Slope Of Term Structure Research Articles

Modeling Conditional Factor Risk Premia Implied by Index Option Returns

ABSTRACTWe propose a novel factor model for option returns. Option exposures are estimated nonparametrically, and factor risk premia can vary nonlinearly with states. The model is estimated using regressions with minimal assumptions on factor and option return dynamics. We estimate the model using index options to characterize the conditional risk premia for factors of interest, such as the market return, market variance, tail and intermediary risk factors, higher moments, and the VIX term structure slope. Together, market return and variance explain more than 90% of option return variation. Unconditionally, the magnitude of the variance risk premium is plausible. It displays pronounced time variation, spikes during crises, and always has the expected sign.

Bonds, Currencies and Expectational Errors

We propose a model in which sticky expectations concerning short-term interest rates generate joint predictability patterns in bond and currency markets. Our parsimonious specification can explain the downward sloping term structure of carry trade returns, difficult to replicate in a rational expectations framework. We offer empirical support for our approach and show that including a sticky short rate expectations channel into a standard affine term structure allows the model to better capture the drift patterns in the data.

The Term Structure of Short Selling Costs

Abstract Short sellers care about (i) how overvalued an asset is and (ii) when the overvaluation will be corrected. Hence, short selling costs should be higher over horizons when negative information is more likely to arrive. This article presents a model formalizing this intuition and tests the model using the put–call parity condition. Forward shorting costs predict future costs and stock returns, consistent with an expectations hypothesis in the shorting market. Additionally, an upward sloping term structure around earnings announcements increases the probability of a negative earnings surprise, evidence that short selling costs are higher over horizons when negative information is more likely to arrive. My findings suggest that the term structure of short selling costs conveys how long overpricings are expected to persist.

Regime-dependent drivers of the EUR/CHF exchange rate

We analyze drivers of the EUR/CHF exchange rate in different regimes between 2000 and 2020. Structural breaks between these subperiods are estimated in an integrated way together with the drivers that are relevant during these subperiods. Overall, the main drivers of the exchange rate include European equity and volatility indices, interest rate and term structure slope differentials, as well as monetary policy interventions. For the “peg period” September 2011–January 2015, in addition to the observed exchange rate we also analyze the drivers of the latent exchange rate that could have been observed in the absence of the peg. Interestingly, the SNB’s foreign currency investments became a significant driver of the EUR/CHF exchange rate only after the end of the peg period when there was no longer an officially communicated target rate.

US macroeconomic surprises and the emerging‐market sovereign CDS market

AbstractOur primary aim is to examine whether US macroeconomic surprises affect the slope of the term structure of ‘sovereign credit default swap’ (SCDS) spreads in emerging markets. Our empirical results show that positive (negative) US macroeconomic surprises are likely to reduce (increase) the term structure slope of SCDS spreads in emerging countries. We find that the slope values in emerging markets are positively related to future market returns over 1‐ and 2‐day horizons. Our results provide general support for the future informational role played by SCDS spreads for the national stock market within emerging markets.

What is the expected return on Bitcoin? Extracting the term structure of returns from options prices

We infer the forward-looking Bitcoin risk premium from options contracts. Using data from 2018 to 2020, we show that the expected excess returns for Bitcoin are time-varying and significantly higher than in equities or gold, averaging almost 80% per annum. A temporal analysis of the term structure of Bitcoin risk premia reveals an upward sloping term structure during Bitcoin bull markets and downward sloping during Bitcoin bear markets.

Stock valuation during the COVID-19 pandemic: An explanation using option-based discount rates

Changes in short-term expected market returns (discount rates) were a significant driver behind the unprecedented fluctuations in equity markets during the first 4 months of the COVID-19 pandemic. Using option-based estimates of the expected market risk premium for 13 international markets, we find that approximately 40% of the change in market values during the COVID-19 pandemic can be attributed to changes in short-term discount rates. We also document sharply downward sloping term structures of equity risk premia at the start of the pandemic, consistent with Hasler and Marfè (2016). Finally, we document a significant increase in the correlation between index returns and changes in the short-term discount rate during the pandemic compared to the period before the pandemic.

The term structure of equity risk premia

We estimate a regime-switching model for the equity term structure with Bayesian methods. Our approach accounts for the data sample being unrepresentative of the population distribution of regimes. We find that (i) the term structure of expected equity dividend strip returns is downward sloping in recessions and upward sloping in expansions, and (ii) the unconditional term structure of expected equity returns is positively sloped. Our estimation shows that the sample unrepresentativeness induces a downward bias in the estimate of the equity term structure slope. We present a regime-switching consumption-based asset-pricing model that matches the empirical findings.

