A comment on: “The solution to the forward-bias puzzle”

Pippenger (2011) recently proposed a solution to the longstanding forward-bias puzzle. He argues that the puzzling estimates obtained using the standard equation for the efficient markets hypothesis are due to omitted variable bias. He identifies the missing variables as the future change in the forward exchange rate and the future interest differential. When these are added to the standard equation, he finds a one-to-one relationship between the future change in the spot rate and the forward premium. However, we argue that his equation can only test covered interest parity and offers no insight into the forward-bias puzzle.     

The solution to the forward-bias puzzle: Reply

My proposed econometric solution to the forward-bias puzzle provoked several comments. Those comments raise three primary objections to my solution. (1) It suffers from multicollinearity, miss-specification and other serious econometric problems. (2) My key test equation is a tautology or identity. (3) My econometric solution has nothing to do with either the forward-bias puzzle or uncovered interest parity. This is my reply to those objections.     

Interpreting deviations from covered interest parity during the financial market turmoil of 2007–08

This paper investigates the spillover effects of money market turbulence in 2007–08 on the short-term covered interest parity (CIP) condition between the US dollar and the euro through the foreign exchange (FX) swap market. Sharp and persistent deviations from the CIP condition observed during the turmoil are found to be significantly associated with differences in the counterparty risk between European and US financial institutions. Furthermore, evidence is found that US dollar term funding auctions by the ECB, supported by US dollar swap lines with the Federal Reserve, alleviated the level of dislocations, as well as the instability, of the FX swap market.     

Co-integrating currencies and yield differentials

This study investigates the relationship between currencies and interest rates of different maturity horizons. The real exchange rate is found to depend both on short-term real domestic and foreign interest rate difference and on long-term real domestic and foreign interest rate difference. Co-integrating regressions of contemporaneous currency rates generate negative and significant coefficients for long-term rate differentials, consistent with uncovered interest parity. Therefore, the expectations hypothesis holds for long horizons. On the other hand, positive coefficients for real short-term interest rate differentials reveal the forward premium puzzle: the failure of uncovered interest parity for short-horizons. Results are partly driven by the very different risk characteristics of short-term bonds and foreign bonds.     

What UIP tests on extreme samples reveal about the missing variable

In their UIP regressions, Huisman et al. (1998. Extreme support for uncovered interest parity, Journal for International Money and Finance 17, 211–228.) focus on extreme forward premia and find much higher coefficients. We show that, for such results, the expectation signal needs to be thicker-tailed than the missing variable. Transaction costs may produce the right sort of bias. It is (i) bounded (i.e. it has no tails at all), (ii) wide (i.e. it may generate betas below 1/2) and (iii) U-distributed, which makes an “extreme” sample quite effective. We derive theoretical and numerical results in the direction of what Huisman et al. observe. We also tighten Fama's moment conditions.     

Covered interest rate parity in emerging markets

This paper finds that while covered interest rate parity holds for large and small triple A rated economies, it holds for emerging markets only for a three-month maturity. For a five-year horizon the size and frequency of violations lead to the conclusion that covered interest rate parity does not hold for longer maturities for Brazil, Chile, Russia and South Korea. Overall this paper finds that aspects of credit risk are the source of violations in CIRP in the long-term capital markets rather than transactions costs or the size of the economy.     

Inflation targeting and the forward bias puzzle in emerging countries

Based on quarterly data on 31 emerging countries (among which 16 are inflation targeting countries) from 1990Q1 to 2014Q3, we obtain a strong support for the conjecture that the implementation of inflation targeting weakens the Fisherian relation between expected depreciation and the interest rate differential (uncovered interest parity condition) and thus is conducive to the appearance of the forward bias puzzle in emerging countries. We show that this reflects the performance of inflation targeting regimes in lowering the level and volatility of inflation. Our finding holds when controlling for country-specific effects, time-specific effects, global disinflation, exchange rate management, crises, and using different econometric techniques.     

