The effects of currency risk hedging on portfolio distribution: a
distinction between crisis and non-crisis periods
João van den Heuvel 10628398 July 1st, 2018
This paper examines the effect of currency risk hedging on portfolio distribution. In addition to the current literature, this research examines whether the effect of currency risk hedging is different for crisis periods. First, hedging benefits are examined for different subsamples. Second, OLS regressions are done of to test the effect of economic variables on hedging benefits. Lastly, these effects are tested with the inclusion of a crisis indicator and the interaction terms of the economic variables and the crisis indicator. The crisis indicator shows that mean and kurtosis benefits are lower during crisis benefits, whereas volatility benefits are higher; the latter can also be seen when comparing different subsamples. The effect on the portfolio skewness shows contradicting results and therefore remains inconclusive.
1 Statement of Originality
This document is written by João van den Heuvel, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
2 1. Introduction
Exchange rate movements can have substantial effects on portfolio performance when holding foreign assets. When an investor holds stocks of a foreign company, currency appreciation or depreciation can easily offset its returns. To protect the portfolio for these potential losses, an investor can take positions in forward contracts, which is also known as currency risk hedging. Since uncertainty is undesirable for most investors this strategy is widely used when holding international portfolios. The traditional view describes currency hedging as an effective method to decrease volatility without altering the portfolio returns, assuming for zero expected returns. Yet, with the presence of a currency risk premium, which suggests that hedging does bring costs, its effectiveness is still a debate. Sufficient research has been done on the risk and return trade-off from currency risk hedging. Although the traditional view was that currency risk hedging could be seen as a ‘free lunch’, later research provides evidence that hedging brings higher costs instead. De Roon, Eiling, Gerard and Hillion (2012) were the first ones to take into account the effects on the higher moments of the portfolio as well. Since most investors are interested in the total risk exposure of the portfolio, just looking at volatility would give an impression based on incomplete information. De Roon et al (2012) indeed find that currency hedging alters the higher moments of the portfolio; the overall skewness decreases and the kurtosis increases, which is an undesirable combination for investors.
The effects of currency risk hedging on all portfolio characteristics might be different in particular time periods. A well-known situation that usually has huge effects on portfolio returns is when an economic crisis returns. Periods of economic crisis usually lead to deteriorating returns, an increase of portfolio volatility and worsening Sharpe ratios. Since risk management is often based on situations of financial distress, the effects of currency hedging on higher moments are important aspects as well. Therefore, this research focuses on the effect of currency risk hedging on total portfolio distribution, and makes a comparison between periods with regular economic circumstances and periods
3
of financial crisis. Carry trade, an investment strategy that is highly comparable to hedging, but rather takes on risk instead of inducing it, has several times been proven to affect portfolio distribution. Brunnermeier, Nagel and Pederson (2008) find a link between carry trade and currency crashes, and explain this by the existence of liquidity spirals that arise in financial downturn. The effect of currency hedging on portfolio distribution in times of financial crisis has, to the best of my knowledge, not been examined yet. Brunnermeier et al (2008) find that carry trade, where high interest rates currencies are bought and low interest rate currencies are sold, leads to higher average returns accompanied by a negative skewness. Currency hedging is expected to lead to more negative returns during financial crises, which can be explained by the presence of a risk premium. Research of Hanson and Hodrick (1980), Fama (1984) provides evidence for a forward premium by looking at UIP deviations. This premium will likely be higher in crises periods since investors are usually reluctant to hold on more risk. This implies that the costs of currency risk hedging increases. Since crisis periods are often accompanied with high volatility, hedging might now be more beneficial for the portfolio’s standard deviation, as hedging aims to reduce this. Except for making a distinction between normal periods and periods of financial crisis, the effect of economic variables is considered as well. If some economic variables that indicate the state of the economy are shown to have significant effects on hedging benefits, these could be a meaningful indicator for hedging strategies. Also, earlier research has focused on the effects of macro-economic variables on carry trade, so the same reasoning should hold for currency hedging. Lustig and Verdelhan (2007), for example, explain the currency risk premium with the effect of consumption growth. Lustig, Roussanov, and Verdelhan (2014) test the effect of multiple macroeconomic variables on carry trade, and find that the macroeconomic factors are important indicators of expected returns. In this research, the explanatory effect of economic variables on hedging benefits is examined by using OLS estimators, with Newey-West standard errors to correct for possible autocorrelation and heteroskedasticity. The
4
economic variables that are included are the change production growth, the change in consumer sentiment and the change in non-farm payrolls, all being for the United States. Hedging benefits are categorized for each distribution characteristic, based on which outcome is desired to be highest. Thereafter, for each hedging benefit, three regressions are done to check for different effects of economic variables during crisis periods. The first regression includes only a crisis indicator in the form of a dummy variable, based on NBER recession dates, to test the effects of crisis periods. The second regression includes the economic variables as well, and the third regression adds the interaction terms of the crisis indicator and the economic variables. These regressions are done over the period from 1985 to 2018, where three U.S. recession periods have occurred.
Over the entire sample period, currency hedging alters the portfolio distribution in a negative manner. The mean and Sharpe ratio decrease, the volatility and the kurtosis increase, and the skewness becomes more negative. Except for the increase volatility, this is all as expected. A possible explanation for the increase in volatility is the use of out-of-sample returns. When using in-sample returns, hedging is shown to decrease volatility, which coincides more with the expectations. When making a distinction between time periods, the results remain equal for the normal periods. For the crisis periods, hedging does not seem to affect mean returns, and decreases portfolio volatility. By looking at the effect of economic variables, industry production growth and the change in non-farm payrolls have significant effects on hedging benefits. The coefficient of industry production growth is positive and significant on both the mean and Sharpe ratio benefits, and negative for the skewness benefits. This suggests that the average returns increase during times of economic growth, but decrease when industry production growth declines. The effect of the change non-farm payrolls is significantly negative for the standard deviation benefits, and significantly positive for the kurtosis benefits. The effect of the recession indicator coincides with this finding, since its coefficient is positive on standard deviation benefits, and negative for the kurtosis benefits. These findings indicate that
5
hedging effects worsen the mean returns during crisis periods, but that it could be a helpful solution to decrease volatility. The unfavourable effect of the decreasing mean returns though overshadows the volatility benefits, since the Sharpe ratios are altered in a negative way. Currency hedging also seems to increase the portfolio kurtosis. The effect of currency hedging on skewness in times of crises remains inconclusive. The findings of the subsamples and the effect of the crisis indicator show contradicting results, and could be related to unknown measurement errors.
The paper is structured as follows. Section 2 describes relevant literature on this subject and includes some theoretical explanations. Thereafter, in section 3 the expectations are described. Section 4 and 5 describe the empirical methodology and the data that has been used. Section 6 provides the empirical results, and section 7 includes a robustness check for a European investor. Section 8 proposes suggestions for further research, and states the possible limitations of this paper. Finally, section 8 describes the conclusion.
