Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums

Empirical studies of bond and commercial mortgage performance often quantify a required risk premium by examining the difference between the promised yield and the realized yield as adjusted for default occurrence. These studies omit the effects of various other sources of risk, however, including collateral asset market risk, interest rate risk, and possibly call risk. These omissions downwardly bias the empirical risk premium estimate on the debt. In this paper, we disentangle and quantify the sources of this bias by modeling secured coupon debt (the commercial mortgage) as used in the calculation of a realized investment return. We consider deterministic and stochastic interest rate economies with mortgage contracts that are either noncallable or subject to a temporary prepayment lockout period. Given realistic parameter values associated with the term structure, underlying asset dynamics, and debt contracting, we show that the magnitude of the bias can be significant.     

交易所国债期限风险溢价的实证研究

本文考察了上海证券交易所国债期限风险溢价的时间变化特征及决定因素。实证结果显示，债券剩余期限越长，平均风险溢价越高；通过对不同期限债券组合的风险溢价序列建立回归模型，发现长短期利差及风险溢价的前期值对中长期债券期限风险溢价的时变性具有明显的解释能力。     

Term premium dynamics in an emerging market: Risk,liquidity, and behavioral factors

This paper contributes to the fixed income research by identifying determinants of term premium in an emerging market’s treasury bond yields with particular attention on ambiguity. We use Nelson–Siegel yield curves generated from daily bond price quotes as input to construct a three-factor affine term structure model which decomposes observed yields into risk-neutral and term premium components. We also construct an ambiguity index using intraday FX return data following Brenner and Izhakian (2018). Our analyses suggest that a combination of factors representing market risk, credit risk, liquidity, ambiguity, and investor sentiments can explain majority of the variation in term premia. Explanatory power of credit risk measures are found to increase while those of volatility, ambiguity, and sentiment measures diminish with the maturity horizon. The results imply that ambiguity aversion of bond investors is a major determinant of the shape of the yield curve as it drives the premia for short end of the yield curve lower in line with the expectation of flight-to-safety behavior.     

A consumption-based model of the term structure of interest rates

This paper proposes a consumption-based model that accounts for many features of the nominal term structure of interest rates. The driving force behind the model is a time-varying price of risk generated by external habit. Nominal bonds depend on past consumption growth through habit and on expected inflation. When calibrated to data on consumption, inflation, and the aggregate market, the model produces realistic means and volatilities of bond yields and accounts for the expectations puzzle. The model also captures the high equity premium and excess stock market volatility.     

Implied liquidity risk premium in the term structure of sovereign credit default swap and bond spreads

In this study, we focus on the dynamic properties of the risk-neutral liquidity risk premium specific to the sovereign credit default swap (CDS) and bond markets. We show that liquidity risk has a non-trivial role and participates directly to the variation over time of the term structure of sovereign CDS and bond spreads for both the pre- and crisis periods. Secondly, our results indicate that the time-varying bond and CDS liquidity risk premium move in opposite directions which imply that when bond liquidity risk is high, CDS liquidity risk is low (and vice versa), which may in turn be consistent with the substitution effect between CDS and bond markets. Finally, our Granger causality analysis reveals that, although the magnitude of bond and CDS liquidity risk is substantially different, there is a strong liquidity flow between the CDS and the bond markets, however, no market seems to consistently lead the other.     

Macroeconomic Sources of Risk in the Term Structure

We develop a new way of modeling time variation in term premia, based on the stochastic discount factor model of asset pricing. The joint distribution of excess U.S. bond returns of different maturity and the observable fundamental macroeconomic factors is modeled using multivariate GARCH with conditional covariances in the mean to capture the term premia. By testing the assumption of no arbitrage we derive a specification test of our model. We estimate the contribution made to the term premia at different maturities through real and nominal sources of risk. From the estimated term premia we recover the term structure of interest rates and examine how it varies through time. Finally, we examine whether the reported failures of the rational expectations hypothesis can be attributed to an omitted time-varying term premium.     

