An explanation of the forward premium 'puzzle'

Existing literature reports a puzzle about the forward rate premium over the spot foreign exchange rate. The premium is often negatively correlated with subsequent changes in the spot rate. This defies economic intuition and possibly violates market efficiency. Rational explanations include non-stationary risk premia and econometric mis-specifications, but some embrace the puzzle as a guide to profitable trading.
We suggest there is really no puzzle. A simple model fits the data: forward exchange rates are unbiased predictors of subsequent spot rates. The puzzle arises because the forward rate, the spot rate, and the forward premium follow nearly non-stationary time series processes. We document these properties with an extended sample and show why they give the delusion of a puzzle.     

Banks as Catalysts for Industrialization

We provide a new theory of the role of banks as catalysts for industrialization. In their influential analysis of continental European industrialization, Gerschenkron and Schumpeter argued that banks promoted the creation of new industries. We formalize this role of banks by introducing financial intermediaries into a “big push” model. We show that banks may act as catalysts for industrialization provided they are sufficiently large to mobilize a critical mass of firms and that they possess sufficient market power to make profits from coordination. The theory provides simple conditions that help explain why banks seem to play a creative role in some but not in other emerging markets. The model also shows that universal banking helps to reduce the cost of acting as catalyst. Journal of Economic Literature Classification Numbers: G21, N2, O14, O16.     

AN ECONOMETRIC ANALYSIS OF EQUITY COSTS AND RISK PREMIUMS IN THE ELECTRIC UTILITY INDUSTRY: 1971–1985

This paper develops a varying parameter econometric model that estimates the cost of equity of individual utility firms from 1971 to 1985. The equity costs estimated in this framework can be analyzed in terms of their statistical precision. The paper also examines, theoretically and empirically, the relationship between the econometric estimates of the equity risk premiums and the risk-free interest rates. The data do not support the hypothesis that risk premiums are independent of interest rates. Also, the relationship appears to vary over time. These results invalidate the risk premium approach in which equity costs are estimated by adding a constant, historical average risk premium to the prevailing interest rates.     

Stock repurchases: How firms choose between a self tender offer and an open-market program

In practice, open-market stock repurchase programs outnumber self tender offers by approximately 10–1. This evidence is puzzling given that tender offers are more efficient in disbursing free cash and in signaling undervaluation – the two main motivations suggested in the literature for repurchasing shares. We provide a theoretical model to explore this puzzle. In the model, tender offers disburse free cash quickly but induce information asymmetry and hence require a price premium. Open-market programs disburse free cash slowly, and hence do not require a price premium, but because they are slow, result in partial free cash waste. The model predicts that the likelihood that a tender offer will be chosen over an open-market program increases with the agency costs of free cash and decreases with uncertainty (risk), information asymmetry, ownership concentration, and liquidity. These predictions are generally consistent with the empirical evidence.     

On Timing and Selectivity

The dichotomy between timing ability and the ability to select individual assets has been widely used in discussing investment performance measurement. This paper discusses the conceptual and econometric problems associated with defining and measuring timing and selectivity. In defining these notions we attempt to capture their intuitive interpretation. We offer two basic modeling approaches, which we term the portfolio approach and the factor approach. We show how the quality of timing and selectivity information can be identified statistically in a number of simple models, and discuss some of the econometric issues associated with these models. In particular, a simple quadratic regression is shown to be valid in measuring timing information.     

Comparison of modeling methods for Loss Given Default

We compare six modeling methods for Loss Given Default (LGD). We find that non-parametric methods (regression tree and neural network) perform better than parametric methods both in and out of sample when over-fitting is properly controlled. Among the parametric methods, fractional response regression has a slight edge over OLS regression. Performance of the transformation methods (inverse Gaussian and beta transformation) is very sensitive to ε, a small adjustment made to LGDs of 0 or 1 prior to transformation. Model fit is poor when ε is too small or too large, although the fitted LGDs have strong bi-modal distribution with very small ε. Therefore, models that produce strong bi-model pattern do not necessarily have good model fit and accurate LGD predictions. Even with an optimal ε, the performance of the transformation methods can only match that of the OLS.     