The Implied Equity Term Structure

We propose a new methodology to estimate the equity term structure, based on the cross-section of stock prices and the implied cost of capital approach. Specifically, instead of focusing on the realized returns of maturity-specific dividend assets, we imply the term structure of expected returns based on the observed market prices and projected firm-level cash flows. Using US data for 1976-2019, we find an unconditionally upward sloping term structure of risk premia with rich cross-sectional patterns. Namely, large and growth firms exhibit an upward sloping term structure, whereas the smallest and value firms mostly have a downward sloping term structure. We also detect that the slope of the term structure changes from negative to positive in the late 1990s for the largest firms, as well as that the slope tends to flatten out or even invert in recessions. Thus, using a direct measure of ex-ante returns, we are able to provide new evidence on the debated properties of the equity term structure.

What Is the Expected Return on Bitcoin? Extracting the Term Structure of Returns from Options Prices

We infer the forward-looking Bitcoin risk premium from options contracts. Using data from 2018 to 2020, we show that the expected excess returns for Bitcoin are time-varying and significantly higher than in equities or gold, averaging almost 80% per annum. A temporal analysis of the term structure of Bitcoin risk premia reveals an upward sloping term structure during Bitcoin bull markets and downward sloping during Bitcoin bear markets.

The Effects of US Macroeconomic Surprises on the Term Structure of Emerging-market Sovereign Credit Default Swaps

Our primary aim in this study is to examine whether US macroeconomic surprises affect the slope of the term structure of national ‘sovereign credit default swap’ (SCDS) spreads in the emerging markets, with our empirical results revealing that positive (negative) US macroeconomic surprises are likely to reduce (increase) the term structure slope of SCDS spreads in the emerging countries. We find that a 1% increase in the slope value of SCDS term structures forecasts a reduction in annual GDP growth at an average rate of 0.0035%, with the slope values in the emerging markets being positively related to future market returns over one-, three- and six-month horizons. Following adjustment by the three global factors of Fama-French (1993), a monthly long-short rebalancing portfolio based upon SCDS slopes in the emerging markets is found to generate an average monthly return of 1.60%. Our results provide general support for the future informational role played by SCDS slopes for national economies within the emerging markets.

Greek-based Bond Factors

The scaled bond Greeks, i.e., the absolute values of the price-scaled derivatives of bond prices with respect to yield, are the relevant characteristics for bond pricing. Two factors---the exposures to which are duration and convexity---explain 99.5% of the total variation in bond yields. A duration (convexity) factor earns a positive (negative) and highly significant premium. The corresponding Sharpe ratios on each factor are comparable in absolute value to that of the equity market. The convexity factor is negatively related to the term structure slope, and its premium can be interpreted as compensation for protection against an increased probability of a recession. Our results also provide explanations for the well-known inverse relation between bond Sharpe ratios and time to maturity as well as the concave shape of the term structure of bond risk premia.

The Price of the Smile and Variance Risk Premia

Using a new specification of multifactor volatility, we estimate the hidden risk factors spanning S&P 500 index (SPX) implied volatility surfaces and the risk premia of volatility-sensitive payoffs. SPX implied volatility surfaces are well-explained by three dependent state variables reflecting (i) short- and long-term implied volatility risks and (ii) short-term implied skewness risk. The more persistent volatility factor and the skewness factor support a downward sloping term structure of variance risk premia in normal times, whereas the most transient volatility factor accounts for an upward sloping term structure in periods of distress. Our volatility specification based on a matrix state process is instrumental to obtaining a tractable and flexible model for the joint dynamics of returns and volatilities, which improves pricing performance and risk premium modeling with respect to recent three-factor specifications based on standard state spaces. This paper was accepted by Gustavo Manso, finance.

Bonds, Currencies and Expectational Errors

We propose a model in which sticky expectations concerning short-term interest rates generate joint predictability patterns in bond and currency markets. Using our calibrated model, we quantify the effect of this channel and find that it largely explains why short rates and yield spreads predict bond and currency returns. The model also creates the downward sloping term structure of carry trade returns documented by Lustig et al. (2019), difficult to replicate in a rational expectations framework. Consistent with the model, we find that variables that predict bond and currency returns also predict survey-based expectational errors concerning interest and FX rates. The model explains why monetary policy induces drift patterns in bond and currency markets and predicts that long-term rates are a better gauge of market’s short rate expectations than previously thought.

