Hedging currency risk of emerging market equities

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UNIVERSITY OF AMSTERDAM

AMSTERDAM BUSINESS SCHOOL

Hedging Currency Risk of Emerging Market Equities

MSC Business Economics: Finance Track

Master Thesis

Marcelo Mozena

Supervisor: dr. P.J.P.M. Versijp

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Statement of Originality

This document is written by Marcelo Mozena, who takes full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Abstract

The goal of this thesis is to evaluate if time conditional hedging strategies reduce the risk of the portfolio invested in emergent market equities. To answer the research question is implemented a DCC-GARCH model of Brown et al. (2012) to hedge currency risk of four portfolios invested in emerging market equity. The suggested model is evaluated against four competing hedging strategies: no-hedge, half-hedge, full hedge, time unconditional hedge ratios. It is also proposed three alternatives rebalance frequencies for the time conditional hedge ratios: monthly, thresholds value, and constraint between 0 and 1. The competing models are evaluated in terms of Hedging Effectiveness, average returns, skewness, kurtosis and Sharpe ratios. The results show that time conditional hedging does not reduce portfolio currency risk, increase returns and Sharpe ratios or affect the distribution of the returns. Among the competing strategies, the full hedge ratio presented superior risk reduction, however, the results are not statistically significant. The findings contradict the literature which shows superior risk reduction of time conditional hedge ratios against the static hedge ratios.

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1. Introduction

A number of factors have been attracting capital to emerging markets. These factors include high GDP growth rates, expansion of the middle class, and abundance of natural resources. However, when investing in emerging markets, developed market-based investor economies face a different investment perspective compared to investing in another developed country. For instance, despite the recent strong globalization, business cycles of rich and developing economies are often not synchronized and their equity markets show low correlation (Bekaert & Harvey 2014). Hence, investing outside developed economies still contributes to portfolio diversification (Bekaert & Harvey 2014). Further, one may argue that emerging markets’ institutional and structural factors, such as political and economic uncertainties, still represent an important source of risk. It must be noted that the expected higher returns compensate investors for bearing these risks (Kearney 2012). With the forecast of low growth in the years ahead for most advanced economies1_{, such as Europe} and Japan, investors cannot forgo this opportunity of diversification and higher expected returns. The question now lies on how much to invest in emerging markets and not anymore on investing or not.

On the one hand investing abroad in fast-growing economies brings diversification and higher expected returns. On the other hand, each asset in the portfolio is pegged to a certain foreign currency and exposes the portfolio to significant exchange rate fluctuations. Those fluctuations may be positive for portfolio returns or even completely eliminate any equity gain. For example, emergent currencies suffered substantial depreciation when the 2013 FED “taper tantrum”2_{led to a} large capital flow from emerging countries into the safety of the US fixed income market (Burns et al. 2014; Cerutti et al. 2015). Investors holding equities in those countries suffered a large reduction in the value of their portfolio. One alternative to use to reduce portfolio exchange volatility can be to hedge the currency risk, in this case shorting the foreign currency position, hence, decreasing the exchange rate volatility. The hedge ratio determines the amount of currency exposure necessary to offset potential losses from exchange rate volatility. Hedging risk is a common practice in the financial industry and has been extensively discussed in the literature. Black (1990) shows that hedging is the appropriated tool to reduce portfolio exchange volatility. However, there is still an ongoing discussion on the real benefits of hedging, and how to construct the hedge ratios. For example, hedging brings no advantages to long-horizon investors according to Froot (1993), but Perold & Schulman (1988) advises investors to fully hedge exchange rate risk. More recently, the

1_{See for example IMF (2015a), IMF (2015b), and Lo & Rogoff (2015).}

2_{The “taper tantrum” was a market reaction to the FEDs announcement that it would slow down}

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discussion has been centred on the “free lunch” argument, where the reduction of the portfolio volatility may bring an adverse effect on portfolio returns, downside risk and Sharpe ratios (De Roon et al. 2012; Walker 2008). Therefore, the decision on whether to hedge or not is not simple. There are several methods to construct a hedging strategy, but the starting point is how to model the covariance between the portfolio assets returns (Cenedese et al. 2015). The more accurate the covariance estimation is, the more effective are the hedge ratios. As the empirical evidence shows since assets have time conditional correlation and covariance, the traditional static hedge ratios might not properly reduce portfolio volatility (Longin & Solnik 1995; Yiu et al. 2010). In general, t research that is more recent adopts the assumption of time-conditional hedge ratios.

Therefore, the goal of this thesis is to evaluate if time conditional hedging strategies reduce the risk of emergent market equities portfolio. Traditionally, the hedging literature explores the situation that investors located in a developed economy invest in another developed economy, though the dynamics of investing in emerging equity might be different. Portfolio managers cannot simply assume that the same hedging strategies will produce the same outcome on developed and developing market portfolios. To answer the research question, this research expands the developed market focused model proposed by Campbell et al. (2010) and Brown et al. (2012) and shows how the model performs on when hedging emerging market equity. This research contributes to the decision making on hedging currency risk of emergent market investments and to the evaluation of time varying hedging ratios with emerging market data.

Hereafter, five competing hedging strategies are implemented: no-hedge, half-hedge, full hedge, time unconditional hedge ratios, and time conditional hedge ratios. The time-conditional hedge ratios are constructed from the variance-covariance matrix of the DCC-GARCH model. The analyses are made in-sample and out-of-sample, from the perspective of investors located in developed markets holding a portfolio of emerging market equity. Further, the time conditional hedge ratios are implemented with four alternatives rebalance frequencies. Hedging may have a diverse consequence for the portfolio performance, from reducing volatility to worsening returns. However, in this thesis we set as the primary objective the portfolio volatility reduction, consequent evaluate which model present the higher Hedge Effectiveness. Then, other portfolio measures are assessed to drawn a clear picture of the effects of hedging on the portfolio’s performance.

In order to achieve its goals, this thesis will be divided into six chapters. Following the introductory chapter, the next chapter of this thesis presents the literature review on hedging currency risk. In the third chapter, the methodology, and the competing models are described. Chapter 4 shows the data and chapter 5 displays and discuss the results. The thesis ends with the conclusions on the research topic and some recommendations for further research.

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2. Literature Review

This chapter presents the relevant literature review on currency hedging and provides the academic background for this research. The chapter starts with an introduction to portfolio currency hedging. Next, the key components necessary to develop a hedging strategy are addressed. Finally, the relevant performance measures used to compare competing portfolios are reviewed.

2.1 Currency Hedging

Exchange rates are one of the main sources of volatility in internationally diversified portfolios (Dumas & Solnik 1995). Henceforth, hedging the currency volatility should be a standard practice for portfolio managers. The initial research on hedging for risk reduction reinforces this argument. For instance, Eun & Resnick (1988) shows that hedging is an essential and the appropriate tool for investors to reduce the exchange rate risk. Perold & Schulman (1988) go further and define currency hedging as a free lunch, that reduce portfolio volatility without any effect on returns and in the distribution of the returns. More recently, De Roon et al. (2003) depict hedging as significantly improving portfolio returns for different the degree risk aversion investors.

However, it is a strong assumption that the free lunch scenario will hold for all international diversified portfolios. Only the hypothesis that currencies have zero expected returns and positive volatility the free lunch argument might hold for different portfolio constructions (De Roon et al. 2012). The literature shows evidence that investors are compensated for holding foreign currency, a currency risk premium (Dumas & Solnik 1995). If currency holdings provide a yield for investors, hedging may negatively affect portfolio performance and not generate the desired currency risk reduction. For instance, Statman & Fisher (2003) find no effect of hedging between the years of 1988 and 2002 for a portfolio of developing markets investments. From the perspective of an emerging market-based investor investing in developing markets, Walker (2008), hedging damages investment returns and raises volatility. According to De Roon et al. (2011), hedging currency risk improves the risk-return trade-off fixed income portfolio, both in-sample and out-of-sample, while it only decreases the risk of equity portfolios. The authors also present that speculative positions on foreign currencies increases portfolio returns and Sharpe ratios. Moreover, Campbell et al. (2010) depicts positive impacts on returns of hedging fixed income portfolios and speculative currency positions. De Roon et al. (2012) also found negative effects of currency hedging on Sharpe ratios and statistical moments, as skewness and kurtosis. To sum up, the literature review shows that the free lunch assumption might not hold for all portfolios. While analysing hedging strategies, it is important to depict clearly the trade-off between risk reduction and portfolio returns.

