for ease of notation. Asan european investor, investing in USD denominated strategy requires buying USD andselling EUR. UHR gtaeur  =  R gtausd  − R s (2) R gtausd  denotes log returns of underlying GTAA portfolio in USD UHR gtaeur  denotes log returns of unhedged GTAA portfolio in EUR R s denotes log returns of EUR/USD spotFor calculating the returns of the fully hedged strategy, we buy the respective futurescontract to hedge currency exposure 2 . FHR gtaeur  =  R gtausd  − R s + R f  + m ∗ CB  (3) FHR gtaeur  denotes log returns of fully hedged GTAA portfolio in EUR R f  denotes log returns of EUR/USD futures m  denotes the margin required for the futures position as a fraction 3 CB  denotes the cost of borrowing USD for margin requirements 4 .Finally, the returns of dynamic hedging strategy overlaid on the GTAA portofolio iscomputed DHR gtaeur  =  R gtausd  − R s + (1  − UHR )  ∗ R f  + m ∗  (1  − UHR )  ∗ CB  (4) DHR gtaeur  denotes log returns of dynamic hedging strategy with GTAA portfolio 2 We have chosen to hedge currency exposure using futures since futures are very liquid exchangetraded products and therefore easier to backtest 3 For the purpose of this article, we have taken a margin requirement of 10% for EUR/USD futurescontract traded at CME. To our knowledge, this a fairly conservative estimate 4 Cost of borrowing is approximated using 6-month interest rate. 4

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Sep 22, 2019

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Sep 22, 2019
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