An Empirical Test of Pricing Kernel Monotonicity

Abstract

Summary A large class of asset pricing models predicts that securities which have high payoffs when market returns are low tend to be more valuable than those with high payoffs when market returns are high. More generally, we expect the projection of the stochastic discount factor on the market portfolio—that is, the discounted pricing kernel evaluated at the market portfolio—to be a monotonically decreasing function of the market portfolio. Numerous recent empirical studies appear to contradict this prediction. The non‐monotonicity of empirical pricing kernel estimates has become known as the pricing kernel puzzle. In this paper we propose and apply a formal statistical test of pricing kernel monotonicity. We apply the test using 17 years of data from the market for European put and call options written on the S&P 500 index. Statistically significant violations of pricing kernel monotonicity occur in a substantial proportion of months, suggesting that observed non‐monotonicities are unlikely to be the product of statistical noise. Copyright © 2014 John Wiley & Sons, Ltd.

The pricing kernel puzzle in forward looking data

“…Jackwerth (2004) and Cuesdeanu and Jackwerth (2016) survey the literature and details the different approaches, which tend to confirm the pricing kernel puzzle using slightly different methods and data sets. More recently, Christoffersen, Heston, and Jacobs (2013) and Beare and Schmidt (2014) confirm the pricing kernel puzzle yet again in the data.…”

“…However, this comes at the cost of assuming iid returns and, hence, unconditional subjective and risk-neutral distributions at each of the three dates, which have been picked in order to represent different market regimes: a bull market, a stable market, and a bear market. Beare and Schmidt (2014) allow for conditional distributions and still find monotonicity violations in the S&P 500 data with two tests based on ordinal dominance curves. Unfortunately, their use of historical returns for obtaining the subjective distribution exposes their results to the criticism of mixing forward and backward looking information.…”

“…The latter value models a risk-averse investor and is close to the estimate of γ = 4.08 in Bliss and Panigirtzoglou (2004), based on a monthly horizon. Statistically, Beare and Schmidt (2014) argue that monotonicity tests should use risk-neutrality (i.e., γ = 0 and m power = 1). The risk-neutral density is then equal to the subjective density.…”

Reference Dependent Preferences and the EPK Puzzle

“…Several studies report the shape of the pricing kernel as being hump-shaped for most months between 2004 and 2007. This holds for both the German DAX 30 index Giacomini and Härdle (2008); Grith et al (2012) and the American S&P 500 index Barone-Adesi et al (2013); Beare and Schmidt (2012); Polkovnichenko and Zhao (2012).…”

“…Beare and Schmidt (2012) test the concavity of the ordinal dominance curve associated with the risk neutral and physical distributions associated with S&P 500 index. Typically, the null hypothesis of nonincreasing EPK was rejected.…”