Unbiased Expectations Hypothesis Research Articles

Markov-modulated jump-diffusion models for the short rate: Pricing of zero coupon bonds and convexity adjustment

In this article, we consider a Markov-modulated model with jumps for the short rate. Using the main properties of a telegraphic process with jumps we compute the expected short rate. We obtain closed formulas for the zero coupon bond price assuming the Unbiased Expectation Hypothesis for the forward rates. Next, we obtain the coupled system of partial differential equations for the bond price using only no-arbitrage arguments. Numerical solutions are provided for some selected examples. The results obtained from both methods are compared and allow to estimate the magnitude of the convexity-adjustment.

Forward Curve Bias and Optimization Errors

We derive optimal hedging ratios for interest rate risk under different assumptions that underpin the relationship between the forward rate and the expected future spot rate. In some instances, full hedging is optimal, and the conditions for the optimality of a partial hedge are identified. Less hedging (more floating debt in our model) is more optimal under the liquidity preference model than under the unbiased expectations hypothesis. This indicates that in times of higher preference for liquidity less hedging is optimal. Higher preference for liquidity correlates with larger term spreads (a steeper yield curve) and periods of monetary easing. Comparison of the analytical results with historical data indicates that partial hedging for interest rate risk is generally preferable over full hedging strategies with some exceptions. Lastly, the paper shows the role of market timing on hedging decisions.

What Explains Deviations in the Unbiased Expectations Hypothesis? Market Irrationality vs. the Peso Problem

What Explains Deviations in the Unbiased Expectations Hypothesis? Market Irrationality vs. the Peso Problem

What explains deviations in the unbiased expectations hypothesis? Market irrationality vs. the peso problem

Evidence from this study suggests that investor sentiment and the peso problem play a significant role in explaining expectation errors, rejecting the unbiased expectation hypothesis (UEH). The deviation of the UEH for long-term rates is mainly attributable to expectation errors, whereas the deviation of short-term rates is tied to the term premium. We decompose expectation errors and find that irrationality is more apparent in crisis periods, and the rational component becomes an influential factor in tranquil periods.

Testing the Foreign Exchange Parity Relations: A Case Analysis of UK Sterling, Japanese Yen and Us Dollar

Since the financial globalization has expanded and developed increasingly fast in recent years, the international parity relationships have been extensively studied due to their importance in international trade and investment. This paper investigates purchasing power parity (PPP), interest rate parity (IRP) and unbiased expectation hypothesis by analyzing three main currencies; UK sterling, Japanese Yen and US dollar during 2008 to 2010. Further, forward premium or discount is calculated and interpret in the study with time series data and ordinary least square (OLS) regression methodologies. It was found that, the unbiased expectation hypothesis and international interest parity holds for Japan-US case but does not hold for Japan-UK case. Finally, the purchasing Power Parity (PPP) holds for both two cases, which is varies with most previous literature.

Term structure information and bond strategies

We examine term structure theories by using a novel approach. We form bond investment strategies based on different theories of the term structure in order to determine which strategy performs best. When using a manipulation-proof performance measure, we find that consistent with prior literature, an active strategy that is based on time varying term premiums can indeed form the basis of a successful bond strategy that outperforms an unbiased expectation inspired passive bond buy and hold strategy. This is true, however, for an earlier time period when the literature first made this claim. In a later time period, we find that the passive buy and hold strategy is significantly superior to all active strategies. This result is confirmed by statistical tests and it suggests that once it became known that an active strategy based on time varying term premiums could outperform a passive buy and hold strategy, the markets adjusted and arbitraged away this opportunity. Overall, it appears that the unbiased expectation hypothesis is the most likely explanation of the behaviour of the term structure during more recent times. This is because economically and statistically significant superior performance cannot be achieved if one uses information from the forward curve or the term structure as a guide to adjusting bond portfolios in response to changes in the term premium.

