Hedging with foreign currency denominated stock index futures: evidence from the MSCI Taiwan index futures market

Transcription

1 J. of Multi. Fin. Manag. 13 (2003) 1 /17 Hedging with foreign currency denominated stock index futures: evidence from the MSCI Taiwan index futures market Changyun Wang a,, Soon Sern Low b a Department of Finance and Accounting, School of Business, National University of Singapore, 10 Kent Ridge Crescent, Singapore , Singapore b Singapore Airlines Ltd, 30 Airline Road, Singapore , Singapore Received 26 October 2000; accepted 2 November 2001 Abstract To hedge with foreign currency denominated stock index futures, the interdependence of equity, futures, and foreign exchange markets is important in formulating hedging strategies. This also results in divergent optimal hedging strategies for international and domestic investors. We derive and compare optimal hedging strategies for the two types of investors. Evidence from the MSCI Taiwan index futures traded on the SGX shows that both types of investors gain from hedging with the futures contract, while international investors tend to benefit more than domestic investors. This result is robust to various commonly used hedging techniques and sample periods. Moreover, both in-sample and out-of-sample results indicate that a GARCH error-correction model persistently outperforms other hedging techniques. # 2002 Published by Elsevier Science B.V. JEL codes: F21; F31; G15 Keywords: Stock index futures; Hedging; Market interdependence; GARCH model Corresponding author. Tel.: / ; fax: / address: bizwcy@nus.edu.sg (C. Wang) X/02/$ - see front matter # 2002 Published by Elsevier Science B.V. PII: S X ( 0 2 )

2 2 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 1. Introduction Emerging stock markets especially in some Far East economies have been experiencing fast-paced real and monetary growth, and continue to attract attention of investors in developed countries who look for opportunities to enhance portfolio performance. However, such markets are noticeably volatile and unpredictable, exposing investors to substantial equity price risk in addition to exchange rate risk. Moreover, an active stock index futures market may not exist in most emerging economies, making foreign equity price risk management more difficult. Recently, a class of innovative derivative instruments have been created to facilitate foreign equity price risk management especially for international investors. An example is the US dollar denominated Morgan Stanley Capital International (MSCI) Taiwan index futures traded on the Derivatives Trading Division of SGX (the Singapore Exchange). 1 Since its inception, the index futures has been quite successful, and is one of the most actively traded contracts on the SGX. The unique feature of the MSCI Taiwan index futures is that it is denominated in foreign currency (US dollars), and supposed to hedge equity price risk in Taiwan. This makes risk management strategy of hedging with foreign currency denominated stock index futures different from the conventional approach studied in the finance literature (e.g. Figlewski, 1984; Junkus and Lee, 1985; Park and Switzer, 1995), 2 because the interdependence of equity returns, futures returns, and exchange rate fluctuations becomes an important factor affecting investors hedging decisions. More importantly, the interdependence may affect differently the hedging strategies of international and domestic investors. The objective of this article is to evaluate the usefulness of the US dollar denominated MSCI Taiwan index futures for managing equity portfolio risks from the perspectives of both international and domestic investors. Based on the above observations, we derive and compare optimal hedging strategies for both types of investors, and assess in-sample and out-of-sample hedging effectiveness of various hedging techniques, including a GARCH error-correction model, the ordinary least squares (OLS) hedge, the OLS hedge with co-integration (OLS-CI), and a naive hedge. We find that both international and domestic investors gain from hedging with the MSCI Taiwan index futures, while international investors appear to benefit more 1 There are other stock index futures markets that share the similar feature to the MSCI Taiwan index futures. For example, the US dollar denominated Nikkei 225 stock average futures traded on the CME, the US dollar denominated Nikkei 225 and Nikkei 300 stock index futures traded on the SGX, and the US dollar denominated Taiwan index futures traded on the HKFE, etc. 2 An alternative risk management strategy for an international investor is international diversification, or a currency hedge in addition to diversification. However, a portfolio manager who manages risk via international diversification has to buy or liquidate his positions, which is more costly compared to a strategy of hedging with forward or futures contacts.

