Philipp Karl
ILLEDITSCH

Published or Forthcoming Papers

• Demand Disagreement (joint with Christian Heyerdahl-Larsen). Journal of Financial Economics, 2026, 75,  1-16. (SSRN version and Online Appendix)   

Abstract. Disagreement about macroeconomic fundamentals accounts for only part of the disagreement about future interest rates, creating a “disagreement correlation” puzzle. This puzzle arises because standard equilibrium models with belief differences predict a strong link between asset return disagreement and fundamental disagreement, a link not supported by the data. We address this puzzle by introducing a model where disagreement about future demand for savings—driven by disagreement over the prevalence of patient versus impatient investors in the economy—generates asset return disagreement. Our mechanism produces stochastic yield volatility, time-varying bond risk premia, and an upward-sloping yield curve. Empirically, we construct a proxy for demand disagreement by isolating the component of yield disagreement unrelated to disagreement about macro-fundamentals. This proxy is positively related to yields and their volatilities, and predicts future bond risk premia, consistent with the predic- tions of our demand disagreement model.  

• Information Inertia (joint with Jayant Vivek Ganguli and Scott Condie). Journal of Finance, 2021, 76 (1), 443-479. (SSRN version and Online Appendix) 

Abstract. We show that aversion to risk and ambiguity leads to information inertia when investors process public news about assets. Optimal portfolios do not always depend on news that is worse than expected; hence, the equilibrium stock price does not reflect this bad news. This informational inefficiency is more severe when there is more risk and ambiguity but disappears when investors are risk neutral or the news is about idiosyncratic risk. Information inertia leads to news momentum (e.g. after earnings announcements) and is consistent with low trading activity of households. An ambiguity premium helps explain the macro and earnings announcement premium.

• Residual Inflation Risk. Management Science, 2018 64 (11), 5289-5314. (SSRN version)

Abstract. I decompose inflation risk into (i) a component that is correlated with factors that determine investors’ preferences and investment opportunities and real returns on real assets with risky cash flows (stocks, corporate bonds, real estate, commodities, etc.), and (ii) a residual inflation risk component. In equilibrium, only the first component earns a risk premium. Therefore, investors should avoid exposure to the residual component. All nominal bonds, including money-market accounts, have constant nominal cash flows, and thus their real returns are equally exposed to residual inflation risk. In contrast, inflation-protected bonds provide a means to avoid cash flow and residual inflation risk. Hence, every investor should put 100% of her wealth in real assets (inflation-protected bonds, stocks, corporate bonds, real estate, commodities, etc.) and finance every long/short position in nominal bonds with an equal amount of other nominal bonds or by borrowing/lending cash; that is, investors should hold a zero-investment portfolio of nominal bonds and cash.

• Disagreement about Inflation and the Yield Curve (joint with Paul Ehling, Michael Gallmeyer, and Christian Heyerdahl-Larsen). Journal of Financial Economics, 2018, 127 (3), 459-484. This article was covered by Knowledge@Wharton. (SSRN version and Online Appendix)

Abstract. We show that inflation disagreement, not just expected inflation, has an impact on nominal interest rates. In contrast to expected inflation, which mainly affects the wedge between real and nominal yields, inflation disagreement affects nominal yields predominantly through its impact on the real side of the economy. We show theoretically and empirically that inflation disagreement raises real and nominal yields and their volatilities. Inflation disagreement is positively related to consumers’ cross-sectional consumption growth volatility and trading in fixed income securities. Calibrating our model to disagreement, inflation, and yields reproduces the economically significant impact of inflation disagreement on yield curves. 

• Risk Premia and Volatilities in a Nonlinear Term Structure Model (joint with Peter Feldhuetter and Christian Heyerdahl-Larsen). Review of Finance, 2018, 22 (1), 337-380. Winner of the best paper award of the World Finance Conference in 2013 and winner of the 2014 outstanding paper prize from the Jacobs Levy Equity Management Center for Quantiative Financial Research. This article was featured by Knowledge@Wharton. (SSRN version)

Abstract. We introduce a reduced-form term structure model with closed-form solutions for yields where the short rate and market prices of risk are nonlinear functions of Gaussian state variables. The nonlinear model with three factors matches the time-variation in expected excess returns and yield volatilities of US Treasury bonds from 1961 to 2014. Yields and their variances depend on only three factors, yet the model exhibits features consistent with Unspanned Risk Premia (URP) and Unspanned Stochastic Volatility (USV).

