Anil Kumar Sharma and Anujit Mitra*

This paper explores the behaviour of the forward premia for US$ vis-à-vis INR during the five-year period of September 2000 to September 2005. Indian forex market experienced a peculiar phenomenon in the years 2003 and 2004 where the forward premia on US$ spot (cash) vis-à-vis Indian rupee became negative. This phenomenon was somewhat uncommon to Indian forex market wherein Indian rupee was always at discount to US$ in the past. The paper tests hypothesis of uncovered interest rate parity in the context of Indian market. The paper also tries to find out the factors that drive the forward premia in the Indian forex market during this period. It is observed that forex premia of US$ vis-à-vis Indian rupee is driven to a large extent by the interest rate differential in the inter bank market of the two economies combined with FII flows, current account balance as well as the changes in the exchange rate of US$ vis-à-vis Indian rupees.

JEL Classification : G13, G15.

Keywords         : Forward Premia, Uncovered Interest Rate Parity

Introduction

Indian forex market experienced a peculiar phenomenon in the years 2003 and 2004 where the forward premia on US dollar spot (cash) vis-à-vis Indian rupee became negative. This phenomenon was somewhat uncommon to the Indian forex market wherein Indian rupee has always been at discount to the US dollar in the past, in conformity with the theory.which says that currency of the country where inflation rate/interest rate is more than that of the other country, its currency should be at discount vis-à-vis other country’s currency. However, years 2003 and 2004 experienced the Indian rupee gaining strength against US dollar despite of India having higher inflation rate / interest rate vis-à-vis US economy. This generates a question as to what drives forward premia in Indian forex market. This also raises question on how deep is the Indian forex market, especially the forward market.

The Indian rupee is still not fully convertible on capital account except for certain transactions carried out by foreign institutional investors, within certain limits, and liberalisation on Investment abroad by Indian Individuals/ companies wherein they can freely convert their foreign currency/rupee assets into Indian/foreign currency assets by way of investment in Indian/ foreign capital market. Recently, Indian companies have also been permitted to invest, up to 25 per cent of its net worth, in shares of foreign companies, having a minimum of 10 per cent of the share capital of a company listed in a recognized stock exchange in India. Mutual Funds are permitted to invest in ADRs/GDRs of the Indian companies, rated debt instruments and also invest in equity of overseas companies with an overall cap of USD 1 billion. Furthermore, under the Liberalised Remittance Scheme of USD 25,000, resident individuals are free to acquire and hold immovable property, shares or any other asset outside India without prior approval of RBI, enabling them to convert their rupee denominated assets into foreign currency denominated assets. These are steps closer to full convertibility of rupee. As all these measures do have an impact on exchange rate of rupee as well as forward premia of US dollar vis-à-vis Indian rupee, developments on these fronts are worth noticing for players active in the Indian forex market. Further, banks can hold both rupee as well as foreign currency deposits and can transmit their influence on interest rates as well as on forward premia.

However, with convertibility of Indian rupee on current account, India’s increasing share in world exports (i.e. 0.84 per cent in 2004 as against only 0.52 per cent in 1990), liberalisation on investment abroad by Indian individuals and Indian companies, as well as almost full convertibility of Indian rupee as regard transactions carried out by nonresident Indians, exchange rate of Indian rupee is largely market determined. Still the share of Indian rupee in the forex market was only 0.15 per cent of global turnover in the year 2004. This was even less in the earlier years, as indicated by the Triennial Central Bank Survey of Foreign Exchange and Derivatives Market Activity by Bank for International Settlements (refer Table 1). With the US dollar still dominating the invoicing pattern of India’s exports, this paper concentrates on forward premia on US dollar vis-à-vis Indian rupee only. As the market decides forward premia in advance after taking into account all the information available in the market at that time it also raises question on whether Indian forex market satisfies the hypothesis of uncovered interest rate parity or not.

