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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
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 ...
Working Paper
The Benefit of Inflation-Indexed Debt: Evidence from an Emerging Bond Market
Portfolio diversification is as important to debt management as it is to asset management. In this paper, we focus on diversification of sovereign debt issuance through greater reliance on inflation-indexed bonds for a representative emerging economy, Colombia. Using an arbitrage-free dynamic term structure model of fixed-coupon and inflation-indexed bond prices, we account for inflation and liquidity risk premia and calculate the net benefit of issuing inflation-indexed bonds over nominal bonds. Our results suggest that the Colombian government could lower its funding costs by as much as ...
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
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
Term structures of asset prices and returns
We explore the term structures of claims to a variety of cash flows: U.S. government bonds (claims to dollars), foreign government bonds (claims to foreign currency), inflation-adjusted bonds (claims to the price index), and equity (claims to future equity indexes or dividends). Average term structures reflect the dynamics of the dollar pricing kernel, of cash flow growth, and of their interaction. We use simple models to illustrate how relationships between the two components can deliver term structures with a wide range of levels and shapes.
Report
Global variance term premia and intermediary risk appetite
Sellers of variance swaps earn time-varying risk premia for their exposure to realized variance, the level of variance swap rates, and the slope of the variance swap curve. To measure risk premia, we estimate a dynamic term structure model that decomposes variance swap rates into expected variances and term premia. Empirically, we document a strong global factor structure in variance term premia across the U.S., U.K., Europe, and Japan. We further show that variance term premia are negatively correlated with the risk appetite of hedge funds, broker-dealers, and mutual funds. Our results ...
Report
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
Equity Volatility Term Premia
Investors can buy volatility hedges on the stock market using variance swaps or VIX futures. One motivation for hedging volatility is its negative relationship with the stock market. When volatility increases, stock returns tend to decline contemporaneously, a result known as the leverage effect. In this post, we measure the cost of volatility hedging by decomposing the prices of variance swaps and VIX futures into volatility forecasts and estimates of expected returns (“equity volatility term premia”) from January 1996 to June 2020.