2. Literature review and theoretical background
To eliminate risk from currency fluctuations in international portfolios, an investor can use several instruments to construct a hedging strategy. Positions in either forward or futures contracts can be taken to equally offset the returns of exchange rate movements. When choosing a position, the future cash flows from the underlying contracts should be the opposite of the expected cash flows from the currency movements. This eliminates the risk of negative returns due to downward fluctuations of the foreign currencies, but it also constraints the positive returns of currency appreciations. These strategies are likely to be most important for investors that focus on cross-border activities, but can be important for the risk induction by financial institutions as well.
If currency returns are expected to be zero, and currency risk hedging reduces portfolio volatility without altering the returns, it seems as a good way of improving the risk return ratio. This traditional view of currency risk hedging
6
describes it as a ‘free lunch’, which was first suggested by Perold and Schulman (1998). In their paper they state that, on average, currency hedging leads to risk reduction without decreasing the expected returns of the portfolio. More recent literature, however, shows rather contradicting results where currency hedging is proven to decrease the portfolio returns, and to have a negative effect on the higher moments as well. De Roon, Eiling, Gerard and Hilion (2012) tested the effectiveness of currency hedging for international portfolios, and were the first to take into account the effect on the higher moments of the portfolio distribution. They consider the skewness and kurtosis to be relevant aspects of a portfolio distribution since most investors benefit from having a clear view on the total risk exposure of the portfolio, and the volatility remains an incomplete indication for this. In their research they construct a portfolio with currencies of seven developed countries, and use currency forward returns for an overlapping hedged portfolio. When looking at the higher moments, they find that the portfolio skewness worsens and that the kurtosis increases1. Having a high kurtosis, which is often referred to as having ‘fat tails’, implies that most outcomes are little deviated from the mean. This means that the variation of the portfolio is largely explained by more extreme outcomes, which reflect the thicker tails of the distribution. A high kurtosis is interchangeably used as having excess kurtosis, where excess kurtosis entails that the outcome exceeds an amount of 3, since that is the kurtosis level of a normal distribution. Although a higher kurtosis is not necessarily disliked by investors, the combination with a negative skewness is regarded as an undesirable trait of the portfolio. The skewness reflects the asymmetry of the portfolio, and a negative skewness thus implies that the distribution’s tail is thicker on its left side. Since the thickness of the tails characterize the amount of outliers, this measure signifies that extreme outcomes are more likely to be negative. As these findings point out the negative
1 De roon et al find that by currency hedging, portfolio skewness decreases from -0.94 to -1.28,
which is a significant decrease of 37%. Looking at portfolio kurtosis, they found an increase from 3.67 to 5.91, which is equal to 61%.
7
effects of currency hedging, De Roon et al (2012) find evidence that hedging also decreases average returns and Sharpe ratios, and suggest that currency risk hedging is no ‘free lunch’ at all. In their findings, the only gain of currency hedging is the decrease in volatility, for where it is originally being used.
An important factor that could explain the cost of currency risk hedging, and therefore the decrease in mean returns, is the presence of a premium for exchange rate risk. If investors want to be compensated for the risk of exchange rate fluctuations, which means that bearing different currencies is priced, this means that hedging does come at a cost. De Santis and Gerard (1998), among others, find supporting evidence on this. When taking into account time variation in the price of risk, they find that both currency risk and market risk are priced factors. Their findings support earlier research of Dumas and Solnik (1995), who show that a currency risk premium is a significant component of the rate of return of a security.
Exchange rate risk, however, is only relevant when there is a difference in purchasing power between countries. This is also known as a violation of the purchasing power parity (PPP), which states that the value of one currency should be equal for every country, and that the exchange rate purely reflects a difference in price levels. If the PPP holds, one dollar should have the same purchasing power in each country, and exchange rate fluctuations do not reflect any risk. However, there are numerous empirical findings and theoretical explanations that suggest that the PPP does not hold for most of the time, and if so, it is only in the long run.2 Transport costs, imperfect competition and productivity differentials are some of the factors that explain differences in purchasing power, and therefore the existence of exchange rate risk. For this reason, these findings form a meaningful argumentation for investors to focus on hedging this risk.
2 Pilbeam (2014), in its book ‘International Finance’, discusses the PPP and its empirical
8
As currency risk hedging strongly relies on the efficiency in forward markets, it must be considered what is the optimal method of constructing forward rates. One could obtain direct forward rates, but a widely used approach is to construct forward rates by using interest rate differentials, which assumes the covered interest parity (CIP) to hold. The CIP condition links the forward and the spot markets, and is known to hold continually by the presence of arbitrage.3 The CIP states that the difference in interest rates between countries is immediately offset by movements in spot and forward exchange rate. The CIP is noted as follows:
1+i = Ft
St 1+i* , (1)
where iis the domestic interest rate, i* the foreign interest rate, St the spot rate and Ft the forward rate. Throughout this paper, the spot and forward rate will be described as the amount of home currency that needs to be exchanged to obtain one unit of the foreign currency, i.e. $/€ for an U.S. investor. The same goes for the forward rate, only this implies a predetermined rate for an exchange in the future. From equilibrium (1) it can be seen that differences in interest rates are offset by the ratio of the forward and the spot rate. The rationale is as follows: if the equilibrium is imbalanced by a change in either the domestic or the foreign interest rate, arbitrageurs aim to make profit by buying the currency with the higher interest rate for the spot rate, and selling it on the forward market at the same time. If it were the foreign interest rate to be the higher one, the spot rate would go up and the forward rate would go down, for which the equilibrium is back to its balance.
A strategy that also relies on interest rate differentials is the ‘carry trade’, which can be regarded as the opposite of currency hedging, since it rather takes speculative positions in currencies. With a carry trade strategy, currencies with high interest rates are bought and currencies with low interest rates are sold. The high interest rate bearing currencies are called investment currencies, whereas
3 However, recent research of Jiang, Krishnamurthy and Lustig (2017) provides new evidence that the CIP does not hold in practice.