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2.2 Hedging Strategies Components

In order to develop this research it is necessary to define the keys components of a hedging strategy, being thus how to add currency exposure to the portfolio, the choice of hedging instrument, the choice between static or dynamic hedge ratios, and how to define the correlations between assets.

The common practice of portfolio managers is adding a hedging instrument position to the portfolio, as simply relying of international portfolio diversification cannot reduce exchange rate exposure (Eun & Resnick 1988). For example, whenever foreign currency and equity are negatively correlated, a straightforward approach for one expecting a positive growth in equity returns is to buy equity and short currency. Independent of the choice of hedging instrument, Jorion (1994) describes three widely adopted approaches on how to combine assets when hedging currency risk of a portfolio. First, the correlation between equity and currency returns is jointly evaluated to determine the size of the equity and currency positions. In this case, an investor is also holding a speculative position in the currency. Second, the currency risk is partially optimized, when the investor first exogenously determines the portfolio equity position, then the currency positions are optimized given the equity holdings. Third, the position on the two assets classes is independently optimized given its expected returns and volatility. The partial and independent methods are generally called currency overlay. Evidence in the literature favours jointly optimization using ex-post data; however, partial optimization outperforms jointly optimization with ex-ante data (Brown et al. 2012).

Portfolio managers often use as hedging instruments currency derivatives such as currency forwards, futures, and options instead of buying and selling the currency. According to De Roon et al. (2001), the returns on forward and futures are actually excess returns, as both require zero investment at the inception. They are contracts to deliver (or not) an asset, in this case currency, at a certain price in the future. Future contracts are more liquid, have lower counterparty risk and are more flexibility than forward contracts mainly because they are traded in organized exchange markets (Caporin et al. 2014). However, futures contracts are not available for a wide number of currency pairs, and most of the hedgers use forwards markets to hedge currency risk (Hautsch & Inkmann 2003). Independent of the choice between futures or forwards, researchers face a shortage of historical data on these hedging instruments, especially when working with developing market currencies. An alternative for researcher is to use the covered interest rate parity condition to construct artificially forward contracts from interest rate differentials (Campbell et al. 2010). It is a common method used to price forwards contracts in the financial markets and it has been generally

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applied in the literature to construct forward contracts to hedge currency risk (Campbell et al. 2010; De Roon et al. 2012). The artificial forward contracts correspond to selling the foreign currency deposit and with the profits, buy domestic currency deposits. Once the returns on domestic and foreign interest rate are equal, the price of the forward contract is left exposed to exchange rate volatility (Walker 2008). As the exchange rates change, the price of the forward contracts changes. Researchers only need data on foreign and domestic interest rates and the exchange rate to construct the artificial currency contract.

The next component to be defined is the hedge ratio, which gives the size of the currency exposure position necessary offsets the portfolio volatility originated from the currency exposure. The straightforward approach would be to counterbalance one hundred per cent of the currency risk or full hedging. However, the literature presents divergences on the optimal hedge ratio. When currency and equities prices are uncorrelated Solnik (1974) and Perold & Schulman (1988) argue for full hedging. Black (1990) recommends hedge ratio 30 to 75%, and Gastineau (1995) states that investor should always target hedge ratio of 50%. There are arguments against hedging, as for instance, according to Froot (1993) since in the end exchange rates are mean reverting long time horizons, investors should adopt no hedging.

However, pre-defined hedge ratios values as proposed by Gastineau (1995) and Solnik (1974) may not eliminate all the currency risks. Different assets have different correlations with the exchange rates. Half hedge might still leave the portfolio exposed to currency and full hedge can make investor take unnecessary hedging positions. The minimum variance hedge ratios overcome these problems since they define the hedge ratios, which minimize the portfolio variance given the historical correlation between the asset and the exchange rates (Celebuski et al. 1990). The ordinary least squares (OLS) is a method commonly adopted to calculate the minimum variance hedge ratios. It gives a static hedge ratio, largely dependent on the asset and currencies input data. The simple OLS regression displays that fixed hedge ratios, as proposed by Black (1990), may not be optimal. Furthermore, the OLS has its own limitations. As asset correlations are changing over time, it will be impossible to produce a perfect ratio ex-ante (Black 1989; Schmittmann 2010). The OLS model assumes that the squared error term is the same at any point in the times series. However, empirical evidence suggests a time-varying correlation between equities and currencies returns (Ang & Bekaert 2002; Longin & Solnik 1995). In these situations, the OLS standard errors and confidence intervals estimated are too narrow, as the error term will vary along the time, and the data will suffer from heteroscedasticity (Engle 2001).

The empirical evidence showing time varying correlation between assets encouraged the research on hedging method capable model time dependent variance and covariances between

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assets. The starting points in the research are the autoregressive conditional heteroscedasticity (ARCH) models, initially proposed by Engle (1982), as the standard framework to analyse and forecast volatility in financial applications. Moreover, to model time-dependent hedge ratios is often implemented a variation of the ARCH model, the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model (

Bauwens et al. 2006

; Lien & Tse 2002). GARCH models consider the present period variance, the most recent squared residuals, and the weighted average of the long-run average variance as the best variance predictor (Engle 2001). The model repeats the process updating the variance prediction as new periods are added to the sample.

Several variations and extensions of ARCH and GARCH models have being applied to estimate volatility, especially when working large datasets. Bollerslev et al. (1998) proposed the vectorised (VECH) model to estimate a time-varying variance-covariance matrix. Due to the large numbers of free parameters estimated trough the likelihood function, it is impractical to apply the VECH with more than two variables (Basher & Sadorsky 2016). Further, the VECH model often violates the assumption of a positively defined variance-covariance matrix. Engle & Kroner (1995) developed the BEKK model, which ensures that the variance-covariance matrix is positive. However, the problem of the BEKK model is that the large quantities of unknown parameters remain. Both, Engle & Sheppard (2008) and Bauwens et al. (2006) state that VECH and BEKK suffer the “The curse of dimensionality”: as the dataset expand the number of parameters requiring simultaneous estimation increase at least quadratically. VECH and BEKK are rarely used to estimate more than four time-series.

The Constant Conditional Correlation (CCC) model and Dynamic Conditional Correlation (DCC) model are designed to address the shortcomings of VECH and BEKK. CCC and DCC can be considered a non-linear combination of univariate GARCH models, where individual conditional variance and the conditional correlation independently specified (Bauwens et al. 2006). These models are more practical with large sample since they have less unknown parameters. But, the CCC-GARCH assumption of constant correlation is not an answer to the critics on OLS hedge ratios. Engle (2002) proposed the DCC-GARCH model allows the dynamic correlation to change over time, and at the same time keeps the variance-covariance matrix positive. It simplifies the volatility estimation of the large multivariate dataset since the two steps estimation approach reduces the number of unknown parameters needing to be estimated.

DCC-GARCH have a more flexible and simple implementation them others multivariate GARCH models and often produces more precise volatility estimations (Engle 2002, Engle & Sheppard 2001). Hence, it has been applied in several times in the literature to construct minimum variance hedge ratios. For instance, Hautsch & Inkmann (2003) shows that DCC-GARCH hedge ratios

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outperform full hedge, half hedge, and no-hedge in reducing portfolio currency of American and European investor when investing in other developed markets. Furthermore, Chang et al. (2011) hedge crude oil prices with BEKK, CCC, DCC, and VARMA-GARCH models and conclude that DCC-GARCH is the best model to reduce the variance of the portfolio. Another example, hedging currency risk of a portfolio of developed market equity between January 2002 to April 2010, Brown et al. (2012) show superior performance of DCC-GARCH model over static and time unconditional variance model.