3 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 3 than domestic investors. We also observe the superiority of the GARCH errorcorrection model over other hedging techniques for both international and domestic investors. Our result holds true for the entire sample and sub-samples, and is robust to both in-sample and out-of-sample comparisons. These findings have important implications for investors and financial service institutions. First, to hedge with foreign currency denominated index futures, the degree of interdependence of equity, futures, and currency markets should be taken into account in formulating hedging strategies. Second, conditional hedging consistently outperforms other hedging techniques. Third, foreign currency denominated derivatives can succeed in the presence of international investors interest in the underlying market. This provides a partial explanation for the high liquidity in the MSCI Taiwan index futures market. Figlewski (1984), Ederington (1979), Junkus and Lee (1985), Ghosh (1993), and Ghosh and Clayton (1996) examine the usefulness of stock index futures in reducing local portfolio risks, and conclude that a stock index futures is an effective tool of risk management for institutional investors. However, these studies focus optimal hedging strategies based on constant hedge models. A large body of literature has established that such models are not as effective as time-varying (conditional) hedge models that take into account all available information when making hedging decisions (e.g. Baillie and Myers, 1991; Myers, 1991; Cecchetti et al., 1988; Park and Switzer, 1995; Gardner and Wuilloud, 1995; Koutmos and Tucker, 1996). In particular, Kroner and Sultan (1993) show that the bivariate GARCH (1,1) errorcorrection model is more effective than the conventional OLS and OLS-CI hedging techniques in reducing foreign currency risks. Kroner and Sultan (1993) also show that, allowing for time varying hedge ratios, there is a significant reduction in variances of portfolio returns as compared to using constant hedge ratios. However, the above studies investigate hedging strategies using a futures contract to hedge local asset price risk. In contrast, in this paper we focus on hedging with a foreign currency denominated stock index futures taking into account the interdependence of equity, futures, and foreign exchange markets. Sener (1998) examines optimal hedging strategies by considering the interdependence of equity and currency markets, and finds that currency surprises do affect investors hedging decisions. Sener s study focuses on the usefulness of currency forward (futures) for hedging foreign equity portfolio currency risk without considering equity price risk. In contrast, we concentrate on evaluating the usefulness of foreign currency denominated stock index futures*/the MSCI Taiwan index futures, for hedging equity price risk from the perspectives of both international and domestic investors. The organisation of the article is as follows. In Section 2, optimal hedge ratios for both international and domestic investors are derived. Section 3 presents the data and empirical procedures. Estimated optimal hedge ratios and the evaluation of hedging effectiveness of various hedging techniques are presented in Section 4. Section 5 concludes.

4 4 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 2. Optimal hedge ratios: international versus domestic investors Assume there are two investors: an international investor and a domestic investor. Both investors hold equity portfolios in the Taiwanese stock market and attempt to utilise the US dollar denominated MSCI Taiwan index futures to manage risk associated with the equity portfolios. For simplicity, both investors are assumed to hold the same equity market portfolio*/the MSCI Taiwan index denominated in New Taiwan dollars (NTD). The international investor based in the US is primarily interested in returns in terms of US dollars, but concerned with both equity price risk and exchange rate risk. Assume that one unit of equity portfolio is purchased. r s and r f are expected spot and futures returns, respectively. r x denotes expected currency surprise, or percentage change in the price of NTD. The investor decides to sell b I units of futures to hedge equity price risk taking into consideration currency fluctuations. Assume that the investor faces a mean-variance utility function in choosing the optimal hedging strategy, which is of the following form U(E(p I ))E(p I ) l 2 var(p I ); (1) where E(p I ) is expected return on the hedged portfolio for the international investor, E(p I )/r s /r x /b I r f, var(p I ) denotes return variance of hedged portfolio, and l denotes the coefficient of risk aversion. Optimisation of Eq. (1) yields the optimal hedge ratio for the international investor as b I rf l cov(r s ; r f ) l cov(r f ; r x ) : (2) l var(r f ) Assuming that the futures rate follows a martingale, that is, r f /0, 3 we then have b I cov(rs ; r f ) cov(r f ; r x ) : (3) var(r f ) Compared to the optimal hedging strategy in the extant literature, a new factor, i.e. the covariance between futures returns and currency surprises (cov(r f, r x )), appears on the left-hand side of Eq. (3). Therefore, the interdependence of futures and currency markets has an effect on the investor s optimal hedging strategy. If the covariance term is negative, currency exposure helps diversify the portfolio and reduces portfolio risk. Consequently, the greater magnitude of the negative covariance, the smaller is the hedge ratio. On the other hand, if the covariance term is positive, the portfolio risk increases, and the optimal hedge ratio becomes larger than that in the case of independence of futures and currency markets. 3 The martingale assumption suggests that the expected return of the portfolio is not affected by the number of contracts held. McCurdy and Morgan (1988) provide empirical evidence on that futures rates follow a martingale in currency futures markets.