Modeling and forecasting expected shortfall with the generalized asymmetric Student-t and asymmetric exponential power distributions

Financial returns typically display heavy tails and some degree of skewness, and conditional variance models with these features often outperform more limited models. The difference in performance may be especially important in estimating quantities that depend on tail features, including risk measures such as the expected shortfall. Here, using recent generalizations of the asymmetric Student-t and exponential power distributions to allow separate parameters to control skewness and the thickness of each tail, we fit daily financial return volatility and forecast expected shortfall for the S&P 500 index and a number of individual company stocks; the generalized distributions are used for the standardized innovations in a nonlinear, asymmetric GARCH-type model. The results provide evidence for the usefulness of the general distributions in improving fit and prediction of downside market risk of financial assets. Constrained versions, corresponding with distributions used in the previous literature, are also estimated in order to provide a comparison of the performance of different conditional distributions.     

Is size dead? A review of the size effect in equity returns

Beginning with Banz (1981), I review 30 years of research on the size effect in equity returns. Since Fama and French (1992), there has been a vigorous, ongoing debate on whether the size premium is a compensation for systematic risk. Since the late 1990s, research on the size effect has been characterized by two developments that are seemingly contradictory. At last, theoretical models have emerged in which the size effect arises endogenously as a result of systematic risk. However, recent empirical studies assert that the size effect has disappeared after the early 1980s. In this review, I address this disconnect between recent theoretical and empirical research.     

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.     

Was it risk? Or was it fundamentals? Explaining excess currency returns with kernel smoothed regressions

This paper uses recently developed kernel smoothing regression procedures and uniform confidence bounds to investigate the forward premium anomaly. These new statistical methods estimate the local time-varying slope coefficient of the regression of spot returns on the lagged interest rate differential. Uniform confidence bands are used to test when uncovered interest parity is violated. The estimated betas in the forward premium smoothed regression are found to vary substantially over time and to be partially explicable in terms of lagged fundamentals and money growth volatilities arising from risk premium. Frequentist model averaging procedures indicate the relative importance of these variables in terms of explaining movements in the betas and hence the apparent causes of regimes where UIP fails.     

Time-varying market,interest rate,and exchange rate risk premia in the US commercial bank stock returns

This paper examines the role of market, interest rate, and exchange rate risks in pricing a sample of the US Commercial Bank stocks by developing and estimating a multi-factor model under both unconditional and conditional frameworks. Three different econometric methodologies are used to conduct the estimations and testing. Estimations based on nonlinear seemingly unrelated regression (NLSUR) via GMM approach indicate that interest rate risk is the only priced factor in the unconditional three-factor model. However, based on ‘pricing kernel’ approach by Dumas and Solnik [(1995). J. Finance 50, 445–479], strong evidence of exchange rate risk is found in both large bank and regional bank stocks in the conditional three-factor model with time-varying risk prices. Finally, estimations based on the multivariate GARCH in mean (MGARCH-M) approach where both conditional first and second moments of bank portfolio returns and risk factors are estimated simultaneously show strong evidence of time-varying interest rate and exchange rate risk premia and weak evidence of time-varying world market risk premium for all three bank portfolios, namely those of Money Center bank, Large bank, and Regional bank.     

On the acquisition of equity carve-outs

We examine the role played by the parent’s motive in undertaking a carve-out; the parent’s post-IPO influence over the carved-out subsidiary; and anti-takeover provisions and industry structure of a carve-out on its acquisition likelihood and its acquisition premium. We find that the probability and hazard of a carve-out acquisition increase when the parent’s objective is to unlock the value of a subsidiary and when the parent and the subsidiary are tied with a product-market relationship. We also find that the post-IPO parent ownership significantly affects the acquisition likelihood and the level of acquisition premium. Additional analyses examining the post-IPO carve-out status suggest that the product-market relationship and post-IPO parent ownership increase the probability of re-acquisition.     

