Currency overlay : the perspective of a euro-investor

Currency Overlay

Daan Mica 9912606

February 15, 2008 Master Thesis

Business Economics: Finance Prof. Dr. Joost Driessen

Faculty of Economics and Business Universiteit van Amsterdam

Table of contents

1 Introduction ... 3

2 Currency markets and currency risk ... 4

2.1 International diversification ... 4 2.2 Currency risk ... 5 2.3 Currency markets ... 5 2.4 Market efficiency ... 8 3 Currency hedging ... 10 3.1 Currency overlay ... 10 3.2 Hedge instruments ... 10 3.2.1 Forwards ... 11 3.2.2 Futures... 12 3.2.3 Options ... 13 3.3 Optimality ... 13 3.4 Benchmarks... 15

3.4.1 Fully hedged benchmark ... 15

3.4.2 Fully unhedged benchmark ... 16

3.4.3 Partial benchmark ... 16

3.5 Conditions for hedging ... 18

4 Hedging strategies ... 22

4.1 Passive hedging strategies... 22

4.1.1 Fully unhedged... 23

4.1.2 Fully hedged... 23

4.1.3 Partial hedge ratio ... 24

4.2 Active hedging strategies ... 25

4.2.1 Forward hedge rule ... 26

4.2.2 Large forward hedge rule ... 26

4.2.3 Real interest rate rule ... 27

4.2.4 Real forward hedge rule ... 28

5 Literature review ... 29 6 Empirical research ... 36 6.1 Investor ... 36 6.2 Data ... 37 6.3 Approach ... 40 6.4 Results ... 43

6.4.1 Results total portfolio ... 43

6.4.2 Differences across countries ... 44

6.4.3 Differences between asset classes ... 46

6.4.4 Hedge efficiency ... 47

7 Conclusion ... 48

1 Introduction

The merits of international portfolio diversification are already common in the financial world. The hedging of the associated currency risk, however, only emerged in the 80’s. Since that time currency overlay is well established in the United States. For the investors in Europe however, it is still reasonably new. That is probably why almost all the existing literature about this subject is from the perspective of US dollar investors. Furthermore, the research is mainly performed on equity markets.

In this thesis different hedging strategies will be tested from the perspective of a euro-investor. By now there is enough data since the introduction of the euro to conduct the research adequately. Furthermore, the effect of currency overlay will not only be tested on equity, but also on bondsand a portfolio combining those two. The foreign markets that are invested in are the bond and equity markets of the United States, the United Kingdom, Japan and Australia.

There are two different types of strategies that will be examined. Passive hedging strategies with various fixed hedge ratios (full, partial or zero). And active strategies with a flexible hedge ratio that will adjust to different market conditions. Those active hedging strategies come from existing literature and are:

• Forward hedge rule (FHR) Eaker and Grant (1990) • Large forward hedge rule (LFHR) Morey (1993)

• Real interest rate rule (RIR) Hazuka and Huberts (1994)

• Real forward hedge rule (RFHR) Vanderlinden, Jiang and Hu (2002) Furthermore, several conditions that will outline when currency hedging becomes efficient will be defined. These conditions can be for example: the size of the portfolio, the percentage of currency exposure, risk-aversion and the investment horizon. This altogether leads to the following research question: Under which conditions is currency hedging for a euro-investor with an internationally diversified portfolio efficient from a practical point of view?

The thesis is organized as follows: Chapter two is about currency markets and currency risk. Chapter three describes currency hedging, followed by a chapter about the various hedging strategies. Chapter five is a literature review about the subject. Then follows the empirical research, where all the different hedging strategies are tested. The thesis ends with a conclusion.

2 Currency markets and currency risk

This chapter will first explain the concept of international diversification. Then the currency risk that results from such an investment allocation will be discussed. To deal with this currency risk, investors have to make use of foreign exchange markets. Therefore this subject is explained also in this section. The chapter ends with an explanation about the efficiency of these foreign exchange markets.

2.1 International diversification

The concept of international diversification has been known to be valuable for portfolio performance since decades. In the traditional Capital Asset Pricing Model (the CAPM), the expected return on equity is the risk-free rate plus a risk premium. In an efficient market you can add less risky assets to the portfolio to lower the total risk. This however, leads also to a decline in the total expected return. International

diversification however, can lower volatility by eliminating non-systematic risk that is associated with the single-market investment, without lowering the total expected return. This is possible because there are low correlations between the stock markets from the different countries. Practitioners previously claimed that the factors that lead to these low correlations were the industrial structure of the country or their different exposures to exchange rates. But recently, Gerard, Hillion and de Roon (2002) investigated this subject, and they found that these small correlations result from the differences in country specific factors.

Despite the advantages of international diversification, several barriers for international trade have discouraged people to take advantage of these opportunities. Examples of such barriers are illiquid markets, high transaction costs, regulatory and tax obstacles and the unavailability of information. Therefore, in the past investors held mostly domestic assets in their portfolios. Nowadays people invest much more abroad since most of the previous barriers have declined or have even disappeared.

Investors now buy assets across borders to enhance their portfolio performance by looking for more profitable investment opportunities, or just to lower risk by diversification. When people started to invest internationally, it began with small amounts relative to the total portfolio. At that time the small currency exposures did

not matter very much in the sense of risk management. Nowadays however, the increasing exposure in foreign currencies has such a big impact on portfolio

performance, that investors cannot disregard these effects any longer. Therefore they seek ways to protect themselves against this risk by entering in currency markets. This risk will be described in the next paragraph.

2.2 Currency risk

When an investor buys a foreign asset, he has to deal with two different types of risk. The specific risk of the asset itself and the currency risk when he wants to sell the asset and exchange the proceeds into his own currency. This latter risk is the

undesirable one. It is undesirable, because the currencies do not provide dividends or a coupon. Literally this means that they do not create value, and therefore have a zero expected return. Because of this reason, the trade in currencies is often called a zero-sum game. Loses to one person will be offset by a profit for another person. There exists no situation where both persons can win. In spite of this lack of returns, the currencies still have a certain amount of risk. This risk can be seen as the potential depreciation of the investor’s home currency against the foreign currency. Because this risk is unrewarded, it does not benefit the performance of the portfolio.

European investors are since a couple of years much less exposed to this currency exposure. This is because since the introduction of the euro in 1999 there is no more currency risk between the participating euro countries. However, outside the European Union, where a substantial part of the European investors’ money is

allocated, there still exists the foreign exchange rate risk.

The major reason for holding currencies is that they are a vehicle for international transactions. In an investment sense, currencies can be seen as non-productive assets, who deliver risk instead of returns. Therefore they cannot be treated as a separate asset class, but more as a tactical asset class that needs to be used in combination with other assets.