2.3 Portfolio Performance

Once defined that portfolio volatility reduction is the main hedging target, an investor can compare portfolio volatilities and Hedge Effectiveness. But, hedging portfolio currency risk may have some drawbacks as it can reduce portfolio returns or even increases total portfolio volatility (Walker 2008). Additional to the volatility measures, other portfolio indicators can allow portfolio managers to take a more informed decision comparing hedging strategies. De Roon et al. (2012) shows that it is necessary to investigate also portfolio total returns, Sharpe ratios, skewness, and kurtosis (De Roon et al. 2012). For instance, it is a stylised fact that some financial times series have a non-normal distribution, and risk-averse investors cannot only depend on returns and volatility for portfolio selection. The non-normality in the returns may distort risk measures and may lead to unreliable Sharpe ratios and is important to use also risk measures that are able to cope with non-normality, as lower tail risk, and also depicts the trade-off between loss and gain (Zakamouline & Koekebakker 2009). To sum up, the mean-variance framework is the starting point but is not enough to compared hedging strategies Investor need to also compared other portfolio measures, as the higher moments.

The Hedging Effectiveness measure is frequently3_{used in order to compare competing} hedging models. It measures the variance reduction between the proposed hedged model and the unhedged model (Ku et al. 2007). Thus, the higher the Hedge Effectiveness, the higher the volatility reduction. Between two models, the one with the higher Hedge Effectiveness is the preferred. Ripple & Moosa (2007) apply the Hedge Effectiveness to evaluate the effect of the of hedge instruments maturity to hedge future oil prices. For example, the Hedge Effectiveness measure is adopted by Basher & Sadorsky (2016) to compare currency hedge performance of DCC, ADCC, and GO-GARCH models.

3_{See for example: Brown et al. (2012), Caporin et al. (2014), Chincarini (2007), Ku et al. (2007),}

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Assuming that investors care more about downside losses than upside gains, Markowitz (1968) suggests the semi variance as a risk measure of the downside expected losses. From this definition, Rockafellar & Uryasev (2000) suggests the Conditional Value-at-Risk (CVaR) as an alternative approach to measuring downside losses. CVaR is a risk metric that averages the worst case losses beyond the Value-at-Risk threshold and quantifies the tail risk of the portfolio. The CVaR, also known as Expected Shortfall, recognises the expected losses in adverse scenarios and is an appropriated measure irrespective of the returns distributions (Acerbi & Tasche 2002). Topaloglou et al. (2002) show effective ex-post realized CVaR prediction when comparing hedging strategies with low volatility data.

Differently from the Sharpe Ratio, which only considers the first two moments (returns and volatility), the Omega Ratio takes into account all moments to calculate a risk-return measure (Keating & Shadwick 2002). The Omega ratio considers the cumulative probability of gains above a certain level over the cumulative probability losses below this level. Hence, is a gain-loss ratio. Further, the Omega ratio divides the portfolio returns into the upper partial moment (gains) and the lower partial moment (losses), without the need of any specific characteristic in the return distributions (Harris & Mazibas 2013; Kane et al. 2009).

To conclude, the simple change in the portfolio variance is not enough to assess the hedging strategy. First, it is necessary to evaluate the Hedge Effectiveness. Next, is necessary to access consequences on the portfolio returns and in the distribution of these returns. But, the final conclusion over a hedging strategy will depend on the initial goal and preferences of investors and researcher. One attempting to reduce only portfolio volatility may ignore the reduction on returns or higher lower tail risk.

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3. Methodology and Model

This chapter presents the methodology and model adopted in this paper in order to answer the research question. For this, the hedging strategy proposed by Campbell et al. (2010) and Brown et al. (2012) is followed. However, this thesis focuses on reducing currency risk of a portfolio of emerging markets equities and not a portfolio formed of developed markets equities. The time-varying variances and covariance are estimated with the Dynamic Conditional Correlation (DCC) GARCH model proposed by Engle (2002). Thus, based on the literature reviewed above and to illustrate the trade-off between risk reduction and portfolio returns, the following hypotheses are tested in this research:

(1) Time conditional hedge ratios decrease portfolio volatility and present significant Hedge Effectiveness;

(2) Time conditional hedge ratio improves portfolio returns; (3) Time conditional currency improve Skewness and Kurtosis; (4) Time conditional hedging increases Sharpe ratio.

Five competing hedging strategies are compared4_{: non-hedge, half-hedge, full-hedge, time} unconditional hedge ratio (OLS), and time-conditional hedge ratio. It is also presented the portfolio Conditional Value at Risk and Omega Ratio, to have clear picture of the portfolio tail risk and gain-loss relation. The strategies are implemented with daily data in-sample and out-of-sample from the standpoint of an investor located in one of the selected four developed markets holding a multi-currency portfolio of emerging market equities. The hedging instrument, the forward multi-currency contract, is added to the portfolio trough currency overlay where the variance-covariance of the assets are calculated on daily basis. Further, a passive equally weight portfolio of emerging equity is adopted. In practice, portfolio managers often use Sharpe ratios, mean-variance and other methods to determine the weights of each asset in the portfolio. Also, investors distribute the portfolio between equities and fixed income (Schmittmann 2010). However, a simplified portfolio construction to focus the evaluation of the results on hedging strategy outcomes is imposed. Nevertheless, it might also mimic the equity exposure of long-term institutional investor.

In the in-sample analyses is used the entire sample to fit the model and generate the hedge ratio and then measured the portfolio volatility and returns. Furthermore, is followed the literature5 and implemented the out-of-sample forecast as the robustness test. It is performed one-day ahead forecast using a rolling window. In the time conditional setting, the fixed size window of data is used to fit the model and predict one day ahead out-of-sample forecast of the variance-covariance matrix.

4_{See for example Brown et al. (2012) and Schmittmann (2010).}

5_{See for example Basher & Sadorsky (2016), De Roon et al. (2012), and Hautsch & Inkmann}

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Them, the in-sample window moves one day in the future and is repeated the fitting and forecast. The process is repeated step by step until the last period(day) in the sample. The same method with the time unconditional model is adopted. But, in this case, the OLS equation forecasts the one-day-ahead hedge ratios. The results out-of-sample exercise better reflects how portfolio managers implement hedge strategies since it uses only the information available at the time to make the forecast and model fitting (Caporin et al. 2014) information that hedgers have to construct models. Given the fact that we are working with the same data, the portfolio returns under the static hedge ratios of non-hedge, half, and full hedge remains equal to the in-sample analyses. Hence, only the unconditional hedge ratio (OLS) and the time conditional hedge ratio are calculated in the out-sample exercise.

The rest of this section is organized in the following way. 3.1 describes the portfolio returns, covariance and how the forward contracts are constructed. Next, 3.2 shows the time unconditional hedge ratios and 3.3 the time conditional variance-covariance model. Section 3.4 the out-of-sample covariance model. Finally, section 3.5 describes the portfolio performance measures.

3.1 Portfolio Returns, Variance, and the Forward Contract

The returns of the unhedged foreign asset, according to Brown et al. (2012), are given by:

, = , _, ,_, − 1 (1)

where P is the value of the asset i at time t, and S is the spot exchange rate of the foreign currency i at time t. Furthermore, the returns on a hedged investment asset are defined as

, = , − ℎ, , (2)

where the hi,t is the hedge ratio and fi,t is the return on the forward contract of currency i. According to Campbell et al. (2010), under the covered interest parity the forward currency contract is described as

, = ,( _, ,) (3)

where the Id,t is the domestic short-term risk-free interest rate and Ii,t is the country i risk-free interest rate. The exchange rate normalized return in the forward contract is given by

, = , _, , (4)

Following Brown et al. (2012), the return on the unhedged portfolio invested at n markets and where wi is the portfolio weights is given by

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= ∑ , (5)

The return of the hedged portfolio is given by

= ′ − ′( ⨀ ) (6)

where W is the vector of the portfolio weights. f is the vector of the forward currency returns fi,t. w is the of portfolio weights. Hence, ⨀ is vector of the one-period return in the forward positions.