During the last twenty-five years, the majority of studies have rejected the hypothesis of uncovered interest rate parity, which states that the (nominal) expected return to speculation in the forward foreign exchange market conditioned on available information is zero. These empirical studies have regressed ex post rates of depreciation on a constant and the forward premium, and have rejected the null hypothesis that the slope coefficient is one. In particular, a robust result in these studies is that this slope is negative, and significantly different from one. This phenomenon is known as the “forward premium puzzle” and implies that, contrary to the theory, high domestic interest rates relative to those in the foreign country, predict a future appreciation of the home currency. Different explanations have been given to this issue. First, rejection of the null hypothesis can be related to the existence of a rational risk premium in the foreign exchange market. Second, other authors have claimed the existence of a “peso problem”, or even the existence of irrational market participants.

To understand the behaviour of forward premia in respect of the Indian forex market, an exploratory analysis is carried out using data available in Database on Indian Economy (culled out from Central Database Management System (CDBMS) of Reserve Bank of India’s Data Warehouse) and other data series available in Telerate. The paper tests the hypothesis of uncovered interest rate parity in the context of Indian market in Section I. Section II discusses the various theoretical explanations that are supposed to determine the forex premia in any market. The paper also tries to find out the factors that drive the forward premia in the Indian forex market in Section III. Section IV concludes the paper.

Section I

This paper has tried to test the UIP hypothesis, in the Indian context. Empirical work on the relation between the forward premia in the foreign exchange market to the expected change in the spot exchange rate has been an area of active research for the last twenty years. In particular, an important building block of this relationship has been the UIP, which states that the (nominal) expected return to speculation in the forward foreign exchange market conditioned on available information is zero: 

where is the logarithm of the spot exchange rate S_t, f_t is the logarithm of the forward rate F_t contracted at t and matures at t +δ_t. As a consequence, the (log) forward exchange rate is an unbiased predictor of the dt -periods ahead (log) spot exchange rate. For this reason, UIP is also known as “Unbiasedness Hypothesis”.
Although one main criticism made against UIP is that it pays no attention to issues of risk aversion and inter-temporal allocation of wealth, Hansen and Hodrick (1983) have given the following formulation, which is consistent with a model of rational maximising behaviour. The conditions needed are that the spot and forward exchange rates and the stochastic discount factor have a lognormal distribution with constant conditional second moments. This proposition is known as “Modified Unbiasedness Hypothesis” (Hodrick (1987), Engel (1996) and Wang and Jones (2002).
Assuming rational expectations (RE) in foreign exchange markets:                           

where μ_t+δ,δt is a rational expectation error with zero mean and uncorrelated with any variable in the time t.

Combining equations (1) and (2)

S_t+δ- S_t = f_t -S_t +μ_{t + δ,δt}

which has motivated the following OLS regression, as in Geweke and Feige (1979), as the usual starting point to test UIP:

as a test of β₀ = 0 and β₁.

However, the RE assumption implies that errors are not autocorrelated as long as the sampling interval is equal or larger than
δ_t. For this reason, different authors, as Frenkel (1977) among others, have sampled data to produce a data set with non-overlapping residuals with the corresponding waste of degrees of freedom.

On the other hand, Hansen and Hodrick (1980) showed how to use overlapping data in order to increase the sample size, which will be reflected in corresponding gains in the asymptotic power of tests. Using Hansen’s Generalised Method of Moments, they obtain asymptotic standard errors that take into account the serial correlation induced into the regression error when the prediction horizon is higher than the sampling interval of the data. In the same way, standard errors robust to conditional heteroscedasticity can also be computed.

Nonetheless, some points with respect to the single equation approach have to be emphasised. First, the asymptotic covariance matrix is very sensitive to the selection of the bandwidth and the kernel chosen in its estimation. Secondly, the construction of the covariance matrix is infeasible if we want to use high-frequency data in order to test UIP, given that the degree of overlapping tends to infinity.

In order to test the UIP in the case of India, this paper has used monthly interval data on forward premia and exchange rate to avoid above- mentioned problems. Accordingly, let S_t+ =log (spot exchange rate of US$ vis-à-vis the Indian rupee at time t+δ),δ_t= 1 month f_t = log (one month forward exchange rate of US$ vis-à-vis Indian rupee).

To test UIP for Indian forex market:

If UIP holds good, i.e. β₀ and β₁ = 1, we estimate error terms and work out its variance-covariance matrix.