2.3 Currency markets

In this section some features about the currency market will be described. Those features will explain why this market is useful for investors. The foreign exchange

market has hundreds of millions of participants. Therefore it is the biggest capital market in the world. All these participants make sure that the market is also very liquid. It is easy accessible for everyone who wants to participate in this market. The market is open for the public 24 hours a day. However, there are big deviations in transaction volume during the day. The largest part of transactions in a certain currency takes place during the office hours in that currencies’ home country. The continuous growth of transactions in the currency market is both a result and a cause for the declining transaction costs. The bid-ask spread for the major currencies is around 0.01 percent. Despite the fact that there are more than 200 currencies sold on this market, the biggest part of all trading consists of only six currencies. Those are the US dollar, the euro, the Swiss franc, the Australian dollar, the Canadian dollar and the Japanese yen. These currencies take credit for about 80 percent of all trading. Because the factors that drive the currency returns are very different from those influencing the stock and bond markets, the currency market presents very low or negative correlations with other markets, like the bond and equity markets.

The foreign exchange market is a relatively efficient market. This is because it is a market in which few restrictions to international trade and investment exist. However, the market is not as efficient as the bond and stock markets. This is because the ongoing prices can sometimes deviate from the efficient prices that reflect all available information. This is the reason why this market is not completely efficient. Nevertheless, it still has some aspects that that will increase the efficiency of a market. The efficiency of the foreign exchange markets will be discussed in more detail in the next paragraph.

Next to the regular currency transactions that are exchanged through the current spot rate, it is also possible to make use of derivative contracts. It is for example possible to set up a contract that allows you to buy or sell an amount of foreign currency in the future. This contract defines the amount of currency that will be exchanged at a certain exchange rate at a certain point in time. These contracts are the so-called forward contracts. The covered interest rate parity states that the forward exchange rate can be calculated from the current spot exchange rate multiplied with the difference between the domestic and foreign short interest rates, as shown in the formula below. This relationship makes sure that investors are indifferent between investing in a domestic bond or in a foreign bond hedged to their home currency, because this would lead to the same results.

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A forward premium arises when there is a difference between the forward rate and the current spot rate. When the forward rate is lower than the spot rate the correct name is a forward discount. When you engage in a certain forward contract, this does not mean that you lock in the future spot rate. This is because the future spot rate can differ from the current forward rate. This means that the forward rate is a biased estimator of the future spot rate.

Eugene Fama (1984) was the first to describe the forward premium puzzle. This puzzle denotes the state when the domestic interest rate exceeds the foreign interest rate. This leads to a bigger demand for the domestic bonds, which has the effect that the domestic currency will appreciate. In the specific situation when the domestic interest rate equals the foreign one, the forward premium should be zero by ‘no arbitrage pricing’. Nowadays this relationship holds within very tight margins, especially for countries with relatively unrestricted capital flows and low credit risk on their domestic government bonds. If this relationship would not hold, arbitrage opportunities will exist. Therefore this puzzle states that currencies with high short-term interest rates deliver high returns on their exchange rates.

Fama (1984) and Bansal and Dahlquist (2000) among others have shown that currency forward returns are related to the current interest rate spread between the two currencies. However, fluctuations in future currency movements are hard to predict. Researches have studied decades of data concerning exchange rates combined with all sorts of macroeconomic data, but did not came up with any robust findings that can correctly predict the future rates. Bos, Mahieu and Van Dijk (2000) for example, found that there is no clear serial correlation pattern between the returns and the squared returns of exchange rates. These are patterns which are found a lot in

high-frequency financial return data, indicating that it is impossible to exactly predict the returns of these variables. However, they argue in their article that there are still some local trends in the levels of exchange rates which can be used in certain actively managed currency trading strategies.

2.4 Market efficiency

The efficient market hypothesis states that prices will reflect all information that is available in the market. The hypothesis is based on two important assumptions. These assumptions state that participants in the market should be rational and that they must act as profit maximizers. The foreign exchange market however, is not in line with these two assumptions. The two biggest players for example, central banks and international corporations, do not act as profit maximizers. Central banks try to control inflation by decreasing the fluctuations in their exchange rates. By altering these exchange rates they engage in the currency market, but not with a profit-maximizing motivation. The other important players in the market, the international corporations, want to hedge their currency risk by entering in some currency contracts. They do not seem to care about the current exchange rates and their expected future course, but are just willing to engage in a contract. This is not in line with the behavior of a profit maximizer. As another example there are of course the tourists who want to exchange their currency for the foreign one, regardless of the current exchange rate and the direction it will move to in the future. Furthermore, there are a lot of reasons why people are forced to use the currency market, and therefore do not have the right trading motives to make the market more efficient.

A lot of participants in the foreign exchange market are also irrational. A good example is the herding behavior they engage in. Herding behavior means that people respond to economic news together in large groups, which leads to an overreaction to this news. This overreaction leads to huge deviations in the exchange rates that cannot be explained by the fundamentals. Another example of irrational behavior comes from the point in time when people engage in a currency transaction. This point in time has generally nothing to do with the beliefs the person has about the future rate of this currency. They just want to make a transaction at that time and do not wait for a better moment when they feel the exchange rate is “right”.

This altogether leads to inefficiencies in the foreign exchange rates which in turn lead to the conclusion that the currency market is not a completely efficient market. The advantage of this situation is that these markets are suitable for arbitrage opportunities. In the foreign exchange market there are far more arbitrage

opportunities to exploit than in the stock or bond markets. An example of such an arbitrage opportunity is the forward bias, which means that the forward exchange rate is not an unbiased predictor of the future spot rate, as mentioned earlier. Therefore one can exploit this bias by using conditional hedging rules, which try to predict the future spot rate better than the forward rate does.

Because the irrational participants in the currency market have no reason to change their behavior in the future, and central banks will keep on intervening in this market, the previously mentioned inefficiencies will continue to persist. Therefore the currency market will probably stay an inefficient market in the future, where it is possible to exploit certain profitable opportunities. Trading strategies that try to make advantage of this situation are discussed further in this thesis.

3 Currency hedging

This chapter will describe how currency hedging works in practice, and which financial instruments can be used. Furthermore, the optimality of currency hedging will be discussed. Next follows a section about the different benchmarks which are used to compare the hedging strategies with. The chapter ends with a summation of conditions that define whether currency hedging becomes efficient.

3.1 Currency overlay

Currency overlay can be defined as the separate management of currency risk that is already present in an internationally diversified portfolio. The management of

currency risk means that one should hedge his foreign exposure to his home currency. Hedging involves taking two negatively correlated positions. The positions are long a certain asset and short a certain positively correlated asset. Therefore hedging must lead to a reduction in the portfolio’s standard deviation. Hedging can be done with different instruments and in different degrees. Both subjects will be discussed in later sections in this chapter.

