Information in the Term Structure of Yield Curve Volatility

Using a novel no‐arbitrage model and extensive second‐moment data, we decompose conditional volatility of U.S. Treasury yields into volatilities of short‐rate expectations and term premia. Short‐rate expectations become more volatile than premia before recessions and during asset market distress. Correlation between shocks to premia and shocks to short‐rate expectations is close to zero on average and varies with the monetary policy stance. While Treasuries are nearly unexposed to variance shocks, investors pay a premium for hedging variance risk with derivatives. We illustrate the dynamics of the yield volatility components during and after the financial crisis.     

A Required Yield Theory of Stock Market Valuation and Treasury Yield Determination

Stock market valuation and Treasury yield determination are consistent with the Fisher effect (1896) as generalized by Darby (1975) and Feldstein (1976) . The U.S. stock market (S&P 500) is priced to yield ex-ante a real after-tax return directly related to real long-term GDP/capita growth (the required yield ). Elements of our theory show that: (1) real after-tax Treasury and S&P 500 forward earnings yields are stationary processes around positive means; (2) the stock market is indeed priced as the present value of expected dividends with the proviso that investors are expecting fast mean reversion of the S&P 500 nominal growth opportunities to zero. Moreover, (3) the equity premium is mostly due to business cycle risk and is a direct function of below trend expected productivity, where productivity is measured by the growth in book value of S&P 500 equity per-share. Inflation and fear-based risk premia only have a secondary impact on the premium. The premium is always positive or zero with respect to long-term Treasuries. It may be negative for short-term Treasuries when short-term productivity outpaces medium and long run trends. Consequently: (4) Treasury yields are mostly determined in reference to the required yield and the business cycle risk premium; (5) the yield spread is largely explained by the differential of long-term book value per share growth vs. near term growth, with possible yield curve inversions. Finally, (6) the Fed model is partially validated since both the S&P 500 forward earnings yield and the ten-year Treasury yield are determined by a common factor: the required yield.     

The increasing default risk of US Treasury securities due to the financial crisis

This paper examines the impact of the current financial crisis on long-term US Treasury yields by testing the impact of a series of events from December 2007 to March 2009 on the spread between 10-year USD LIBOR swap and 10-year US Treasury (constant maturity) rates to measure risk associated with Treasuries. Controlling for the liquidity of the two markets, the default risk of the swap, and the net foreign purchases of Treasury securities, we find that 13 of the tested 20 events have significantly negative coefficients. We conclude that the lower spread is consistent with greater default risk for US Treasury securities.     

Aggregate earnings and stock market returns: The good,the bad,and the state-dependent

Prior research documents a negative aggregate earnings-returns relation. In contrast, we posit that the sign of the relation varies, depending upon the macroeconomic and financial market conditions that exist in the earnings announcement quarter. We argue that the existing macroeconomic and financial market conditions influence market participants’ frame of reference, which in turn affects whether they interpret aggregate earnings surprises to be informative about the expected inflation component of the discount rate, the market risk premium component of the discount rate, or aggregate future cash flows. Consistent with this, we find that the sign of the aggregate earnings-returns relation changes numerous times across our sample period. We also find that market participants interpret aggregate earnings to be informative about changes in expected inflation (market risk premium) when the sign of the aggregate earnings-returns relation is negative (positive). Finally, we identify macroeconomic and financial market conditions under which the aggregate earnings-returns relation is more (less) likely to be negative (positive).     

Economic determinants of the nominal treasury yield curve

Macroeconomic shocks account for most of the variability of nominal Treasury yields, inducing parallel shifts in the level of the yield curve. We develop a new approach to identifying macroeconomic shocks that exploits model-based empirical shock measures. Technology shocks shift yields through their effect on expected inflation and the term premium. Shocks to preferences for current consumption affect yields through their impact on real rates and expected inflation. For both shocks, the systematic reaction of monetary policy is an important transmission pathway. We find little evidence that fiscal policy shocks are an important source of interest rate variability.     

Inflation ambiguity and the term structure of U.S. Government bonds

Variations in trend inflation are the main driver for variations in the nominal yield curve. According to empirical data, investors observe a set of empirical models that could all have generated the time-series for trend inflation. This set has been large and volatile during the 1970s and early 1980s and small during the 1990s. I show that log utility together with Knightian uncertainty about trend inflation can explain the term premium in U.S. Treasury bonds. The equilibrium has two inflation premiums, an inflation risk premium and a Knightian inflation ambiguity premium.     

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.     

Inflation Expectations and Risk Premiums in an Arbitrage‐Free Model of Nominal and Real Bond Yields

Differences between yields on comparable‐maturity U.S. Treasury nominal and real debt, the so‐called breakeven inflation (BEI) rates, are widely used indicators of inflation expectations. However, better measures of inflation expectations could be obtained by subtracting inflation risk premiums (IRP) from the BEI rates. We provide such decompositions using an affine arbitrage‐free model of the term structure that captures the pricing of both nominal and real Treasury securities. Our empirical results suggest that long‐term inflation expectations have been well anchored over the past few years, and IRP, although volatile, have been close to zero on average.     

