Currency Hedging; Should I Bother?
Bob Looij 10688110
Finance & Organization
Supervicer: Ieva Sakalauskaite 22-‐01-‐2016
Abstract
The purpose of this thesis is to investigate whether the use of a currency hedge improves the Sharpe ratio for international diversified portfolios during the global financial crisis (2008-‐
2012). The origination of the overall risk of an international diversified portfolio will be examined. Where after unprotected portfolios and hedged counterparts will be constructed and
compared. Conclusively, my hypothesis of a Sharpe ratio improvement, by the means of a currency hedge, for an internationally diversified portfolio during the global financial crisis, will
be confirmed.
Table of Content page INTRODUCTION 3 1.DIVERSIFICATION 4-‐5 2. INTERNATIONAL DIVERSIFICATION 5-‐6 3. EXCHANGE RATE RISK 6-‐7 4. CURRENCY HEDGE 7-‐8 5. INTERNATIONAL DIVERSIFICATION DURING CRISIS PERIODS 8-‐9 6. EMPIRICAL ANALYSIS 9-‐14 6.1. METHODOLOGY 9 6.2. RESULTS 9-‐12 6.3. PORTFOLIOS 12-‐14 7. CONCLUSION & DISCUSSION 15 REFERENCE LIST 16
Introduction
Solnik (1974) showed the great benefits of international rather than domestic
diversification. However he emphasizes the importance of exchange rate risk, especially in days of internationally monetary instability. In such times fluctuating exchange rates are likely to mitigate the potential gains from international diversification by making investment in foreign securities more risky.
Exchange rate risk can be hedged by applying forward exchange contracts.
A forward contract imposes the obligation to either make or take a foreign currency payment in some point in the future. This leaves the investor fully protected should the currency depreciate below the contract level. However, he gives up all benefits if the currency appreciates. One could wonder if the risk return tradeoff would benefit most from the protection against exchange rate risk or from the possible gains of currency appreciation. At least I did by asking the question; Does currency hedging for
international diversified portfolios increase the Sharpe ratio during the global recession (2008-‐2012)? An answer to this question would give insight to in which extent a variety
of investors who hold an international portfolio should be concerned with exchange rate risk.
It is interesting to look at the time period of the global recession (2008-‐ 2012) because in these times portfolio diversification is ever more important and
simultaneous exchange rates are volatile due to international monetary instability. The First part of this thesis is theoretical and encloses how diversification works and why it is used. This will lead to the topic of international diversification. However when
investing internationally investors are confronted with exchange rates and the associated risk. Therefore exchange rate risk will be discussed followed by the use of forward contracts to hedge this risk. Subsequently, in the empirical part, the
methodology is explained and the results of this research are discussed from which a conclusion is drawn.
1. Diversification
Diversification is used as a mechanism to lower the variance of a portfolio’s return by allocating investments among imperfectly correlated categories. For risk-‐averse investors, such diversification is attractive because it can reduce portfolio risk for any given level of expected return. Risk-‐averse investors require a risk premium in the form of expected excess return for bearing risk. The utility of a risk-‐averse investor is derived from the trade-‐off between return and risk, and thus not simply maximizing return. The mechanism of diversification uses the fact that although the mean return of a portfolio is the average of asset returns and does not change when assets with the same expected return are added to the portfolio, the portfolio risk can change. The variance of the portfolio is not a weighted average of the individual asset variances and depends on their covariance’s and thus can be reduced when the covariance terms are negative or less than one. This can been seen from the following formula demonstrated by Bodie, Kane, and Marcus (2014).
var 𝑅! = 𝑤!!var 𝑅
! + 𝑤!!var 𝑅! + 2𝑤!𝑤!cov(𝑅!, 𝑅!) (1)
Where X and Y are different assets, 𝑅! and 𝑅! the respective returns and 𝑤! and 𝑤! the associated weights invested in those assets. 𝑅! is the portfolio return.
By combining the returns of multiple assets, the idiosyncratic share of risk can be diversified, as the distribution of portfolio return gets closer to its mean value.