This study will focus on using currency overlay to hedge the foreign currency risk already existing in an investment portfolio. It is also possible to use currency overlay as a pure alpha strategy, where it is solely used to create value. The currency market can be a suitable place for a pure alpha strategy because of the inefficiencies that exist in the market and the low transaction costs. These strategies are also relatively new, which makes it easier to make advantage of these opportunities. However, the pure alpha strategy is beyond the scope of this paper, so it will not be discussed here any further.

3.2 Hedge instruments

The three most commonly used tools to hedge are forwards, futures and options. They will be described in the next section. There are also other techniques available but those are not as frequently used. This is because they have certain undesirable properties compared to the other three instruments. Money market transactions for

example can be used to hedge, but unfortunately the desirable ones are often

impossible to set up. Swaps can also be used, but most of the time they are unsuitable because they are very expensive, and their maturities are too long. Delaloye and Porchet (2004) state that the costs of these swaps are around an average of 75 basis points.

3.2.1 Forwards

Forward contracts are most frequently used to hedge currency risk. These contracts make an agreement about a certain amount of currency that will be exchanged against a certain exchange rate on a certain point in time. Most of the contracts have a length of one, three or six months. When the contract is set up, nothing has to be bought or sold yet. Therefore, at the beginning of the contract it has very little value. After that time, changes in the exchange rate will generate gains or losses and therefore will create value. However, these gains or losses are only settled at the expiry of the contract.

The reason why these contracts are used so often for hedging is that these contracts have more desirable properties compared to the other financial products. First of all there are no direct costs associated. The bid-ask spread is therefore very low. It turns out that the most liquid currencies cost about 5 basis points for each month hedged. This is demonstrated for example by Hazuka and Huberts (1994), Dunis and Levi (2001) and Vanderlinden, Jiang and Hu (2002). Dunis and Levi also computed the transaction costs for less liquid currencies. They found this value by computing bid-ask spreads from DataStream. For most of those “exotic” currencies, they found a value of 10 basis points for each month hedged. For some very illiquid currencies however, those costs were even higher.

The market in which forward contracts are sold is also very liquid. This makes it easy to obtain such a contract. Because there is such a big supply of these contracts, they come in a lot of variations. Another advantage is that the contracts are very flexible; they can be tailored to very specific demands. Also the contracts are easy to price, through a straightforward computation.

3.2.2 Futures

Futures contracts have a lot of similar properties as forward contracts. They also make an agreement about a certain amount of currency to be exchanged in the future. The big difference between these contracts however, is that they must be marked to market. This means that after each trading day when the exchange rates have changed, the resulting profit or loss on the contract must be settled. Therefore one should have a margin account which contains enough money to make these settlements. Most of the time this is a fixed percentage of the total value of the underlying contract. This is in contrast with the forward contract where the settlement only takes place at expiry of the contract. But there are more points from which futures contracts differ from forward contracts (Briys and Solnik, 1992, p. 434). First of all futures contracts are standardized, which means that they are less flexible. When the margin account has declined due to losses on the futures contract, there comes a margin call, which requires that the account will be filled with extra resources. This will lead to

intermediary cash flows, which can alter the portfolio performance. Furthermore, in some countries futures contracts do not even exist.

Abraham Lioui (1997) tested whether the need for hedging with forwards or futures varied under different circumstances. He found that when looking at hedging in the narrow sense, which means measuring the volatility of a portfolio, it does not matter whether forwards or futures are being used. They both delivered the same results.

When looking at hedging in a wider sense, which concerns the risk-return trade-off, there are some differences. When interest rates are stochastic, which means that there is interest rate risk present, futures and forwards do not deliver the same results. The choice between the two contracts is determined by the correlations between the domestic and foreign term structure of interest rates. Nevertheless, most of the time forward contracts are more suitable to be used by the investors. This is because the conditions under which futures contracts are more suitable are not likely to prevail in international financial markets.

3.2.3 Options

Options have far more risk than the other contracts mentioned earlier. Under bad circumstances you can lose more money than the option price itself. But on the other hand, you can exploit certain opportunities better because of the upside potential. A useful application of options is to buy out-of-the-money options which are very cheap. These options can provide security against some low probability events with very large impacts, against very low costs.

Acar and Lequeux (2001) also show that hedging through the use of options instead of forwards was not to be recommended. The main reason for this outcome is the premium costs. In some situations the options outperformed the forwards upward, but also had a bigger maximum drawdown. So the major reason for hedging, lowering risk, was not accomplished through the use of options. Also in practice very few overlay managers use options as their major strategy.

3.3 Optimality

This paragraph describes the optimality of currency hedging. This subject was first mentioned in an article by Glen and Jorion (1993). They found that there is no significant performance improvement from adding currencies to predetermined positions in either stocks or bonds. Therefore they argue that optimizing separately over assets and currencies does not take advantage of the correlations between these two. This leads to the conclusion that the delegation of currency management to overlay managers may be suboptimal. In the article “Mean/Variance Analysis of Currency Overlays” (1994) Philippe Jorion goes deeper into this subject. He discusses three approaches for optimizing a portfolio of assets and currencies in a

mean/variance framework, where he sets the currencies as a separate asset class. The first approach is the joint optimization over the total portfolio, which includes all assets and currencies. In this approach the portfolio manager has specific knowledge about all the asset classes. This way, he can take advantage of the

correlations between the assets and the currencies. This approach should therefore give the most optimal portfolio composition.

The second approach is partial optimization over the currencies, which takes place after the optimal portfolio of assets has been determined. This is a type of

currency overlay, where the currency hedge decision is made separately, after the asset allocation has been determined. This happens when the core portfolio manager has not enough knowledge about the currency market. Therefore the currency

allocation decision will be transferred to a specialist currency manager, who has more specific knowledge about this field than the manager of the total portfolio. Because the asset allocation has already been determined, the manager cannot fully exploit the correlations between the assets and the currencies. Therefore, this method should be less optimal than the first one.

The third approach is a separate optimization over the assets and over the currencies. This is also a type of currency overlay. But in this case the addition of currencies to the portfolio has no relation to the other assets, and has therefore no hedging purpose. The currencies in this case are only held for pure speculative reasons, like in a pure alpha strategy. In this situation the total portfolio comprises of two different portfolios, one with assets only, and one only consisting of currencies. Because the allocation of the two portfolios is made separately, they do not take account at all for any correlations between each other. Therefore, this would lead to the least optimal outcome for the three different types of portfolio allocation.

Using these three approaches we can conclude that when the currency hedge decision is made separately from the asset allocation, like in a currency overlay, this would always lead to a suboptimal portfolio allocation. Especially approach three, the separate optimization, will always be the least efficient method and should therefore be cancelled out in favor of the other two methods.

