Smaller Pricing Errors Research Articles

Upside and downside correlated jump risk premia of currency options and expected returns

This research explores upside and downside jumps in the dynamic processes of three rates: domestic interest rates, foreign interest rates, and exchange rates. To fill the gap between the asymmetric jump in the currency market and the current models, a correlated asymmetric jump model is proposed to capture the co-movement of the correlated jump risks for the three rates and identify the correlated jump risk premia. The likelihood ratio test results show that the new model performs best in 1-, 3-, 6-, and 12-month maturities. The in- and out-of-sample test results indicate that the new model can capture more risk factors with relatively small pricing errors. Finally, the risk factors captured by the new model can explain the exchange rate fluctuations for various economic events.

The time-varying risk price of currency portfolios

This paper formally implements time-varying risk price models for currency returns. Focusing upon time variation in risk prices, the paper explores four currency risk factors. In addition to dollar and carry factors, we employ momentum and value factors which are widely used by currency investors. We find time variation in risk prices for the dollar factor is associated with the U.S. business cycle, with notable increases at the end of economic downturns. Constant beta models moreover have smaller pricing errors across all currency portfolios, which is in contrast to the stock and bond markets.

The Time-Varying Risk Price of Currency Portfolios

This paper formally implements time-varying risk price models for currency returns. Focusing upon time variation in risk prices, the paper explores four currency risk factors. In addition to dollar and carry factors, we employ momentum and value factors which are widely used by currency investors. We find time variation in risk prices for the dollar factor is associated with the U.S. business cycle, with notable increases at the end of economic downturns. Constant beta models moreover have smaller pricing errors across all currency portfolios, which is in contrast to the stock and bond markets.

Reconstructing the yield curve

The constant maturity zero-coupon yield curve for the US Treasuries is one of the most studied datasets. We construct a new yield curve using a non-parametric kernel-smoothing method with a novel adaptive bandwidth specifically designed to fit the Treasury yields. Our curve is globally smooth while still capturing important local variation. Economically, we show that applying our data leads to different conclusions from using the leading alternative data of Gürkaynak et al. (2007) (GSW) when we repeat two popular studies of Cochrane and Piazzesi (2005) and Giglio and Kelly (2018). Statistically, we show our dataset preserves information in the raw data and has much smaller pricing errors than GSW. Our new yield curve is maintained and updated online, complemented by bandwidths that summarize information content in the raw data.

Flexible Time-Varying Betas in a Novel Mixture Innovation Factor Model with Latent Threshold

This paper introduces a new methodology to estimate time-varying alphas and betas in conditional factor models, which allows substantial flexibility in a time-varying framework. To circumvent problems associated with the previous approaches, we introduce a Bayesian time-varying parameter model where innovations of the state equation have a spike-and-slab mixture distribution. The mixture distribution specifies two states with a specific probability. In the first state, the innovation variance is set close to zero with a certain probability and parameters stay relatively constant. In the second state, the innovation variance is large and the change in parameters is normally distributed with mean zero and a given variance. The latent state is specified with a threshold that governs the state change. We allow a separate threshold for each parameter; thus, the parameters may shift in an unsynchronized manner such that the model moves from one state to another when the change in the parameter exceeds the threshold and vice versa. This approach offers great flexibility and nests a plethora of other time-varying model specifications, allowing us to assess whether the betas of conditional factor models evolve gradually over time or display infrequent, but large, shifts. We apply the proposed methodology to industry portfolios within a five-factor model setting and show that the threshold Capital Asset Pricing Model (CAPM) provides robust beta estimates coupled with smaller pricing errors compared to the alternative approaches. The results have significant implications for the implementation of smart beta strategies that rely heavily on the accuracy and stability of factor betas and yields.

Estimating latent asset-pricing factors

We develop an estimator for latent factors in a large-dimensional panel of financial data that can explain expected excess returns. Statistical factor analysis based on Principal Component Analysis (PCA) has problems identifying factors with a small variance that are important for asset pricing. We generalize PCA with a penalty term accounting for the pricing error in expected returns. Our estimator searches for factors that can explain both the expected return and covariance structure. We derive the statistical properties of the new estimator and show that our estimator can find asset-pricing factors, which cannot be detected with PCA, even if a large amount of data is available. Applying the approach to portfolio data we find factors with Sharpe-ratios more than twice as large as those based on conventional PCA and with smaller pricing errors.

