حق بیمه ریسک و غیرجانبداری در بازار معاملات آتی ارز هندی

This paper explores the relationship between currency futures and realised spot rates for the Indian rupee US dollar exchange rate. Using futures contracts with maturities of one, two and three months, we examine the unbiasedness of futures quotes as a predictor of the future spot exchange rate as well as the nature of time-varying risk premiums in this emerging market. Empirical estimates, obtained using monthly data, suggest the biasedness of futures quotes as a predictor of the future spot rate for contracts with maturities of two and three months. We also find significant time-varying risk premiums in the considered futures market, while the premium is of greater magnitude and more significant with increasing maturity of the contracts. We then examine the relationship between realised risk premiums and explanatory variables such as spot currency returns, the futures basis and realised volatility, skewness and kurtosis of spot currency returns. Our results show that spot currency returns and the futures basis can be considered as significant determinants of realised risk premiums in the considered futures market.

The relationship between currency forward or futures rates and realised spot rates has been one of the central issues in the literature of international financial markets. As pointed out by Pippenger (2011), it is one of the most important puzzles in the area of international finance. The uncovered interest rate parity (UIP) and the forward rate unbiasedness hypothesis (UH) are the most commonly used theories to establish the relationship between current forward rates and future spot rates. UIP theory suggests that the expected future change in the spot rate is determined by the interest rate differential (or forward premium under the assumption of no arbitrage) between two countries (Bai and Mollick, 2010) such that high yield currencies are expected to depreciate against currencies with lower interest rates (Bekaert et al., 2007). The UIP theory under the assumption of no-arbitrage leads to the UH which states that the forward rate should be an unbiased predictor of the future spot rate at maturity of the contract (Tai, 2003 and Nikolaou and Sarno, 2006). Hereby, unbiasedness means that the currency futures price should not be significantly different from the corresponding future spot prices. In other words, a regression of the spot rate at maturity on the current forward rate should yield a slope coefficient of one under the assumption of risk neutrality and rational expectations. Alternatively, a slope coefficient of one should also be obtained in the regression of percentage change in spot rates between now and maturity on the current forward-spot basis (forward premium) divided by the current spot rate. For an extensive review of the empirical literature on foreign exchange rate expectations, we refer, for example, to Engel (1996), Sarno (2005) and Jongen et al. (2008). The unbiasedness of the forward rate has been overwhelmingly rejected in a number of studies (Kodres, 1993, Cavaglia et al., 1994, Baillie and Kilic, 2006 and Nikolaou and Sarno, 2006) and the slope coefficient has been found to be significantly different from one, often even negative in a number of cases. The puzzle of the biasedness of the forward rate has been coined as the forward premium puzzle by Fama (1984) who states that the reason for the failure of UIP is a time-varying risk premium. Baillie and Bollerslev (2000) suggest the forward premium anomaly as a widespread empirical result in the literature and find that returns on most of the nominal exchange spot rates are negatively correlated to the forward premium. This finding implies that the forward rate is not an unbiased predictor of future spot rates. Tai (2003) states that the speculative return from holding a forward contract results from a risk premium that has to be paid to risk averse speculators who takes the risk of future changes in the exchange rates. The presence of a time-varying risk premium in currency forward markets is also confirmed by other studies, e.g. Wolff (1987), Theobald (1991), Panigirtzoglou (2004), just to mention a few. Ehsani and Shahrokhi (2003) have tried to explain this puzzling relationship and put forward that the main reason for a negative relationship between the future currency spot rate and the forward rate can be attributed to surrogate variables1 used in place of expectations conditional on all the available information. Frankel and Poonawala (2010) study a sample of 14 emerging market currencies and state that the bias in the forward rate for emerging market currencies is lower than that of advanced market currencies. According to Baillie (2011), the forward premium anomaly remains a paradox in international financial markets which is important and worthwhile to be better understood. Chang (2011) has tried to solve the forward premium puzzle using covered interest parity, but suggests that this is not feasible. Due to the complex nature of the forward premium puzzle, Müller (2011) states that we should stop trying to work out this anomaly and should start looking for fundamentally better models for the determination of exchange rates. Note that the majority of these studies focus on the relationship between the forward and spot rates, and not on the relationship between futures quotes and the spot rate. For futures there is no natural equivalent to the forward rate unbiasedness hypothesis available. Also futures contracts differ in several ways from forward contracts such that forward and futures prices for delivery of a currency on the same maturity date may deviate. However, a variety of studies, including for example, Cornell and Reinganum (1981), Hodrick and Srivastava (1987), argue that often forward rates and futures prices have been found to be approximately equal. As a consequence, the relationship between futures contracts and the spot rate could be analysed in a way very similar to the relationship between the forward and currency spot rate, since there is generally very little difference between the two speculative prices (Baum and Barkoulas, 1996). Also de Roon et al. (1998) point out that they ignore the difference between forward and futures markets when analysing risk premiums for currency and commodity futures contracts. Therefore, with futures quotes of foreign exchange rates being