The degree of correlation between assets determines the diversification benefits that can be achieved in a given economy. The value of diversification depends on the share of systemic versus idiosyncratic risk in asset returns: across firms, idiosyncratic risks that influence individual companies can be diversified, but the part of their returns determined by macroeconomic conditions that affect all firms in the economy cannot. For instance macroeconomic conditions like the business cycle, inflation, interest-‐ and exchange rates, influence the returns of all firms in a given economy, and are thereby correlated and non-‐diversifiable. However firm specific conditions like accomplishments in research and development or restructurings affect the firm returns without affecting other firms in the economy. Because the firm specific risk sources are independent they can be diversified. Furthermore as Meric and Meric (1984) show, are separate industries within a country differently affected by macroeconomic conditions. For instance the
aviation industry reacts differently relative to the agricultural industry to economic downturns. When a country has a diversity of industries that are among not perfectly correlated the market-‐risk can be diversified to a larger extent then a country with only one industry.
2. International Diversification
Systematic risk determined by macroeconomic conditions that affect all firms in the economy can only be diversified to some extent when holding only a national portfolio. However when holding an international portfolio macroeconomic risk can be diversified if not perfectly correlated across markets. The fundamentals of international
diversification were established in the 1960 and 1970. Solnik (1974) shows that
diversifying internationally rather than domestically can attain even a greater reduction of portfolio risk. Also more recent studies have shown the benefits of international diversification due to low correlations between international markets. For instance Cheol, Resnik and Resnik (1984) and also Meric and Meric (1989) find supportive evidence in their study of 17 developed countries over the period1973-‐1987. They conclude that diversification across countries, even within a single industry, produces greater risk reduction benefits than diversification across industries within countries. Michaud, Bergstrom, Frashure, and Wolahan (1996) study two different relatively long time periods, 1959-‐1973 and 1976-‐1995, and states that international equity
diversification can improve the risk/return characteristics. They explain that for an actively managed portfolio, the most potential is in the increase in returns from an increase in opportunities to add value. For a passively managed portfolio the most potential is in risk reduction.
The less correlated countries are the higher the benefits from international diversification. Gilmore and McManus (2002) found that due to relaxation and
liberalization in the financial markets around the world, global markets are becoming more integrated. The integration of global markets can raise the correlations between them and thereby reduce the gains from international diversification. The developed countries demonstrate higher correlations between each other than emerging markets do. In general, investors in emerging markets can gain more diversification benefits than those in developed markets (Chiou 2008). Despite what Gilmore and McCanus (2002) found, Bekaert and Harvey (2002) and Chiou (2009) conclude with their empirical
analyses that the correlation between the international markets remains low enough to achieve diversification benefits.
However, exchange rates do also have an effect on the returns of international diversified portfolios. Solnik (1974) emphasizes the importance of exchange rate risk, especially in days of international monetary instability. Fluctuating exchange rates are likely to mitigate the potential gains from international diversification by making investment in foreign securities more risky. More recent studies by Cheol, Resnik and Resnik (1988) as well Glen and Jorion (1993) indeed find that exchange rates do increase the volatility of international portfolios. Depreciation or appreciation of the foreign currency against the domestic currency can have great negative/positive effects on the return rate of a foreign investment.
3. Exchange Rate Risk
To get a better understanding on exchange rate risk a simple example follows. It shows what the dollar denominated return is for a foreign investment.
Starting with a dollar amount 𝑋$ and the original exchange rate 𝐸! at 𝑡 = 0 denoted in ($/€). This dollar amount 𝑋$ is exchanged for 𝑋$/𝐸! Euros.