′ is a vector the one-period spot return of the equity positions.

The variance of the hedged portfolio returns is defined by Brown et al. (2012) at time t can be defined as:

( ) = ( ) − ( ( ⨀ )) − 2 ( , ( ⨀ )) (7)

3.2 Time Unconditional Hedge Ratios

The equation 6 describes the hedged portfolio returns for the half-hedge (h=0.5), full-hedge (h=1), time unconditional hedge ratio, and time-varying hedge ratio. The hedge ratio for the last two strategies is calculated as follows.

The hedging main objective when hedging is to minimize portfolio variance. Hence, assuming that variance and covariances are constant over time, according to Brown et al. (2012) and Schmittmann (2010) the first order condition of the equation 7 with respect to the hedge ratio h is:

( ) (8)

( ⨀ )ℎ − ( , ⨀ ) = 0 (9)

∗₌ , ⨀

( ⨀ ) (10)

where h* is the static hedge ratio that minimizes the portfolio variance.

The optimal and time unconditional hedge ratio (h*) can be estimated trough OLS regression (Schmittmann 2010), where the spot prices returns( ) are the dependent variable and the spot returns in the forward contract ( ⨀ ) are the regressors:

= + ( ⨀ ) + (11)

where is the time unconditional hedge ratio for each one of the assets in the portfolio (Nx1 vector of coefficients). The OLS estimation will produce constant hedge ratios for the sample period.

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3.3 Time Conditional Hedge Ratios

According to Brown et al. (2012), under the assumption that correlation between assets are time-dependent, equation 7 is set to be conditional on the time, as follow

( )| = ( )| − ( ⨀ ) | − 2 ( , ( ⨀ ))| (12)

To derive the hedge ratio, which minimizes portfolio variance is necessary to minimize the portfolio variance equation

( )| (13) Hence ( ⨀ )ℎ| − ( , ⨀ )| = 0 (14) and ∗₌ ( , ⨀ ) ( ⨀ ) (15)

where h* is the time-dependent hedge ratio (Brown et al. 2012; Schmittmann 2010).

The time conditional correlations and covariances depicted in the equation 15 are estimated through a DCC-GARCH model, which is derived in the remaining of this section according to Brown et al. (2012), Engle (2002), and Engle & Sheppard (2001). The choice of model relies on its

implementation simplicity and capacity to deal with the problem of heteroscedastic when modelling time-varying correlation between different assets.

The DCC-GARCH is described as follows. First, the conditional mean asset returns Xt=[R,f]’ are modelled trough vector autoregression (VAR) as follow:

= + + + ⋯ + + (16)

where the residuals et|It-1~N(0, t) and It-1 is the information at time t-1. t is the variance-covariance matrix of the assets returns and currency forward returns at time t. The number of lags is determined with the AIC.

Afterwards, is constructed the Dynamic Conditional Correlation (DCC) GARCH model which later will provide the variance and the correlation necessary to calculate the hedge ratios. The variance-covariance matrix is given as:

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where  is the ( × ) time varying correlation matrix. Dt =(  , … ,  ) is the ( × ) diagonal matrix of the time varying standard deviations.

The standard deviations are calculated from univariate GARCH models. The GARCH (p,q) model is defined as:

, = + ∑ , , + ∑ , , (18)

where , is the conditional variance of the assets returns (here, equity index or forward

contract of given country). , is the squared residuals of the VAR (equation 16). It is

commonly adopted in the literature that the GARCH(1,1) specification is sufficient, since it is able to account for volatility dynamics and is easier to implement compared to high lag orders

(Hautsch & Inkmann 2003)6_._{The parameter α}_i,p_{denotes the short run persistence of shocks to the}

returns, or the ARCH effects. βi,q are the GARCH effects and ∑ , + ∑ , represents the

long run persistence. ωi,αi,p and βi,q are non-negative scalar parameters and ∑ , + ∑ , <

1. The GARCH model parameters are calculated through the maximum likelihood estimation. It is also imposed the condition of the data to be stationary. If the GARCH model is correctly specified the residuals would have constant mean and variance, in other words, residuals are not autocorrelated (Engle 2001).

In the second stage, the residuals generate by the VAR model of the returns are adjusted by their conditional standard deviation obtained in the first stage. Hence, = ~ (0, Λ ) is the vector of the standardized returns residuals. Next, it is estimate the parameters of the dynamic correlation structure, as follow:

= 1 − ∑ − ∑ + ∑ ( ) + ∑ (19)

where δm and ηl are non-negative DCC (M,N) parameters, and ∑ − ∑ < 1, and is the n x n unconditional variance matrix of the standardized residuals(εt). It is adopted here DCC

(1,1) specification following the related literature7_._{The DCC-GARCH δ and η parameters in the}

equation 19 are calculated trough the maximum log likelihood estimation, expressed as

= − ∑ ( (2 ) + 2 | | + | | + ) (20)

6_{Further the out-of-sample results tend to deteriorate when using higher lag orders. See also: Basher}

& Sadorsky (2016), Brown et al. (2012), Chang et al. (2013), Engle & Sheppard (2001), Sheppard (2003).

7_{The reasons for the DCC(1,1) specification are similar if not the same when justifying the choice for}

the GARCH(1,1). This specification accounts for the volatility dynamics, is simple to implement, and produce better results out-of-sample. See: Basher & Sadorsky 2016, Brown et al. 2012, Chang et al. 2013, Engle & Sheppard 2001, Hautsch & Inkmann 2003, and Sheppard 2003.

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Next, the variance matrix is used to calculate the dynamic correlation matrix is defined as:

= [ ] / _{[ ]} / ₍₂₁₎

The typical element of Λ will be of the form , = , ⁄ . The covariance matrix t has to be positive, since Dt is positive t has to be positive definite (Bauwens et al. 2006; Engle & Sheppard 2001).

Finally, with the variances and covariances from the dynamic correlation matrix (equation 21) we calculate the time-dependent hedge ratios of equation 15.

3.4 Out-Of-Sample Time Conditional Hedge

According to Engle & Sheppard (2001), the r-step ahead GARCH(1,1) model is described as

, = ∑ ( , + , ) + ( , + , ) , (22)

where , and , are the GARCH(1,1) parameters .The DCC(1,1) estimator is

, = 1 − , − , + , , , + , , (23)

where and are parameters from the DCC (1,1) estimator. Further

= [ ] / _[ _] / ₍₂₄₎

However, equation 23 cannot directly forecast r-steps ahead, according to Engle & Sheppard (2001) one should make the approximation

≈ ( ) for i ∈ (1, ... , r) (25) Then, is calculated the r-step ahead forecast of Qt

, [ , ] = ∑ 1 − , − , ( , + , ) +( , + , ) −1 , (26)

The next step is to replace the forecast of the dynamic correlation (equation 26) into the dynamic correlation matrix (equation 21) (Engle & Sheppard 2001). Finally, with the variances and covariances of the dynamic correlation matrix the time-conditional hedge ratios are calculated according equation 15.

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3.5 Portfolio Performance Measures

This section briefly describes the portfolio measures and statistical tests used to evaluate the competing hedging methods.

The Hedge Effectiveness, which compares the risk reduction between the hedged portfolio and the unhedged portfolio. It is defined by Caporin et al. (2014), as follow

= (27) where is the variance of the unhedged portfolio and is the variance of the hedged portfolio.

This Hedge Effectiveness is adopted by Brown et al. (2012) and Caporin et al. (2014) as the main comparative between competing hedging strategies. According to Ripple & Moosa (2007), the significance test for the Hedge Effectiveness is the test of the change in volatility between both portfolios. The null hypothesis is that both unhedged and hedge portfolio present the same variance. The mean returns of the portfolio are evaluated with the Student's t-test, under the hypothesis of equal mean returns between the unhedged portfolio returns (equation 5) and the hedged portfolio returns (equation 6) (Harvey & Siddique 2000).