9
the low interest rate bearing currencies are called funding currencies. This strategy relies on violations of the uncovered interest rate parity (UIP), which is comparable to the CIP, except that the exchange rate movements are not being covered by the forward rate. The formula is similar, but now the expected future spot rate ESt+1 is the balancing factor. Instead of arbitrage, it is speculation that ensures the UIP to hold. The equation is as follows:
1+i = ESt+1
St (1+i*). (2)
Early work from Hanson and Hodrick (1980), and Fama (1984), brings evidence for UIP violations, which is often referred to as the ‘forward premium puzzle’. Where currency risk hedging is proven to exhibit lower returns, carry trade strategies rather have supporting evidence of improvement in portfolio returns. Burnside, Rebelo and Eichenbaum (2008) find that carry trade strategies increase Sharpe ratios by over 50%. In their research, they base the effectiveness on three different strategies. The equally weighted carry trade strategy gives an equal weight to all currencies, at each point in time for which data is available, and for which the spot rate differs from the forward rate. The other two strategies concern a currency-specific carry trade and a high-low carry trade.4 All of these strategies result in higher Sharpe ratios, which are explained by an imperfect correlation between the payoffs for different currencies, and are mostly due to a decrease in volatility. For the currency specific and the high low carry trade, the returns have lower means and show a fat tailed distribution. Only for the equally weighted carry trade, the rise in Sharpe ratios is not followed by an increase in tail risk, since this strategy even leads to a less negative skewed distribution than that of the excess return to the value-weighted U.S. stock market. Moreover, for all their strategies, Burnside et al (2008) reject their hypothesis that the payoffs of the returns are normally distributed. If carry trade is proven to affect the higher moments of the portfolio, it could be the case that the same holds for currency risk hedging. Both strategies are highly comparable in taking positions, where
4 For a detailed explanation of the different carry trade strategies, see Burnside, Eichenbaum
10
hedging is used to induce risk, and carry trade rather takes on risk for making profit.
An important reason to distinguish the effect of currency hedging for normal periods and crisis periods is the existence of currency crashes, which are linked to carry trade strategies by Brunnermeier, Nagel and Pedersen (2008). In their earlier work, they explain the existence of liquidity spirals that arise because of financial constraints that investors face. In their model, they show that investors typically invest in securities with high average returns and a negative skewness. With the asymmetric response to fundamental shocks, the situation worsens when investors unwind their positions, funding problems increase, and the problem continues. They argue that the same situation might occur in a currency setting, where interest rates are altered. A change in interest rate should lead to capital inflows or outflows, which would insure the UIP to hold. However, when investors face liquidity constrains, which therefore eliminates the assumption of full capital mobility, exchange rates only adapt gradually and are often disrupted by speculative capital withdraws. When investors hold on to their initial position, and the exchange rate does not move back to its fundamental value, a currency bubble might occur. Just like a regular pricing bubble, investors do not know when others will revise their positions. The inevitable consequence is that a currency crash occurs when the first investors unwind their positions. Brunnermeier et al (2008) indeed find evidence that carry trade leads to negatively skewed returns, and document that currency crashes are linked to the unwinding positions in these currencies.
Jurek (2014) distinguishes regular carry trade strategies from crash risk strategies by using foreign exchange options. He tests the hypothesis whether the currency risk premium reflects the risk of currency crashes, where high interest rate currencies devaluate quickly. Although his findings support that carry trade strategies yield positive returns, the returns also show to be extremely negative in times of rapid devaluations, which lead to a negative skewness of the portfolio. Jurek (2014) finds that the excess returns are unlikely to be reflection of
11
a ‘peso problem’, which could have been the problem whenever currency crashes are not represented enough in the sample period.5 By his research, he finds that the peso problem is unlikely to explain the excess currency returns, since carry trades that are hedged for crash risk result in positive and significant returns as well. Furthermore, he investigates what amount of the excess returns is actually attributable to a currency risk premium. He decomposes the currency risk premium into a diffusive part, which is estimated by the mean return of a portfolio that is constructed by carry trades, and a jump (crash) risk part, that is estimated by the difference between mean returns of the hedged and unhedged portfolios.
Except for looking solely at outcomes in hedged returns, it can be useful to find whether economic variables can indicate the effectiveness of hedging, so that investors can base their positions on these indicators. The macroeconomic indicators are used to declare the state of the economy, and could therefore make a distinction in normal periods and periods of financial crisis. If these variables are shown to be related hedging benefits, it could be suggested for which economic state hedging is more beneficial. For example, Lustig and Verdelhan (2007) link consumption growth to the currency risk premium, which is an important factor that explains the cost of hedging. They find that a large part of the variance in average currency excess returns is explained by U.S. consumption growth risk. In crisis periods, U.S. consumption growth is usually below average, which should lead to a higher currency risk premium, and therefore to higher costs of hedging. More recent literature of Lustig, Roussanov and Verdelhan (2014) focuses on a dollar version of the traditional carry trade strategy, where baskets of interest rates are compared to the U.S. dollar. According to their theory, the risk premium is attributed to the risk exposure of dollar appreciations in U.S. recession periods, since this highly affects returns from taking speculative
5 The peso problem is referred to as a situation where inference is caused by events that are
not represented in the sample and are unlikely to occur, but can have a large impact on portfolio performance
12
positions. Therefore, they also include business cyclical and financial variables to explain future currency returns. They find that aggregate returns in currency markets are highly predictable and that expected currency returns are strongly countercyclical. They conclude that the most important predictors for expected returns are U.S. macroeconomic variables, mostly for longer holding periods. 3. Expected findings
With respect to the current literature, currency risk hedging is expected to affect the portfolio distribution in several ways. As the effect on total portfolio distribution is previously documented by De Roon et al (2012), it is tested whether this effect differs in periods of financial crisis.
Regarding the first moment of the distribution, the portfolio mean, it is expected to decrease by using currency hedging, due to the findings of a currency risk premium. Hedging this risk would therefore bring costs, which negatively alters portfolio returns. The risk premium is expected to be present in both normal and crisis periods. This is in line with the earlier findings of De Roon et al (2012), who prove that hedging decreases mean returns. When making a distinction between normal and crisis periods, it has to be considered for which period the risk premium is higher. Intuitively, the amount of insurance mostly depends on the both the probability and the amount of loss that is expected to occur. Therefore, since losses are more likely to occur in crisis periods, it is reasonable to suggest that investors require higher premiums during financial crises. Moreover, crisis periods can be seen as times of insecurity in general, when taking factors as moral hazard and adverse selection into account. Inducing this risk by hedging would therefore be more costly, which entails that the mean of the hedged portfolio is expected to be lower during crisis periods than during normal periods. The economic variables are expected to be positively related to the mean benefits, since they indirectly indicate the state of the (U.S.) economy, and therefore the crisis periods.
13
portfolios at all times, since inducing risk is the main purpose of currency hedging. This also follows the earlier findings on the decrease in volatility. The question is whether this effect is stronger during crisis periods. Since crisis periods are usually more volatile than normal periods, hedging is therefore expected to be more beneficial in these times. For the economic variables, they are expected to be negatively related to hedging benefits, since economic stability decreases the urge of risk reduction.
As the Sharpe ratio can be seen as the combination between the mean- and volatility benefits, the effect of currency hedging during crises should depend on which effect dominates. The expected decrease in mean returns would negatively affect the numerator of the Sharpe ratio, whereas the decrease in volatility has positive effect on the denominator. Combining these affects makes that the Sharpe ratio could go either way. The same holds for the expectations on the economic variables.