5 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 5 The domestic investor is interested in local currency returns, but concerned with equity market risk. The investor attempts to hedge equity price risk using the MSCI Taiwan stock index futures. Assume that the investor also holds one unit of equity market portfolio, and sells b D units of futures contracts to optimise the following mean variance utility function U(E(p D ))E(p D ) l 2 var(p D ); (4) where E(p D ) is expected return on the hedged portfolio for the domestic investor, which is equal to r s /b D (r f /r x ), and var(p D ) is the return variance of the hedged portfolio. Optimisation of Eq. (4) gives the optimal hedge ratio for the domestic investor as b D cov(rs ; r f ) cov(r s ; r x ) var(r f ) var(r x ) 2cov(r f ; r x ) : (5) From Eq. (5), it is clear that hedging with foreign currency denominated stock index futures is different from the conventional strategy of hedging with stock index futures in local currency. In addition to the covariance between equity returns and futures returns as well as futures variance affecting the domestic investor s hedging decisions, exchange rate variability, the covariance between equity returns and currency surprises, and the covariance between futures returns and currency surprises enter into the equation. In Eq. (5), a positive correlation between futures returns and currency surprises requires the investor to hedge more, while a positive correlation between equity returns and currency surprises and currency surprise variability force the investor to cut back hedging. 3. Data and empirical procedures 3.1. Data We collect daily settlement prices of the MSCI Taiwan Index futures contract traded on the Derivatives Trading Division of SGX over the interval from January 1997 to June To avoid thin trading and expiration effects, we use the nearest contract, and roll over to next nearest contract prior to expiration month of the current contract. We also obtain daily MSCI Taiwan Index closing prices in New Taiwan dollars and NTD/USD mid rates over the same sample period. These data are collected from Datastream International. Several diagnostic checks on distributional properties of the data are performed, and the results are reported in Table 1. Panel A reports stationarity test results for (natural log) spot and futures series. For the level (natural log) prices, unit root tests fail to reject the null hypothesis of the presence of a unit root in both the (log) spot and futures prices, indicating non-stationarity of these series. The hypothesis of the existence of a unit root in the first differenced log spot and futures price series is

6 6 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 Table 1 Summary statistics for spot and futures prices and return series (January 1997 to June 2000) Panel A: Unit root tests (natural log prices) Prices First differences PPT PP PPT PP MSCI Taiwan index in NTD / / / / MSCI Taiwan futures in USD / / / / % critical value / / / / Panel B: Descriptive statistics for spot and futures returns and currency surprises Mean (%) S.D. Skewness Kurtosis Bera/Jarque Ljung/Box (24) MSCI Taiwan spot in NTD MSCI Taiwan futures in USD Currency surprise / / % critical value PPT is the Phillips/Perron t statistic in an estimated model with a time trend. PP is the corresponding t statistic in the estimated model without a time trend. rejected at the 1% level. Panel B of Table 1 reports summary statistics for spot and futures returns as well as the currency surprises over the sample period. The results indicate that the average daily returns on spot and futures markets are and 0.025%, respectively. Despite returns on spot and futures markets are similar in magnitude, the MSCI Taiwan index futures market is about 50% more volatile than the spot market. The average daily change in the price of New Taiwan dollar is / 0.022%, suggesting that New Taiwan dollars, on average, depreciate against US dollars over the sample period. It seems that the distributions of futures and spot returns are skewed to the right. The distribution of currency surprises is skewed to the left. The Bera /Jarque tests reject the hypothesis of normality for the three series. The Ljung/Box Q statistics also reveal that the hypothesis of no autocorrelation is not rejected for spot return series. To test for cointegration between spot and futures, we regress log spot prices on log futures prices ln S t nd ln F t o t : (6) Should spot and futures price show an equilibrium relationship, we need to add this cointegration measure to account for this long-run behaviour between spot and futures prices. The results of estimating Eq. (6) that are reported in Table 2 show that the slope coefficient estimate, d; is close to unity. The null hypothesis of no cointegration is rejected at the 1% level, indicating the difference between spot and futures prices is stationary. We thus impose the restriction d/ /1 in the ensuing analysis.

