Asset prices and portfolio holdings encode information about investor beliefs about the future and about investors' concerns for risk. A natural empirical exercise is to use the financial market data to extract such information. In this post, I briefly outline a few approaches that have emerged (relatively) recently.
Authors employ a revealed-preference approach to estimate investor expectations of stock market returns. The underlying idea is that demand for assets embodies the investor's risk aversion and expectation of the asset's financial value, so with (minor) structural assumptions we can extract the parameters of interest.
For identification, they make use of the fact that investors choose investment options from a menu of several ETFs with different risk/return profiles and fee structures.
One important assumption in the paper is that investors only care about the mean and volatility of the ETFs. This assumption seems empirically at odds with the key insight in Koijen and Yogo (2019): the size of the latent demand is quite large, which points to the existence of "investor taste" not captured by traditional financial metrics.
Authors formalize the following intuition: stock prices of the riskiest, most volatile firms should be particularly sensitive to investor perceptions of risk. Therefore, they measure perceived risk indirectly through the variable $PVS_t$, defined to be the average book-to-market ratio of low-volatility stocks minus the average book-to-market ratio of high-volatility stocks.
Given the simplicity of the construction, the measure inherits the granularity of the stock returns and can be used to construct high-frequency measure of risk appetite.
Authors note that $PVS_t$ "captures a broad notion of perceived risk that operates simultaneously in many asset classes." An interesting question therefore is to decompose $PVS_t$, especially in terms of other metrics such as volatility expectations and uncertainty.