The two remaining approaches will give identical results in two situations. When the returns on the assets are uncorrelated with the currencies, there are no benefits from managing them together. Furthermore, when the expected returns on the exchange rates are zero, there is no reason to invest in these currencies. In that case the two approaches will also lead to the same portfolio, which will consist of assets only. In practice however, those two assumptions together will never hold, and therefore the separate allocation will always lose from the joint optimization. Based on historical data, it turns out that this efficiency loss is around 40 basis points for equity portfolios.

The main conclusion of the article by Jorion (1994) states that the performance of the currency overlay must be evaluated in the context of the entire portfolio. The core portfolio manager must therefore frequently communicate his positions to the

overlay manager, who would use this extra information to evaluate the risks and returns for the entire portfolio. Furthermore, Jorion states that despite the fact that partial optimization is a second-best alternative, it can still be an acceptable solution for managing currencies in an internationally diversified portfolio.

3.4 Benchmarks

The choice for an appropriate benchmark to compare the currency overlay with is an important decision. Gastineau (1995) states that an inappropriate benchmark can stimulate an inappropriate hedging policy, or may even prevent the portfolio manager from paying attention to the possibilities of active currency management. A fully hedged benchmark can for example discourage a manager to look at the currency hedging possibilities, because he is only evaluated on the performance of his assets, since the currency returns are filtered out of his results.

There are different opinions about the appropriate benchmark one should use to evaluate the currency hedge decision. There are people (for example Hazuka and Huberts, 1994) who state that the decision to hedge is an extra action you can

undertake, along with the “normal” asset allocation. Therefore, whether one takes this decision should be compared with the original benchmark for the portfolio, which means no hedging at all. These people advocate a fully unhedged benchmark. But there are other people with different reasoning. Therefore the various benchmarks will be discussed in the next paragraphs. They can be subdivided in the unitary

benchmarks which are fully hedged and fully unhedged, and the partial benchmarks that have a hedge ratio somewhere between zero and one.

3.4.1 Fully hedged benchmark

Perold and Schulman (1988) wrote an influential article about currency overlay. They argued that the risks resulting from currency exposure can be removed easily with a currency overlay against very little costs. Therefore they saw this as a free lunch. Keeping exposed to this risk was therefore seen as an active currency decision. In that time most investors (mostly US-based pension funds) followed this reasoning and fully hedged their foreign currency exposure. This was seen as the optimal portfolio decision and was therefore seen as the benchmark investors should follow. Other

proponents of full currency hedging (for example Jorion, 1994) argued that

international portfolio performance should always be measured against a fully hedged benchmark.

However, after that time there came a period of dollar weakness, which pointed out the drawbacks of a fully hedged benchmark. During that time the dollar weakened against the foreign currencies, which made their overseas investments rise in value. Therefore there was no need to hedge these exposures, and this currency management had to cope with big losses. The cash flows that were needed to compensate these negative results on the currency overlay were causing problems. Assets must be sold to make up for these losses, which in turn lead to dramatic portfolio performances.

3.4.2 Fully unhedged benchmark

Froot (1993) is a proponent of the purchasing power parity (PPP). This parity states that identical transferable goods must have the same prices between nations. So the returns in exchange rates should make up for the differences in prices across countries. When an investor has a long investment horizon, the currency deviations tend to clear out in the long run, which would minimize the risk. Therefore under this assumption the currency exposure does not have to be hedged. This would only lead to hedging costs that are useless in the long run. So the benchmark should be dependent on the investment horizon. Froot advices therefore to use a fully unhedged benchmark because the majority of the investors has a long investment horizon. However, he argues that for investors with small investment horizons, currency overlay can indeed reduce the portfolio volatility, and may be efficient in that situation.

Unfortunately, it is shown that the PPP does not work so well in practice. This is because some factors that support this parity are not arbitrageable, such as

transportation and labor costs, taxes and certain specifications of the product. Furthermore, history shows that some currencies have had long periods of

appreciation or depreciation, without returning to a certain level which is set by the PPP.

As shown earlier, both the fully hedged and fully unhedged benchmarks have quite some disadvantages. Return volatility (which is related to the fully hedged benchmark) and cash flow volatility (related to the unhedged benchmark) are both important and the minimization of those two variables cannot be separated from each other.

Therefore a lot of funds now use the “benchmark of least regret” which is in the middle between the two unitary hedge ratios and is therefore equal to a 50 percent hedge. However, this does not solve the two problems stated before, but tries to benefit from both approaches.

A partial benchmark is most suitable when the portfolio’s hedge ratio is restricted between zero and one. This is the case with most pension funds, where overhedging and/or underhedging are prohibited. In that case it is not possible to take advantage of certain opportunities when you are already at a border of the hedge restrictions. For example, you cannot outperform the fully hedged benchmark when the hedged currency depreciates, because you cannot increase the hedge ratio to more than 100 percent. So the decision of which benchmark to take is not only based on the performance measurement, but also on the freedom you want to give to the portfolio manager.

Among others, Binny (2001) argues that there is no optimal benchmark. There is no “black box” possible to define the benchmark exactly. He therefore came up with a methodology that can help define a certain benchmark based on some specific factors. It is a sort of guidance to support the decision-making process. Binny uses eight different factors, which together determine the benchmark. They are measures of how important some aspects are for the company, like volatility control, cash flow control, downside protection, upside capture, peer group risk, minimization of

portfolio risk, costs of hedging and the maximization of return. Those factors are then given a weight, which is used to combine them to a single benchmark hedge ratio for the company.

This approach may be a guideline for some investors, but for others it is not. But one point all investors can agree on, is that it shows how difficult it is to

determine a suitable benchmark. Furthermore, it shows that a benchmark can differ across all investors, and it can change for a single investor across time. It is also possible to use a conditional benchmark which will change under different conditions, but those are not commonly used in the market. To see which hedge ratios are used in practice, the next figure is included. It comes from an article by Michenaud and

Solnik (2005), and shows a distribution of different hedge ratios for investors from several base currencies. The hedge ratios come from institutional investors who have their currencies hedged by special overlay managers. The data comes from a survey conducted in 2004 by Mellon/Russel. The numbers under the countries represent the amount of included investors from that country.

Figure 1: benchmark hedge ratios

Michenaud and Solnik (2005, p.2)

3.5 Conditions for hedging

This section will discuss under which conditions it is suitable for an investor to hedge the foreign exposure of his portfolio. It depends for example on whether the currency is hedgeable or not. Some currencies are very illiquid, and are therefore unsuitable for hedging because they are not easy available or just too expensive. Other conditions for a currency to become hedgeable are whether the spot and forward markets exist and are developed, whether the bid-ask spread is not too high and whether there no exchange control or tax exists (Delaloye and Porchet, 2004). However, sometimes a non-hedgeable currency can still be hedged by using a proxy. This means that another currency can be used that is highly correlated with the non-hedgeable currency.