The Europe Investment grows to 𝑋$/𝐸! 1 + 𝑅€
The Euro proceeds from the investment are converted back to dollars at 𝑡 = 1 at the exchange rate 𝐸!, for total dollar proceeds of 𝑋$(𝐸!/𝐸!) 1 + 𝑅€
The dollar denominated return on the European investment, therefore, is:
1 + 𝑅$ = 1 + 𝑅€ (𝐸!/𝐸!) (2)
From the example above it follows that exchange rates fluctuations over time have effect on the dollar denominated return of a foreign investment. To further investigate the effects of exchange rate risk on foreign investments, formula (3 & 4) also used by Cheol et al. (1988) will be examined. It shows that the variance of the dollar rate of return of a foreign investment can be approximated as
The above equation makes clear that the exchange rate change not only contributes to the variance of dollar returns via its own variance but also through its covariance with the local stock market returns.
The above analyses can be extended into a portfolio context. The variance of the portfolio return then can be written as;
var 𝑅!$ ≈ Σ!Σ!X!X!cov 𝑅!, 𝑅! + Σ!Σ!X!X!cov 𝑒!, 𝑒! + 2Σ!Σ!X!X!cov 𝑅!, 𝑒! (4)
From this last equation can be seen that the benefits of the total portfolio variance reduction achieved by international diversification can be mitigated by the additional total portfolio variance resulting from the exchange rate changes. Namely if the covariance, among the exchange rates, or among the exchange rate and stock market return are positive they will increase the overall portfolio risk. Which is the opposite effect of the risk reduction tried to accomplish by diversification.
Cheol et al. (1988) found that during their sample period of 1980 trough 1985 the volatility of the dollar exchange rates of such major currencies as the German mark and the Japanese yen exhibit nearly as much volatility as their respective stock markets. Furthermore, they conclude that the correlations among the exchange rate changes are higher than among the stock market returns. From the above result they deduce that the local stock market risk can be diversified away to a larger extent than the exchange rate risk. Another important result of their research is that the local market movements are reinforced by those countries exchange rates. From equation 3 can be seen that this will further increase overall portfolio risk.
4. Currency Hedge
Since the exchange rate risk might be non-‐diversifiable to a large extent it thereby contributes to the overall portfolio risk. The use of forward contract to hedge the exchange rate risk could be beneficial. A forward contract imposes the obligation to either make or take a foreign currency payment in some point in the future. This leaves the investor fully protected should the currency depreciate below the contract level. However, he gives up all benefits if the currency appreciates. The question than is if the use of forward contracts to hedge an internationally diversified portfolio indeed
the exchange rate risk is only beneficial if the risk reduction is not accompanied by an offsetting decrease in returns. Over the period 1974 to 1990 they conclude that a hedged portfolio significantly outperforms an unprotected portfolio. Another study by Cheol et al. (1988) also found that a hedging strategy with forward contracts
outperformed any unhedged strategy by far over the 1980 to 1985 time period.
5. International Diversification during Crisis Periods
The data sample for this research over the period (2008-‐2012) includes at least some of the timeframe of the global financial crisis. I expect that the effects of international diversification will be different due to the implications of the financial crisis. Because a common observation from several crises that occurred during the 1990’s, like the Exchange Rate Mechanism attacks of 1992, the Mexican peso collapse of 1994, the East Asian crisis of 1997, the Russian collapse of 1998, and the Brazilian devaluation of 1999, is that an initially national shock is transmitted to different markets around the globe. A phenomenon that is called contagion. Several studies for contagion make use of cross-‐ market correlation coefficients. They test whether correlations between country market returns in stable periods significantly increases after a shock occurs. If that is indeed the case it suggest that the transmission mechanism between markets increased from which the existence of contagion is deduces. Lee and Kim (1993) analyse the price co-‐
movements between stock market indices of the world’s 12 major stock markets during the October 1987 crash. They find evidence for contagion in the fact that average weekly cross-‐market correlations increased from 0.23 before the 1987 crash to 0.39 afterwards. Baig and Goldfajn (1998) further strengthen the evidence of contagion with their study on cross-‐market correlation increases in stock indices, currency prices, interest rates, and sovereign spreads in emerging markets during the 1997-‐98 East Asian crisis. The increase in cross-‐market correlation of equity and currency markets could have implication for international diversification.
