Options on Leveraged ETFs: A Window on Investor Heterogeneity

Abstract

A risk-neutral probability distribution (RND) for future S&P 500 returns extracted from index options contains investors' true expectations and also their risk preferences. But the empirical pricing kernel that emerges in a representative agent framework, which suppresses investor differences, is inconsistent with investor rationality. The anomalous shape can be generated easily in a model with heterogeneous investors facing limits to arbitrage, however. We explore investor heterogeneity directly via RNDs extracted from options on three exchange traded funds with leveraged short and long exposures to the S&P 500 index, and find large differences that are not arbitraged away. For example, holders of ETFs with short exposure to the market value payoffs in negative return states significantly more than those with long exposure do. Separating true expectations from risk premia requires further assumptions, so we consider polar cases in which either all investors have the same expectations but different risk preferences, or the reverse. The results are largely consistent with the expectations differences we anticipate from investors choosing short or leveraged long market exposure. We then look at changes in RNDs to see how realized returns affect investors with different expectations. A large negative realized return raises the median future return expected by bulls but lowers it for bears. Uncertainty over future returns widens for both types of investors when they are wrong and narrows when they are right.

Keywords: investor heterogeneity, risk neutral density, exchange-traded funds

JEL Classification: G14, G13, G11