The rise of risk-based pricing of mortgage interest rates in Italy

This paper assesses how much mortgage interest rates in Italy are priced on credit risk as proxied by the probability of household mortgage delinquency estimated using the EU-Silc database. Owing to data availability, we restrict the analysis of mortgage pricing to Italian households. Consistent with the more widespread use of credit scoring, estimates indicate that Italian lenders have increasingly priced mortgage interest rates on household credit risk. For mortgages granted between 2000 and 2007, we find that a 1% point increase in the probability of default is associated with a 21 basis point rise in mortgage interest rates, lower than the 38 basis point premium Edelberg (2006) estimated for the US at the end of the 1990s.     

Financial literacy,present bias and alternative mortgage products

Choosing a mortgage is one of the most important financial decisions made by a household. Financial innovation has given rise to more complex mortgage products with back-loaded payments, known as ‘Alternative Mortgage Products’ (AMPs), or ‘Interest-Only Mortgages’. Using a specially designed question module in a representative survey of UK mortgage holders, we investigate the effect of consumer financial sophistication on the decision to choose an AMP instead of a standard repayment mortgage. We show poor financial literacy and present bias raise the likelihood of choosing an AMP. Financially literate individuals are also more likely to choose an Adjustable Rate Mortgage (ARM), suggesting they avoid paying the term premium of a fixed rate mortgage.     

Inflation risk premia and the expectations hypothesis

We study the properties of the nominal and real risk premia of the term structure of interest rates. We develop and solve the bond pricing implications of a structural monetary version of a real business cycle model, with taxes and endogenous monetary policy. We show the relation of this model with the class of essentially affine models that incorporate an endogenous state-dependent market price of risk. We characterize and estimate the inflation risk premium and find that over the last 40 years the ten-year inflation risk premium has been has averaged 70 basis points. It is time-varying, ranging from 20 to 140 basis points over the business cycle and its term structure is sharply upward sloping. The inflation risk premium explains 23% (42%) of the time variation in the five (ten)-year forward risk premium and it plays an important role in help explain deviations from the expectations hypothesis of interest rates.     

The Variation of Economic Risk Premiums in Real Estate Returns

We examine the predictable components of returns on stocks, bonds, and real estate investment trusts (REITs). We employ a multiple-beta asset pricing model and find that there are varying degrees of predictability among stocks, bonds, and REITs. Furthermore, we find that most of the predictability of returns is associated with the economic variables employed in the asset pricing model. The stock market risk premium is highly important in capturing the predictable variation in stock portfolios, and the bond market risk premiums (term and risk structure of interest rates) are important in capturing the predictable variation in bond portfolios. For REITs, however, both the stock and bond market risk premiums capture the predictable variation in returns. REITs have comparable return predictability to stock portfolios. We conclude that there is an important economic risk premium for REITs that are not captured by traditional multiple-beta asset pricing models.     

Payout yield,risk, and mispricing: A Bayesian analysis

We develop a simple parametric model in which hypotheses about predictability, mispricing, and the risk-return tradeoff can be evaluated simultaneously, while allowing for time variation in both risk and expected return. Most of the return predictability based on aggregate payout yield is unrelated to market risk. We consider a range of Bayesian prior beliefs about the risk-return tradeoff and the extent to which predictability is driven by mispricing. The impact of these beliefs on an investor's certainty-equivalent return when choosing between a market index and riskless T-bills is economically significant, in both ex ante and out-of-sample analyses.     

Mortgage convexity

Most home mortgages in the United States are fixed-rate loans with an embedded prepayment option. When long-term rates decline, the effective duration of mortgage-backed securities (MBS) falls due to heightened refinancing expectations. I show that these changes in MBS duration function as large-scale shocks to the quantity of interest rate risk that must be borne by professional bond investors. I develop a simple model in which the risk tolerance of bond investors is limited in the short run, so these fluctuations in MBS duration generate significant variation in bond risk premia. Specifically, bond risk premia are high when aggregate MBS duration is high. The model offers an explanation for why long-term rates could appear to be excessively sensitive to movements in short rates and explains how changes in MBS duration act as a positive-feedback mechanism that amplifies interest rate volatility. I find strong support for these predictions in the time series of US government bond returns.     