Given the importance of incorporate higher moments in the selection of the hedge strategy, we compare the hedged portfolio skewness and kurtosis against the unhedged portfolio. Further, the quantile-quantile (QQ) plot is used to verify if the distribution in the returns of the unhedged and hedge portfolios have a similar shape (Gencay & Selcuk 2004). The quantiles of each distribution are plotted against each other. The greater the departure from the 45-degree line, the greater the evidence that both samples have different distributions.

The Sharpe ratios measure the risk-adjusted returns, and are defined according to Leung & Wong (2006) as

ℎ = (28)

where is the portfolio returns, is the risk-free rate the investor domestic market and is the portfolio standard deviation. The Sharpe ratios are tested for statistical significance through the method developed by Leung & Wong (2006), where is tested the null hypothesis of the equality between the Sharpe ratios of the unhedged and of the hedged portfolio (Dupuy et al. 2016; Lean et al. 2010).

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4. Data

Four different portfolios are constructed in the empirical analyses with daily data from January 2000 to January 2016. Each portfolio represents an investor located in one of the following developed markets: the Eurozone, Japan, the United Kingdom, and the United States. The results are depicted in terms of the investor domestic currency. Hence, the returns on emerging market equity index are converted to the developed market currency. In other words, the returns on the Chilean equity index is converted into US dollar for the American based investor. The forward currency contract returns are also denominated in terms of the developed domestic currency. The selected emerging markets8_{are Brazil, Chile, China, India, Indonesia, Malaysia, Mexico, Philippines, Poland,} Russia, South Africa, South Korea, Taiwan, Thailand, and Turkey. All the datais available at Reuters (via DataStream) and comprises of spot exchange rates, risk-free interest rates, and equities indexes. The indexes are the MSCI single-country equity index of each developed market. Appendix 1 depicts a complete list of the data and its respective DataStream code. The currencies and equity indexes returns are tested for stationarity through the Augmented Dickey-Fuller (ADF) statistic test.

Given the choice of mode, it is important to test the data for the presence of ARCH and GARCH effects (Bauwens et al. 2006; Malhotra & Krishna 2014). Hence, it is applied the Lagrange Multiplier to test the presence of a dynamic conditional variance process in the time series, or ARCH effects. The Lagrange Multiplier tests the null hypothesis of the presence of homoscedasticity in the data. The GARCH effects are tested using the Ljung-Box test, where the null hypothesis is no serial autocorrelation in the standardized residuals. If the null hypothesis is rejected in both Lagrange Multiplier and Ljung-Box test, the data is said to be appropriate for the GARCH based models. These analyses are performed on the equity indices returns and spot exchange rates9_{. Further, it is also} verified if the data follows a normal distribution with the Jarque-Bera test statistics, under the null hypothesis of the skewness and excess kurtosis being both zero.

Next, the summary statistics for the equity returns and the spot exchange rate returns in US dollars is presented. The equity returns and currency return denominated in Euro, British Pound, and Japanese Yen present similar summary statistics and are depicted in Appendix 2. Table 1 describes the relevant summary statistics for the equity indexes returns denominated in US dollars for the entire sample period. The average daily returns values at table 1 are presented times 100 for better visualisation of the returns. For instance, Brazil and Chile equity indexes have a daily average returns of 0,00031% and 0,00023%. Moreover, all equity indexes present a similar level of daily average

8_{Emerging market portfolio construction in based on the MSCI Emerging Markets Index,}

available at: https://www.msci.com/emerging-markets.

9_{The forward contract returns are not tested ARCH and GARCH effects, since they are calculated}

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returns and volatility. The equity returns skewness close to zero meaning no heavy tails. Most of the indexes present leptokurtic distribution of the returns, given the high kurtosis. The Jarque-Bera test corroborates the results and rejects the null hypothesis of the excess of skewness and Kurtosis being zero, at 1% confidence interval. The Augmented Dickey-Fuller tests are significance at 1% confidence interval. Hence we can reject the null hypothesis of the presence unit root in the data. Further, both Lagrange Multiplier and Ljung-Box reject the null hypothesis of no ARCH and GARCH effects. The equity returns denominated Euro, British Pound, and Japanese Yen present similar characteristics. Where we reject the hypothesis of the excess of skewness and Kurtosis being zero, the presence of unit root is also rejected and ARCH and GARCH effects are found in all the data.

Table 1: Summary Statistics – Emerging Markets Equity Indexes Daily Returns, denominated in US dollars. January 2000 to March 2016.

Note: 4217 observations.† mean returns are show times 100. The ADF tests are applied to test the null hypothesis of a unit root for the returns; Ljung-Box statistics for up to 10th order serial correlation in the returns, under the null hypothesis of no GARCH effects; LM is the Lagrange test for the null hypothesis of no ARCH effects (up to the 5th order); J-B is the Jarque-Bera test for normality, null hypothesis of the skewness and excess kurtosis being both zero; * indicates significance at the 1% level, ** indicates significance at the 5% level, *** indicates significance at the 10% level.

Table 2 shows the spot exchange rate returns for the emerging markets currencies against the US Dollars. The exchange rates present often negative average daily mean, such as the Turkish Lira with the average daily return of -0.00033%. Most of the currencies indicate skewness closer to zero, apart from the right side tail of the Philippines and South Korea and the Turkey left side tail. Similar to the equity returns, the kurtosis indicates a leptokurtic distribution of all exchanges rates returns. The Jarque-Bera rejects the null hypothesis of normally for all contracts at 1% confidence interval. The Augmented Dickey-Fuller tests are significance at 1% confidence interval. Hence, we can reject the presence unit root in the exchange rate data. Further, both Lagrange Multiplier and Ljung-Box reject the null hypothesis of no ARCH and GARCH effects. Once more, the exchange rates between Euro, British Pound, and Japanese Yen and the emerging markets currencies show comparable results and are depict in Appendix 2

Brazil Chile China India Indonesia Malaysia Mexico Philippines

Mean Return 0.031 0.023 0.033 0.039 0.048 0.019 0.039 0.027 Standart Deviation 0.023 0.013 0.018 0.017 0.020 0.010 0.017 0.016 Skewness 0.162 0.202 0.199 0.139 -0.108 -0.280 0.270 1.088 Kurtosis 7.535 13.471 5.824 9.327 4.986 6.349 8.954 23.235 ADF -14.284 -15.031 -15.201 -14.454 -14.293 -15.504 -15.366 -15.383 LM 797.39 651.86 682.00 200.59 257.30 253.51 779.84 78.95 Ljung-Box 19.57** 85.98*** 31.37*** 59.72 40.55 71.79 40.81 66.61 J-B 10006.53 31953.34 5996.86 15316.67 4382.07 7148.40 14157.13 95790.80

Poland Russia South Africa South Korea Thailand Taiwan Turkye

Mean Return 0.019 0.040 0.032 0.038 0.009 0.032 0.035 Standart Deviation 0.020 0.026 0.018 0.021 0.016 0.017 0.028 Skewness -0.051 0.055 -0.414 0.219 -0.106 -0.260 0.215 Kurtosis 3.798 10.719 6.658 11.370 2.946 6.849 6.506 ADF -15.102 -15.597 -15.785 -17.013 -15.342 -15.397 -14.680 LM 579.95 420.63 664.42 429.97 400.37 458.43 446.78 Ljung-Box 23.37 49.42 24.45 22.97** 31.53 26.34 41.03 J-B 2541.12 20213.83 7920.68 22775.02 1535.27 8301.41 7481.24

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Table 2: Summary Statistics – Daily Spot Emerging markets exchange returns against US dollars. January 2000 to March 2016.

Note: 4217 observations.† mean returns are show mes 100. The ADF tests are applied to test the null hypothesis of a unit root for the returns; Ljung-Box statistics for up to 10th order serial correlation in the returns, under the null hypothesis of no GARCH effects; LM is the Lagrange test for the null hypothesis of no ARCH effects (up to the 5th order); J-B is the Jarque-Bera test for normality, null hypothesis of the skewness and excess kurtosis being both zero; * indicates significance at the 1% level, ** indicates significance at the 5% level, *** indicates significance at the 10% level.