7 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 7 Table 2 Cointegration tests (for natural log prices): OLS estimation of Eq. (6) (January 1997 to June 2000) 3.2. Methodology PP ADF n d MSCI Taiwan index / / (3.57) (88.95) 95% critical value / / PP is the Phillips/Perron t statistic in an estimated model without a time trend. The ADF statistic is a fourth-order augmented Dickey/Fuller test. Figures in the parentheses are t-statistics that are for the hypothesis the relevant coefficient is zero, computed using Newey/West heteroskedasticity consistent standard errors. Denotes significance at the 1% level. A GARCH (1,1) error correction model is proposed to estimate optimal hedge ratios for both the international and domestic investors. The GARCH (1,1) model is chosen because there is substantial evidence on the model s adequacy of characterising the dynamics of the second moment of financial asset prices. This model involves in parameterising the first two conditional moments of distributions of r s, r f, and r x. Error correction is essential as spot and futures prices share the same long run stochastic trend under weak assumptions and the error correction term ensures that the long run relationship between spot and futures prices is maintained (e.g. Engle and Granger, 1987). A theoretical generalisation of the simultaneous multivariate GARCH structure is discussed in Engle and Kroner (1995). However, unrestricted Vector GARCH structure is seldom used in empirical applications due to convergence problem. The positively defined conditional variance/covariance matrices may resolve the convergence problem, however, this results in asymmetric variance/covariance matrix. That is, the conditional covariance between equity and futures returns differs from the conditional covariance between futures and equity returns. For computational ease, following Bollerslev (1986, 1990), Kroner and Sultan (1993), Ghosh and Keong (1994), a constant correlation GARCH (1,1) model is used for the estimation of time varying variance/covariance in this study. There are separate equations for spot and futures returns as well as currency surprises. The second moment is parameterised with a multivariate constant correlation GARCH (1,1) structure. We thus have the following specifications r s t a 0 a 1 (ln S t1 d ln F t1 )os t ; (7) r f t b 0 b 1 (ln S t1 d ln F t1 )of t ; (8) r x t v 0 v 1 rx t1 ox t 2 3 ; (9) o st 4o ft 5jV t1 N(0; H t ); o xt

8 8 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 / h ss;t h sf;t h sx;t H t 4h sf;t h ff;t h fx;t 5 h sx;t h fx;t h xx;t 2 32 h s;t h f;t r r 2 h s;t 0 0 4r 1 1 r h f;t 0 5; (10) 0 0 h x;t r 2 r h x;t h 2 st c s a s o2 s;t1 b s h2 s;t1 ; (11) h 2 ft c f a f o2 f;t1 b f h2 f;t1 ; (12) h 2 xt c x a x o2 x;t1 b x h2 x;t1 ; (13) where r s t, r f t, and r x t are returns for equity, futures, and currency markets at time t respectively, V t1 represents the information set at t/1, r 1, r 2, and r 3 are the constant correlations between o st and o ft ; o st and o xt ; o ft and o xt ; respectively. The error-correction term in Eqs. (7) and (8), i.e., (ln S t1 d ln F t1 ); is to impose the long-run relationship (cointergration) between spot and futures prices into this short run model. d is cointegration parameter that links spot and futures prices together. Wahab and Lashgari (1993) and Ghosh (1993) show that an error correction representation for stock index and futures price series is appropriate. Using timing varying variance/covariance as parameterised by the GARCH structure, we can rewrite the optimal hedge ratios in Eqs. (3) and (5) as b I;t ĥsf;t ĥ ĥfx;t ; f f;t ĥ ff;t (14) and ĥ sf;t ĥ sx;t ; (15) ĥ ff;t ĥ xx;t 2ĥ fx;t b D;t where b I,t and b D,t are optimal hedge ratios for the international and domestic investors, respectively. Optimal hedge is to minimise the conditional variance of hedged portfolio returns. The primary innovation in deriving the optimal hedge using foreign currency denominated stock index futures is that we take into account exchange rate fluctuations and the interdependence of equity, futures, and currency markets for both types of investors. To obtain b I,t and b D,t, parameters in Eqs. (7)/(13) are estimated using maximum likelihood estimation (MLE) Comparison among hedging techniques To gain an understanding of the potential strength of GARCH error-correction model, we compare hedging effectiveness of four hedging techniques for the two investors: the international investor and the domestic investor. These four hedging techniques are: a naïve hedge, an OLS hedge, an OLS hedge with cointergration