Considering the higher moments, the expectations are a bit more complicated to determine. With reference to research of Jurek (2014) and Brunnermeier et al (2008), the effect of currency hedging on skewness can be compared to the effect of carry trade strategies. They find that carry trade leads to more negative skewed returns, and link this to the occurrence of currency crash risk that is caused by the unwinding positions of investors. When investors face liquidity problems, the problem worsens, and a currency bubble occurs. The quick deteriorations of currencies with high interest rates result in high losses, which explains the negative skewed returns for carry trade. If offsetting positions are taken in these currencies, hedging should rather lead to less negative skewed returns during crisis periods, assuming that currency crashes occur at the same time. However, De Roon et al (2012) find that a combination of a carry trade strategy and a hedging strategy leads to negative skewed returns for all the examined currencies. It has to be tested whether this effect differs in crisis periods. Looking at the kurtosis, a higher excess kurtosis reflects that large outliers are more likely to occur, which is also expected in crisis periods. If
14
hedging is able to induce these outliers, hedging benefits will likely increase during recession periods.
4. Empirical methodology
Following De Roon et al (2012), Campbell (2010), and many others, constructing a hedged portfolio will be done by an overlay strategy, where currency forward returns are added to an unhedged base portfolio with a certain weight. As a base portfolio, a global equity portfolio is used to insure international exposure, and therefore exchange rate risk. For the global equity portfolio the MSCI world index is used, and the returns are calculated on a monthly basis. The currency returns reflect the difference between the forward and spot rates, and are based on interest rate differentials, assuming the CIP to hold. By rewriting equation (1), the forward rates can be constructed as:
Ft = St1+i*1+i . (3)
After constructing the forward rates, the currency forward returns can be calculated as:
ft= FSt
t-1:t. (4)
To decide what amount of the currencies should be hedged, the method of minimum variance hedging is being used. This uses past information to determine the correlation between the currencies and the unhedged portfolio, and constructs weights by using OLS estimates. The weights per currency are the negatives of the regression coefficients. The OLS equation is thus as follows:
RτMSCI= α+ β1RτCurrency1,…,+ β2RτCurrencyn+ετ, τ=t-1,…, t-60,
(3)
with βi= Cov RVar RMSCICurrencyi, RCurrencyi = -wi. (4)
The rationale is as follows: when the hedged portfolio consists of both an unhedged equity part and of currency forward returns, the total portfolio will be diversified when both parts move the opposite direction. Therefore, negative weights are given to currencies that are estimated to have a positive effect on the
15
base portfolio. To construct the weights, a window of 60 months is used for a base period of input. The hedged returns can then be constructed as:
Rthedge = RtMSCI+wi,tfi,t
.
(5)
All hedged returns are calculated out-of-sample, which means that the weights of the estimation period are multiplied with the returns for the subsequent period. Both out of sample hedged and unhedged returns are calculated for each month, which is based on a rolling window basis, and for the entire out-of-sample period. The calculation for the entire period uses all available input, and is used to see what impact currency risk hedging has on the overall portfolio distribution. The monthly rolling window calculations slightly changes the currency weights and gives estimates for the portfolio distribution over time. By this way, the portfolio characteristics can be compared for normal periods and periods of financial crisis.
The calculations for the mean and the standard deviation are straightforward and are widely known, so the formulas will not be explained. The Sharpe ratio is used as a measure of the mean return and the volatility ratio. This gives a clearer view of portfolio performance, since higher mean returns can also stem from higher volatility. The Sharpe ratio combines these two aspects with the following formula:
SR
=
R-Rfσ
.
(6)As stated earlier, both the skewness and the kurtosis are relevant statistics because of risk aversion from investors, and the volatility does not fully reflect the portfolios risk exposure. The skewness measures the level of asymmetry in the returns over a given period. Taking a normal distribution as a starting point, a positive skewness implies that more data is centred at the left side of the mean, and that the tails are thicker on the right. By having a portfolio with a positive skewness, positive outliers are more likely to occur. A negative skewness describes the opposite situation. More data is centred on the right side of the mean, but outliers are also more likely to be negative. A negative skewness can
16
therefore be seen as an undesirable characteristic. The formula for the skewness is:
S = N
Ni=1(Xi-X)3( Ni=1(Xi-X)2)
3
2
(7)
The kurtosis measures the thickness of the distribution’s tails. A high kurtosis means that the peak of the distribution is higher than that of the normal distribution, and implies that most returns are centred around the mean. Although this seems like a more precise measure of the real average return, a high kurtosis implies that the variance is explained by more extreme outcomes. A lower kurtosis assumes that outcomes are more deviated from the mean, but that these outcomes together result in the given variance. Whether a high kurtosis is desirable or not depends on the investor’s preferences, but the combination with a negative skewness is mostly regarded as unwanted, since the variance is attributed to more extreme outcomes, and these extreme outcomes are likely to be negative. The formula for the kurtosis is as follows:
K = N
Ni=1(Xi-X)4( Ni=1(Xi-X)2)
2
(8)
Sometimes the kurtosis is also described as excess kurtosis, which compares the outcome to the normal distribution. In this research, however, this measure is being used.
The same calculations as for the entire sample period are also done on a monthly basis. For the estimation window a time frame of 60 months is used. Since the hedged returns require input from past information, the out of sample period for the returns is from 1980-2018. The rolling window statistics start exactly 5 years later, since the statistics also require past information. To compare normal periods with periods of financial distress, two subsamples are created, with a dummy variable indicating whether the U.S. is in a recession or not.
The currency hedging benefits are constructed for every statistic separately to give more precise and clear results. For example, if for a given period the hedging strategy leads to a higher Sharpe ratio but to a more negative
17
skewness as well, it is difficult to determine which is more beneficial. Therefore, all portfolio characteristics are considered individually. When a positive outcome implies a hedging benefit, the outcome for the unhedged portfolio is subtracted from the hedged portfolio. Obviously, investors desire a higher mean return, so the hedging benefit is constructed by subtracting the unhedged mean returns from the hedged mean returns. The same goes for the Sharpe ratio and the skewness. Investors usually rather dislike volatility, so now the hedging benefits are constructed by subtracting the standard deviations of the hedged returns from the standard deviations of the unhedged returns. For the kurtosis, the hedging benefit is not as one sided as the previous characteristics, but since the combination of a high kurtosis and a more negative skewness is usually disliked, a lower kurtosis implies a hedging benefit.