Some “exotic” emerging market currencies seem to be unsuitable to use in a hedging strategy, because they are not very liquid and sometimes quite expensive. But Dunis and Levi (2001) showed that even despite the fact that they seem not suitable for hedging, they still can improve the risk-adjusted performance of currency overlays. This may be due to the fact that these markets are less developed, and less liquid. Also the central banks tend to intervene more. Therefore, it can be argued that these

inefficiencies make sure that the future development of the emerging market currencies can be easier to forecast with some trading rules than the other major currencies. So when an investor has some knowledge about such rules these markets can be very suitable for profitable trading strategies.

The investment horizon is also important for the hedging decision. Froot (1993) states that the shorter the horizon, the more hedged one should be. He comes to this conclusion because he found that the value of hedging disappears after a period of eight years. So hedging for more than eight years will lead to too high transaction costs in the long run. This is because exchange rates are mean reverting in the long run according to the purchasing power parity. Mean reversion implies that long-horizon currency exposure is low, which makes sure that the risk is also low. Despite that the fact that people know that the PPP does not work so well in practice, they all agree that currency returns are more volatile in the short run, and that hedging is more beneficial for investors with short-term horizons.

Another condition for hedging is the type of asset that needs to be hedged. Vanderlinden, Jiang and Hu (2002) argue that because of the fact that bond returns and exchange rates are both very sensitive to fluctuations in interest rates, they tend to fluctuate more and therefore have more risk. This leads them to the conclusion that it is more beneficial to hedge bonds than stocks. This is in contrast with Jorion (1994). He states that because of these correlations bonds and currencies must be managed together, in a joint optimization. Otherwise it is not beneficial. Therefore he states that stocks are more suitable for hedging than bonds. The literature varies about this subject, so it is useful to determine for each situation whether the asset is suitable for hedging or not.

Another factor that has influence on the hedging efficiency is the numeraire

effect (Vanderlinden, Jiang and Hu, 2002, p. 80). This means that the kind of base

currency the investor has is also important. The US dollar has always been the most influent currency in the world. Because of this role of the dollar, this currency has

some special features that other currencies do not posses. As an example, almost all the central banks from other countries are holding the dollar as a reserve currency. There has been shown that this may lead to correlations between the different dollar exchange rates (Gadkari and Spindel, 1990). Therefore, when a US-investor hedges his currency risk, this leads to a reduction in the correlations of his portfolio, which in turn leads to a reduction of total risk. This hedging benefit does not work so well for non-US investors, because they already have lower correlations among their exchange rates. Therefore the need for hedging for such investors is lower, because they

experience already more diversification benefits by holding assets in a variety of currencies.

Because the euro is more and more starting to play a similar role as the dollar when looking at the role of a reserve currency, this can be a reason that the euro-investors might enjoy the same hedging benefits as the dollar euro-investors. Simpson and Dania (2005) indeed found that the correlations among European exchange rates increased significantly since the introduction of the euro. The Swiss franc has also some equal features as the euro and the dollar. They are all negatively correlated with the world equity market, and are almost uncorrelated with their domestic equity markets (Campbell, Serfaty-de Medeiros and Viceira, 2006). The negative

correlations can be explained by the fact that big shocks in risk aversion of investors will lower the demand for equity, and will transfer that demand to currencies as a store of value.

There are some studies which show indeed that hedging is less beneficial for currencies other than the dollar. For example, Eaker, Grant and Woodward (1991) and Eun and Resnick (1994) both showed that investors with the dollar as base currency benefit more from hedging than Japanese yen-based investors.

The composition of the portfolio has also influence on the hedge decision. Because there are very different sorts of portfolios, they all can have a different need for hedging. Important features are the correlations among the assets where the portfolio consists of (Filatov and Rappoport, 1992). Also the correlations between the assets and the currencies have their influence. Solnik (1974) argues that when equities and currencies are uncorrelated, full currency hedging is optimal. Because of the negative correlation between currencies and their domestic bond and equity markets one should not have a currency exposure in the same market as he has invested in bonds and stocks (Delaloye and Porchet, 2004, p.33). When the portfolio is already

well diversified, the need for hedging is lower, because the portfolio has already lower risk.

The level of risk aversion of an investor is also very important to determine how much hedged the investor should be (Inwegen, Hee and Yip, 2003). When an investor is extremely risk averse, he does not care about the expected returns, but only wants to minimize volatility. Therefore they are also called the minimum-variance investors (Roon, Nijman and Werker, 2003). To minimize the risk, a fully hedged portfolio is acceptable because this will completely remove the foreign exchange rate volatility. When the risk aversion of the investor is lower, the appropriate hedge ratio will also decline. Investors with very low risk aversion do not care about short-run fluctuations, but are more interested in the long-run returns on their portfolio. Because theory suggests that in the long-run returns on currencies are near zero, these investors are not very interested in hedging their foreign exposure.

4 Hedging strategies

This chapter describes the different hedging strategies that come from the existing literature about this subject. The strategies can be divided in two subgroups, namely active and passive hedging strategies. Active strategies will use different hedge ratios according to different conditions, for example distinctions among real interest rates across countries.

The passive strategies set a fixed hedge ratio that will not be adjusted under different conditions. Briys and Solnik (1992) decomposed this hedge ratio in different components, to get more feeling about the factors one should consider when setting an appropriate hedge ratio. They show that the ratio can be decomposed in a

macroeconomic part, which is based on the interest rate and its covariance with the currency movements. Next is an ‘asset-specific’ term, which is the covariance between the foreign currency asset return and the interest rate. Another part is a ‘speculative’ term which is a function of the risk aversion of the investor and the conditional risk premium of the exchange rate. And finally there are two stochastic opportunity set hedging terms. With this decomposition they try to show which factors are important to determine a hedge ratio.

4.1 Passive hedging strategies

The only goal of passive hedging strategies is to minimize risk. Such strategies will lock out losses, but also lock out profits. This will decrease the volatility of returns. The drawback of such strategies is that they do not let you benefit from profitable movements of the exchange rate. When a foreign currency appreciates, your

investments in that country will rise in value in your base currency, but the hedge will lose money.

There are two different types of fixed hedge ratios, namely unitary and partial hedge ratios. The unitary ratios have a hedge ratio equal to zero or one. The partial ratios have a hedge ratio somewhere between zero and one. All these ratios will be described in the next section.

4.1.1 Fully unhedged

The first hedge strategy is to fully unhedge the foreign exposure, which actually means no hedging at all. This will lead to a large volatility in the returns, but no costs have to be made for the purchase of the hedging instruments. In this situation you accept risk without any returns. Therefore it may be an inefficient strategy because the portfolio performance can be enhanced through a currency overlay strategy.