9 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 9 between spot and futures prices (OLS-CI hedge), and the GARCH error-correction model. To compare these hedging techniques, the model in Eqs. (7) /(13) is first estimated with no restrictions, which gives the parameter estimates for the GARCH error-correction model. The model that is estimated with restriction: a s b s a f b f a x b x a 1 b 1 0inEqs. (6)/(12), gives the parameter estimates for the OLS hedge. The model that is estimated with restriction: a s b s a f b f a x b x 0inEqs. (11)/(13), gives the parameter estimates for the OLS-CI hedge. Lastly, the naive hedge has a constant hedge ratio of one. 4. Empirical evidence 4.1. Computed optimal hedge ratios The parameter estimates of the GARCH error-correction model are reported in Table 3. The parameter estimate associated with the error-correction term in the futures equation is statistically significant at the 1% level. Parameters a s, a f, a x, b f, and b x are statistically significant, suggesting that the variances and covariances, and therefore the risk-minimising hedge, is indeed changing over time. It is also noted that the covariance between local stock returns and currency surprises, the Table 3 Maximum likelihood estimates of the GARCH model Coefficient t -value a a 1 / /0.34 b 0 / /0.88 b v v c s c f c x a s a f a x b s b f b x r r r Numbers in parentheses are z-statistics computed using Bollerslev /Wooldrige robust standard errors and covariance. Significance at the 1% level. Significance at the 5% level. Significance at the 10% level.

10 10 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 covariance between local stock returns and futures returns, and the covariance between futures returns and currency surprises, are all positive, implying that the optimal hedge ratio for the international investor is likely to be larger than that for the domestic investor. The finding of a positive correlation between local stock returns and currency surprises is also consistent the extant literature, for example, Eun and Resnick (1988). Using the estimated model parameters, we can compute, b I,t and b D,t, the optimal hedge ratios for the international and domestic investors, respectively. The OLS and OLS-CI hedge ratios for the two types of investors are also computed. We denote the OLS and OLS-CI hedge ratios by b OLS and b OLS-CI, respectively. For the naive hedge, b/1. The Asian financial crisis triggered by the substantial devaluation of Thai Bhat in July 1997 may have greatly changed the degree of interdependence of equity, futures, and currency markets. Therefore, we also compute the hedging ratios for the crisis period (July 1997 to July 1998) and post crisis period (August 1998 to June 2000). These periods are conveniently and reasonably chosen as we find difficulties in ascertaining the end date of the crisis, with the Asian economies recovering at dissimilar speeds. Computed hedge ratios for the international and domestic investors are reported in Table 4. Two results are worth noting. First, the hedge ratio for the international investor is always larger than that for the domestic investor for all hedging techniques and all sample periods. Second, the GARCH hedge ratio is consistently larger than the OLS and OLS-CI hedge ratios for all sample periods and both types of investors. For example, for the whole sample period, the OLS and OLS-CI hedge ratios are and for the international investor, and and for the domestic investor respectively. The daily average of the GARCH hedge ratios is and for the international and domestic investors respectively. The different hedge ratios for the international and domestic investors result from the interdependence of equity, futures, and currency markets. The positive correlation between futures returns and currency surprises requires the international investor to hedge more in order to manage risk optimally. On the other hand, the variability of currency surprises and the positive correlation between equity returns and currency surprises force the domestic investor to hedge less compared to hedging with local Table 4 Computed hedge ratios for the international and domestic investors International investor Domestic investor Overall Crisis Post crisis Overall Crisis Post crisis b OLS b OLS-CI b GARCH The entire sample period is from January 1997 to June 2000, the crisis period is from July 1997 to July 1998, and the post crisis period is from August 1998 to June b GARCH is the mean of daily conditional hedge ratios over the sample period.