Forward exchange market unbiasedness: the case of the Australian dollar since 1984

This paper implements a robust statistical approach to regression with non-stationary time series. The methods were recently developed in other work and are briefly exposited here. They allow us to perform regressions in levels with non-stationary time series data, they accommodate data distributions with heavy tails and they permit serial dependence and temporal heterogeneity of unknown form in the equation errors. With these features the methods are well suited to applications with frequently sampled exchange rate data, which generally display all of these empirical characteristics. Our application here is to daily data on spot and forward exchange rates between the Australian and US dollars over the period 1984–1991, following the deregulation of the Australian foreign exchange market. We find big differences between the robust and the non-robust regression outcomes and in the associated statistical tests of the hypothesis that the forward rate is an unbiased predictor of the future spot rate. The robust tests reject the unbiasedness hypothesis but still give the forward rate an important role as a predictor of the future spot rate.     

INFLATION MEASUREMENT,INFLATION RISK,AND THE PRICING OF TREASURY BILLS

One explanation for the high real interest rates on Treasury bills during the period from 1980 to 1985 is that the risk premium had risen. A procedure for testing this hypothesis is to apply the Black version of the capital asset pricing model to real Treasury bill returns. This paper examines that procedure in detail. The main conclusion is that nonstationarity and measurement error, which are always impediments to empirical implementation of the CAPM, are particularly difficult to handle when estimating changes in Treasury bill risk premiums. Furthermore, the behavior of the premium depends on the index used to measure inflation.     

The residual market factor,the APT,and mean-variance efficiency

The rapidly increasing volume of both published and unpublished work on the arbitrage pricing theory (APT) of Ross (1976) has given rise to a number of misunderstandings at the interface of theoretical and econometric work. In this article we extend the theoretical structure of our previous work (McElroy and Burmeister, 1985, 1988; Burmeister and McElroy, 1987, 1988) to provide a broad yet rigorous framework both for econometric estimation and for better economic interpretation of new empirical results. We begin with the case where allK factors are observed, and then present the second case ofK−1≡J observed APT factors and one unobserved factor, theresidual market factor introduced in McElroy and Burmeister (1985). The economic interpretations for equivalent specifications of this model are discussed, and we enumerate several immediate payoffs to these specifications. The main new results are concerned with the sometimes intricate relationships among APT models withK factors and APT models withK factors that are constrained to satisfy mean-variance efficiency restrictions. These results are not only of theoretical interest, but more importantly they provide the basis for econometric estimation and testing of nested hypotheses. These econometric issues are discussed in detail.     

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.     

An Asymptotic Theory for Estimating Beta-Pricing Models Using Cross-Sectional Regression

Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two-stage cross-sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t -value of a premium may converge to infinity in probability even when the true premium is zero. However, when a beta-pricing model is misspecified, the t -values for firm characteristics generally converge to infinity in probability, which supports the use of firm characteristics in cross-sectional regressions for detecting model misspecification.     

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.     

On the (in)feasibility of covered interest parity as a solution to the forward bias puzzle

This paper examines Pippenger's (2011) proposed solution to the forward bias puzzle, which is based on the covered interest parity (CIP) condition. It is argued that the CIP-based approach does not solve this well known and long-standing puzzle in international finance in a meaningful way. Moreover, it is shown that empirical results from such an approach follow mechanically from the identity-like nature of the theory of covered interest parity, which, aside from small deviations due to transaction costs, is assumed to hold in all periods (as if it were an identity). We show that rather than leading to new insights, the simple reconfiguration of CIP to solve for the time t + 1 spot exchange rate leads to tautological expressions that, when estimated, might appear to successfully explain the forward bias, but in actuality are trivial. Results from simple simulation exercises further illustrate the inconclusiveness of the proposed solution method.     

Habit-based asset pricing with limited participation consumption

We calibrate and estimate a consumption-based asset pricing model with habit formation using limited participation consumption data. Based on survey data of a representative sample of American households, we distinguish between assetholder and non-assetholder consumption, as well as the standard aggregate consumption series commonly used in the CCAPM literature. We show that assetholder consumption outperforms non-assetholder and aggregate consumption data in explaining bond returns, bond yields, and the volatility of bond yields. We further show that the high volatility of assetholder consumption enables the model to explain the equity premium puzzle and the risk-free rate puzzle simultaneously for a reasonable value of relative risk aversion.