very similar to forward rates for the same maturities, they could then also be described as containing predictions of future exchange rates plus risk premiums. Therefore, it is worthwhile to examine whether the rejection of the unbiasedness hypothesis and the nature of time variation in risk premiums found in forward markets carries over into the considered futures market, see e.g. Hodrick and Srivastava (1987). In this paper we provide a pioneer study on the relationship between currency spot and futures contracts traded at the National Stock Exchange of India Limited (NSE). The NSE introduced rupee/dollar futures trading in India only in August 2008. In our analysis we focus on the relationship between currency futures rates and realised spot rates for the Indian rupee US dollar exchange rate using futures contracts with maturities of one, two and three months. Our results suggest that the futures rate is not an unbiased predictor of the future spot rate, at least for longer maturity contracts. Further, we find that observed risk premiums in the market become more significant with increasing maturity of the currency futures contracts. In other words, for the considered market, the assumption that futures quotes provide unbiased estimates for the spot rate at maturity cannot be rejected for shorter maturity contracts while it is unlikely to hold for contracts with longer maturities. Our results are in line with Inci and Lu (2007) who investigate the significance of UIP for the Japanese yen, British pound, Swiss franc and German mark against the US dollar. They state that the currency risk premium may be an important component of the basis for long-term futures contracts while the same may not be true for contracts with shorter maturities. Their findings also suggest that the basis of long-maturity contracts cannot predict changes in the spot rate between now and maturity, thus rejecting UIP. On the other hand, they suggest that the basis for short-maturity contracts is a useful indicator to predict the changes in the spot exchange rate between now and maturity. We also examine observed risk premiums and conduct tests in order to investigate whether observed risk premiums are significant for the different maturities. We find that realised risk premiums for the considered one month futures contracts are not significant, while risk premiums for the two-month and three-month contracts are significantly different from zero and negative. A reason for the insignificant short-term premiums could be that hedging activities in currency futures markets are mostly concentrated upon the contracts with longer maturities, such that the pricing of short-term contracts is less affected by hedging. Breuer (2000) states that derivatives contracts with longer maturities carry a great risk of valuation changes; hence they might have slope coefficients that are biased downwards and significantly smaller than one. Unlike for stock markets, the intertemporal risk-return relationship in foreign exchange markets is still very much unexplored. Hence, in this paper we also investigate the relationship between observed ex-post risk premiums and explanatory variables including returns of the currency spot rate, the basis, as well as measures such as realised volatility, skewness and kurtosis of spot currency returns. For stock markets, e.g. Pindyck (1984) suggests that US stock market returns vary positively with the expected volatility of market returns. Examining currency forward rates, Jiang and Chiang (2000) state that volatility of currencies or equity markets might possibly explain excess returns in these markets since investors are rewarded for risk that can be measured by volatility. Hence, one could expect that also risk premiums in the Indian rupee US dollar currency futures market are positively related to volatility. The higher the volatility in the market, the higher might be the compensation investors will demand in the form of an additional risk premium. Such an argument is based on risk-averse investors and excess returns being closely tied to expected risk premiums which in turn are believed to be correlated to market volatility. Next to volatility in our analysis we also include higher moments of spot currency returns such as skewness and kurtosis. Some studies in the literature suggest that the mean-variance analysis is not sufficient to explain the risk-return relationship in emerging markets. Bekaert et al. (1998) state that the application of standard mean-variance analysis is problematic for emerging market economies, since, typically in these markets, returns exhibit significant skewness and excess kurtosis. Moreover, Harvey and Siddique (2000) put forward that assets that decrease the skewness are less desirable and should command higher expected risk premiums and vice versa. Therefore, we also examine whether risk premiums of currency futures contracts in the Indian market can be better explained by the inclusion of higher moments of the return distribution. Another reason for the inclusion of such measures stems from the recent literature on carry trades. For example, Brunnermeier et al. (2009) state that carry trades are prone to crash risk, that is, exchange rate movements between high interest rate and low interest rate currencies being negatively skewed. Hence, these findings also motivate us to use the realised skewness and kurtosis of spot currency returns as an explanatory variable for the risk premium. Further, Christiansen (2011) investigates the intertemporal risk-return trade-off of foreign exchange rates using measures such as realised volatility, realised skewness and value-at-risk. Investigating monthly excess returns and monthly foreign exchange risk measures calculated from daily observations, the author reports a strong contemporaneous risk-return relationship for ten currencies against the US dollar. Based on the above justification, we also expect to find a relationship between observed risk premiums in the futures market and realised measures of the currency spot returns. The remainder of the article is organised as follows. Section 2 provides a brief review of the literature on the unbiasedness of forward and futures rates as well as on risk premiums in foreign exchange markets. Section 3 describes the methodology used in our analysis, while Section 4 provides the data and results of our empirical analysis. Section 5 concludes.