A Liquidity-Based Resolution of the Uncovered Interest Parity Puzzle

A new monetary theory is set out to resolve the “uncovered interest parity (UIP)” puzzle. It explores the possibility that liquidity properties of money and nominal bonds can account for the puzzle. A key concept in our model is that nominal bonds carry liquidity premia. We show that the UIP can fail to hold under the economic environment where collateral pledgeability and/or liquidity of nominal bonds and/or collateralized credit-based transactions are relatively bigger. Our liquidity-based theory can help understanding many empirical observations that risk-based explanations find difficult to reconcile with.     

Possible solutions to the forward bias paradox

This note outlines the economic theory behind the theory of uncovered interest parity and some of the econometric issues involved in testing and interpretation. I illustrate some of the issues involved by estimating a rolling regression of the forward premium regression from 22 years of eight major currencies. I also conclude that Pippenger's model is not consistent with the theory of UIP and that furthermore there are severe econometric problems in estimating his model. The forward premium anomaly remains a paradox in international finance that is important and worthwhile to understand more fully.     

Monetary policy and covered interest parity in the post GFC period: Evidence from the Australian dollar and the NZ dollar

After the global financial crisis (GFC), most major currencies had higher interest rates than the US dollar on forward contract because of increased demand for the US dollar as international liquidity. However, unlike the other major currencies, the Australian dollar and the NZ dollar had lower interest rates than the US dollar on forward contract in the post GFC period. The purpose of this paper is to explore why this happened through estimating the covered interest parity (CIP) condition. In the analysis, we focus on a unique feature of Australia and New Zealand where short-term interest rates remained significantly positive even after the GFC. The paper first constructs a theoretical model where increased liquidity risk causes deviations from the CIP condition. It then tests this theoretical implication by using daily data of six major currencies. We find that both money market risk measures and policy rates had significant effects on the CIP deviations. The result implies that unique monetary policy feature in Australia and New Zealand made deviations from the CIP condition distinct on the forward contract.     

When can you immunize a bond portfolio?

This paper presents a condition equivalent to the existence of a Riskless Shadow Asset that guarantees a minimum return when the asset prices are convex functions of interest rates or other state variables. We apply this lemma to immunize default-free and option-free coupon bonds and reach three main conclusions. First, we give a solution to an old puzzle: why do simple duration matching portfolios work well in empirical studies of immunization even though they are derived in a model inconsistent with equilibrium and shifts on the term structure of interest rates are not parallel, as assumed? Second, we establish a clear distinction between the concepts of immunized and maxmin portfolios. Third, we develop a framework that includes the main results of this literature as special cases. Next, we present a new strategy of immunization that consists in matching duration and minimizing a new linear dispersion measure of immunization risk.     

Solving exchange rate puzzles with neither sticky prices nor trade costs

We present a simple framework in which both the exchange rates disconnect and forward bias puzzles are simultaneously resolved. The flexible-price two-country monetary model is extended to include a consumption externality with habit persistence. Habit persistence is modeled using Campbell Cochrane preferences with ‘deep’ habits along the lines of the work of Ravn, Schmitt-Grohe and Uribe. By deep habits, we mean habits defined over goods rather than countries. The model is simulated using the artificial economy methodology. It offers a neo-classical explanation of the Meese–Rogoff puzzle and mimics the failure of fundamentals to explain nominal exchange rates in a linear setting. Finally, the model naturally generates the negative slope in the standard forward market regression.     

Deviations from Covered Interest Rate Parity

We find that deviations from the covered interest rate parity (CIP) condition imply large, persistent, and systematic arbitrage opportunities in one of the largest asset markets in the world. Contrary to the common view, these deviations for major currencies are not explained away by credit risk or transaction costs. They are particularly strong for forward contracts that appear on banks' balance sheets at the end of the quarter, pointing to a causal effect of banking regulation on asset prices. The CIP deviations also appear significantly correlated with other fixed income spreads and with nominal interest rates.     

The role of covered interest parity in explaining the forward premium anomaly within a nonlinear panel framework

This paper investigates the dynamic properties of uncovered interest parity (UIP) depending on deviations from covered interest parity (CIP) in a nonlinear panel framework. By employing a panel smooth transition regression model, the threshold level of the CIP deviation in which UIP tends to hold is found to be outside the band of inaction where deviations from CIP would fail to be arbitraged away. This paper shows how reversals of UIP observed during the global financial crisis can be, to some extent, accounted for by funding liquidity constraints. Simulation experiments also suggest that the data-generating process from the nonlinear panel model can produce data consistent with the failure of UIP.     