Table 3 reports the time unconditional daily correlation between the emerging markets equity returns denominated in the local currency. The equity returns of all markets present a positive degree of correlation, which increases with the geographic proximity. This is expected given the stronger economic ties within neighbour economies. For instance, the correlation among Latin American and among Asian countries is higher than the correlation between Asian and Latin American markets.

Table 3: Time Unconditional Daily Correlations Emerging Markets Equity Indexes Returns - January 2000 to March 2016.

Furthermore, emerging markets were severely affected by the 2008 Financial Crises (Bekaert & Harvey 2014). Hence, the full sample analyses may be subject to a structural data break since it

Brazil Chile China India Indonesia Malaysia Mexico Philippines

Mean Return -0.013 -0.004 0.006 -0.010 -0.013 -0.002 -0.012 -0.003 Standart Deviation 1.067 0.645 0.108 0.440 0.658 0.368 0.723 0.469 Skewness 0.08 -0.17 0.35 -0.34 0.22 0.44 -0.52 3.94 Kurtosis 8.97 3.97 59.09 12.77 29.76 9.88 13.08 107.74 ADF -14.00* -15.23* -13.98* -14.50* -12.52* -14.88* -15.74* -14.76* LM 727.60* 297.80* 78.05* 583.81* 113.67* 451.46* 1150.23* 12.59* Ljung-Box 38.27* 20.32* 51.04* 47.76* 32.28* 38.86* 73.34* 81.34* J-B 14164.4* 2798.05* 614185.72* 28776.58* 155830.26* 17302.01* 30264.57* 2052594.22*

Poland Russia South Africa South Korea Thailand Taiwan Turkye

Mean Return 0.005 -0.021 -0.016 0.001 0.003 -0.001 -0.033 Standart Deviation 0.909 0.765 1.126 0.822 0.484 0.310 1.126 Skewness -0.17 0.72 -0.42 1.34 0.72 0.25 -2.76 Kurtosis 4.20 89.95 15.61 29.55 138.54 24.16 50.90 ADF -14.75* -13.83* -16.21* -15.79* -14.27* -14.39* -14.87* LM 746.74* 1078.57* 483.18* 331.18* 1414.20* 1018.93* 470.73* Ljung-Box 29.72* 77.89* 28.78* 115.97* 192.94* 88.65* 85.13* J-B 3118.07* 1423462.95* 42990.07* 154857.96* 3376059.55* 102723.20* 461081.88* 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 (1) Brazil 1 (2) Chile 0.51 1 (3) China 0.29 0.28 1 (4) India 0.25 0.25 0.44 1 (5) Indonesia 0.19 0.23 0.43 0.36 1 (6) Malaysia 0.15 0.22 0.41 0.29 0.37 1 (7) Mexico 0.64 0.51 0.27 0.26 0.18 0.15 1 (8) Philippines 0.12 0.16 0.33 0.23 0.34 0.34 0.11 1 (9) Poland 0.34 0.35 0.35 0.34 0.28 0.24 0.36 0.18 1 (10) Russia 0.38 0.33 0.36 0.31 0.26 0.24 0.37 0.16 0.48 1 (11) South Africa 0.36 0.36 0.39 0.36 0.30 0.28 0.40 0.22 0.46 0.49 1 (12) South Korea 0.21 0.23 0.54 0.36 0.36 0.35 0.24 0.29 0.32 0.30 0.36 1 (13) Thailand 0.17 0.20 0.46 0.31 0.35 0.35 0.16 0.30 0.26 0.25 0.31 0.55 1 (14) Taiwan 0.24 0.27 0.45 0.35 0.38 0.37 0.25 0.30 0.29 0.29 0.31 0.39 0.34 1 (15) Turkye 0.27 0.26 0.26 0.23 0.20 0.20 0.25 0.16 0.37 0.39 0.32 0.25 0.21 0.24 1

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covers crises period. Therefore, the in-sample and out-of-sample analyses are replicated in three distinct sample periods, as depicts table 4. First, is selected the period before the 2008 crises. Next, the two years’ period during the crises. Finally, a data period representing the post crises period, from 2010 to most recent date.

Table 4: Sample and Sub-Samples Periods

Period Number of Observations*

Full Sample 01/01/2000 to 01/03/2016 4217

Before Crises 01/01/2016 to 01/01/2008 1825

Crises Period 01/01/2008 to 01/01/2010 784

After Crises 01/01/2010 to 01/03/2016 1608

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5. Empirical Results and Discussion

This section presents the in-sample and out-of-sample results where the forward currency contract is added to the portfolio trough currency overlay. The results are presented from the perspective of investors based in the US, Europe, the United Kingdom, and Japan investing in emerging markets equities. For both In-sample and out of sample the time unconditional hedge ratio is calculated according to equation 11, the time conditional covariance’s with a DCC(1,1)-GARCH(1,1) model10_{and time conditional hedge ratios with equation 15.}

In the in-sample analyses differently from the OLS hedge ratios, the DCC-GARCH hedge model produces a daily update of the hedge ratios. However, some investors are not willing to bear the transaction costs of daily changes in the hedging instrument positions. Hence, four alternatives to rebalance frequencies are presented: daily, monthly, minimum threshold, and constraint hedge ratio. The daily rebalance mimics a continuous rebalancing of the portfolio forward currency contract position and is often adopted in the literature when using GARCH models (Brown et al. 2012; Caporin et al. 2014; Engle 2002). Moreover, Hautsch & Inkmann (2003) suggests that the hedge ratio should be updated only when the newly estimated hedge ratio is larger or smaller than current hedge ratio by certain percentage11_{amount. For instance, with a threshold of 10% portfolio} managers should only update the hedge ratios if the new estimated hedge ratio is 10% larger or smaller than the current hedge ratios. The monthly rebalance frequency is based on the common practice in the financial markets12_{, where the currency hedge ratio of portfolios are updated in the} first trading day of the month and estimated with the most recent available information.

Hedge ratio larger than 1 infers the use of leverage and lower them zero to short sell the hedging instrument. However, portfolio managers are often not allowed to take such speculative positions. Hence, the results are also presented when the time conditional hedge ratio is constrained between 0 and 1.

5.1 In-sample analyses – January 2000 to March 2016

This section reports the in-sample results for the full sample period, from January 2000 to March 2016. Figure 1 depicts the time conditional correlation between equity returns and the forward contracts returns denominated in Euros for four developing countries. It reinforces the criticism

10_{Appendix 4 reports the in-sample DCC-GARCH model parameters for the full-sample period and also}

for the subsample periods.

11_{Hautsch & Inkmann (2003) without any extensive discussion adopt a threshold of 25%.}

12_{For example, the MSCI Japan U.S. Dollar Hedged Index currency risk is hedged on monthly basis,}

available at: https://etfus.deutscheam.com/US/EN/resources/insights/market-insights/CURRENCY-WHITE_4Q15.pdf

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against the assumption of constant asset correlations, as it is clear that the correlations are time dependent. Similar behaviour holds for all other countries’ equity-forwards returns independent on the underlying currency (US Dollars, Euro, British Pound, and Japanese Yen). Furthermore, as the correlation and covariance between assets are an important determinant of the minimum variance hedge ratios, we can extend the criticism to time static ratios. The static hedge ratios cannot follow the correlation peaks and troughs the peaks show at figure 1 and represent the most recent available information. Portfolio managers need to update promptly investment strategies when macroeconomic and other exogenous shocks change the underlying correlation among assets. Time conditional hedging ratios give this flexibility to sudden changes in the markets dynamics and portfolio managers can quickly react.

Figure 1: Time Conditional Correlation Between Equity and Forward Currency Contracts – January 2000 to March 2016

Figure 2 shows the time unconditional hedge ratio (OLS) and time conditional hedge (DCC-GARCH) for four different portfolio-emerging markets match. It is clear that hedge ratios fluctuation in the time dependent hedge ratios and the difference them and the time unconditional hedge ratio. The hedge ratios of the Brazilian equity indexes for the American portfolio oscillate above zero for most of the period. However, the fixed time unconditional hedge ratio is negative. The hedge ratio of Poland equity in the European portfolio fluctuates between negative and positive value. In the British portfolio, the hedge ratio of the Mexican equity show significate peaks and troughs. Finally, the hedge ratio of the Turkish equity in the Japanese portfolio present large fluctuation before the in the initial years and slowly decreases after 2005. To sum up, figure 2 illustrates that time conditional hedge ratios do not follow the same path across the sample. They present some similarities, as on

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average oscillate on between the same upper and lower bounds and show at some points a relative large difference from the time unconditional hedge ratios.