Rentestrukturen og Forventningshypoteserne: En Betragtning Under Usikkerhed (The Yield-Curve and the Expectation Hypothesis)

In this paper we analyse the relationship between the 4 different Expectation Hypothesis that has been suggested in the litterature. These 4 Expectation Hypothesis are: 1) The unbiased expectation hypothesis (UEH); 2) The return-to-maturity expectation hypothesis (RTM-EH); 3) The yield-to-maturity expectation hypothesis (YTM-EH) and 4) The local expectation hypothesis (LEH).In a deterministic setting it is shown that all the 4 Expectation Hypothesis are identical. However, In a world of uncertainty, they impose different hypothesis about the future Yield-Curve. It is in this connection - in continuous-time - shown that the only Expectation Hypothesis with does not violate the risk-free arbitrage argument is LEH.The market price of risk is also being analysed and proof is being presented that show that in order for the LEH to be valid it is required that the market price of risk is 0 (zero). Furthermore, it is being shown that one cannot freely define the market price of risk as there exist an interactive relationship between the market price of risk and the variance in the bond-price that need to be satisfied in order to be consisting with the risk-free arbitrage argument.

Volatility models of currency futures in developed and emerging markets

This paper examines volatility models of currency futures contracts for three developed markets and two emerging markets. For each contract, standard models of the Unbiased Expectations Hypothesis (UEH) and Cost-of-Carry hypothesis (COC) are extended to derive volatility models corresponding to each of the two standard approaches. Each volatility model is formulated as a system of individual equations for the conditional variances of futures returns, spot returns and the domestic risk-free interest rate. The empirical results suggest that the conditional volatility of futures returns for emerging markets is significant in explaining the conditional volatility of returns in the underlying spot market. For developed markets, however, the conditional volatility of the spot returns is significant in explaining the conditional volatility of futures returns. Moreover, it is found that the domestic risk-free interest rate has little impact on the conditional variances of the futures, spot and domestic risk-free interest rates.

A COMPLETE YIELD CURVE DESCRIPTION OF A MARKOV INTEREST RATE MODEL

This paper aims to present a complete term structure characterisation of a Markov interest rate model. To attain this objective, we first give a proof that establishes the Unbiased Expectation Hypothesis (UEH) via the forward measure. The UEH result is then employed, which considerably facilitates the calculation of an explicit analytic expression for the forward rate f(t, T). The specification of the bond price P(t, T), yield rate Y(t, T) and f(t, T) gives a complete set of yield curve descriptions for an interest rate market where the short rate r is a function of a continuous time Markov chain.

Efficient Estimation and Testing of Alternative Models of Currency Futures Contracts

An efficient systems approach is used to estimate and test two alternative models regarding the pricing of Australian dollar futures contracts traded on the International Monetary Market of the Chicago Mercantile Exchange. Cointegrating relationships among the Australian dollar spot and futures prices, and the US and Australian risk‐free rates of interest, suggest alternative error‐correction representations for the cost‐of‐carry model which, with appropriate zero restrictions, yields the unbiased expectations hypothesis. A structural break in the futures price series permits estimation of appropriate models for the full sample in the presence of the break, for the full sample without explicitly modelling the break, and for two separate sub‐samples created by the structural break. The restricted and unrestricted cost‐of‐carry formulations are estimated for all sample sets, the models obtained are found to be statistically adequate, and the qualitative results are reasonably robust across different sample sets for both models. On the basis of the tests of zero restrictions, the cost‐of‐carry model is found to be empirically superior to the unbiased expectations hypothesis for the four sample sets considered, regardless of the number of cointegrating relations.

The False Teachings of the Unbiased Expectations Hypothesis

The unbiased expectations hypothesis is the basis for many current investment strategies, despite its shortcomings. Yet the spot–forward parity theorem and the unbiased expectations hypothesis cannot both hold. Why do some in the investment community continue to believe that there is any more information in forward prices or rates than spot prices or rates? The authors show that forward prices have to be biased predictors of future spot prices, or arbitrage opportunities would arise. The bias is fair compensation for the difference in the timing of the cash flows between the spot and forward markets. The authors argue that the unbiased expectations hypothesis often forms the basis for trading strategies only because of the zero initial value and non–zero future value, the misuse of forwards in performance attribution, and a misunderstanding of the symmetry of risk premiums.