Furthermore, the effect of economic indicators on currency hedging benefits is examined, with the U.S. recession date being used as a dummy variable (USREC). The economic variables that are included in the regression are: industry production growth, consumer sentiment and total non-farm payrolls, all for the United States. The industry production growth is calculated as the monthly percentage change of the U.S. industry production index (Indpro), and the consumer sentiment as the monthly percentage change of the consumer sentiment (Umcsent). The total non-farm payrolls (Payems) is also calculated as a monthly percentage change, and is regarded as a more precise measure of the labour market condition compared to the unemployment rate. The GDP growth is omitted from the regression, since its availability is on a quarterly basis and would therefore only lead to more imprecise estimates of the other variables. When including it as an explanatory variable, it did not show to have significant effects on hedging benefits and excluding it did not alter the estimates of the other explanatory variables.
Since the same variables are measured over time, a multiple OLS regression is done, but with Newey-West standard errors to cover for
18
autocorrelation and heteroskedasticity in the error terms. The regression equation is:
Hedging benefitt= α + β1Umcsentt+ β2Indprot+ β3Payemst+ εt,
(9)
which is done for al portfolio characteristics. To examine the effect of crisis periods, a dummy variable USREC is included in the regression, and the interactions with the economic variables are included as well. For each characteristic three regressions are done. The first regression is with the recession indicator being the single explanatory variable. The second variable includes the economic variables, and the third regression adds the interaction terms between the crisis indicator and the economic variables. It is expected that the coefficients remain being the same in all three regressions. In case of a significant effect of the interaction terms, this might suggest that the effects of the explanatory variables are stronger or weaker during crisis periods. Since economic variables are almost inevitably different in crisis periods, this situation is not being unexpected. 5. Data
The MSCI World Total Return Index is used for the unhedged equity portfolio. The MSCI world index has over 1600 constituents of large- and mid-cap stocks from 23 developed countries6. The sample period is from 1975 to 2018, since it covers all years for which data is available. Several crises are taken into account when examining a period from 1975 until 2018. The most obvious crisis to be considered is the Great Financial Crisis (August 2008 – December 2009), but the early 1980s recession (August 1981 – November 1982), the early 1990s recession (August 1990 – March 1991) and the early 2000s recession (April 2001 – November 2001) are being considered as well. The early 1980s recession, however, is not being used for the regressions with the economic variables, since
6 Markets covered: Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany,
Hong Kong, Ireland, Israel, Italy, Japan, Netherlands, New Zealand, Norway, Portugal, Singapore, Spain, Sweden, Switzerland, the U.K. and the U.S.
19
the hedged benefits could be calculated from 1985. All recession dates are based on the NBER recession indicators for the United States.
The currencies that are used for the hedging strategy are the U.S. Dollar, the U.K. Pound, the Euro, the Australian and the Canadian Dollar, the Japanese Yen and the Swiss Franc. For the period before 1999, the German Mark is used as an approximation for Europe, since it Germany is Europe’s largest market. For the risk free interest rates, the one-month deposit middle rates are used, for the same countries of which the currencies are from. The monthly interest rate differentials are used to construct forward rates. The MSCI world index and the monthly interest rates are both retrieved from DataStream. The monthly exchange rates are retrieved from the IFS database.
Table 1
This table shows the summary statistics for the base portfolio and for the currency forward returns per country. The period is from February 1975 to February 2018. The currency forward returns are based on monthly interest rate differentials, and are calculated from an U.S. investor’s perspective. The mean and standard deviation are presented as annual percentages.
Summary statistics for the MSCI and the currency forward returns (U.S. $)
MSCI Eur Aus Can Jap Swi UK
Mean (% p.a.) 11.25 0.32 2.66 0.38 0.5 0.2 1.07 Stdev (% p.a.) 15.32 10.83 12.02 6.91 11.03 11.84 10.22
Skewness -0.634 -0.034 -0.458 -0.483 0.392 0.078 0.082 Kurtosis 4.912 3.956 9.143 7.755 4.472 4.121 4.898 The currency forward returns all show positive annual mean returns, ranging from 2.66% of the Australian dollar to 0.2% for the Swiss franc. For the Euro, and for the Australian and the Canadian dollar, the currency forward returns are negatively skewed, just as the MSCI world index. For the remaining currencies, the returns are positively skewed. For all currencies and for the MSCI, the distributions show an excess kurtosis, since they all exceed an amount of 3. The distributions therefore have fatter tails compared to a normal distribution.
The economic variables are retrieved from FRED database. The monthly changes in the industry production growth index (INDPRO) are used to measure U.S. production growth. Consumer sentiment is estimated by the monthly
20
change in the U.S. consumer sentiment index (UMCSENT). The labour market conditions are estimated by the monthly change in non-farm payrolls (PAYEMS). All variables are used for the same window as the hedged and unhedged returns, from 1985 to 2018. The U.S. recession dates are also retrieved from the FRED database, and are based on the NBER recession indicators.
Graph 1: U.S. consumer sentiment
Graph 2: industry production growth
21 Table 3, 4, 5
These tables show the summary statistics for the explanatory economic variables for the United States in different time periods. Table 1 shows the statistics for the total period, table 2 for non-crisis periods and table 3 for crisis periods.
U.S. economic variables: total period
Umcsent Indpro Payems
Mean (% p.a.) 0.19 1.91 1.29
Stdev (% p.a.) 16.45 2.14 0.55
Skewness -0.087 -1.585 -1.436
Kurtosis 5.322 12.233 6.584
U.S. economic variables: non-crisis periods
Umcsent Indpro Payems
Mean (% p.a.) 0.73 2.97 1.67
Stdev (% p.a.) 14.79 1.71 0.40
Skewness -0.082 -0.030 -0.431
Kurtosis 4.229 3.690 3.597
U.S. economic variables: crisis periods
Umcsent Indpro Payems
Mean (% p.a.) -5.53 -9.31 -2.76
Stdev (% p.a.) 29.03 3.31 0.69
Skewness 0.055 -1.988 -0.896
Kurtosis 3.545 8.274 2.618
Looking at the summary statistics of the economic variables, we see that there is a clear difference in crisis- and in non-crisis periods. The biggest difference in means is for the industry production growth, which is 2.97% per year for non-crisis periods, and -9.31% for non-crisis periods. All variables show negative averages and higher standard deviations in crisis periods. The skewness is always negative for all variables and the distributions all show fat tails, except for the non-farm payrolls in crisis periods (2.618). The variable Umcsent seems to be highly volatile comparing to the other variables. A possible explanation could be that consumer sentiment depends on numerous things, such as news messages and political events.
22 Table 6
This table shows the correlation matrix of the U.S. economic variables in the period 1985 to 2018.
Umcsent Indpro Payems
Umcsent 1
Indpro -0.0829 1
Payems 0.0317 0.4648 1
The correlation matrix shows that industry production growth and the change in non-farm payrolls are correlated with a correlation coefficient of 0.46. Since both should reflect economic circumstances, this is to be expected. However, this amount should not give problems of multicollinearity. The correlation coefficient of consumer sentiment and industry production growth is negative, but small. Due to the high level of volatility of consumer sentiment, there are several reasons that could explain this, such as the difference in timing. Below shows the graphs of the explanatory variables, with the recession periods being highlighted. 6. Empirical results
1. Portfolio characteristics for the total period
Below, all graphs of the portfolio characteristics are shown over the total period. The highlighted periods indicate crisis periods.