11 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 11 currency denominated stock index futures in the extant literature. Thus, our results suggest that the failure to account for the interdependence of equity, futures and currency markets can result in a sub-optimal hedging strategy. Notice also that the post crisis hedge ratios are significantly larger than those for the crisis period and those for the whole sample period. This result holds true for all hedging techniques and for both types of investors. The hedge ratios are lower in the crisis period because the correlation between futures and spot markets tends to be lower, or/and the futures price variability is larger during crisis than post crisis. Consequently, it is advisable that investors adopt smaller hedge ratios when futures and spot markets are less highly correlated and when futures prices are considerably volatile. Consistent with the previous finding, the GARCH hedge ratios are uniformly larger than those of other hedging techniques for all sample periods and for both types of investors. Fig. 1 plots the GARCH hedge ratios for the international and domestic investors. The GARCH hedge ratio for the international investor is consistently larger than that for the domestic investor. Moreover, the GARCH hedge ratio is substantially larger for the international investor than for the domestic investor at certain periods, namely, October 1997 to July 1998 and January 2000 to February The period from October 1997 to July 1998 coincides with the ongoing Asian financial crisis, which first hit Thailand on 2 July 1997 when it called upon the International Monetary Fund (IMF) for assistance. This move seriously devalued the Thai Bhat and was a trigger for the Asian financial crisis. Fig. 1. GARCH hedge ratios for international and domestic investors (January 1997 to June 2000).

12 12 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 / In-sample comparisons of hedging effectiveness To compare the performances of various hedging techniques, we use the estimated hedge ratios to calculate holding period returns for a hedged portfolio with one unit investment in the Taiwan stock market portfolio each week (Friday) for the international and domestic investors. Then the variance of portfolio returns for all sample periods and for both types of traders is computed. The variance of portfolio returns for the GARCH model is computed as var(r s r x b I;t r f ) for the international investor, and var(r s b D;t r f b D;t r x ) for the domestic investor. Similarly, for the international investor, the portfolio return variance using the OLS and OLS-CI hedge can be computed as var(r s r x b I;OLS r f ) and var(r s r x b I;OLS-CI r f ); respectively. For the domestic investor, the portfolio return variance for the OLS and OLS-CI hedge can be computed as var(r s b D;OLS r f b D;OLS r x ) and var(r s b D;OLS-CI r f b D;OLS-CI r x ) respectively. The top Panel of Table 5 reports the resultant portfolio variances using various hedging techniques over the entire sample as well as sub-samples. To facilitate comparisons, we also report the portfolio return variance for an unhedged investor. There are several observations worth highlighting. First, an unhedged international investor has a larger portfolio variance compared to an unhedged domestic investor. This is because the international investor has to face additional exchange rate risks. This can be seen from the extra currency surprise component in expected total return for the international investor (see Eq. (1)). Second, the international investor also seems to face larger portfolio return variances compared to the domestic investor despite hedging. The larger portfolio return variances for the international investor may be attributable to the greater exchange rate risk in his hedged portfolio compared to that of a domestic investor. Third, the four hedging techniques, i.e. a Table 5 In-sample comparisons of hedging performance International investor Domestic investor Overall Crisis Post crisis Overall Crisis Post crisis Variance of returns Unhedged position a Naive (b /1) OLS conventional hedge OLS-CI hedge GARCH model Percentage reduction in variance over (%) Unhedged position Naive (b /1) OLS conventional hedge OLS-CI hedge a For unhedged positions, the expected returns to the international investor and domestic investor are p/r s /r x and p/r s, respectively.