This paper explores the relationship between currency futures rates and realised spot rates for the Indian rupee US dollar exchange rate. To our best knowledge this is the first study to use data on spot and futures contracts from the National Stock Exchange of India Limited (NSE) where rupee/dollar currency futures trading was introduced only in August 2008. Using futures contracts with maturities of one, two and three months, we examine the unbiasedness of the futures rate as a predictor of the spot exchange rate as well as the nature of realised time-varying risk premiums in this relatively new market. Like several studies on more mature foreign exchange markets, we find that the futures remium cannot be considered as an unbiased predictor of changes in the spot rate for the Indian rupee US dollar. In particular for contracts with maturities of two and three months, estimated coefficients in a model regressing realised changes in the spot exchange rate on the forward premium deviate significantly from their expected coefficients under the null hypothesis of unbiasedness. Results also become more significant for contracts with longer maturities. In other words, the unbiasedness hypothesis possibly holds for futures contracts with a short maturity, but it is unlikely to hold for contracts with longer maturities of two and three months. Thus, we confirm results on the relationship between bias and maturity in other currency futures markets, e.g. by Inci and Lu (2007), who investigate the significance of UIP for the Japanese yen, British pound, Swiss franc and German mark against the US dollar. Based on our results, we argue that one of the reasons for the poor performance of the futures premium as an unbiased predictor of changes in the spot exchange rate is the presence of a timevarying risk premium in the Indian rupee US dollar futures market. We suggest that risk premiums start playing a more important role with increasing maturity of the currency futures contracts. To further investigate this assumption empirically, we examine observed risk premiums and conduct tests on their significance for different maturities. We find that realised risk premiums for the considered one month futures contracts are not significant, while realised risk premiums for the two-month and threemonth contracts are negative and significantly different from zero. We also investigate the relationship between observed ex-post risk premiums and explanatory variables such as spot currency returns, the futures basis, as well as measures like realised volatility, skewness and kurtosis of currency returns. Our results indicate that spot returns on the xchange rate as well as the futures basis are significant determinants of the risk premium. We also find that the explanatory power of these variables increases as the maturity of the contract gets longer. While observed risk premiums are also positively related to the realised variance and negatively related to the realised skewness and kurtosis of spot currency returns, these variables are not significant in the estimated models. We suggest the following reasons for our results: First, since hedging activities in currency futures markets are mostly concentrated on contracts with longer maturities, the pricing of short-term contracts is less affected by hedging activities. On the other hand, for two and three month futures contracts, the risk premium will be an important determinant of the futures rate and can be expected to be more pronounced as the maturity of the contract gets longer. Our second explanation can be related to covered interest parity (CIP) and the notion that the futures-spot basis is equivalent to the interest rate differential between two countries’ currencies. While short-term interest rates are generally set by central banks and are, therefore, not affected by market risk premiums, interest rates for longer maturities are more related to market forces and expectations. Therefore, for longer maturities risk premiums start to play a more important role in the determination of interest and futures rates. As a consequence, for short maturity contracts UIP and the unbiasedness of the futures rate are more likely to hold while for longer-term contracts we can expect to find significant risk premiums in currency futures quotes. Furthermore, these risk premiums might be dependent on the behaviour of the currency spot rate, i.e. variables such as spot currency returns, realised volatility, skewness and kurtosis of the currency returns. Overall, our results suggest that the relationship between currency spot and futures rates in the Indian rupee US dollar market shows dynamics that are similar to more established currency futures markets. However, given that this is a relatively new and emerging market, we recommend further research on the nature and dynamics of currency futures risk premiums when more data is available. Another direction for future work is to expand analysis to other emerging markets to examine the same issue and possibly compare the results with major currency futures markets.