Econometric Analysis of Present Value Models When the Discount Factor Is near One

Econometric analysis of present value models when the discount factor is near one

Stationary time-varying risk premia in forward foreign exchange rates

ONE OF THE MOST widely used models dealing with the effects of speculation on the forward foreign exchange rate is the so-called Modern Theory of the Forward Foreign Exchange Rate which stresses the role of both interest arbitrage and speculation in the determination of the forward rate (see Grubel [2]). Traditionally, the reduced form of the model expresses the forward foreign exchange rate as a weighted average of the covered interest-parity exchange rate on one hand and of the future spot rate expected to prevail at the maturity date of the forward contract on the other hand. Empirical work based on this reduced form is found in Stoll [6], Kesselman [4], Haas [3], and McCallum [5]. This specification, in which speculation on the forward foreign exchange market is implicitly analyzed in terms of the current forward exchange rate and the expected future spot exchange rate only, is unduly restrictive. The options facing the speculator are indeed much broader. The speculator does not need to get out of his speculative position by buying or selling the relevant currency on the spot market at the date of delivery. He can take his gain at any time between the date of the initial contract and the delivery date by entering into an offsetting transaction on the forward market for the same delivery date as soon as the corresponding forward rate is lower than the rate at which he sold forward initially. For example, a speculator expecting a depreciation of sterling and having sold forward sterling in January at $2.00 for delivery in July may take his gain by buying the sterling forward in April if at that time the three-month forward rate of sterling is, say, $1.85. The possibility to speculate by combining two offsetting forward transactions contracted at two different moments in time but for the same delivery date, without any operation on the spot market at that date, has an important implication: the expected future spot rate is not the only key variable determining speculators' decisions. Speculators can decide to speculate on a future forward rate, following exactly the same principles as when speculating on the future spot rate. They will thus sell forward foreign exchange if the current forward exchange rate is higher than the expected value of a future forward rate for contracts involving the same delivery date, and buy forward in the opposite case. If, for example, speculators anticipate that, in three months, the three-month forward exchange rate for sterling will be lower than the present forward exchange for sixmonth contracts, they expect to make a speculative gain by selling sterling today on the six-month forward foreign exchange market and buying sterling forward

The Unbiased forward rate hypothesis (UFRH) stipulates that the forward rates should be a perfect predictor for the future spot rates. A number of studies conducted in order to test the UFRH and foreign market efficiency, have come to the conclusion that the hypothesis does not hold. This phenomenon is dubbed as the UFRH puzzle. A number of studies that reject the UFRH have made use of ordinary least square methods and support a linear adjustment between spot and forward exchange rates. This paper establishes that the use of a linear model in testing the UFRH can lead to a misspecification problem if indeed there is a nonlinear adjustment between the forward and spot exchange rates. In order to overcome the problem of model misspecification, this paper applies the nonlinear method of the class of the Smooth Transition Regression (STR) model in assessing the relationship between the rand-US dollar future spot and forward exchange rates. With the aid of a series of diagnostic tests, the paper shows that there is indeed a nonlinear adjustment process between the rand-US dollar spot and forward exchange rates and that there exists a regime in the STR model where the UFRH eventually holds.

This paper re-considers cointegrating behaviour between forward and spot exchange rates and the implications for the forward rate unbiasedness hypothesis. Extant empirical evidence examining forward and future spot rates is mixed, offering results both for and against cointegration; the forward rate as an unbiased predictor of the spot rate; and the existence of a time-varying risk premium. However, recent research has suggested that such analysis may be subject to bias and that models of cointegration between forward and current spot rates should instead serve as a starting point for analysis of exchange rate behaviour. Johansen cointegration analysis supports this contention showing that erroneous inferences can be made by merely using future spot rate data. Subsequently both single equation and panel estimation methods support cointegration between forward and current spot rates, but that the forward rate is a biased predictor. Further, single equation tests are conducted over a rolling window of five ...

In a no-arbitrage environment, the both assumptions of risk neutrality and rational expectations imply that the forward foreign exchange rate should be an unbiased predictor of the corresponding spot rate. This paper focused on Chinese foreign exchange market and examined whether RMB-USD forward exchange rate is unbiased estimate of the spot rate and tried to look for the reasons of the biased estimation by means of using a GARCH-in-mean approach. The results showed that the spot rate has a unit root while the forward exchange rate is 1(d) with d, 1, implying long memory and forward exchange rate of RMB-USD is not unbiased estimate of the future spot exchange rate. Moreover, we found that a time-varying premium existing maybe was one reason of the biased estimation in China's foreign exchange market.