中国市场利率流动性溢酬实证分析

市场利率的流动性溢酬(liquiditypremium),也称为期限溢酬(termpremium),是为了弥补投资者投资于长期证券所承担的额外利率波动风险(Hicks,1942)。这种风险一般随着期限的延长而增加,因此,相应的流动性溢酬也要随着期限的延长而增加。本文在郑振龙、林海(2003)对中国利率期限结构的静态估计的基础之上,通过一个直接的通用模型对中国市场利率的流动性溢酬进行了实证考察和分析,这个模型直接使用总收益率而不是利率的概念,从而就可以避免Nelson(1972)所提出的问题,而且没有对利率的分布做任何假定。同时为了比较分析不同期限的流动性溢酬,这个模型还进行了标准化处理。检验结果表明,中国存在比较明显的流动性溢酬,而且这个流动性溢酬水平随着期限的延长而上升。而且,通过对流动性溢酬随时间变动情况的分析,发现不同期限的流动性溢酬都随时间变动,因此常数流动性溢酬假设就被拒绝。     

Noise as Information for Illiquidity

We propose a market‐wide liquidity measure by exploiting the connection between the amount of arbitrage capital in the market and observed “noise” in U.S. Treasury bonds—the shortage of arbitrage capital allows yields to deviate more freely from the curve, resulting in more noise in prices. Our noise measure captures episodes of liquidity crises of different origins across the financial market, providing information beyond existing liquidity proxies. Moreover, as a priced risk factor, it helps to explain cross‐sectional returns on hedge funds and currency carry trades, both known to be sensitive to the general liquidity conditions of the market.     

Understanding liquidity and credit risks in the financial crisis

This paper develops a structured dynamic factor model for the spreads between London Interbank Offered Rate (LIBOR) and overnight index swap (OIS) rates for a panel of banks. Our model involves latent factors which reflect liquidity and credit risk. Our empirical results show that surges in the short term LIBOR-OIS spreads during the 2007-2009 financial crisis were largely driven by liquidity risk. However, credit risk played a more significant role in the longer term (twelve-month) LIBOR-OIS spread. The liquidity risk factors are more volatile than the credit risk factor. Most of the familiar events in the financial crisis are linked more to movements in liquidity risk than credit risk.     

The Relation Between Default-Free Interest Rates and Expected Economic Growth Is Stronger Than You Think

The relation between default-free interest rates and expected economic growth is substantially stronger than suggested by extant literature. Futures-implied Treasury bill yield spreads are more highly correlated with future real consumption, investment, and GNP growth than spot spreads. This stronger relation arises because using futures removes a component of the spot term structure that covaries negatively with real economic growth. Treasury forward rates from spot bills contain a premium for the risk that short-sellers will default. This risk premium is negatively related to expected economic growth.     

Estimating the Equity Risk Premium and Expected Equity Rates of Return: The Case of Canada

It is common to use the average excess return of equities over bonds estimated over long time periods as an expected equity risk premium on the grounds that going back far enough covers most possible economic scenarios. But although this data is useful in guiding the exercise of judgment, it cannot substitute for judgment. Adding more years of data to the near century of Canadian stock and bond returns that inform today's estimate of the equity risk premium will not produce a “random walk” for a simple reason: the historic bond series is the result of a specific historic monetary policy. This is particularly true of and important for the case of Canada, where today's very low current bond yields reflect the emergence of the Canadian dollar as a reserve currency as well as the impact of unconventional monetary policy elsewhere. After analyzing the historic record of the Canadian equity risk premium and noting the need for adjustments when this premium is applied to the current anomalously low Canadian long‐term bond yields, the author reaches the following conclusions:

• The historic Canadian equity risk premium is approximately 5.0% (based on arithmetic returns), which is slightly lower than the roughly 6.0% value for the U.S.
• The historic equity risk premium has not been constant because of obvious changes in the Canadian bond market. To some extent, the huge cycle in which bond yields began their increase from the 4.0% level starting in 1957, when markets were liberalized, and then fell back to the 4.0% level in 2007‐2008 completed an adjustment to changes in fiscal versus monetary policy. However, in 2016, average long Canada bond yields dropped to an anomalously low 1.8%, which is below the long‐term inflation target of the Bank of Canada, and have barely recovered since. It is difficult to view this as an equilibrium rate determined by private investors.
• Of the drop in bond yields, about 0.50% is unique to Government of Canada bonds as they became attractive to sovereign investors as a rare AAA‐rated issuer.
• Using an indicator variable for the post‐2010 years, a simple regression analysis indicates that current long Canada bond yields should be about 2.75% higher but for the recent changes. And for 2018, this means that the 2.35% average long Canada bond yield should have been about 5.0%. Apart from the impact of higher government deficits, this is consistent with average yields before the 2008 financial crisis.
• Adding an adjusted 5.0% long Canada bond yield to the historic equity risk premium in Canada of 4.50% gives 9.50% for the cost of the overall equity market or, given the Bank of Canada's target inflation rate of 2.0%, a real equity return of 7.5%, both slightly higher than the long‐run averages.