These kind of portfolios are only likely to be optimal in some special cases. One such case is when there are high negative correlations between domestic assets and currencies. Negative correlations lead to a reduction of risk in the portfolio, so in that case it may be efficient to stay exposed to that currency. Another situation is when the expected returns from the unhedged currency exposure tend to be

significantly positive. However, this is impossible to predict for the future. When the investor is not too risk averse and has a long investment horizon he can wait to the fluctuations in the currencies will cancel out in the long run. Therefore under these conditions not hedging may also be suitable because in that case he has no transaction costs to bear. In all other cases, it seems that hedging a part or all of the exposure will lead to an improvement of the portfolio performance.

4.1.2 Fully hedged

Opposite to fully unhedged is the fully hedged strategy. In this case all the foreign currency exposure is hedged away. This means that the exposure of the hedge contracts equals the total amount of the foreign assets. This strategy may be suitable for an investor that is very risk-averse. Risk-averse investors are primarily concerned about the volatility of their returns. When the portfolio is fully hedged the investor will not be affected at all by fluctuations in the exchange rate. Another situation when this strategy is suitable is when the domestic exchange rate tends to decrease in the coming investment horizon. But as mentioned earlier, this is impossible to predict correctly. Finally, in the situation when there are no correlations between the assets and currencies at all, there exist no diversification benefits from holding these

different exposures, because currency risk is in this situation pure noise. Therefore, in this case full hedging might also be optimal.

4.1.3 Partial hedge ratio

Fisher Black (1989) was one of the first people that wanted to determine a universal hedge ratio. He states that fully hedging is never optimal because of two reasons. First of all there are correlations between the exchange rates and the local returns, which already take part in the diversification process and therefore lower risk. And as a second reason he mentions the speculative motives for engaging in currency positions. He therefore defines a universal hedge ratio which is equal for all investors over the world. However, this universal hedge ratio holds only under the assumptions that all investors have the same risk aversion and each national wealth is equal to the total value of the country’s stock market. Unfortunately those two assumptions will not hold in practice, which indicates the weakness of Black’s universal hedge ratio.

Inwegen, Hee and Yip (2003) also show that the optimal portfolio for an investor in one country does not have to be the same as the optimal portfolio of an investor in another country. However, some parts of Black’s theory are still quite useful. He states that the optimal hedge ratio will lie somewhere between 0 and 100 percent, but certainly not on the borders. He argues that the most appropriate hedge ratios lie between 0.30 and 0.77. The universal hedge ratio is too unstable to hold in practice, but it gives some reasoning that the half hedged/half unhedged ratio might be a suitable one.

Gardner and Stone (1995) argue that there is no optimal hedge ratio. To calculate an optimal hedge ratio, you need estimates of expected returns, variances and covariances. Because the correct values are all unknown, they must be estimated. Therefore they are random variables that will always contain certain amounts of errors, no matter what statistical techniques are being used. All these errors are being used in the calculation of the optimal hedge ratio. When these errors are large, they lead to a very big confidence interval around the true value of the optimal hedge ratio. This is not very useful when you want to determine the amount of foreign currency in your portfolio you want to hedge. In their article they come to the conclusion that the estimation error in the variables is so large that the estimation of an optimal hedge ratio has almost no practical use for a U.S-based investor with a small or moderate risk aversion. Glen and Jorion (1993, p. 1882) also state that there is no optimal hedge ratio. They argue that it differs across countries, investors, risk aversion, assets, etc.

Furthermore, the optimality of universal or unitary hedge ratios is rejected by the time-varying nature of the hedges.

Sebastien Michenaud and Bruno Solnik (2005) looked at the currency hedge decision from a different point of view. They looked at it from a behavioral

economics viewpoint. They came up with a regret-theoretic approach for hedging currency risk. During their study they found out that regret-averse investors let the expected pain of future regret play a big part in their hedging decision. The decisions they made differed significantly from traditional investors. Regret is such a powerful negative emotion, that the prospect of a negative future experience can change an investor’s behavior dramatically. It may lead to irrational, sub-optimal decisions compared with the expected utility paradigm.

When investors let regret dominate their risk aversion they are called highly-regret-averse investors. Those investors disregard speculation motives and

covariances and base their decision solely on their regret, which will lead to a 50% hedge ratio. In this case, they are always a little bit right. When the domestic currency appreciates, they profit from being partly hedged, and when the domestic currency depreciates, they still profit (partly) from the positive currency returns. When the investors risk-aversion gets more influence compared to the regret-aversion part, the hedge ratio moves from the half hedged ratio to the fully hedged one.

4.2 Active hedging strategies

Hedging strategies that are actively managed will reduce the volatility of the portfolio, but also try to make advantage from certain positive movements in the currency market. Therefore they are much more flexible than passive strategies. They will try to limit losses but do not limit upside potential. Because the potential extra returns they can deliver, these strategies can outperform passive strategies when the investor is not very risk-averse.

Selective hedging is theoretically superior to full hedging because of the correlations among the exchange rates and rates of return. As mentioned earlier, the forward exchange rate is a biased estimator of the future spot rate and therefore it is possible to take advantage of this bias by using conditional hedging rules instead of passive hedging. In the next section four active hedging strategies will be discussed,

and later in this thesis they will be tested in practice from the perspective of a euro-investor.

4.2.1 Forward hedge rule

The forward hedge rule (FHR) was tested for the first time by Eaker and Grant (1990) who found that it significantly outperformed the two unitary benchmarks. The rule works under the assumption that the current spot exchange rate follows a random walk. This means that the current spot rate has an expected return of zero with a certain nonzero standard deviation. Therefore, the current spot rate gives a better approximation of the future spot rate than does the prevailing forward rate. So when the foreign currency is trading at a forward premium, which means that the forward rate is higher than the current spot rate, this would suggest that it is a suitable situation to hedge the foreign currency. Under the assumption of the random walk, this should be profitable because this way one can lock in a higher exchange rate in the future than the expected spot rate would be. Another way to look at this rule is that it recommends to hedge currencies with a high nominal interest rate, because these currencies tend to appreciate in the future due to a growing demand.

This forward hedge rule is well known nowadays in the economic world and has been shown to be quite robust in empirical tests. Such tests are done for example by Eaker and Grant (1990), Glen and Jorion (1993) and Eun and Resnick (1994). What should be mentioned is that these tests are all performed with the dollar as a base currency, so it would be interesting to see if those results also hold when the research is conducted with another base currency. Furthermore, Vanderlinden, Jiang and Hu (2002, p.79) argue that this rule might be a better hedging rule for bonds than for equity. This is because the rule is based on interest rates, which have a bigger impact on bonds than on stocks. This might also be something interesting to investigate.