Nominal exchange rates in low-inflation advanced countries are nearly random walks. Engel and West (2003a) offer an explanation for this in the context of models in which the exchange rate is determined as the discounted sum of current and expected future fundamentals. Engel and West show that if the fundamentals are I(1), then as the discount factor approaches one, the exchange rate becomes indistinguishable from a random walk. An alternative explanation for the random-walk behavior of exchange rates is that there are some unobserved variables that drive exchange rates that follow near random walks. This paper takes the approach that both explanations are possible. We are able to measure how much of exchange-rate variation could be accounted for by the Engel-West explanation, despite the fact that we do not observe the information set of financial markets. We find that the observable fundamentals (money, income, prices, interest rates) may account for about 40 percent of the variance of changes in exchange rates under the assumption of discount factors near unity.

Further evidence on expectations and the demand for money during the German hyperinflation

This paper explores how consistent two-dimensional families of forward rate curves can be constructed on an international market. Applying the approach in Björk and Christenssen (1999) and Björk and Svensson (2001), we study when a system of inherently infinite dimensional domestic and foreign forward rate processes in a two-country economy with spot (forward) exchange rate possesses finite dimensional realizations. In the system with the forward exchange rate, the forward interest rate equations are supplemented by a third infinite dimensional stochastic differential equation representing the forward exchange rate dynamics. We construct and fit consistent families to observed Euro and USD yields as well as the forward (spot) EUR/USD exchange rate.

In this research, monthly forward exchange rates are evaluated for possible existence of time varying risk premia in Singapore forward foreign exchange rates against US dollar. The time varying risk premia in Singapore dollar is modeled using non-Gaussian signal plus noise models that encompass non-normality and time varying volatility.The results from signal plus noise models show statistically significant evidence of time varying risk premium in Singapore forward exchange rates although we failed to reject the hypotheses of no risk premium in the series. The results from Gaussian versions of these models are not much different and are in line with Wolff (1987) who also used the same methodology in Gaussian settings.Our results show statistically significant evidence of volatility clustering in Singapore forward exchange rates. The results from Gaussian signal plus noise models also show statistically significant evidence of volatility clustering and non-normality in Singapore forward foreign exchange rates. Additional tests on the series show that exclusion of conditional heteroskedasticity from the signal plus noise models leads to false statistical inferences.

Forward foreign exchange rates and risk premia—a reappraisal

A Re-Examination of the Forward Exchange Rate Unbiasedness Hypothesis. — This paper applies the Phillips and Hansen estimation and inference procedures to re-examine the hypothesis that the forward exchange rate is an unbiased predictor of the future spot exchange rate. The results indicate that the 90-day forward exchange rate is not an unbiased predictor. However, the 90-day forward and future spot exchange rates are cointegrated. Only for the U.K. pound/U.S. dollar exchange rate is there an error correction representation. Overall, however, the evidence is consistent with the hypothesis that risk-averse agents in the forward foreign exchange market form expectations rationally.

This study aims to determine whether the spot exchange rate and forward exchange rate, either partially or simultaneously influence the projection of the futures exchange rate on the rupiah against the dollar. The data include spot exchange rate , the forward exchange rate and the future spot rate using middle rate value from the the Bank Indonesia for the Rupiah exchange rate against the US Dollar.The results of this study indicate that the spot exchange rate has a positive effect on the projected futures exchange rate on the rupiah against the dollar, the forward exchange rate has a negative effect on the projected futures exchange rate on the rupiah against the dollar, spot exchange rate and forward exchange rate collectively have a positive effect on the projected futures exchange rate on the rupiah against the dollar.

Forward exchange rates and expectations during the 1920s: A re-examination of the evidence

This study explores the viability of the PPP (Purchasing Power Parity) theory in predicting short-term exchange rate movements in Bangladesh. We aim to construct a forecast model, exclusively based on PPP theory, to accurately estimate the 30, 60, and 90-day forward exchange rates of BDT-USD (Bangladeshi Taka - US Dollar) with minimal error. Drawing from approximately 9 years of monthly data, we utilize monthly nominal CPI values from Bangladesh and the USA to compute six inflation differentials across various periods (30, 60, 90, 120, 150, and 180 days). To determine the lagged impact of inflation on exchange rates, we employ a straightforward correlation matrix with associated p-values. Among these sets, the one exhibiting the highest correlation (along with the lowest p-value) with the percentage change in the 30-day forward rate is identified as the very variable having the highest impact on the next 30-day forward rate. This process is repeated for the 60 and 90-day forward rates, leading to three distinct equations for forecasting each duration. Finally, error-adjustment variables are incorporated in these equations. Our model relies on five readily available data points to forecast forward exchange rates. Results indicate that this model accurately forecasts the 30-day forward exchange rate with a ±0.58% error margin and 98.84% accuracy, with statistical robustness at a 5% significance level across the sample period. However, the performance diminishes when forecasting 60 and 90-day forward exchange rates. This study underscores the effectiveness of PPP theory in predicting up to 30 days of forward exchange rates in Bangladesh, highlighting its practical applicability in economics and finance.