13 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 13 naïve hedge, the OLS hedge, the OLS-CI hedge and the GARCH error-correction model, appear to yield lower portfolio variances compared to an unhedged position. In addition, a naive hedge is the worst form of hedging for both types of investors, evident from its largest hedged portfolio variance. Fourth, although the OLS-CI hedge ratio is larger than the OLS hedge ratio, resultant portfolio variances are not significantly different for both types of investors. For the international investor, the portfolio return variances are and for the OLS and OLS-CI hedge respectively, while these are of similar magnitude for the domestic investor. Therefore, there appears to be no significant advantage in using OLS-CI hedge over OLS hedge. Finally, for both types of investors, portfolio variances are larger in the post crisis period than those of the crisis period. This may be attributable to the generally increased equity, futures, and exchange rate risks in the post crisis period, resulting from larger return variability and the persistence property of return variability. More importantly, it appears that the GARCH error-correction model is superior to other hedging techniques for both types of investors and all sample periods. The GARCH model yields a resultant variance of and for the entire sample period, the lowest amongst that of all hedge models for the international investor and domestic investor respectively. This result also holds true for the sub-samples. The evidence on the superiority of conditional hedge model is consistent with the findings in Baillie and Myers (1991), Kroner and Sultan (1993), Ghosh and Keong (1994), Gardner and Wuilloud (1995), and Koutmos and Tucker (1996). To assess the extent of superiority of the GARCH error-correction model over other hedging techniques, we calculate percentage portfolio variance reduction brought about by the GARCH model over an unhedged position, a naïve hedge, the OLS hedge, and the OLS-CI hedge. The percentage variance reduction is calculated as var Others var GARCH 100%; var Others where var Others and var GARCH are the resultant portfolio variance for one of other hedging methods and portfolio variance for the GARCH error-correction model respectively. The results on the variance reduction are reported in the lower panel of Table 5.In the whole sample period, it appears that the GARCH model significantly outperforms the naive hedge, reflecting a variance reduction of and 54.75% for the international and domestic investors respectively. The GARCH hedge model also outperforms the OLS and OLS-CI hedge in portfolio variance reduction for both the international and domestic investors. Moreover, the GARCH model appears to result in larger variance reduction for both types of investors. For example, the conditional hedge outperforms the OLS-CI hedge, with improvements of 2.56% for the international investor, and 1.96% for the domestic investor. This suggests that the international investor appears to benefit more from hedging with the MSCI Taiwan index futures than the domestic investor. These regularities also apply to the

14 14 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 sub-samples. For example, the reduction in variance of GARCH model over the OLS-CI hedge for the crisis and post crisis periods is 2.60 and 4.41% for the international investor, and 1.02 and 1.65% for the domestic investor, respectively Out-of-sample comparisons of hedging effectiveness In-sample comparisons provide us a broad picture of hedging effectiveness of various hedging techniques for both international and domestic investors. However, these resultant hedging strategies are not practical since investors do not know future return distributions of futures, currency, and equity markets when formulating their hedging strategies. Therefore, we also conduct out-of-sample comparisons of hedging effectiveness. The following procedure is used to examine out-of-sample hedging performance of various hedging techniques for both types of investors. To have sufficient data for the GARCH error-correction model estimations, we first estimate the parameters for the GARCH model using daily data over the interval from 3/1/1997 to 8/1/1999, which are then used to compute hedge ratios and portfolio returns for both types of investors for the week 11/1/1999 to 15/1/1999. The estimation period is sequentially rolled forward, one week at a time via a fixed-length moving window, throughout the hedging period of 26/06/2000 to 30/6/2000. For the OLS and OLS-CI hedge, the hedge ratios are estimated using daily data over the same estimation period, but assumed constant throughout the end of June Then, the mean weekly portfolio returns and variances of these hedging techniques for both types of investors are computed. Table 6 Out-of-sample comparisons of hedging performance International investor Domestic investor Mean Variance Mean Variance Unhedged position Naive (b /1) OLS Conventional hedge OLS-CI hedge GARCH hedge Percentage reduction in variance of GARCH model over (%) Unhedged position Naive (b /1) OLS conventional hedge OLS-CI hedge The GARCH model parameters and hedge ratios are estimated using the daily data over the interval from 3/1/1997 to 8/1/1999, and used to compute the portfolio returns for the week 11/1/1999 to 15/1/1999 for both types of investors. This procedure continues till the end of sample period via a fixed-length moving window. Returns are measured as weekly holding period returns, in percent. The hedge ratios for the OLS hedge and the OLS-CI hedge are estimated using the daily data over the same estimation period and assume constant in the hedging period.