Moody and Dissatisfied: A Possible Resolution of Asset Pricing Puzzles

Recent microeconomic evidence suggests that risk aversion is largely determined by the changes in the state of the economy and mostly insensitive to the fluctuations in idiosyncratic wealth. I propose a consumption-based asset pricing model that is consistent with this evidence and capable of explaining various stylized facts about the U.S. stock market. In the model, agents have a power-utility type instantaneous utility function whose curvature explicitly depends on a stationary macroeconomic state variable. The model can produce a high equity risk premium with a low, stable and wealth-insensitive relative risk aversion if the utility curvature is mildly countercyclical (i.e., if the agents are mildly moody) and consumption is sufficiently smaller than a predetermined benchmark (i.e., if the agents are sufficiently dissatisfied) at the steady state. It also gives a low and stable risk-free rate, procyclical price-dividend ratio, countercylical risk premium and price of risk, return predictability, an upward sloping real yield curve and a downward sloping equity term structure.

Decomposing the Term Structure of Interests Rates: Evidence from a Small Open Economy

This paper uses Israeli data of inflation-indexed and nominal government bonds to estimate a discrete-time essentially affine term structure model. To estimate the model, I use a uniquely long-spanned sample of monthly real yields for the period of 01/1985-03/2018. The nominal yields data spans the period of 05/2001-03/2018. I document an unconditional upward sloping real term structure that the model ascribes to a rising real term premium while the average expected real short rates are relatively flat. A decomposition of the break-even inflation shows that the unconditional term structure of the inflation premium is increasing with maturity and most of the variance in the short end is due to expected inflation. However, in the long end, most of it is due to the inflation term premium.

Systematic Currency Volatility Risk Premia

I show that volatility risk of the dollar factor --- an equally weighted basket of developed U.S. dollar exchange rates --- carries a significant risk premium and that it is priced in the cross-section of currency volatility excess returns. The dollar factor volatility risk premium is negative on average with an upward sloping and concave term structure. Consistent with this pattern, I find that dollar factor volatility risk is most significantly priced in the cross-section of volatility excess returns at shorter maturities. A trading strategy that sells (buys) volatility insurance on currencies with high (low) exposure to dollar factor volatility risk delivers high mean excess returns and Sharpe ratios. At shorter maturities, the profitability of this strategy cannot be explained by exposure to traditional currency factors, equity factors, or currency volatility carry factors.

Long Forward Probabilities, Recovery, and the Term Structure of Bond Risk Premiums

We show that the martingale component in the long-term factorization of the stochastic discount factor due to Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) is highly volatile, produces a downward-sloping term structure of bond Sharpe ratios, and implies that the long bond is far from growth optimality. In contrast, the long forward probabilities forecast an upward sloping term structure of bond Sharpe ratios that starts from zero for short-term bonds and implies that the long bond is growth optimal. Thus, transition independence and degeneracy of the martingale component are implausible assumptions in the bond market.

Term Structure(s) of the Equity Risk Premium

By simultaneously using dividend and variance swap data, we show how the term structure of the equity risk premium varies over time and how its shape is affected by liquidity risk premia. The term structure is always positively sloped, while funding liquidity premia and betas explain the high unconditional returns for all dividend claims. Alphas for short-dated dividend claims are actually negative implying that their returns are too low, whereas alphas for long-dated claims seem to be positive. The term structure slope varies positively with the market risk premium, but it is never negative relative to the first contract -- due to the nearly zero risk premium in the first maturity -- and rarely hump-shaped in some empirical models. We show how the maturity term structure -- the risk premium for dividend strips with different maturities -- is connected to both the horizon term structure -- linked to the variance swap term structure -- and various funding liquidity measures. The risk premium is on average increasing with investment horizon, while the maturity risk premium depends primarily on the short-horizon risk premium, implying that short-horizon investors are the marginal ones. All our results hold in the US, the UK, Europe and Japan.

Asset Prices and No-Dividend Stocks

We develop a stationary model of the aggregate stock market featuring both dividend-paying and no-dividend stocks within a familiar, parsimonious consumption-based equilibrium framework. We find that such a simple feature leads to profound implications supporting several stock market empirical regularities that leading consumption-based asset pricing models have difficulty reconciling. We show that the presence of no-dividend stocks in the stock market leads to a lower correlation between the stock market return and aggregate consumption growth rate, a non-monotonic and even a negative relation between the stock market risk premium and its volatility, and a downward sloping term structure of equity risk premia. When we quantify these effects, we find them to be economically significant. We also find that no-dividend stocks command lower mean returns but have higher return volatilities and higher market betas than comparable dividend-paying stocks, consistently with empirical evidence. We provide straightforward intuition for all these results and the underlying economic mechanisms at play.