Trading frequency and asset pricing on the London Stock Exchange: Evidence from a new price impact ratio

This study proposes a new price impact ratio as an alternative to the widely used Amihud’s (2002) Return-to-Volume ratio. We demonstrate that the new price impact ratio, which is deemed Return-to-Turnover ratio, has a number of appealing features. Using daily data from all stocks listed on the London Stock Exchange over the period 1991–2008, we provide overwhelming evidence that this ratio, while being unequivocal to construct and interpret, is also free of a size bias. More importantly, it encapsulates the stocks’ cross-sectional variability in trading frequency, a relatively neglected but possibly important determinant of stock returns given the recently observed trends in financial markets. Overall, our findings argue against the conventional wisdom that there is a simple direct link between trading costs and stock returns by strongly suggesting that it is the compound effect of trading frequency and transaction costs that matters for asset pricing, not each aspect in isolation.     

A computing bias in estimating the probability of informed trading

This study identifies a factor that leads to a bias in estimating the probability of informed trading (PIN), a widely-used microstructure measure. It is shown that, along with the numerical maximization of the likelihood function for PIN, the floating-point exception (i.e., overflow or underflow) may eliminate feasible solutions to the actual parameters in the optimization problem. Approximately 44% of PIN estimates for recent stock market data may have been subject to a downward bias that is more pronounced for active stocks than for inactive stocks. This study develops a remedy to mitigate the resulting bias.     

Covered interest parity with default risk

In this paper we derive a simple model of covered interest parity (CIP) with the assumption that interbank money market rates are risky. The model assumes that the default risk of uncollateralised loans can be hedged perfectly by credit default swap contracts. We show that the no-arbitrage condition is satisfied by a band. The location of this no-arbitrage band depends on the relative riskiness of the two counterparties in the CIP trade. We present evidence on the performance of the model for developed currency pairs in 2008–2011. We find that FX swap spreads (CIP deviations calculated from interbank interest rates of two countries) either fluctuated within the no-arbitrage bands or were close to the edges of the no-arbitrage bands.     

General equilibrium pricing of currency and currency options

This paper presents a consumption-based general equilibrium model for valuing foreign exchange contingent claims. The model identifies a novel economic mechanism by exploiting highly but imperfectly shared consumption disaster with variable intensities which are the concerns to the representative investor under recursive utility. When applied to the data, the model simultaneously replicates (i) the moderate option-implied volatilities; (ii) substantial variations in the risk-neutral skewness of currency returns; (iii) the uncovered interest rate parity puzzle; and (iv) the first two moments of carry trade returns. Furthermore, the model rationalizes salient features of the aggregate stock, government bonds, and equity index options.     

LONG-RUN RELATIONS IN EXCHANGE MARKETS: A TEST OF COVERED INTEREST PARITY

We examine long-run relations implied by covered interest parity (CIP) in possibly cointegrated and nonstationary data series. Empirical evidence suggests that, ignoring market imperfections, CIP failed over January 6, 1984, through December 6, 1991, using weekly data from four major currencies relative to the U.S. dollar. The multivariate maximum likelihood vector autoregressive (VAR) methodology does not require data differencing and hence retains valuable information lost in previous research examining international market flows. Rejections are robust to both subperiod analysis and alternative interest rate series. Although test rejections are highly statistically significant, attainable economic profits appear small. Practitioners will find economic profits inconsequential relative to reasonable bounds on market frictions such as transaction costs. Nonetheless, the use of CIP to determine forward rates identically from interest rates and spot rates in academic studies is called into question.     

Triangular arbitrage in the spot and forward foreign exchange markets

Imad Moosa shows that the effect of triangular arbitrage in the forward market is similar to the combined effect of triangular arbitrage in the spot market and covered interest arbitrage. He also shows that when the forward rates are inconsistent then this implies inconsistency of the spot rates and/or the violation of covered interest parity. When the bid-offer spreads are allowed for, the equilibrium conditions hold only approximately.