Reconstructing the Yield Curve

The constant-maturity zero-coupon Treasury yield curve is one of the most studied datasets. We reconstruct the yield curve using a non-parametric kernel-smoothing method with a novel adaptive bandwidth specifically designed to fit the Treasury yield curve. Our curve is globally smooth while still capturing important local variation. Economically, we show that applying our data leads to different conclusions from using the leading alternative data of Gurkaynak et al. (2007) (GSW) when we repeat two popular studies of Cochrane and Piazzesi (2005) and Giglio and Kelly (2018). Statistically, we show our dataset preserves information in the raw data and has much smaller pricing errors than GSW. Our new yield curve is maintained and updated online, complemented by bandwidths that summarize information content in the raw data. Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Estimating Latent Asset-Pricing Factors

We develop an estimator for latent factors in a large-dimensional panel of financial data that can explain expected excess returns. Statistical factor analysis based on Principal Component Analysis (PCA) has problems identifying factors with a small variance that are important for asset pricing. We generalize PCA with a penalty term accounting for the pricing error in expected returns. Our estimator searches for factors that can explain both the expected return and covariance structure. We derive the statistical properties of the new estimator and show that our estimator can find asset-pricing factors, which cannot be detected with PCA, even if a large amount of data is available. Applying the approach to portfolio data we find factors with Sharpe-ratios more than twice as large as those based on conventional PCA and with significantly smaller pricing errors.

Portfolio Choice with Model Misspecification: A Foundation for Alpha and Beta Portfolios

Our objective is to investigate the effect of model misspecification on mean-variance portfolios and to show how asset-pricing theory and asymptotic analysis (for large number of assets) can be used to provide powerful solutions to mitigate misspecification. The starting point of our analysis is the Arbitrage Pricing Theory (APT). We extend the APT to show that it can capture not just small pricing errors that are independent of factors, but also large pricing errors from mismeasured or missing factors. Our key insight is that, instead of treating misspecification directly in the mean-variance portfolio, it is better to first decompose the portfolio into components that correspond to the two components of returns in the APT: a ``beta'' portfolio that depends on factor risk premia and an ``alpha'' portfolio that depends only on pricing errors. For the beta portfolio, we treat misspecification using asymptotic analysis: as the number of assets increases, we show that the weights of the alpha portfolio dominate those of the beta portfolio, leading to an expression for mean-variance portfolio weights that is immune to beta misspecification. For the alpha portfolio, we treat misspecification by imposing the APT restriction on alphas, which serves both as an identification condition and a shrinkage constraint. Finally, we demonstrate that our approach achieves an out-of-sample Sharpe ratio that is more than double that of the equally weighted portfolio.

Pricing errors and the geography of trade in the foreign exchange market

Pricing errors in exchange rates are largest during Asian trading hours and decrease until European–New York overlapping trading hours at which point the cycle begins again. Substantial heterogeneity exists in this pattern across exchange rates. Currencies have smaller pricing errors during their home trading hours, which can be explained by traders facing both lower information-unrelated costs and lower information-related costs during a currency׳s home trading hours. Using methods that are able to unambiguously identify the relative importance of information-related and information-unrelated costs for pricing errors, information-unrelated costs are of first-order importance while information-related costs are of second-order importance.

Pricing Errors, the Geography of Trade, and Expected Returns in the Foreign Exchange Market

Pricing errors in exchange rates are largest during Asian trading hours and decrease until European-New York overlapping trading hours at which point the cycle begins again. Substantial heterogeneity exists in this pattern across exchange rates. Currencies have smaller pricing errors during their home trading hours which can be explained by traders facing both lower information-unrelated costs and lower information-related costs during a currency's home trading hours. Using methods that are able to unambiguously identify the relative importance of information-related and information-unrelated costs for pricing errors, information-unrelated costs are of first-order importance while information-related costs are of second-order importance.

The Supply and Demand Factor in the Bond Market: Implications for Bond Risk and Return

In the United States and United Kingdom, the supply of bonds is occasionally found to have a substantial pricing impact that is not accounted for by popular term structure models. In emerging markets, where the supply factor can be much more pronounced, the authors show that the pricing effects are even greater and constantly present. They propose ways to modify the standard affine models to account for the supply effects, thereby yielding much smaller pricing errors and predicting better the time variation of risk. The results are of substantial economic significance for global bond portfolios in managing risk and boosting expected returns.

An application of nonparametric volatility estimators to option pricing

We discuss the impact of volatility estimates from high frequency data on derivative pricing. The principal purpose is to estimate the diffusion coefficient of an Ito process using a nonparametric Nadaraya–Watson kernel approach based on selective estimators of spot volatility proposed in the econometric literature, which are based on high frequency data. The accuracy of different spot volatility estimates is measured in terms of how accurately they can reproduce market option prices. To this aim, we fit a diffusion model to S&P 500 data, and successively, we use the calibrated model to price European call options written on the S&P 500 index. The estimation results are compared to well-known parametric alternatives available in the literature. Empirical results not only show that using intra-day data rather than daily provides better volatility estimates and hence smaller pricing errors, but also highlight that the choice of the spot volatility estimator has effective impact on pricing.

