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Equity Volatility Term Premia
This paper estimates the term-structure of volatility risk premia for the stock market. Realized variance term premia are increasing in systematic risk and predict variance swap returns. Implied volatility term premia are decreasing in risk initially, but then increase at a lag, predicting VIX futures returns. By modeling the logarithm of realized variance, the paper derives a closed-form relationship between the prices of variance swaps and VIX futures. The model provides accurate pricing and highlights periods of dislocation between the index options and VIX futures markets. Term premia ...
Working Paper
Forecasting with Shadow-Rate VARs
Interest rate data are an important element of macroeconomic forecasting. Projections of future interest rates are not only an important product themselves, but also typically matter for forecasting other macroeconomic and financial variables. A popular class of forecasting models is linear vector autoregressions (VARs) that include shorter- and longer-term interest rates. However, in a number of economies, at least shorter-term interest rates have now been stuck for years at or near their effective lower bound (ELB), with longer-term rates drifting toward the constraint as well. In such an ...
Report
Anxiety in the face of risk
We model an ?anxious? agent as one who is more risk averse with respect to imminent risks than with respect to distant risks. Based on a utility function that captures individual subjects? behavior in experiments, we provide a tractable theory relaxing the restriction of constant risk aversion across horizons and show that it generates rich implications. We first apply the model to insurance markets and explain the high premia for short-horizon insurance. Then, we show that costly delegated portfolio management, investment advice, and withdrawal fees emerge as endogenous features and ...
Working Paper
Does the Yield Curve Predict Output?
Does the yield curve have the ability to predict output and recessions? At some times and in certain places, of course! But many details are matters of dispute: When and where does the yield curve predict successfully, which aspects of the curve matter most, and which economic forces account for the predictive ability? Over the years, an increasingly sophisticated set of tools, both statistical and theoretical, have addressed these issues. For the US, an inverted yield curve, particularly when the spread between the yield on 10-year and 3-month Treasuries becomes negative, has been a robust ...
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Option-implied term structures
This paper proposes a nonparametric sieve regression framework for pricing the term structure of option spanning portfolios. The framework delivers closed-form, nonparametric option pricing and hedging formulas through basis function expansions that grow with the sample size. Novel confidence intervals quantify term structure estimation uncertainty. The framework is applied to estimating the term structure of variance risk premia and finds that a short-run component dominates market excess return predictability. This finding is inconsistent with existing asset pricing models that seek to ...
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Horizon-Dependent Risk Aversion and the Timing and Pricing of Uncertainty
Inspired by experimental evidence, we amend the recursive utility model to let risk aversion decrease with the temporal horizon. Our pseudo-recursive preferences remain tractable and retain appealing features of the long-run risk framework, notably its success at explaining asset pricing moments. In addition, our model addresses two challenges to the standard model. Calibrating the agents’ preferences to explain the equity premium no longer implies an extreme preference for early resolutions of uncertainty. Horizondependent risk aversion helps resolve key puzzles in finance on the valuation ...
Discussion Paper
The Law of One Price in Equity Volatility Markets
Can option traders take a square root? Surprisingly, maybe not. This post shows that VIX futures prices exhibit significant deviations from their option-implied upper bounds—the square root of variance swap forward rates—thus violating the law of one price, a fundamental concept in economics and finance. The deviations widen during periods of market stress and predict the returns of VIX futures. Just as the stock market struggles with multiplication, the equity volatility market appears unable to take a square root at times.
Working Paper
Quantitative Easing and the Supply of Safe Assets: Evidence from International Bond Safety Premia
Through large-scale asset purchases, widely known as quantitative easing (QE), central banks around the world have affected the supply of safe assets by buying quasi-safe bonds in exchange for truly safe reserves. We examine the pricing effects of the European Central Bank’s bond purchases in the 2015-2021 period on an international panel of bond safety premia from four highly rated countries: Denmark, Germany, Sweden, and Switzerland. We find statistically significant negative effects for all four countries. This points to an important international spillover channel of QE programs to bond ...
Report
Betting against beta (and gamma) using government bonds
Purportedly consistent with ?risk parity? (RP) asset allocation, recent studies document compelling ?low risk? trading strategies that exploit a persistently negative relation between Sharpe ratios (SRs) and maturity along the U.S. Treasury (UST) term structure. This paper extends this evidence on betting against beta with government bonds (BABgov) in four respects. First, out-of-sample tests suggest that excess returns may have waned somewhat recently and that the pattern seems most pronounced for USTs given data on ten other previously unexamined government bond markets. Second, BABgov ...
Discussion Paper
Are Stocks Cheap? A Review of the Evidence
We surveyed banks, we combed the academic literature, we asked economists at central banks. It turns out that most of their models predict that we will enjoy historically high excess returns for the S&P 500 for the next five years. But how do they reach this conclusion? Why is it that the equity premium is so high? And more importantly: Can we trust their models?