In sum, the conventional practice of adding a historic market risk premium to the current low Canada long bond yields would impart a sharp downward bias to current equity cost estimates; use of this method would not be appropriate until long Canada bond yields increase to at least the 4.0% level.     

On the Structural Interpretation of the Smets–Wouters “Risk Premium” Shock

This article shows that the “risk premium” shock in Smets and Wouters (2007) can be interpreted as a structural shock to the demand for safe and liquid assets such as short‐term U.S. Treasury securities. Several implications of this interpretation are discussed.     

Inflation and the stock market: Understanding the “Fed Model”

The so-called Fed model postulates that the dividend or earnings yield on stocks should equal the yield on nominal Treasury bonds, or at least that the two should be highly correlated. In US data there is indeed a strikingly high time series correlation between the yield on nominal bonds and the dividend yield on equities. This positive correlation is often attributed to the fact that both bond and equity yields comove strongly and positively with expected inflation. Contrary to some of the extant literature, we show that this effect is consistent with modern asset pricing theory incorporating uncertainty about real growth prospects and habit-based risk aversion. In the US, high expected inflation has tended to coincide with periods of heightened uncertainty about real economic growth and unusually high risk aversion, both of which rationally raise equity yields.     

Short-term determinants of the idiosyncratic sovereign risk premium: A regime-dependent analysis for European credit default swaps

This study investigates the dynamics of the sovereign CDS term premium, i.e. difference between 10Y and 5Y CDS spreads. It can be regarded a forward-looking measure of idiosyncratic sovereign default risk as perceived by financial markets. For some European countries this premium featured distinct nonstationary and heteroskedastic pattern during the last years. Using a Markov-switching unobserved component model, we decompose the daily CDS term premium of five European countries into two unobserved components of statistically different nature and link them in a vector autoregression to various daily observed financial market variables. We find that such decomposition is vital for understanding the short-term dynamics of this premium. The strongest impacts can be attributed to CDS market liquidity, local stock returns, and overall risk aversion. By contrast, the impact of shocks from the sovereign bond market is rather muted. Therefore, the CDS market microstructure effect and investor sentiment play the main roles in sovereign risk evaluation in real time. Moreover, we also find that the CDS term premium response to shocks is regime-dependent and can be ten times stronger during periods of high volatility.     

Treasury Safety,Liquidity, and Money Premium Dynamics: Evidence from Debt Limit Impasses

Treasury securities enjoy a “money premium” because they are ultra-safe and liquid. However, during debt limit impasses, the safety and liquidity of Treasury securities temporarily deteriorate, eroding the money premium. Using past impasses, we find the money premium eroded by roughly six basis points across all Treasury securities and up to 50 basis points for the shortest maturities at the greatest risk of a delayed principal payment. Safety and liquidity each accounted for about half of the erosion. The deterioration of safety and liquidity also appears to interact, consistent with theories of default-driven liquidity risk and the information sensitivity of debt.     

Consumption risk and the cross-section of government bond returns

In this paper we provide a consumption-based explanation of risk in nominal US Treasury bond portfolios. We use a consumption-CAPM with Epstein–Zin–Weil recursive preferences. Our model introduces two sources of risk: uncertainty about current consumption (reflected in contemporaneous consumption growth) and uncertainty about prospects of consumption in a long run (reflected in innovations to expectations about future consumption growth). We use a novel approach to estimate pricing factors in our model: we employ a factor-augmented VAR model with common factors, extracted from a large panel of macroeconomic and financial data, as state variables. We find that the important source of risk in US bonds is related to uncertainty in prospects in future consumption and it induces a positive and significant risk premium. We find as well that covariance risk related to innovations in expectations about future consumption growth is greater for long term bond portfolios than for short term bond portfolios, which is consistent with a duration measure of risk and justifies why long term bonds require greater premium than short term bonds. Our model explains well the cross-sectional variation in average excess returns of bonds with different maturities over the period 1975–2011 and compares favorably with competing models.     

The seeds of a crisis: A theory of bank liquidity and risk taking over the business cycle

We examine how the banking sector could ignite the formation of asset price bubbles when there is access to abundant liquidity. Inside banks, to induce effort, loan officers are compensated based on the volume of loans. Volume-based compensation also induces greater risk taking; however, due to lack of commitment, loan officers are penalized ex post only if banks suffer a high enough liquidity shortfall. Outside banks, when there is heightened macroeconomic risk, investors reduce direct investment and hold more bank deposits. This ‘flight to quality’ leaves banks flush with liquidity, lowering the sensitivity of bankers’ payoffs to downside risks and inducing excessive credit volume and asset price bubbles. The seeds of a crisis are thus sown.     

A liquidity-augmented capital asset pricing model

Using a new measure of liquidity, this paper documents a significant liquidity premium robust to the CAPM and the Fama–French three-factor model and shows that liquidity is an important source of priced risk. A two-factor (market and liquidity) model well explains the cross-section of stock returns, describing the liquidity premium, subsuming documented anomalies associated with size, long-term contrarian investment, and fundamental (cashflow, earnings, and dividend) to price ratios. In particular, the two-factor model accounts for the book-to-market effect, which the Fama–French three-factor model fails to explain.