4.2.2 Large forward hedge rule

Morey (1993) and later also Morey and Simpson (2001) argue that the forward hedge rule can be enhanced, because in the form which is described above, no distinction is made between different magnitudes of the forward premium. Sometimes it is possible

that the spot rate will come out higher than the forward rate at which the contract was purchased, even though the forward was selling at a premium. This situation is less likely to happen when the premium is larger. Therefore they state that when the premium is large it may be more advisable to hedge then in the case when there is only a small premium. Therefore a certain condition to the FHR is added which states that one should only hedge in the situation when the premium is larger than the average premium. This rule is therefore called the large forward hedge rule (LFHR). To determine whether the forward premium is large, Morey and Simpson (2001) used a trailing 36-month average of the absolute value of the premia.

4.2.3 Real interest rate rule

This approach tries to make advantage of the differences in real interest rates between different countries. Hazuka and Huberts (1994) argue that the exchange rates tend to revert to a mean according to the purchasing power parity (which is discussed earlier in this thesis). The relative purchasing power parity means that differences in inflation across countries will be offset by a change in the foreign exchange rate. This makes sure that the relative purchasing power in the different countries stays the same. In theory it is reasonable to assume that identical transferable goods have the same price across countries, at least in the long run.

So according to this view the return on a currency forward contract is based on the differences in expected inflation between the two countries combined with the interest rate parity. The interest rate parity states that the forward rate is equal to the spot rate adjusted by the interest rate differentials, that is, the difference between the domestic nominal interest rate and the foreign nominal interest rate. Combining this interest rate parity with the purchasing power parity leads to a formula which states that hedging is efficient when the real domestic interest rate is higher than the real foreign interest rate.

Unfortunately, the expected inflation is not measurable. Therefore Hazuka and Huberts use a proxy which is related to the “adaptive expectations” model. This model assumes that a trailing six month average of Consumer Price Index (CPI) inflation is a good measure to predict the one month expected inflation. However, this is an assumption that they make. Therefore they do not argue that their model

explains the future exchange rates perfectly, but they think that especially in the long-run those relationships will hold to some level.

Unfortunately, it is well known that the PPP does not work well in practice. This is because of various restrictions that hinder free trading. Therefore the PPP is a poor short-term predictor of the future spot rate. Nevertheless, their results report significant outperformance compared to the full-, half- and unhedged benchmarks. This leads to the conclusion that despite the fact that the PPP does not predict the spot rate well, it still has more predictive power than the forward premium or discount. This rule is only tested on the dollar, so whether it also works on other currencies is still unknown.

4.2.4 Real forward hedge rule

Vanderlinden, Jiang and Hu (2002) confirm that some active trading rules indeed deliver significant results. They argue however, that those rules do not work perfectly, so they try to come up with an improved technique. The earlier mentioned forward hedge rule is based on differences in interest rates between countries. But that rule does not make a distinction between the sources of the discrepancies between those two. This leads to the suggestion that it is possible to improve the FHR. Therefore they propose to combine the FHR with the real interest rate rule. This new rule states that it is only useful to hedge when two conditions are met. The foreign currency must be trading at a forward premium and the real domestic interest rate is higher than the real foreign interest rate.

These two conditions make sure that the real forward hedge rule (RFHR) should be invoked less than the other two rules it consists of, because the intersection of those two is smaller that each of the other hedge dimensions individually. Yet should the accuracy be improved, because the percentage of “correct” hedge decisions should be higher. A hedge decision is correct when the future spot rate turns out to be lower than the forward rate for which the contract is settled. A big advantage of a higher hedge accuracy is that less hedging means lower transaction costs.

5 Literature review

There have been various studies about the concept of hedging currency risk. The studies differ in methodology, countries, currencies, asset classes, time periods, and several other factors. This chapter will present the main results of some of the more influential studies in a chronological order.

Eun and Resnick (1988) are probably one of the first researchers who performed a study about the hedging of currency risk. In their article they show that stock portfolios perform better when they are fully hedged. Perold and Schulman (1988) confirmed that statement. They argued that every internationally diversified investor should fully hedge their exposure. This is because they saw currency hedging as a “free lunch”. This is because such a strategy lowered volatility against very little costs. Therefore they proposed a fully hedged benchmark for such investors, and lifting the hedge, which would increase the currency exposure, should be seen as an active investment decision.

Black (1989) tried to find a universal hedge ratio that is suitable for all

investors around the world. This aggregate hedge ratio is based on a weighted average of each individual’s wealth and preferences, which unfortunately does not hold in practice. Furthermore, optimal currency hedge ratios among different countries do vary, so a universal hedge ratio has little practical importance. Nevertheless, some points from his theory are quite useful. He argued for example that full hedging may not be optimal, because of the correlations between the currencies and the assets. Therefore he advocated a lower hedge ratio, somewhere between 0.30 and 0.77, but certainly not on the borders at zero and one.

Another study that tried to determine an optimal hedge ratio was by Briys and Solnik (1992). They decomposed the hedge ratio in five parts, indicating that it is very difficult or even impossible to determine an optimal hedge ratio. Furthermore, they found empirical evidence that the optimal hedge ratio would differ between countries, assets and time. These results stroked with Black’s findings about the existence of a universal hedge ratio.

From the 1990’s and on there came support for actively managed hedging strategies instead of the passive strategies that were supported earlier. Glenn and Jorion (1993) were one of the first to test such conditional hedging strategies. First of

all they found that the unitary hedge ratio is suboptimal because it ignores correlations between exchange rates and local returns. This fact was also demonstrated in the article by Fischer Black. Both the conditional hedging strategies and the unconditional hedging strategies significantly improved the performance of the portfolios. However, they found that there is no statistical evidence that adding an optimal combination of forward contracts to a portfolio of fully hedged assets will improve performance. This leads to the conclusion that the risk reduction part of full hedging has the biggest contribution to the improvement of the portfolio performance. They found also that the separate management of currencies may be sub-optimal because it does not fully exploit correlations between equity, bonds and currencies.

Jorion (1994) investigated this separate optimization in more detail. He tested mean/variance optimal positions for five stock and bond markets with ex-post data in the period 1978 – 1991. His study shows that unhedged stock returns have positive correlations with the currencies. Therefore, optimizing the allocation separately is never optimal. Hedged stock returns however, appear uncorrelated with currencies, and are therefore suitable for full currency hedging. In contrast, bonds delivered high correlations for both the hedged and unhedged returns, which shows that bond yields are negatively correlated with foreign currencies. Therefore, he states that partial optimization and full hedging are not efficient for bonds. He argues that this is the reason why mainly equity is being hedged against currency risk.