A market-augmented model for SIMEX Brent crude oil futures contracts

Brent crude oil futures contracts are traded on both the Singapore International Monetary Exchange (SIMEX) and the International Petroleum Exchange (IPE). Through a mutual offset system between SIMEX and IPE, Brent crude oil futures contracts can be traded up to nineteen hours each day. The inter-relationship between the two futures contracts, the spot price of Brent crude oil and the riskfree interest rate, suggest the existence of cointegration among SIMEX Brent crude oil futures prices, lagged IPE Brent crude oil futures prices, Brent spot prices and the London Inter-bank Offer Rate (LIBOR). Error-correction representations of two standard futures pricing models, namely the unbiased expectations and cost-of-carry hypotheses, are formulated for SIMEX Brent crude oil futures contracts. These formulations are augmented by including the lagged IPE futures price in the mispricing error. The resulting Augmented Unbiased Expectations Hypothesis (AUEH) and the Augmented Cost-of-Carry (ACOC) models are estimated and tested against each other, and also against the standard unbiased expectations and cost-of-carry models, using nested and non-nested testing procedures. Forecasting comparisons are also made among the various models and the autoregressive integrated moving average models fitted to SIMEX Brent crude oil futures prices. Results from the nonnested tests and the forecasting criteria show clearly that the augmented models outperform their standard (non-augmented) counterparts.

Futures and realized cash or settle prices for gold, silver, and copper

AbstractThis article examines the relation between 15‐, 30‐, 45‐, and 60‐day gold, silver, and copper futures, and their realized cash or delivery settle prices, for deliveries on the first, middle, and last business day (FD, MD, and LD, respectively) of the delivery month. Samples of futures prices for gold, silver, and copper, and the realized cash or delivery settle prices, based on fixed maturities for a cross‐section of contracts are used, because time‐series over fixed maturities are unfeasible owing to the restrictive maturity periods in these contracts. This study contrasts with similar studies for forwards, which are not hampered by this problem (e.g., Baillie and Bollerslev in 1989), studies that use contemporaneous time‐series of futures and cash prices to obtain optimal hedge ratios (e.g., Ghosh and Clayton in 1996), and studies that examine for parity between different futures prices (e.g., Franses and Kofman in 1991). Near‐term gold, closest to delivery silver and all copper futures (the latter only with settle prices at delivery) are good predictors of the future cash price, except for silver and copper deliveries on the last day of delivery months. These results are consistent with previous studies on short‐term cash (Ma in 1985) and futures (Ma and Soenen in 1988) parity between gold and silver, and with Gross's (1988) results for copper. The longer‐term gold (45‐ and 60‐day) and silver (30‐, 45‐, and 60‐day) futures reject an unbiased expectations hypothesis. This result is consistent with Leistikow (1990) because cash prices respond less than futures prices in these instances.

The pricing of bank bill futures and FRA contracts in New Zealand

This study examines pricing in the bank bill futures and forward rate agreement (FRA) markets. The study finds (i) the bill futures market is more transactionally efficient than the FRA market, and (ii) the unbiased expectations hypothesis generates more accurate estimates of bill futures and FRA yields than the cost of carry hypothesis. The first result reflects impediments to FRA market arbitrage such as illiquidity, minimum trade sizes and credit limits. The second result contradicts US evidence but is consistent with the leading role played by the bank bill and interbank dealers in New Zealand interest rate markets.

Around and Around: The Expectations Hypothesis

We show how to construct models of the term structure of interest rates in which the expectations hypothesis holds. McCulloch (1993) presents such a model, thereby contradicting an assertion by Cox, Ingersoll, and Ross (1981), but his example is Gaussian and falls outside the class of finite‐dimensional Markovian models. We generalize McCulloch's model in three ways: (i) We provide an arbitrage‐free characterization of the unbiased expectations hypothesis in terms of forward rates; (ii) we extend this characterization to a whole class of expectations hypotheses; and (iii) we show how to construct finite‐dimensional Markovian and non‐Gaussian examples.