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Table 5 shows the fixed time unconditional (OLS) and the average daily time conditional hedge ratios hedge ratios for the four portfolios. Once more, both models present clear distinct hedge ratios. In the American portfolio, the South African equity has a fixed and negative OLS hedge ratio, but a positive average hedge ratio for time conditional strategy. The magnitude of the hedge ratio also presents relevant difference, for instance, for the Japanese investor hedging Chinese and South Korean equity.

Table 5: In-sample Daily Hedge Ratios – January 2000 to March 2016

Note: † ﬁxed hedge ra o value for the entire period; all other hedge ratios are the daily averages. Shows the hedge ratios for each developing market equity index for all four portfolios. Unconditional hedge ratios are generated by regressing(OLS) the unhedged portfolio onto the return on the

currency forward contracts The time conditional hedge ratios are computed with conditional covariance matrix estimated from the DCC-GARCH model.

Table 6 illustrates the changes in the average time-dependent hedge ratios for three alternative hedge ratios rebalance frequencies. These results are important for portfolio managers concerned with trading costs and the complexity of the daily operations. In the monthly rebalance frequency, the portfolio hedge ratios are updated with the time conditional hedge ratios estimated for the last day of the previous month. Hence, the hedge ratios reflect only the information that portfolio managers have available in the first day of the month13_{. Table 6 shows no change in the} average hedge ratio; however, this does not denote that portfolio volatility remains the same. For

13_{The out-of-sample exercise, where the model produces one-period ahead of forecasts of the hedge}

ratios, provides a more realist simulation of the daily implementation of hedging strategies (Caporin et al. 2014). US EU UK JP US EU UK JP Brazil -0.046 0.181 0.166 0.225 0.045 0.169 0.181 0.172 Chile 0.087 0.028 0.024 -0.010 -0.001 -0.014 -0.019 -0.010 China 0.365 -0.076 -0.132 0.247 -0.011 -0.043 -0.073 -0.331 India 0.109 -0.043 0.017 0.097 0.147 -0.064 -0.004 0.030 Indonesia 0.233 0.084 0.103 0.321 0.165 0.048 0.066 0.223 Malaysia -0.068 -0.058 -0.055 -0.012 -0.101 -0.038 -0.055 -0.027 Mexico -0.130 0.099 0.055 0.012 0.013 0.072 0.071 -0.018 Philippines -0.205 -0.101 -0.103 0.371 -0.034 -0.024 -0.061 0.211 Poland -0.008 0.057 0.004 0.096 -0.004 0.013 0.012 0.054 Russia 0.180 0.089 0.062 0.000 0.036 -0.008 0.043 0.000 South Africa -0.065 0.008 0.002 0.047 0.016 -0.014 0.004 0.005 South Korea -0.119 -0.108 -0.127 0.566 0.057 -0.033 -0.044 0.164 Thailand -0.077 -0.042 -0.059 0.267 0.137 -0.014 0.009 0.093 Taiwan -0.102 -0.063 -0.023 0.030 0.209 0.048 0.047 0.051 Turkye 0.027 0.162 0.161 0.335 0.133 0.109 0.118 0.288

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instance, the monthly rebalance will not update the hedge ratios for sudden changes in correlations and covariance that may occur during the month. Next, table 6 depicts the average hedge ratios when the most recent hedge ratio estimates by the model is 50% greater or smaller them the current portfolio hedge ratio. For instance, if the current hedge ratio is 1 and the threshold is 50%, the portfolio hedge ratio would only be updated if the model estimates a hedge ratio larger than 1.5 or lower than 0.5. The threshold of 50% is defined according to Figure 3, which depicts the average time conditional hedge ratios for thresholds ranges from 1 to 100%. The same occurs for other combinations of developed and developing markets, where the average hedge ratio remains constant until around a threshold of 75-85%. Hence, a threshold of 50%for the remainder of the analysis is selected since this level has a small effect on the average hedge ratio but decreases the number of rebalances hedging position. Table 6 confirms figure 2 and shows almost now a significant change in the average time depended on hedge ratios. Finally, table 6 shows the average hedge ratio when they are constraints between zero and 1. It is clear the consequence of the lower bound constraint as now there are no negative hedge ratios. The upper bound 1 brings apparently no effect since the hedge ratio never reaches the values larger than 1 in the in-sample analyses of the complete data sample. The small effect of the alternative rebalances frequencies can be attributed the low variation in the hedge ratios in the full sample period. For instance, the average time-dependent hedge ratios maximum of 0,288 and a minimum of -0.311 (table 6) for the four portfolios.

Table 6: In-sample Daily Time Conditional Hedge Ratios – January 2000 to March 2016

Note: † ﬁxed hedge ratio value for the entire period; all other hedge ratios are the daily averages. Shows the hedge ratios for each developing market equity index for all four portfolios. Unconditional hedge ratios are generated by regressing(OLS) the unhedged portfolio onto the return on the currency forward contracts The time conditional hedge ratios are computed with conditional covariance matrix estimated from the DCC-GARCH model. US EU UK JP US EU UK JP US EU UK JP Brazil 0.044 0.168 0.179 0.170 0.044 0.170 0.184 0.175 0.047 0.169 0.181 0.172 Chile 0.000 -0.015 -0.020 -0.010 0.000 -0.013 -0.018 -0.009 0.014 0.012 0.011 0.004 China -0.010 -0.044 -0.074 -0.334 -0.009 -0.042 -0.073 -0.331 0.120 0.017 0.011 0.000 India 0.151 -0.064 -0.004 0.031 0.151 -0.064 -0.003 0.032 0.149 0.004 0.022 0.033 Indonesia 0.162 0.047 0.066 0.219 0.174 0.050 0.070 0.242 0.165 0.058 0.069 0.223 Malaysia -0.100 -0.037 -0.055 -0.027 -0.101 -0.038 -0.055 -0.027 0.006 0.002 0.002 0.003 Mexico 0.013 0.071 0.070 -0.018 0.014 0.075 0.074 -0.018 0.024 0.080 0.080 0.003 Philippines -0.036 -0.026 -0.062 0.215 -0.034 -0.023 -0.061 0.215 0.011 0.020 0.007 0.211 Poland -0.004 0.011 0.013 0.054 -0.004 0.013 0.012 0.055 0.009 0.034 0.025 0.055 Russia 0.038 -0.011 0.044 0.000 0.039 -0.007 0.046 0.000 0.081 0.042 0.069 0.000 South Africa 0.016 -0.015 0.004 0.005 0.016 -0.014 0.005 0.006 0.018 0.010 0.019 0.017 South Korea 0.057 -0.033 -0.044 0.165 0.058 -0.033 -0.044 0.165 0.061 0.016 0.020 0.164 Thailand 0.137 -0.013 0.009 0.094 0.139 -0.013 0.010 0.094 0.138 0.018 0.034 0.093 Taiwan 0.209 0.046 0.046 0.050 0.214 0.050 0.049 0.053 0.210 0.057 0.058 0.058 Turkye 0.132 0.108 0.118 0.283 0.134 0.109 0.119 0.301 0.133 0.112 0.119 0.288

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Figure 3: Average Daily Hedge Ratios for different Thresholds (%) – January 2000 to March 2016