The study shows also that there is no evidence that currencies add value to internationally diversified equity portfolios. Bonds have more advantage from adding currencies to their portfolios in a joint optimization, because of the high correlations among bonds and currencies. But their optimal allocation must be determined together, not separate. So a currency overlay is not very suitable in that situation.

Gary Gastineau (1995) came to the same conclusion as the article by Philipe Jorion. He emphasizes the importance of currency management, and states that the currency allocation decision should always be integrated with the overall asset allocation of the portfolio.

Hazuka and Huberts (1994) used the fact that central banks have certain behavior that influences the exchange rates in such a way, that investors can use these discrepancies in real interest rates to adjust their currency holdings. Therefore

investors should increase positions in currencies with high real interest rates and decrease positions in currencies with relative low real interest rates. Hazuka and

Huberts were the first to test a hedging strategy based on this relative purchasing power parity. They found that for US dollar-investors in the period 1974 through 1992 this strategy significantly outperformed the unhedged as well as the fully hedged benchmarks.

The main result by the article of Braccia (1995) is that an investor should never fully hedge his exposure. He argues that it is optimal to keep the hedge ratio less then 80 percent, to make advantage of the correlations that exist between the currencies and the assets. Gardner and Stone (1995) found that the estimation error in the optimal hedge ratio is so large, that these estimates are of little use for an investor with low or average risk aversion.

Bos, Mahieu and van Dijk (2000) took a different approach to analyze the implications of currency risk management. They modeled the daily exchange rate of the US dollar versus the German mark. They focused primarily on the returns instead of the variances of these returns, which are generally studied in other studies. They found that modeling the exchange rate in an integrated framework may be successful, as long as the level of risk aversion is not too high. Furthermore, they mention that they did not include theories like the covered interest rate parity and the purchasing power parity in their model. Because other studies have shown that these parities have indeed some predictive power, they argue that their results may be enhanced when those theories are added to the model.

Morey and Simpson (2000) examined different active hedging strategies in the period between 1989 and 1998 for a US dollar-based investor. Their study showed that an unhedged strategy performed better than a passive hedging strategy.

Furthermore, all the passive strategies were dominated by the active ones. In the short-run, the forward hedge rule delivered the best results. The strategy that hedges when the forward premium is large (LFHR) outperformed all the other strategies in the long-run.

De Roon, Nijman and Werker (2003) performed a very sophisticated study where they determined the hedge performance by using the investors risk aversion and different utility functions. It turned out that static hedging with currency forwards did not lead to portfolio performance improvements, unless the investor had an extremely high risk aversion. The dynamic strategies however, which use the interest rate spread as a conditional factor, did enhance the portfolio performance in all cases. There was a significant difference in forward positions between the power utility

investors and the mean/variance investors. However, hedging was beneficial for both types of utility functions. They found these results for a dollar-based investor in the period 1975-1998, who invested in assets from the G5 countries.

Dunis and Levy (2001) looked at the hedging benefits of exotic currencies. They found that the low correlations between emerging markets and developed

markets lead to risk diversification. Furthermore, the market for exotic currencies may be more inefficient than the other currency markets in the world. This would also suggest an added benefit of diversification into emerging markets when those

inefficiencies can be used with active trading strategies. However, they find that there is a maximum amount of exotic currencies one should add to his portfolio, namely about 15 to 25 percent.

Vanderlinden, Jiang and Hu (2002) tried to improve earlier tested strategies by combining hem into a new rule, the real forward hedge rule. This rule turned out to be the best performing one in their research, where it significantly outperformed the standard benchmarks. Furthermore, dominance tests showed that over a 10-year horizon, the RFHR outperformed all the other active strategies. When they tested the performance of the strategies with other numeraires, they found that hedging was far more beneficial for a dollar-based investor than for investors in other countries, such as Japan, the United Kingdom, France and Germany. This finding is completely in line with the numeraire effects that a major currency as the dollar may exhibit, as mentioned earlier in this thesis.

Inwegen, Hee and Yip (2003) studied different kind of hedge ratios and tested them on various types of investors. The investors were categorized based on their risk aversion, their expectations regarding the future development of currency returns, and the constraints that were placed on their currency holdings. Their results show that full currency hedging is only suitable for minimum-variance investors. This makes sense because fully hedging generally reduces portfolio volatility. All the other investors were recommended to use various optimal hedge ratios. They mentioned that they did not test any active strategies, but that there may be some opportunities in this field because of the existence of time-varying currency risk premiums.

The main result of the article by Beltratti, Laurant and Zenios (2003) is that investors based in a relatively low interest rate country should always hedge their portfolio against currency risk. This is because the low interest rate will induce investors to switch to the higher interest rate countries, which will lower their

exchange rates. This decrease should be hedged regardless of their investment horizon, risk aversion, transaction costs and asset mix.

All the previous studies were looking for a hedge ratio which would minimize risk measured as the variance of the portfolio. Harris and Shen (2004) however, made some adjustments to this method. These two authors came up with the idea to

minimize the Value at Risk (VaR) instead of using the minimum variance for hedging strategies. They argue that variance as a measure of risk can only be justified under the assumption that the total portfolio skewness and kurtosis are the same as the skewness and kurtosis of the assets that make up the portfolio. Skewness is the lack of symmetry of the distribution (fatness of one tail) and kurtosis is the fatness of the two tails (also known as the volatility of volatility). Their study shows that the skewness and kurtosis of returns are not preserved when the assets are formed into a portfolio. This leads to the conclusion that the standard deviation is therefore no longer an appropriate measure of portfolio risk, because this measure does not capture all the important characteristics that are significant for the investors.

So therefore they propose a minimum-VaR hedging strategy, which also tries to minimize the risk of the portfolio, but then with another risk measure. This more general risk lowering method offers a significant improvement in the hedging performance of the portfolio in terms of VaR, with an average reduction in VaR of about fifteen percent. The portfolio variance does not change much compared to the minimum variance approach. In some cases the minimum VaR approach even lowers the variance. In all cases the minimum VaR method leads to a lower hedge ratio compared to the minimum variance approach. This means that smaller short positions are needed to lower the VaR of a portfolio than to lower variance. This lower hedge ratio has also the benefit of less hedging costs.

Nevertheless, one remark must be made, which is that the VaR is not a perfect risk measure. It has been used nowadays by a lot of practitioners, but it has still some shortcomings. One of those shortcomings is the fact that it does not contain any information about the size of the expected loss when the VaR of a portfolio is exceeded.

Simpson and Dania (2005) were the first researchers to study the performance of hedging strategies for a euro-based investor. The study was performed on equity markets in the period between 1999 and 2003. The results were that all the selective hedging strategies outperformed both the fully hedged and the unhedged portfolios.