From Chart 1, it is clear that spot rate of Indian rupee vis-à-vis US dollar started appreciating in as early as June 2002, however, one month forward premia became negative for the first time only in October 2003. To smoothen the volatile movements of Indian rupee, RBI absorbed almost US $ 10 billion from the market in November, December 2003 and January 2004 (refer Table 2). While carrying out regression as suggested in equation (3) above, it can be observed from the results presented below that UIP hypothesis do not hold good for Indian market as the slope coefficient is significantly different from one and is negative. The negative slope coefficient

means market is expecting a steady appreciation of Indian rupee vis-à-vis US dollar irrespective of the positive forward premia and in spite of higher domestic interest rate in Indian market as compared with US market. Further, the relationship with spot exchange rate and forward premia in Indian market is found to be very weak. This means future spot rate of US dollar vis-à-vis Indian rupee is driven by some other factors in addition to forward premia. Based on equations (1), (2) and (3) above with µ=0 (i.e. assuming rational expectation) for the period September 2000 to December 2005, the regression equation in Indian context takes the following form

R² = 0.0002; t-statistic are give in parenthesis.

Question then arises is what does forward premia in Indian forex market represent and what factors are accounted for by the market players while determining the forward premia itself. The paper endeavoured to analyse these factors in Section II in general and in section III in respect of Indian forex market in particular.

Section II

Forward Market for foreign exchange is extremely important particularly for importers and exporters. This is so because international trade results in exposure in foreign currencies. Forward Market helps the traders in hedging the risks of this inevitable exposure in foreign currency. On the other side there are players in foreign exchange market who offer the forward rates for the foreign currency. A well-developed market helps in getting the better rates for the traders promoting international trade and consequently the general economic development.

Offering forward rates for any commodity always involve trying to forecast the future price of the commodity keeping in view the opportunity cost. It may require knowledge about how the price of the underlying product is determined in the market. One also needs to be aware about the factors influencing the price of the product. Countries are free to decide the type of exchange rate arrangements, which could be described to vary in different degrees from fixed to flexible exchange rate. It is practically impossible to strictly follow either a completely fixed or flexible exchange rate. International Monetary Fund publishes an annual report listing the different regimes followed by its member countries. There are many countries that are following ‘pegged exchange rate’ mechanism whereby their domestic currencies are fully pegged with some other major foreign currency like USD. Forecasting the exchange rate and thereby working out the forward rates for currencies following different regimes would be different.

From the perspective of the economists there are three classes of explanatory variables, viz., price level, interest rates and the balance of payments to explain the behaviour of the exchange rate. The Purchasing Price Parity or PPP hypothesis tries to explain how the price levels affect the exchange rates. It says the relative exchange rate S =  kP/P*, where P is the price level in the domestic economy, P* is that in the other country and k is a constant parameter. Taking differences after taking logarithms gives us Δ_s= Δ_p - Δ_p^* giving us the idea how the forward rates could be influenced by the change in the level of prices in the two economies. However, it is noted that over a short or medium term, PPP hypothesis is conclusively rejected.

Though, it cannot be said that the price levels have no impact on exchange rate movement or the forward rates.
In the earlier section the paper has already talked about the influence of interest rates on the exchange rates. Both the major Interest Rate Parity hypotheses, i.e., Covered Interest Rate Parity (CIP) and Uncovered Interest Rate Parity (UIP) have drawn lot of attention of the researchers, but UIP is more interesting in the context of this paper because it involves the variable, expected future spot rate, unlike CIP.

That the trade imbalances would have a bearing on the behaviour of exchange rates has been recognised very early. However, the earliest models to relate the current account to the exchange rate followed the Marshallian tradition of treating the exchange rate as a relative price to clear the market with the “elasticities approach”. The limitations of this approach led to the emergence of “absorption approach” in the 1950s. Among the series of subsequent models, the Mundell– Fleming model is most referred. The Mundell-Fleming Model adds a balance of payments equilibrium condition to the IS-LM Model. This extends the closed economy IS-LM framework to examine the interplay between monetary policy and exchange rate policy. In particular, the model emphasises the differences between fixed and floating exchange rates.