23
Graph 5: difference in standard deviations
Graph 6: difference in Sharpe ratios
Graph 7: difference in skewness
24 Table 7, 8, 9
The following tables show the characteristics for the unhedged and the hedged portfolio. Table 1 shows the results for the overall period, table 2 for the normal periods and table 3 for crisis periods. The results are based on the perspective of an U.S. investor, where the currency returns are calculated vis-à-vis the U.S. dollar. The sample period is from 1980 to 2018. The benefits are calculated by subtracting the outcomes of either the hedged or the unhedged portfolio from the other, depending on which characteristic is desired to be higher.
Portfolio distribution (U.S. $) – total period
Mean Stdev Sharpe Skewness Kurtosis
Unhedged 0.93% 4.42% 0.118 -0.634 4.912
Hedged 0.83% 4.53% 0.091 -0.753 5.374
Benefit -0.11% -0.11% -0.027 -0.119 -0.462
N 457 457 457 457 457
Portfolio distribution (U.S. $) – non-crisis period
Mean Stdev Sharpe Skewness Kurtosis
Unhedged 1.16% 3.88% 0.198 -0.601 4.857
Hedged 1.04% 4.19% 0.153 -0.700 5.630
Benefit -0.12% -0.23% -0.045 -0.099 -0.462
N 407 407 407 407 407
Portfolio distribution (U.S. $) – crisis period
Mean Stdev Sharpe Skewness Kurtosis
Unhedged -0.90% 7.32% -0.204 -0.005 2.657
Hedged -0.90% 6.53% -0.226 -0.355 3.183
Benefit -0.00% 0.79% -0.022 -0.350 -0.526
N 50 50 50 50 50
It can be seen that for the overall period, currency risk hedging leads to an undesirable outcome for all portfolio characteristics. Outcomes that are desired to be higher are lower when a hedging strategy is applied. The mean for the hedged portfolio decreases by 0.11%, which implies that the by hedging, monthly average returns decrease with 12%. Whereas both means are rejected to be zero, the difference of 0.11% between the hedged and the unhedged portfolio is not statistically significant.7 For the overall period, currency hedging is not beneficial to the other portfolio characteristics either. Except for the negative effect on standard deviation, the results are all as expected, following research of De Roon et al (2012). The increase in volatility is also different from what is expected by theory, since the aim of hedging is mainly to induce risk rather than amplifying
25
it. This could possibly be a result of the out-of-sample hedging strategies, where the weights might be imprecisely attributed to the different currencies. Since the hedged returns are calculated out-of-sample, the currency returns for the subsequent period could be different from what is expected by OLS estimation. The hedging strategy is also done for an in-sample period, which means that hedging is done for the same period as for which the returns are already known. For this period, hedging now does seem to decrease volatility, which matches the expectations. The results can be found in table A2.
Since the mean decreases, followed by an increase in volatility, the Sharpe decreases from 0.12 to 0.09, which is a decrease of 23%. Regarding the higher moments, currency hedging also leads to undesirable results. The skewness decreases from -0.63 to -0.75 and the kurtosis increases from 4.91 to 5.37. These findings all signify that hedging comes at cost when different time periods are not being considered.
For the different sub-samples, hedging seems to be more beneficial in crisis periods when looking at the first moments of the portfolio. The mean returns are equal for both portfolios, which is different from what is expected. When only the first three recession periods are being considered (including the 1980s crisis that is not displayed in the graph), and therefore excluding the Great Recession of 2008, the mean of the unhedged portfolio is -0.33%, whereas for the hedged portfolio it is -0.53%, which is a decrease of 60%. This decrease is still not statistically significant though. The volatility also improves during crisis periods, with 7.32% for the unhedged portfolio, and 6.53% for the hedged portfolio, which is more in line with the related theory. The difference in the skewness, however, is three times as much for the crisis period than for the other periods. The impact on the kurtosis seems to be equal for all periods.
26 2. Effect of economic variables on hedging benefits
To see whether the effectiveness of currency risk hedging can be predicted for certain economic circumstances, the relation between several economic variables and hedging benefits is tested by OLS regression.
Table 3
This table reports results from the OLS regressions of the hedging benefits on economic indicators. The regressions are done with Newey-West standard errors to correct for possible autocorrelation and heteroscedasticity in the error terms. The hedging benefits represent the difference between the hedged and the unhedged results. All the portfolio characteristics are based on 60 months of returns, and are calculated for every month on a rolling window basis. The total period is from April 1985 to February 2018, a total of 395 months. The explanatory variables represent the change in consumer sentiment, the industry production growth, the change in non-farm payrolls and the TED spread, are all on a monthly basis. The t-statistics are in parentheses. * p < 0.05, ** p < 0.01, *** p < 0.001.
Effect of economic variables on hedging benefits
Mean Stdev Sharpe Skewness Kurtosis
Umcsent 0.0037 0.0016 0.0894 -0.618 0.246 (1.71) (0.52) (1.86) (-1.65) (0.19) Indpro 0.0653* 0.0869 1.628** -6.881* -12.21 (2.55) (1.68) (2.05) (-2.21) (-1.14) Payems -0.0703 -0.895*** -3.710 18.04 274.6*** (-0.40) (-3.61) (-1.00) (0.83) (3.63) Constant -0.0011*** -0.0008*** -0.0297*** -0.0970* -0.831*** (-3.78) (-1.86) (-4.79) (-2.22) (-5.53) N 395 395 395 395 395
Except for the U.S. consumer sentiment (Umcsent), the economic variables show ambiguous effects on the different portfolio characteristics. Looking at the mean benefits, industry production growth has a positive effect that is significant at the 5% level. The same goes for the Sharpe ratio, where the variable Indpro has the only positive significant effect. This implies that when industry production growth increases, the mean returns increase as well. Stating that industry production growth increases in good economic times, profits can be even more increased if currency risks are being hedged. The question is whether this is relevant for investors, since hedging is primarily used to induce risk, and not to boost profits. This does not necessarily state that the mean of the hedged
27
portfolio is higher than for the unhegded portfolio, but the decreases could also be less severe.
For the volatility, the only significant effect is that of non-farm payrolls. Since the effect is negative, it could indicate that volatility rather decreases during crisis periods. For the skewness, the effect of Indpro is negative and significant, which indicates that the benefit decreases when the economy is in a bad state. Following this finding, the risk of negative outliers rather increases during crisis periods. Payems shows to have a positive significant effect of kurtosis, which indicates that the kurtosis decreases in periods of financial downturn. It can also be seen from both graphs that the change in payrolls and the standard deviation seem to move the opposite directions over time. The increase in volatility logically matches the positive effect on portfolio kurtosis, since the kurtosis benefit is stated as a decrease, so a lower (excess) kurtosis is desired. This means that most of the variance is attributed by frequent but relatively small deviations from the mean.
