Using Asset Prices to Measure the Persistence of the Marginal Utility of Wealth

Abstract

We derive a lower bound for the size of the permanent component of investors' marginal utility of wealth, or more generally, asset pricing kernels. The bound is based on return properties of long-term zero-coupon bonds, risk-free bonds, and other risky securities. We find the permanent component of the pricing kernel to be very large; its volatility is about at least as large as the volatility of the stochastic discount factor. We also show that, for many cases where the pricing kernel is a function of consumption, innovations to consumption need to have permanent effects.

Very Long-Run Discount Rates

“…The level of the yield curve shifted down during this latter period and the yield curve became hump-shaped. 26 Our estimates of long-run discount rates provide further support for the volatility bounds on the permanent component of pricing kernels derived by Alvarez and Jermann (2005) not only via the direct observation of low U.K. 40-year real yields, but mostly by observing the discount rates for assets very far into the future, 100 or more years. Since housing is a risky asset, our estimated total discount rates provide an upper bound for the risk-free discount rates that Alvarez and Jermann (2005) are directly interested in.…”

The Long Bond, Long Forward Measure and Long-Term Factorization In Heath-Jarrow Morton Models

“…This martingale accomplishes the change of probabilities from the data-generating (physical) measure P to the risk-neutral measure Q. More recently, Alvarez and Jermann (2005), Hansen et al (2008), Hansen and Scheinkman (2009), Hansen (2012) and Qin and Linetsky (2017) study an alternative long-term factorization of the SDF. The long-term factorization decomposes the pricing kernel (PK) process in an arbitrage-free asset pricing model…”

“…Alvarez and Jermann (2005) originally introduced the long-term factorization in discrete-time ergodic economies. Hansen and Scheinkman (2009) introduced and studied the long-term factorization in continuous-time Markovian economies and expressed it in terms of the Perron-Frobenius principal eigenfunction of the pricing operator.…”

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AbstractThis paper proves existence of the long bond, long forward measure and long-term factorization of the stochastic discount factor (SDF) of Alvarez and Jermann (2005) and Hansen and Scheinkman (2009) in Heath-Jarrow-Morton (HJM) models in the function space framework of Filipović (2001). A sufficient condition on the weight in the Hilbert space of forward rate volatility curves is given that ensures existence of the long bond volatility process, the long bond process and the long-term factorization of the SDF into discounting at the rate of return on the long bond and * likuanqin2012@u.northwestern.edu † linetsky@iems.northwestern.edu 1 a martingale component defining the long forward measure, the long-term limit of T -forward measures.

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Long-term factorization of affine pricing kernels

“…This martingale accomplishes the change of probabilities to the risk-neutral probability measure. More recently Alvarez and Jermann (2005), Hansen et al (2008), Hansen and Scheinkman (2009) and Hansen (2012) introduce and study an alternative long-term factorization of the SDF. The transitory component in the long-term factorization discounts at the rate of return on the pure discount bond of asymptotically long maturity (the long bond).…”