From theory it can be reasoned that with higher correlation between markets the benefits of diversification will decrease. With higher co-‐movements between currency markets during crisis periods the exchange rate risk can be diversified to a lesser extent. Which is why I expect that the volatility of the exchange rate will add more risk to the total portfolio risk than in an out of crisis sample. Thereby making the use of a currency hedge to eliminate the exchange rate risk, pay of relatively more. From this follows my
hypothesis that the Sharpe ratio of the hedged portfolio will outperform that of the unhedged portfolio. 6. Empirical Analysis 6.1 Methodology
The approach of this paper is to investigate an equity portfolio with and without a hedging strategy. The portfolios will consist of the country stock market indices from Japan, United Kingdom, Canada, Australia and the Netherlands. These countries all have a flexible exchange rate regime, which is required to investigate the exchange rate risk of the portfolios. For this thesis I used daily data over the period 2008-‐2012. The data exists of the daily local currency return rates on the country stock market indices and the corresponding exchange rates against the dollar. To see how the portfolio variance consists and is influenced by different elements, the dollar rate of return for the different country indices is decomposed. Where after a correlation matrix is constructed for the countries subject to investigation. For the construction of the portfolios, I will use an equally weighted portfolio (EQW) and also identify the weights of the historical (ex post), maximum Sharpe portfolio (MAX SR) and invest accordingly. For the portfolios the viewpoint of an American investor who measures returns in US dollars is taken. Further a risk-‐free rate of zero is assumed. The unhedged strategy exists of the combined return of the asset and the currency i.e. 𝑅!$ ≈ 𝑅! + 𝑒!
For the hedged strategy a perfect protected portfolio is assumed. Excluding the exchange rates against the dollar does this and will thereby treat the local currency return rates as if they were US dollar return rates. The Sharpe ratio for the portfolio’s and their hedged counter parts will be calculated and compared.
6.2 Results
In table 1 the dollar rate of return for the different country indices is decomposed into different components. Column (1) shows the variances of the local returns of the country indices. Column (2) shows the variance of the local exchange rate returns. If we compare those columns it is clear that for all countries the exchange rates are substantially less volatile then their respective stock market returns.
Column (3) shows the covariance between the local index return of a country and the associated exchange rate return. Column (4) shows the correlation between the local
index return of a country and the associated exchange rate return. For all countries except for the Japan the covariance between the local stock market return and their exchange rate returns are positive. So only for Japan the exchange rate returns are found to offset the stock market movements, in case of the other countries they rather
reinforce the stock market movements.
Column (5) shows the variance of the dollar rate of return for each country index. It consists of the variance of the country index return in local currency plus the variance of exchange rate return plus two times covariance of the local index return with the local exchange rate return. As can been seen from equation 3 it is a measure for the total variance of a country’s stock market index return in dollars. And in case of this thesis it represents the total volatility of the unhedged country stock market index returns. Columns (6), (7) and (8) indicate to which percentage, the variance of the local index returns, the local exchange rate return and the covariance between them contribute to the variance of the dollar rate of return for each country index. They suggest that the exchange rate changes substantially contribute to the variance of the dollar rate return, via its own variance and the covariance with the stock market return. In particular, exchange rate volatility contributes 40,7% of total return volatility in both the UK and Canada, 58,7% in Australia and 18,3% in the Netherlands. Only in japan due to the negative covariance between the local stock market and the exchange rate, exchange rate fluctuations reduce total return volatility by 10,2%.
Table 1
Decomposition of the stock market returns in U.S. Dollars
(Daily data: January 2008 – December 2012)
(1) (2) (3) (4) (5) (6) (7) (8)
Stock
Market var 𝑅! var 𝑒! cov 𝑅!, 𝑒! cor 𝑅!, 𝑒! var 𝑅$ (1)/(5)x100% (2)/(5)x100% 2x(3)/(5)x100%
Japan 0,00036 0,000059 -‐0,000046 -‐0,317* 0,00033 110,2 18,1 -‐28,3 UK 0,00023 0,000062 0,000049 0,405* 0,00039 59,3 15,8 24,9 Canada 0,00025 0,000067 0,000053 0,411* 0,00043 59,2 15,7 25,0 Australia 0,00022 0,000143 0,000084 0,473* 0,00053 41,3 27,1 31,6 Netherlands 0,00034 0,00006 0,000008 0,057** 0,00042 81,8 14,4 3,9 USA 0,00030 -‐ -‐ -‐ 0,00030 100 -‐ -‐
The variances and covariances of columns (1), (2), (3), and (5) are stated in squared percentages * Correlation coefficient is significantly different from zero at the five percent level. ** Correlation coefficient is significantly different from zero at the ten percent level.
