Retail investors’ return expectations affect market momentum and risk premia. The rise of ETFs with varying and inverse leverage offers an opportunity to estimate the distribution of such expectations based on actual transactions. A new paper shows how to do this through ETFs that track the S&P 500. The resulting estimates are correlated with investor sentiment surveys but more informative. An important empirical finding is that expectations are extrapolating past price actions. After a negative return shock, investor beliefs become more pessimistic on average, more dispersed, and more negatively skewed.

Egan, Mark and Alexander MacKay and Hanbin Yang (2019), “Recovering Investor Expectations from Demand for Index Funds” (December 19, 2019)

The below summary consists of quotes from the paper. Cursive text and text in brackets have been added.
The post ties in with this site’s summary on endogenous market risk.

The basic idea

“We develop a flexible model of demand for exchange-traded funds (ETFs) that allows us to recover the distribution of investor expectations of stock market returns based on observed investment decisions…At each point in time, we recover the distribution of expectations across investors rather than just the average expectation. We find that heterogeneity in expectations is meaningful and varies over time.”

“Exchange-traded funds are passive investment funds designed to track another underlying asset… We focus on ETFs that track the S&P 500 Index, as well as those that provide leveraged and inverse exposures. The S&P 500 Index covers approximately 80% of available market capitalization.
Leveraged and inverse ETFs provide investors a menu of different exposure to the underlying indices. They offer discrete leverage categories of 2x or 3x in the long side and -1x, -2x and -3x in the short side. Leveraged and inverse S&P 500 ETFs were among the first of such products introduced in 2006 and they became popular especially during the crisis in 2008… Relative to all S&P 500 linked ETFs held by retail investors, leveraged ETFs accounted for roughly one quarter of assets under management…. … These products offer active retail investors access to leveraged exposure with limited liability as an alternative to other more complicated derivative contracts, which require margins and more specialty knowledge.”

How to extract investor beliefs from ETF data

“In each month, we observe the fraction of consumers purchasing S&P 500 linked ETFs in each leverage category…. we apply a model of investor choice to observed market shares for investments linked to the performance of the S&P 500. Our data on market shares comes from monthly trading volumes for exchange-traded funds (ETFs) by retail (non-institutional) investors…We do not observe an investor’s portfolio; we only observe purchases.”

Studying leveraged index funds offers a clean setting for separately identifying investor expectations of stock market returns and risk aversion. Investors have the choice of different leverage options when purchasing ETFs. By choosing a higher leverage, an investor increases the expected mean return, but also the risk associated with the investment [and thus] reveals his expectations about the future performance.”

“We model this decision and estimate the model to recover a time-varying distribution of investor expectations of stock market returns that rationalize aggregate choices. Presumably, an investor that purchases a -3x leveraged ETF has more pessimistic expectations of the future performance of the stock market than an investor who purchases a 3x leveraged ETF. Because we observe the fraction of consumers purchasing leveraged ETFs in each category (-3x, -2x, …, 3x), we have information about the distribution of expectations across investors.”

“We interpret our revealed choice estimates of investor expectations as the investor’s beliefs about the expected future return of the stock market.”

Empirical lessons

“Using maximum likelihood, we estimate a flexible, time-varying distribution of expectations at a quarterly frequency over the period 2008-2018. Our framework allows us to quantify those expectations in terms of the expected annualized return of the stock market. “

“We confirm a prior finding, based on survey evidence, that beliefs are extrapolative…Mean expected return is extrapolative, based on past stock market returns.”

“The dispersion in expectations, or investor disagreement, also reflects past returns. Following a period of negative stock market performance, investor beliefs become more pessimistic on average, more dispersed, and more negatively skewed. This suggests that a subset of investors become very pessimistic following negative returns. In contrast, disagreement across investors tends to decline following periods of high stock market returns. In other words, investors tend to agree during stock market booms and disagree during stock market busts.”

“While beliefs are extrapolative for the average investor, they do not appear extrapolative for all investors. For example, we find that following downturns, while the average investor becomes more pessimistic, a substantial fraction of investors become more optimistic.”

“Further, we find that expectations are persistent: one month of poor stock market performance impacts investor expectations up to two years in the future.”

Relation to market surveys

“A growing number of surveys have been designed to elicit such beliefs from households, investment professionals, and managers.

  • The Duke CFO Global Business Outlook, surveys CFOs at a quarterly frequency about their views on the stock market and macroeconomic outlook. As part of the survey, CFOs are asked to report their expectations of the market risk premium over the upcoming year.
  • The Wells Fargo/Gallup Investor and Retirement Optimism index is constructed using a nationally representative survey of U.S. investors with USD10,000 or more invested in stocks, bonds and mutual funds. The index is designed to capture a broad measure of U.S. investors’ outlook on their finances and the economy based on their survey responses and Gallup’s proprietary index construction methodology.
  • The University of Michigan Survey…asks consumers about the probability that the stock market increases. Specifically, the survey asks a set of nationally representative of US consumers to report the percent chance that a ‘one thousand dollar investment in the stock market will increase in value a year ahead.’
  • The American Association of Individual Investors surveys its members each week about their sentiment towards the stock market over the next 6 months. Specifically, the survey asks respondents whether they believe the stock market over the next six months will be up (bullish), no change (neutral), or down (bearish).
  • The Shiller US Individual One-Year Confidence Index measures the percentage of individual investors who expect the stock market (Dow Jones Industrial) to increase in the coming year.”

Our estimates are aligned with the survey evidence commonly used in the literature… Overall, the survey responses implied by the estimated distribution of our beliefs from the structural model are statistically and positively correlated with the survey data.”

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Ralph Sueppel is founder and director of SRSV, a project dedicated to socially responsible macro trading strategies. He has worked in economics and finance for over 25 years for investment banks, the European Central Bank and leading hedge funds. At present, he is head of research and quantitative strategies at Macrosynergy Partners.