Correlated interest rate risk and funding strategies for nonfinancial firms

This paper considers appropriate funding strategies for nonfinancial firms when operating cash flows are correlated with interest rates. An example expression is provided for the optimal funding position when the firm has a two-period investment horizon. The conclusion is that matching will be the best strategy if the unbiased expectations hypothesis of the term structure holds and operating cash flows are uncorrelated with interest rates. Since the optimal funding position will be the minimum-risk one if the expectations hypothesis holds, the properties of the minimum-risk funding strategy are also investigated. The primary result is that maturity matching will not necessarily be the optimal funding strategy even when, on average, the cost of long- and short-term funds is the same. Finally, some empirical estimates of minimum risk funding positions for nonfinancial firms are provided using data from the Quarterly CompuStat files. The data indicate that changes in corporate operating earnings are, on average, significantly positively correlated with changes in short-term interest rates, but that there is substantial cross-sectional variation across companies in our sample.

Testing the rationality of exchange rate and interest rate expectations: an empirical study of Australian survey-based expectations

This paper examines the rationality of the Australian survey-based expectations, 1- and 4-week-ahead $US/$A exchange rate and 2 and 4-week-ahead Australian 90-day bank bill and 10-year bond rates. The actual and expected variables are found to be cointegrated, indicating that the expected future values and the future realizations of the exchange rate and interest rates have long-run equilibrium relationships. OLS estimations with the Newey - West corrections are employed for testing the unbiased expectations hypothesis (UEH) where the frequency of the expectations data is finer than the forecast horizons, and the exponential-GARCH models that take into account the time-varying nature of the forecasterror variance are employed for testing the weak rational expectations hypothesis (WREH). The evidence shows that the WREH could not be rejected in any case, except for the two-week-ahead forecast of the 90-day interest rate, which indicates that all available information is used at the time of forming relevant forecasts. The UEH, however, is decisively rejected in all cases. This indicates that strong rationality, which requires both UEH and WREH, is rejected in all cases. It is concluded that forecasters are weakly rational; however, their forecasts are not unbiased because the data available to them when forming expectations are inadequate.

A class of Health-Jarrow-Morton models in which the unbiased expectations hypothesis holds

The unbiased expectations hypothesis states that forward rates are unbiased estimates for future short rates. Cox, Ingersoll and Ross [1] conjectured that this hypothesis should be inconsistent with the absence of arbitrage possibilities. Using the framework of Heath, Jarrow and Morton [4] we show that this is not always the case. The unbiased expectations hypothesis together with the existence of an equivalent martingale measure is equivalent to a certain condition on the volatilities of the forward rates.

Around and Around: The Expectations Hypothesis

We show how to construct arbitrage-free models of he term structure of interest rates in which various expectations hypotheses can hold. McCulloch (1993) provided a Gaussian non-Markovian example of the unbiased expectations hypothesis (U--EH), thereby contradicting the assertion by Cox, Ingersoll, and Ross (CIR, 1981) that only the so-called local expectations hypothesis could hold. We generalize that example in three ways: (i) We characterize the U--EH in terms of forward rates; (ii) we extend this characterization to a class of expectations hypotheses that includes all of those considered by CIR; and (iii) we construct stationary Markovian and non-Gaussian economies. The building block is a maturity-dependent vector that travels around a circle at a constant speed as maturity increases.

Interest rate futures: Evidence on forecast power, expected premiums, and the unbiased expectations hypothesis

Journal of Futures MarketsVolume 14, Issue 5 p. 531-543 Article Interest rate futures: Evidence on forecast power, expected premiums, and the unbiased expectations hypothesis Tim Krehbiel, Tim Krehbiel Tim Krehbiel is an Assistant Professor of Finance at Oklahoma State University.Search for more papers by this authorLee C. Adkins, Lee C. Adkins Lee C. Adkins is an Associate Professor of Economics at Oklahoma State University.Search for more papers by this author Tim Krehbiel, Tim Krehbiel Tim Krehbiel is an Assistant Professor of Finance at Oklahoma State University.Search for more papers by this authorLee C. Adkins, Lee C. Adkins Lee C. Adkins is an Associate Professor of Economics at Oklahoma State University.Search for more papers by this author First published: August 1994 https://doi.org/10.1002/fut.3990140504Citations: 17 AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat Citing Literature Volume14, Issue5August 1994Pages 531-543 RelatedInformation