By keeping equation 4 in mind, it is easier to see that when the correlation among the exchange rate returns (panel B in table 2) and the cross-‐correlation between the local stock market returns and the exchange rate returns (panel C in table 2) are largely positive, fluctuations of the exchange rate returns increases the total portfolio risk. However when the entries in panel A and B in table 2 are negative the fluctuation of exchange rate returns actually decrease the portfolio risk.
To identify the stock market correlations, the exchange market correlation and the stock/exchange market cross-‐correlation among all countries table 2 is constructed.
Table 2
Correlation Matrices of Six Major Countries
(Daily data: January 2008 – December 2012)
Japan UK Canada Australia Netherlands US
A: Stock Market Returns in Local Currencies
Japan 0,478 0,334 0,749 0,445 0,227 UK 0,609 0,514 0,871 0,596 Canada 0,332 0,656 0,810 Australia 0,471 0,234 Netherlands 0,659
B: Exchange Rate Changes against Dollar
Japan -‐0,0934 -‐0,2019 -‐0,2363 -‐0,0094 0,000 UK 0,5649 0,6208 0,1038 0,000 Canada 0,7423 0,1014 0,000 Australia 0,0745 0,000 Netherlands 0,000
C:Stock/Exchange Market CrossCorrelations
Japan -‐0,317 0,324 0,366 0,495 0,190 0,000 UK 0,416 0,405 0,590 0,640 0,113 0,000 Canada -‐0,465 -‐0,584 0,411 0,493 0,083 0,000 Australia -‐0,992 -‐0,999 -‐0,779 0,473 0,200 0,000 Netherlands -‐0,197 -‐0,092 -‐0,068 -‐0,103 0,057 0,000 US -‐0,316 0,306 0,397 0,428 0,060 0,000
Each entry in panel C denotes the correlation among the column stock market returns in local currencies and the row exchange rates. All nonzero entries are statistically significant at a five percent level except for the cross-‐correlation of the Netherlands with itself, which is significant at the ten percent level. The only exception is the correlation between the Japanese stock market and the Dutch exchange market, which is not significant at all.
When panel A and panel B from table 2 are compared it can be seen that most of the time the correlations between the local stock market returns are higher then among the exchange rate changes against the dollar. Namely the average correlation of the stock market return is 0,532 and the (absolute) average correlation of the exchange rate changes is (0,275)/ 0,1667. This implies that the exchange rate risk can be diversified away to a larger extent then the market risk. In contrary, Cheol et al. (1988) find in their weekly data from the period of January 1980 through December 1985 that for each country the correlations are much higher among the exchange rate changes than among the local stock market returns.
In panel C the (absolute) average cross-‐correlation is (0,312)/ 0,0512, which is quite low in comparison to what Cheol et al. found in 1988, their average was 0,189. Corresponding with my finding, their average cross-‐correlation was relatively low in comparison to the market return and exchange rate change correlations. In contrary to my findings they found that every entry in panel C was positive which implies that the exchange rate change in a given country reinforces the stock market movements in the same country as well as in the other countries examined. From equation (4) follows that this reinforcement increases the overall portfolio risk. Cho, Choi, Kim, and Kim (2016) find in their overall period and sub-‐periods of 1996-‐2002 and 2003-‐2009 that in global down markets, capital tends to move, induced by the flight to safety, out of the emerging markets into the developed markets. The increase for the demand of developed markets currencies results in the appreciation of those currencies. When the returns on stock market indices in developed countries go down and their currencies appreciate it will cause a negative correlation between currency and equity in developed markets. This could explain why I found, in contrast to Cheol et al. (1988), 11 out of the 30 entries in panel C to be negative correlations. For a negative cross-‐correlation in panel C holds that the movements in that given country’s stock market is offset by the movement in the accompanying exchange market. This phenomenon will lead to a decrease of the over all portfolio risk.