3. Effect of economic variables on hedging benefits for crisis and non-crisis periods
To see whether the economic variables show different effects in different time periods, a dummy variable is included to indicate whether there is an economic crisis. It is usually expected that the coefficients of the variables are similar for every period. Since the variables are not rejected for a unit root, the effects could also be amplified or impaired during crisis periods. Therefore, for each portfolio characteristic, three regressions are done. The first regression includes just a crisis dummy indicator, the second regression includes the economic variables, and the third regression includes the interaction terms of the recession indicator and the explanatory variables. All regressions are done by using Newey-West standard errors. The graphs show a plot of the difference in hedged and unhedged returns over time.
28
Graph 9: hedging benefits for mean returns
Table 4
This table shows three different regressions on mean benefits. The first regression only considers the effect of USREC, a dummy that is 1 for U.S. recession periods, and zero otherwise. The recession indicator is based on the NBER recession dates. The second regression includes explanatory economic variables, the third regression includes interaction terms. The t-statistics are in parentheses. * p < 0.05, ** p <
0.01, *** p < 0.001.
Effect of economic indicators on hedging benefits during U.S. recession periods: mean returns
(1) (2) (3)
Mean benefit Mean benefit Mean benefit
USREC -0.0145 0.0522 -0.104 (-0.19) (0.58) (-1.07) Umcsent 0.376 0.198 (1.73) (0.84) Indpro 7.029** 9.988*** (2.64) (3.42) Payems -1.946 12.47 (-0.10) (0.62) USREC*Umcsent 0.190 (0.39) USREC*Indpro -7.893 (-1.82) USREC*Payems -77.59* (-2.30) Constant -0.105*** -0.120*** -0.148*** (-3.69) (-3.85) (-4.78) N 395 395 395
Table 4 shows that the recession indicator itself does not have significant impact on mean benefits. In other words, during recession periods, hedging does not lead to significant different average returns than during normal periods. Although the coefficient of USREC is not significant, the negative sign coincides
29
with the positive effect of industry production growth. By including interaction terms in the third regression, the effect of industry production growth is slightly amplified. In regression 3, the interaction term of the recession with the change in non-farm payrolls is now significant (and of much greater magnitude), whereas in regression 2 it is not. Looking at graph 3, where the change in non-farm payrolls is plotted over time, the trend shows abnormal breaks during the recession periods. For all recession periods, the change in non-farm payroll is negative, in contrary to normal periods. This could be a possible explanation for the significant effect of the interaction term in the third regression.
30
Graph 10: hedging benefits for volatility
Table 5
See table 4 for explanation
Effect of economic indicators on hedging benefits during U.S. recession periods: standard deviations
(1) (2) (3)
Stdev benefit Stdev benefit Stdev benefit
USREC 0.197* -0.0813 -0.142* (2.17) (-0.89) (-2.02) Umcsent 0.145 -0.0695 (0.48) (-0.20) Indpro 7.908 10.43 (1.64) (1.87) Payems -97.47** -92.89** (-3.28) (-2.79) USREC*Umcsent 0.448 (0.55) USREC*Indpro -8.267 (-1.19) USREC*Payems -17.38 (-0.42) Constant -0.175*** -0.0587 -0.0712 (-4.38) (-1.10) (-1.25) N 395 395 395
The same regressions are done for the standard deviations. For the standard deviation, the effect of the recession indicator seems to change for all regressions. In the first regression, where the economic variables are omitted, USREC shows to have significant positive effect on volatility benefits, i.e., decreases more during crisis periods than during non-crisis periods. This result seems intuitively, and is in line with the expectations. During recessions, markets are mostly more volatile, and hedging aims to reduce this. However, when including economic
31
variables, the effect switches to being negative, and when including interaction terms, this negative effect is now significant as well. An explanation for this could be the possibility of omitted variable bias. Because all economic variables are omitted in the first regression, all the positive change is being attributed to the recession period. When including all variables and interaction terms, hedging seems to be less beneficial for volatility during crisis periods. Furthermore, the other effects in regression 2 and 3 remain stable. Just as in the overall period, the change in non-farm payroll affects volatility benefits in a negative way. This coincides with the finding that hedging volatility increases during crisis periods, since the change in non-farm payrolls is negative for all crisis periods.
32
Graph 11: hedging benefits for the Sharpe ratio
Table 6
See table 4 for explanation
Effect of economic indicators on hedging benefits during U.S. recession periods: Sharpe ratios
(1) (2) (3) Sharpe benefit Sharpe benefit Sharpe benefit USREC -0.172 0.312 -3.225 (-0.10) (0.17) (-1.80) Umcsent 8.992 4.483 (1.84) (0.82) Indpro 165.8** 239.2*** (2.68) (3.57) Payems -340.5 -21.95 (-0.84) (-0.05) USREC*Umcsent 5.096 (0.51) USREC*Indpro -207.6* (-2.23) USREC*Payems -1675.5* (-2.45) Constant -3.090*** -3.030*** -3.653*** (-4.81) (-4.42) (-5.42) N 395 395 395
The Sharpe ratio benefit combines the earlier characteristics of the mean and the standard deviation. The rationale is also roughly the same as for the previous regression tables. The effect of USREC is negative in both regression 1 and 3, although it is not statistically significant. The effect of industry production growth is positive and significant, just as in the overall period. This is probably attributed to the increase in average returns, which is also shown in the tests for the mean. The effect of the economic variables does not change in regression 2
33
and 3, but the interaction terms of USREC with Indpro and Payems are negative and significant. Regarding the non-farm payroll, the same happens when testing for the mean benefits. What is noticeable is the interaction term of Indpro and USREC in regression 3. A possible explanation could be that the effect of a crisis period on Sharpe ratio benefit is negative but not significant. During crisis periods, the effect of the lower industry production growth is significantly lower in the sense that it amplifies the total effect.