Term structure determinants of time-varying risk of 1-year bond returns

Term structure drivers of 1-year bond premia and conditional bond return risk are distinct. Consequently, the Cochrane–Piazzesi factor captures aggregate price of risk and not the amount of risk in 1-year bond returns. One linear combination of forward rates captures most of the variation in bond return risk across maturities. Interest rate level captures substantial amount of variation in the conditional return risk, a finding consistent with rising inflation uncertainty with level of inflation and interest rates. The 4-5 yield spread, an important positive predictor of bond return premia, has an opposing but limited impact on the conditional volatility.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

Pricing the term structure with linear regressions

We show how to price the time series and cross section of the term structure of interest rates using a three-step linear regression approach. Our method allows computationally fast estimation of term structure models with a large number of pricing factors. We present specification tests favoring a model using five principal components of yields as factors. We demonstrate that this model outperforms the Cochrane and Piazzesi (2008) four-factor specification in out-of-sample exercises but generates similar in-sample term premium dynamics. Our regression approach can also incorporate unspanned factors and allows estimation of term structure models without observing a zero-coupon yield curve.     

Can hedging tell the full story? Reconciling differences in United States aggregate- and industry-level exchange rate risk premium

While the importance of currency movements to industry competitiveness is theoretically well established, there is little evidence that currency risk impacts US industries. Applying a conditional asset pricing model to 36 US industries, we find that all industries have a significant currency premium that adds about 2.47 percentage points to the cost of equity and accounts for approximately 11.7% of total risk premium in absolute value. Cross-industry variation in the currency premium is explained by foreign income, industry competitiveness, leverage, liquidity, and other industry characteristics, while its time variation is explained by US aggregate foreign trade, monetary policy, growth opportunities, and other macro variables. The results indicate that methodological weakness, not hedging, explains the insignificant industry currency risk premium found in previous work, thus resolving the puzzle that currency risk premium is important at the aggregate stock market level, but not at the industry level.     

Time-varying risk premium yield spread effect in term structure and global financial crisis: Evidence from Europe

The global financial crisis had a significant effect on the interest rates and the term structure of interest rates around the globe. In this paper we apply the GARCH-in-mean (GARCH-M) to study the effect of the global financial crisis on the term structure volatility, persistence of volatility, risk premium, and effects of the yield spread in five European markets; Portugal, Ireland, Italy, Greece and Spain (PIIGS). To the best of our knowledge this is the first such study in the field, and thus represents the main contribution of the paper to the literature. We investigate both the longer end and the shorter end of the term structure. We study two versions of the longer end based on the 10-year bond (long-term rate) and the two short-term rates, (three- and six-month rates). The shorter end of the term structure is based on the two short-term rates. Results indicate a substantial change in the term structure volatility, persistence of volatility, risk premium, and the effects of the yield spread due to the financial crisis. These results are found for both the longer end and the shorter end versions of the term structure.     

A Defense of Traditional Hypotheses about the Term Structure of Interest Rates

Expectations theories of asset returns may be interpreted either as stating that risk premia are zero or that they are constant through time. Under the former interpretation, different versions of the expectations theory of the term structure are inconsistent with one another, but I show that this does not necessarily carry over to the constant risk premium interpretation of the theory. I present a general equilibrium example in which different types of risk premium are constant through time and dependent only on maturity. Furthermore, I argue that differences among expectations theories are second-order effects of bond yield variability. I develop an approximate linearized framework for analysis of the term structure in which these differences disappear, and I test its accuracy in practice using data from the CRSP government bond tapes.     

Household Income, Termination Risk and Mortgage Pricing

The premium embedded in home mortgage loans to compensate investors for their exposure to prepayment risk is a significant component of the cost of home mortgage lending. Moreover, there is some reason to believe that prepayment risk may be lower for loans to lower-income housing borrowers, especially those that are first-time home owners. If so, investor recognition of this advantage should facilitate greater willingness to acquire portfolios of lower-income housing loans, and encourage more competitive pricing in this segment of the market. This study investigates the possibility of differential mortgage prepayment behavior between lower-income home owners and non-low income home owners. The investigation relies on samples of the American Housing Survey spanning ten years of experience from 1985 to 1995. We find no significant difference between the termination or refinancing behavior of non-low income and low-income households. This result is robust to a number of alternative specifications such as restricting the low-income test group to non-moving households and to first-time owners. The same conclusions are derived from both aggregate prepayment rates and from analysis of individual household prepayment behavior.     

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.