6.3 Portfolios
Next the portfolios of the hedged and unhedged strategies are presented. Each including two portfolios, one for which equally weights are invested in the
different countries indices, and one for which the weights are derived from maximizing the Sharpe ratio. The last column of the unhedged and hedged portfolios represents the
Sharpe ratio, which is the average return of the portfolio divided by the standard deviation of the portfolio.
The Sharpe ratios of the unhedged equally weighted and maximum Sharpe portfolios are respectively -‐0,003 and 0,032. The negative Sharpe-‐ratio of the EQW portfolio is caused by the negative return of this strategy. By making use of a strategy that maximizes the Sharpe ratio a Sharpe ratio of roughly ten times as larger as the EQW portfolio can be achieved. For the hedged portfolios, the Sharpe ratio (-‐0,002) of the EQW strategy is also negative due to a negative portfolio return. The Sharpe ratio (0,058) of the MAX SR portfolio is almost thirty times larger than the Sharpe ratio of the EQW portfolio. Comparison of the unhedged and hedged portfolios suggest that both the Hedged EQW and MAX SR strategies outperform the unhedged counterparts in term of Sharpe-‐ratio. The higher Sharpe ratios of the hedged portfolio are mostly caused by their lower standard deviations.
Unhedged portfolio
Daily returns and standard deviations
EQW MAX SR Japan 20% 492% UK 20% 2330% Canada 20% 450% Australia 20% -‐588% Netherlands 20% -‐2584%
Sum of Weights 100% 100%
E(R$) -‐0,005% 1,000%
St.Dev 1,688% 31,309%
E(R$)/St.Dev -‐0,003 0,032
Hedged portfolio
Daily returns and standard deviations
EQW MAX SR Japan 20% -‐9% UK 20% 888% Canada 20% 49% Australia 20% -‐179% Netherlands 20% -‐649%
Sum of weights 100% 100%
E(R$) -‐0,003% 0,389% St.Dev 1,331% 6,655% E(R$)/St.Dev -‐0,002 0,058
7. Conclusion & Discussion
From comparing the above portfolios by first sight, it is clear that the Sharpe ratios of the hedged portfolios are higher for both the equally weighted and maximum Sharpe ratio strategy relative to the unhedged counterparts. I therefore can positively confirm that at least a perfect currency hedge for international diversified portfolio indeed increases the Sharpe ratio of an international diversified (equally weighted and max-‐ Sharp) portfolio during the time period 2008-‐2012 (Global recession).
In this study no statistical test is conducted to check whether the differences in the Sharpe ratios are actual statistically significant.
Further research could include, the investigation on how the Sharpe ratios are
distributed in the data samples used in this study. After which a matching statistical test can be conducted and inferences about the significance of the difference in Sharpe ratios can be made. For the portfolios multiple holding periods over different time horizons could be investigated. Also the use of forward contracts to hedge the exchange rate could be used which would also introduce the estimation of expected returns that need to be converted back in dollars. This study made use of ex ante investment strategies that made it possible to identify the optimal weights, and thereby estimation risk was excluded. It could be informative to see how these ex ante strategies perform in out of sample data.
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Verklaring eigen werk
Hierbij verklaar ik, Bob Looij, dat ik deze scriptie zelf geschreven heb en dat ik de volledige verantwoordelijkheid op me neem voor de inhoud ervan.
Ik bevestig dat de tekst en het werk dat in deze scriptie gepresenteerd wordt origineel is en dat ik geen gebruik heb gemaakt van andere bronnen dan die welke in de tekst en in de referenties worden genoemd.
De Faculteit Economie en Bedrijfskunde is alleen verantwoordelijk voor de begeleiding tot het inleveren van de scriptie, niet voor de inhoud.