15 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 15 The out-of-sample results are reported in Table 6. Also reported are the weekly average portfolio returns in the out-of-sample period. Overall, the GARCH errorcorrection model results in higher mean returns and lower risk compared to other hedging techniques and the unhedged position for both types of investors. The superiority of the GARCH model over the OLS and OLS-CI hedge in the out-ofsample analysis becomes more pronounced compared to the in-sample result, although it appears that the variances of portfolio returns are larger for all hedging techniques. Furthermore, in line with the in-sample result, the portfolio return variance reduction brought about by the GARCH model is consistently larger for the international investor than for the domestic investor. The GARCH model yields and 8.78% more variance reduction compared to the OLS and OLS-CI hedge for the international investor, while the risk reduction is only 3.39 and 2.56% from the in-sample result. This is not surprising because the GARCH model makes use of the most updated information, while the OLS and OLS-CI hedge employ the constant hedge ratios estimated from the estimation period. The GARCH model results in 8.78 and 19.74% risk reduction over the OLS-CI and OLS hedge respectively for the international investor, which are 5.23 and 18.86% respectively for the domestic investor. It is also noted that the naïve hedge actually increases portfolio variances and decrease portfolio returns for both types of investors, and thus, the performance of naïve hedge is worse than that of an unhedged position. The benefit from the OLS hedge is difficult to assess since the hedge results in smaller return variance, but also lower portfolio returns compared to the unhedged position. 5. Conclusions It is evident that international investors have increased asset holdings in foreign countries especially in the fast growing Asian economies, for the purpose of enhancing profitability. However, this requires investors to effectively manage both equity price risk and exchange rate risk. A foreign currency denominated stock index futures is shown to be useful for managing portfolio risk. This tends to result in divergent optimal hedging strategies for the international and domestic investors due to the perceived comovements of equity, futures, and foreign exchange markets. The evidence from the US dollar denominated MSCI Taiwan index futures market shows that both international and domestic investors gain from hedging with the futures contract, however, international investors tend to benefit more than domestic investors. The estimated optimal hedge ratio for international investors taking into account the interdependence of equity, futures, and currency markets tends to be larger than that for domestic investors. This result holds true for various hedging techniques in the whole sample as well as sub-samples. We also observe the superiority of the GARCH error-correction model over conventional hedging techniques in reducing portfolio risks for both international and domestic investors. This is attributable to the fact that a conditional hedge model appropriately allows investors to utilise the most updated information when making hedging decisions. Conventional hedging techniques make an over-

16 16 C. Wang, S. Sern Low / J. of Multi. Fin. Manag. 13 (2003) 1 /17 Fig. 2. Futures trading volume of the MSCI Taiwan index futures and the TAIEX index futures (January 1998 to June 2000). simplified assumption of a constant variance/covariance matrix between spot and futures prices, leading to sub-optimal hedging decisions. From the out-of-sample results, the advantage of the GARCH error-correction model over other hedging techniques is more pronounced for both international and domestic investors, although international investors appear to benefit more from this hedging strategy than domestic investors. Our results suggest that, to hedge with foreign currency denominated stock index futures, the interdependence of equity, futures, and currency markets becomes an important factor in determining hedging strategies. Moreover, this interdependence can affect differently the optimal hedging strategies of international and domestic investors, resulting in divergent hedging performance for the two types of investors. These results thus have implications for investors to hedge with foreign currency denominated stock index futures. Our findings also imply that, in the presence of international investors interest in the underlying market, a foreign currency denominated stock index futures is likely to succeed. This tends to provide an explanation for the perceived liquidity of the MSCI Taiwan index futures contract. The trading volume of the MSCI index futures is also consistently larger than that of Taiwan Stock Exchange Capitalisation Weighted Index (TAIEX) futures contract traded on the Taiwan Futures Exchange. As shown in Fig. 2, on 25 November 1999, the trading volume of the MSCI Taiwan Index futures reached contracts, while that of the TAIEX index futures market amounted to only 2756 contracts. Acknowledgements The authors thank an anonymous referee, Ike Mathur (the editor), and participants at the APFA 2001 Annual Conference in Bangkok for helpful comments and suggestions. The financial support from the NUS Academic Research Fund is greatly acknowledged.

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