Pricing TIPS and Treasuries with Linear Regressions

We present an affine term structure model for the joint pricing of TIPS and Treasury yield curves that adjusts for TIPS’ relative illiquidity. Our estimation via linear regressions is computationally efficient and can accommodate a large number of pricing factors. The baseline specification with seven principal components extracted from Treasury and TIPS yields as well as a liquidity factor generates negligibly small pricing errors for both real and nominal yields. Model-implied expected inflation adjusted for risk premia and liquidity provides a better prediction of actual inflation than unadjusted breakeven inflation. Analysis of model-implied Treasury and TIPS decompositions shows that the Federal Reserve’s large-scale asset purchases lowered nominal and real Treasury yields primarily via a reduction of real term premia, the compensation investors demand for bearing real short-rate risk. Real term premia also account for the large response of long-term real forward rates to monetary policy surprises. The deflation floor embedded in TIPS is generally small in magnitude, but spiked during the recent crisis. We also show that the nominal and real term structures from the United Kingdom have qualitatively similar features to the U.S. yields.

The performance of VIX option pricing models: Empirical evidence beyond simulation

AbstractWe examine the pricing performance of VIX option models. Such models possess a wide‐range of underlying characteristics regarding the behavior of both the S&P500 index and the underlying VIX. Our tests employ three representative models for VIX options: Whaley (1993), Grunbichler and Longstaff (1996), Carr and Lee (2007), Lin and Chang (2009), who test four stochastic volatility models, as well as to previous simulation results of VIX option models. We find that no model has small pricing errors over the entire range of strike prices and times to expiration. In particular, out‐of‐the‐money VIX options are difficult to price, with Grunbichler and Longstaff's mean‐reverting model producing the smallest dollar errors in this category. Whaley's Black‐like option model produces the best results for in‐the‐money VIX options. However, the Whaley model does under/overprice out‐of‐the‐money call/put VIX options, which is opposite the behavior of stock index option pricing models. VIX options exhibit a volatility skew opposite the skew of index options. © 2010 Wiley Periodicals, Inc. Jrl Fut Mark31:251–281, 2011

Evaluating asset pricing models using the second Hansen-Jagannathan distance

We develop a specification test and a sequence of model selection procedures for non-nested, overlapping, and nested models based on the second Hansen-Jagannathan distance, which requires a good asset pricing model to not only have small pricing errors but also be arbitrage free. Our methods have reasonably good finite sample performances and are more powerful than existing ones in detecting misspecified models with small pricing errors but are not arbitrage-free and in differentiating models that have similar pricing errors of a given set of test assets. Using the Fama and French size and book-to-market portfolios, we reach dramatically different conclusions on model performances based on our approach and existing methods.

Feasibility of the Fama and French three factor model in explaining returns on the JSE

ABSTRACTWe test the feasibility of the Fama and French (1993) three factor model on the JSE Limited (JSE) to explain the size and value effects. In time-series tests on grouped data, we show that both the models can capture a substantial amount of time-series variation in most assets, and yield small pricing errors. In tests on ungrouped data, the three factor model can explain the value effect, and goes in the right direction to explain the size effect. Given these results, we propose that our three factor model could be used in expected return estimation for firms listed on the JSE.

Testing conditional asset pricing models: An emerging market perspective

The CAPM as the benchmark asset pricing model generally performs poorly in both developed and emerging markets. We investigate whether allowing the model parameters to vary improves the performance of the CAPM and the Fama–French model. Conditional asset pricing models scaled by conditioning variables such as Trading Volume and Dividend Yield generally result in small pricing errors. However, a graphical analysis reveals that the predictions of conditional models are generally upward biased. We demonstrate that the bias in prediction may be the consequence of ignoring frequent large variation in asset returns caused by volatile institutional, political and macroeconomic conditions. This is characterised by excess kurtosis. An unconditional Fama–French model augmented with a cubic market factor performs the best among some competing models when local risk factors are employed. Moreover, the conditional models with global risk factors scaled by global conditioning variables perform better than the unconditional models with global risk factors.

A skeptical appraisal of asset pricing tests

It has become standard practice in the cross-sectional asset pricing literature to evaluate models based on how well they explain average returns on size- B/ M portfolios, something many models seem to do remarkably well. In this paper, we review and critique the empirical methods used in the literature. We argue that asset pricing tests are often highly misleading, in the sense that apparently strong explanatory power (high cross-sectional R 2s and small pricing errors) can provide quite weak support for a model. We offer a number of suggestions for improving empirical tests and evidence that several proposed models do not work as well as originally advertised.

A Skeptical Appraisal of Asset Pricing Tests

It has become standard practice in the cross-sectional asset-pricing literature to evaluate models based on how well they explain average returns on size-B/M portfolios, something many models seem to do remarkably well. In this paper, we review and critique the empirical methods used in the literature. We argue that asset-pricing tests are often highly misleading, in the sense that apparently strong explanatory power (high cross-sectional R2s and small pricing errors) in fact provides quite weak support for a model. We offer a number of suggestions for improving empirical tests and evidence that several proposed models don't work as well as originally advertised.