Graph 12: hedging benefits for the skewness
Table 7
See table 4 for explanation
Effect of economic indicators on hedging benefits during U.S. recession periods: skewness
(1) (2) (3)
Skew benefit Skew benefit Skew benefit
USREC 0.130 0.227 0.492* (0.76) (1.20) (2.12) Umcsent -0.577 -0.269 (-1.67) (-0.89) Indpro -4.693 -6.381 (-1.67) (-1.85) Payems 40.22 8.449 (1.73) (0.39) USREC*Umcsent -1.103 (-1.36) USREC*Indpro -6.882 (-1.18) USREC*Payems 198.0*** (3.36) Constant -0.0998** -0.144*** -0.0957* (-3.26) (-3.35) (-2.24) N 395 395 395
34
In the first two regressions, neither one of the economic variables, nor the U.S. recession indicator seem to have significant effect on skewness benefits. This is different from the regression in table 3, where the effect of Indpro was negative and significant. In the third regression, the recession indicator is positive and significant, which implies that the skewness benefit of hedging is higher during recession periods. Also, the interaction term of non-farm payroll is highly significant, whereas the effect of Payems itself was significant in the previous regressions. This implies that the slope of Payems differs in times of financial crisis, which is explained in the discussion of the other characteristics. The change in non-farm payroll seems to show another trend in recession periods than in normal periods, which is likely to explain the significant effect of the interaction term for multiple distribution characteristics.
35
Graph 13: hedging benefits for the kurtosis
Table 8
See table 4 for explanation
Effect of economic indicators on hedging benefits during U.S. recession periods: kurtosis
(1) (2) (3)
Kurt benefit Kurt benefit Kurt benefit
USREC -1.302* -0.761 -0.474 (-2.19) (-1.11) (-0.48) Umcsent 0.108 -0.0503 (0.09) (-0.06) Indpro -19.53 -16.57 (-1.73) (-1.37) Payems 200.4** 162.1** (2.72) (2.59) USREC*Umcsent 0.0474 (0.01) USREC*Indpro -25.90 (-0.81) USREC*Payems 260.9 (0.90) Constant -0.442*** -0.674*** -0.627*** (-4.44) (-4.66) (-4.56) N 395 395 395
The last portfolio distribution characteristic that is discussed is that of the Kurtosis. As stated earlier, for the Kurtosis the benefits are not as explicit as for the other characteristics. The benefit is now stated as a lower excess kurtosis for the hedged portfolio compared to the unhedged portfolio. Only in the first regression the effect of USREC seems to be significant, when the economic variables are included the effect decreases in magnitude. Just as for the overall regression in table 3, the effect of Payems is significant, both with and without
36
the interaction terms. In contrast to the standard deviation, the change in non-farm payrolls positively affects kurtosis benefits. In other words, a positive change in non-farm payrolls decreases the excess kurtosis by using currency hedging. The intuition behind this is that volatility increases, and therefore the kurtosis decreases, since now most of the variance is explained by more even deviations, instead of a few extreme outcomes.
Overall, the estimated effects of the economic variables stay roughly the same when taking crisis indicators into account. The effect of the U.S. consumer sentiment stays insignificant for all characteristics, in all of the regressions. The effect of industry production growth stays positive and significant for the mean- and Sharpe ratio benefits. For the skewness benefit, the effect of industry production growth remains negative, only the effect loses its significance. An explanation for this could be that the effect of the recession indicator, USREC, shows to be significant and positive in the third regression, where interaction variables are included. Since industry production growth is shown to be lower for crisis periods, the combination of these effects seems intuitive. Moreover, the negative interaction term of industry production growth and USREC indicates that the effect of industry production growth is amplified during recession periods. The coefficients of the change in non-farm payrolls remain approximately the same when including recession indicators, but the interaction term of both seems to have significant effect on mean benefits, Sharpe ratios and the skewness. This effect is now ambiguous when looking at the total hedging benefits. The interaction term for the mean and the Sharpe ratio indicates that in crisis periods, a decrease in non-farm payroll negatively affects average returns, whereas in normal periods this cannot be supported with statistical significance. Furthermore, the interaction term on portfolio skewness is positive, which supports the positive outcome of the recession indicator.
When using the economic variables as indicators of financial circumstances, the positive effect of industry production growth the mean return and the Sharpe ratio would indicate that hedging is more beneficial in economic
37
good times. This is in line with the expectations, since in crisis periods the risk premium is expected to be higher than in non-crisis periods. When looking at the sub-periods, however, the mean of the hedged returns does not seem to be different than from the unhedged portfolio. The negative effect of non-farm payrolls on the standard deviation benefit indicates that in economic good times, the benefits on volatility decreases. This is somewhat in line with the finding that the standard deviation is lower for the hedged portfolio in times of financial crisis. When looking solely at the recession indicator effect on standard deviation benefits, the coefficient is positive and significant as well. Hedging seems to be more beneficial in crisis periods when looking solely at the crisis indicator on the portfolio skewness, but this contradicts the interaction with Payems, and differs from the finding when looking at the subsamples. Therefore, no strong conclusions could be drawn from these findings. The kurtosis benefit is only positively affected by the change in non-farm payroll. However, in both normal and crisis periods the kurtosis increases.
7. Robustness check for a European investor
The same method as for the U.S. investor is done from the perspective of a European investor. The base portfolio is still the MSCI world index, but the currency forward returns are now calculated based on the EU exchange rate and interest rates. Since the base portfolio is the same, the results for the unhedged portfolio do not change. The outcomes of the hedged portfolio are presented in the following table.
38
Table 9
This table shows the characteristics for both the unhedged and hedged portfolios. The results are based on the perspective of an U.S. investor. The unhedged portfolio represents the MSCI world index, and the hedged portfolio includes currency forward returns. All calculations are out-of-sample. The total period is from February 1975 to February 2018. The first 5 years are used as input for the OLS regressions and are therefore not used for the calculations of the distribution characteristics. The benefits are calculated by subtracting the outcomes of either the hedged or the unhedged portfolio from the other, depending on which characteristic is desired to be higher.
Portfolio distribution (€) – total period
Mean Stdev Sharpe Skewness Kurtosis
Unhedged 0.94% 4.42% 0.118 -0.634 4.912
Hedged 0.84% 4.45% 0.068 -0.773 5.395
Benefit -0.10% -0.03% -0.05 -0.139 -0.483
N 457 457 457 457 457
Portfolio distribution (€) – non-crisis period
Mean Stdev Sharpe Skewness Kurtosis
Unhedged 1.16% 3.88% 0.198 -0.601 4.857
Hedged 1.06% 4.14% 0.131 -0.698 5.651
Benefit -0.10% -0.26% -0.067 -0.097 -0.794
N 407 407 407 407 407
Portfolio distribution (€) – crisis period
Mean Stdev Sharpe Skewness Kurtosis
Unhedged -0.90% 7.32% -0.204 -0.005 2.657
Hedged -0.94% 6.41% -0.263 -0.400 3.164
Benefit -0.04% 0.91% -0.059 -0.395 -0.507
N 50 50 50 50 50
The results are roughly the same for the European investor as for the U.S. investor; only now the difference in standard deviations is now reduced to 0.3%. This is more in line with the expectations, although it still does not show that currency hedging leads to less volatility. Concerning the other characteristics, the outcomes are similar as for the U.S. investor, hedging leads to lower average returns and Sharpe ratios, worsens the skewness and increase the kurtosis.