The annualised performance measures of the full sample are depicted in table 7. The half hedge and full hedge strategies present the largest volatility reduction among all portfolios. The half hedge outperforms full hedge for American and European investors, and full-hedge outperforms half hedge for the British and Japanese investor. There is a small difference in volatility between time unconditional and the variants of the time conditional hedging strategies; however, time unconditional produces a slightly lower volatility on average. Thereafter, the Hedge Effectiveness, which measures the percentage risk reduction relative to the no hedged portfolio, confirms the superior performance of the static half hedge and full hedge ratio. The F-test results show no statistical significance for variance reduction in the US, European and Japanese portfolios for all hedging strategies. However, the volatility reduction is significant at the 5% confidence interval for all strategies in the UK portfolio. The volatility reduction of the half-hedge and full hedge comes with the cost of reduction of the portfolio returns compared to the no hedge. The portfolio returns remained unchanged with the time conditional and unconditional strategies relative to the no hedge. Hedging show no effect on the skewness and kurtosis since there is no significative difference in the distributional shapes or location in the quantile-quantile plots (Appendix 5) of the hedge portfolios compared to the unhedged portfolio. The time unconditional and time conditional just slightly changes the Sharpe ratios. The static hedge shows a larger change in the Sharpe ratios especially for the European, British and Japanese portfolios. For instance, for the Japanese investor the Sharpe ratios decreased from 0.457 and 0.672 for the half and full hedge compared to 0.296 when there is no hedge. On the other hand, the static hedge decreases Sharpe ratio in the UK portfolio. The changes in the Sharpe ratios are not statistically significant, since we cannot reject the

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null hypothesis of Sharpe ratio being equal to the unhedged portfolio. Neither of the strategies is able to improve Conditional VaR and the gain-loss ratio of the four portfolios. To conclude, the conditional and unconditional hedging do not achieve the primary goal of risk hedging. The static hedging does produce better results, but the results are significant only for one portfolio. Further, the different rebalance frequencies do not generate any significant different in the portfolio volatility and other measures.

The results show that time conditional hedging does not reduce emerging market portfolio risk. Emergent market currency might yield a risk premium, as the full hedge ratio decreased the portfolio average returns. However, we develop here two possible arguments that can explain the results. First, one of the possible reasons might be the low correlation between the data currency returns and equity returns. The correlation matrixes between equity and forward contract returns (Appendix 3) show an average correlation with between 0 and 0.116 for the four portfolios. Low correlations imply a low covariance between the assets and consequent low hedge ratio. Macroeconomic policies of developed and developing markets governments might have an important weight in this correlation. For instance, the fixed peg of the Chinese Yuan to the US Dollar is well known. Under a free float exchange rates, the rising in return in the Chinese equity markets would attract an inflow of foreign capital. The growing inflow would lead to a depreciation of the Chinese Yuan. However, the exchange rate peg does not allow such adjustments and may eliminate any co-movement between the exchange rate and equity returns. Even though not all developing economies in the sample have a fixed exchange rate regime, most of them continuously make use of currency interventions as a macroeconomic policy tool (Burns et al. 2014). Secondly, the reason for the failure of time conditional strategies to reduce portfolio risk reason might be the low correlation between the equity returns and the returns on the artificially constructed forward currency contracts. Forward and Futures derivatives might provide a better risk relation currency and equity, as they provide a more accurate and up-to-date market perception of country risk. However, there are few to no data available for forwards and futures derivatives for emergent market currencies and the artificial forward currency contracts used here might be the only technique to simulate long sample periods.

Since the in-sample data comprehends a period between 2000 and 2016, structural breaks might be another reason for the low performance of time-dependent hedge ratios. The next section presents the results for three distinctive periods: before, during, and after the 2008 financial crises.

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Table 7: Annual In-sample Results – January 2000 to March 2016

Note: No hedge is the unhedged portfolio; time unconditional is the OLS model; time conditional is the DCC-GARCH model. Student’s t-test are applied to test the null hypothesis equal returns of the hedged portfolio against the unhedged portfolio. F-test test the Hedge Effectiveness, under the null hypothesis of equal variance between the hedged and unhedged portfolio. The skewness and kurtosis quantile-quantile plots are display in the Appendix 5. The Sharpe ratios are tested for the null hypothesis of equal variance between the hedged and the unhedged portfolio. * indicates significance at the 1% level, ** indicates significance at the 5% level, *** indicates significance at the 10% level.

5.2 In-sample analyses – Subsample Periods

Table 08 presents the hedge ratio for the period before the financial crises, between January 2000 and January 2008. There is clear changes in the magnitude of the hedge ratios compared to the full sample period. For example, under the time conditional DCC-GARCH model, the full sample suggests an average hedge ratio of 0.045 (table 5) to the Brazilian equity in the US portfolio. Table 8 on the other hander, suggest an average hedge ratio of 0.155. The change in magnitude is also present on other portfolios emerging market equity. Comparing time unconditional and time conditional hedge ratios, the larger changes are for the Asian countries for four all portfolios. The

No Hedge Half Hedge Full Hedge _{Unconditional}Time _ConditionalTime Conditional Time Monthly Time Conditional Threshold Time Conditional Constraint

Average Annual Return 0.114 0.099 0.085 0.114 0.112 0.112 0.112 0.112

Standart Deviation 0.342 0.300 0.260 0.342 0.338 0.338 0.338 0.337 Hedge Effectiveness 0.123 0.240 0.001 0.012 0.013 0.014 0.015 Skew 0.24 0.15 0.03 0.22 0.23 0.24 0.23 0.23 Kurtosis -0.70 -0.60 -0.46 -0.71 -0.68 -0.68 -0.67 -0.67 Sharpe Ratio 0.07 0.02 -0.05 0.07 0.06 0.06 0.06 0.06 CVaR -0.51 -0.46 -0.43 -0.51 -0.50 -0.50 -0.50 -0.50 Omega Ratio 2.45 2.46 2.42 2.44 2.44 2.43 2.44 2.44

Standart Deviation 0.303 0.279 0.261 0.300 0.301 0.302 0.301 0.300 Hedge Effectiveness 0.080 0.137 0.012 0.005 0.004 0.007 0.010 Skew 0.14 0.07 0.07 0.12 0.13 0.12 0.13 0.13 Kurtosis -0.55 -0.50 -0.45 -0.54 -0.56 -0.55 -0.56 -0.56 Sharpe Ratio -0.18 -0.18 -0.18 -0.18 -0.18 -0.18 -0.17 -0.17 CVaR -0.47 -0.45 -0.43 -0.47 -0.47 -0.48 -0.47 -0.47 Omega Ratio 2.28 2.31 2.33 2.29 2.27 2.27 2.27 2.28

Standart Deviation 0.274 0.265 0.260 0.270 0.273 0.273 0.274 0.273 Hedge Effectiveness 0.032** 0.049** 0.012** 0.002** 0.002** 0.000** 0.004** Skew 0.22 0.14 0.03 0.20 0.20 0.20 0.20 0.20 Kurtosis -1.23 -0.89 -0.49 -1.23 -1.20 -1.20 -1.19 -1.19 Sharpe Ratio -0.32 -0.39 -0.45 -0.32 -0.32 -0.33 -0.32 -0.32 CVaR -0.38 -0.39 -0.42 -0.37 -0.38 -0.38 -0.38 -0.38 Omega Ratio 2.56 2.51 2.44 2.57 2.55 2.55 2.54 2.55

Standart Deviation 0.326 0.292 0.259 0.314 0.321 0.321 0.320 0.320 Hedge Effectiveness 0.104 0.203 0.037 0.014 0.015 0.018 0.017 Skew -0.34 -0.15 0.08 -0.28 -0.31 -0.31 -0.32 -0.31 Kurtosis -0.64 -0.48 -0.36 -0.60 -0.59 -0.59 -0.58 -0.60 Sharpe Ratio 0.20 0.35 0.55 0.25 0.21 0.21 0.21 0.22 CVaR -0.56 -0.50 -0.43 -0.54 -0.55 -0.55 -0.55 -0.55 Omega Ratio 2.40 2.36 2.28 2.37 2.40 2.40 2.41 2.39 Ameican Portfolio European Portfolio British Portfolio Japanese Portfolio

Hedging currency risk of emerging market equities

UNIVERSITY OF AMSTERDAM

AMSTERDAM BUSINESS SCHOOL