Section III

As observed in Section I, UIP hypothesis does not hold good for the Indian market, as the slope coefficient is significantly different from one. Furthermore, there are other factors, which also influence the forward market in India. This section has tried to identify the factors that affect forward premia in Indian forex market, i.e., “What drives forward premia in Indian forex market?”

• Is it inflation-differential?
• Is it interest-rate differential?
• Is it FII flows?
• Is it the current account balance in BoP?

To answer this question, an attempt is made to carry -out some exploratory exercise based on Forward Premia - annualized (INR vis-à-vis US$), Inflation differential between Indian and US economy (i.e. WPI for India^* – CPI for US economy) (Chart 2), Interest Rate differential between 91 Day Treasury Bills in India and US (Chart 3); Interest Rate differential between MIBOR - one month and LIBOR-one month (Chart 4), FIIs inflows and Current Account Balance (Chart 5).

Chart 2 indicates that forward premia has a weak relationship with Inflation-differential in US and Indian Economy.

Chart 3 indicates the relationship between 3 months forward premia (annualised) and interest rate differential in Government of India and the US T Bills is also not strong, though there is good co-movement some of the time. Hence the variable is considered for further analysis.

Chart 4 indicates that relationship between forward premia - 1 month (annualised) and interest rate differential between one month MIBOR and 1 month LIBOR, is stronger than the above two.

However, there are other factors (supply side as well as demand side), viz., fresh flows by Foreign Institutional Investors (FIIs) and current account balances play important roles in determining the forward premia as can be seen from the respective regression equation and its analysis given below. In Chart 5 below the premia is shown with the

current account balance (USD 100 million) and FII net investment (in USD 100 million).

Performing the regression of one month Forward Premia for USD vis-à-vis INR (Annualised) vs Inflation Differential, Interest Rate Differential (one month MIBOR – one month LIBOR), FII Portfolio Investment (net flows) and India’s current account balance (CAB) over the entire period Septemer 2000 to September 2005, it is observed that the coefficient for Inflation differential is not statistically significant, thereby prompting us to drop from final analysis. Since, the information

on current account balances is available to the market with a lag, introduction of lagged value of current account balance (1 quarter lag) showed improvement. Furthermore, balance of payments (BoP) current account quarterly balance is distributed equally for intervening months for regression analysis, due to non-availability of monthly CAB data. In this connection, instead of CAB, trade balance data, which is available on monthly frequency was also tried, but did not show good result.

Equation:
Forward Premia (Y) = f (Interest rate differential (IRD), Current Account Balance –lagged (CAB), FIIs Net flows (FIINF))

Furthermore to check the influence of RBI intervention on forward premia, RBI’s Intervention (Net Purchase of USD) has also been tried as regressor and it was found that the variable is not statistically significant indicating that RBI intervention in forex market does not make significant impact in determination of forward premia and it only helps in smoothing the volatility in forex premia. Similarly

inclusion of Trade Balance as regressor in place of Current Account Balance has not resulted in improvements.

Though the regression above shows a reasonable fit with expected signs, in the actual and estimated premia plot in Chart 6 some change in pattern is observed over the period. This motivated breaking the period of observation into two parts, i.e., September 2000 to March 2003 and April 2003 to September 2005 and explores the behaviour separately.

For the September 2000 to March 2003 period, the regression gives the following result:

For the period April 2003 to September 2005 period, the regression gives the following result:

As observed there is a marked difference in the regression results in the two periods. Also, the Durbin Watson D statistics, for the regression run for the full study period, indicates the possible presence of first order autocorrelation. One way to deal with the autocorrelation is to include the lagged value of the dependent variable as a regressor. However, it is felt that the past forward premia might have less influence on the current forward premia compared to the observed change in the exchange rate in the immediately preceding period. It was indeed found out that introducing the lagged forward premia was not improving the regression. Therefore, another variable AOCER : Annualised observed change in exchange rate of USD vis-à-vis INR was introduced. This variable captures the immediate trend in the exchange rate. Further, this also goes well with self-fulfilling nature as observed during the times of volatility in any financial market. The regression results based on the four variables for the period of October 2000 to September 2005 are as follows: