This paper introduces a theoretical framework for extracting investors’ subjective beliefs by combining holdings data with option prices under the assumption of no-arbitrage. We demonstrate methods to estimate investor-specific expected returns and risk, as well as to derive consensus beliefs in a market with heterogeneous investors. Analyzing buy and sell orders on S&P 500 options, we find that the statistical characteristics of subjective expected returns and Sharpe ratios vary significantly between investor types and are heavily influenced by portfolio composition. Notably, while expected returns derived solely from price data exhibit countercyclical behavior, expected returns inferred from institutional investor holdings can change signs, exhibit acyclicality, and align closely with professional investor survey data. In contrast, option market makers’ expected returns show a strong correlation with price-based measures.

Option market makers' intermediation of S&P 500 index options with zero-days-to-expiration (0DTE) lowers the index volatility, on average. Exploiting exogenous variation in contract expiration days, we show that the index volatility decreases by 60–90 annualized basis points on days with 0DTE trading. We find that market makers match most 0DTE order flows, but absorb end-users' trades in long-dated options that eventually become 0DTE positions. Hedging these expiring positions creates intraday order flow in the index futures that dampens volatility. The results run counter to concerns that 0DTE market makers amplify volatility. Instead, their increased hedging activity has attenuated the volatility of the underlying index.

Using comprehensive new contract level data (EMIR) for the period 2019-2023, we explore how the FX derivative trading by 2,806 European funds with discretionary hedging mandates compares to a feasible theoretical benchmark of optimal hedging. A

minority of funds engage in hedging policies close to the optimal hedging benchmark. The FX derivative trading of most investment funds is partial, unitary (i.e., with a single currency focus), or even currency risk augmenting. Overall, FX derivative trading does not significantly reduce the return risk of the average European investment funds, although optimal hedging strategies could do so without incurring substantial trading costs.