• Ambiguous Information, Portfolio Inertia, and Excess Volatility. Journal of Finance, 2011, 66 (6), 2213-2247. (SSRN version and Online Appendix)

Abstract. I study the effects of risk and ambiguity (Knightian uncertainty) on optimal portfolios and equilibrium asset prices when investors receive information that is difficult to link to fundamentals. I show that the desire of investors to hedge ambiguity leads to portfolio inertia and excess volatility. Specifically, when news is surprising, investors may not react to price changes even if there are no transaction costs or other market frictions. Moreover, I show that small shocks to cash flow news, asset betas, or market risk premia may lead to drastic changes in the stock price and hence to excess volatility.

Working Papers

• Effects of Financial Speculation on Households (joint with Christian Heyerdahl-Larsen and Petra Sinagl, Revise and Resubmit a the Journal of Financial and Quantitative Analysis). December 2025.

Abstract. Financial speculation is often blamed for market instability, yet its impact on households that do not invest in speculative markets is less understood. We study the impact of financial speculation, driven by cash flow disagreement, on the welfare of households that do not participate in the stock market and save in the risk-free asset. Without additional frictions, households forego the equity premium, which reduces their consumption share, though speculation itself does not affect it. While speculation increases asset price volatility and causes significant fluctuations in speculators’ consumption shares, it does not affect the volatility of households’ shares. Our findings challenge the view that speculation negatively affects households, instead suggesting that financial exclusion, not speculative excess, is the key barrier to wealth accumulation. Our framework serves as an important benchmark for identifying the economic mechanisms through which financial speculation impacts households.

• Market View: Reconciling Survey and Statistical Equity Premia (joint with Christian Heyerdahl-Larsen). September 2025.
  
  Abstract. Survey-based excess stock return forecasts are procyclical, less volatile, and more persistent than countercyclical statistical forecasts. These patterns challenge rational representative-agent models. We show that they arise naturally in fully rational heterogeneous-belief models with speculative trade. Prices reflect the market view, a consumption and risk tolerance weighted belief of investors rather than the survey consensus views, which ignores gains from trade when aggregating beliefs. In a general framework, we derive sufficient conditions for the negative correlation between consensus and statistical equity premia. Three simple examples show how trade on differing beliefs about cash flows or valuations makes some investors contrarian and others trend-chasing. Because prices aggregate beliefs differently than surveys, the consensus premium is procyclical, extrapolates past returns, and is less volatile and more persistent than the statistical view of the equity premium in all three examples.

• Economic Growth through Diversity in Beliefs (joint with Christian Heyerdahl-Larsen and Howard Kung, Submitted to the Journal of Financial Economics). May 2025.

Abstract. We study a macro-finance model with entrepreneurs who have different views on identifying the “next big idea,” leading them to pursue distinctly different paths. Their different views and consequent engagement in a broad array of strategies and actions serve to tap into the full spectrum of societal ideas, thereby fostering economic growth that would be unattainable without such diversity. The resulting benefits for future generations come at the cost of higher wealth and consumption inequality. Venture capital funds and taxes enhance risk sharing among entrepreneurs, stimulating innovation and growth unless high taxes deplete entrepreneurial capital.  

• Asset Pricing with the Awareness of New Risks (joint with Christian Heyerdahl-Larsen and Petra Sinagl, Submitted to the Review of Financial Studies). May 2025.
  
  Abstract. Recessions cause substantial but delayed drops in output, followed by recoveries with abnormally high growth. We propose a new theory where the awareness of new risks negatively impacts growth, leading to recessions of varying duration and severity. Our model shows that risk premia and return volatilities exhibit a hump-shaped pattern at the onset of recessions, not rising immediately, unlike in most non-expected utility models (Ai and Bansal, 2018). These results align with empirical patterns of output, risk premia, and volatilities observed during recessions and expansions. Hence, our model explains a stronger link between fundamentals and asset prices observed during economic recessions and recoveries.

• Model Selection by Market Selection (joint with Christian Heyerdahl-Larsen and Johan Walden). November 2022.
  
  Abstract. We define the concept of market beliefs in an economy with disagreement, such that equilibrium in a representative agent economy with market beliefs is equivalent to equilibrium in the disagree- ment economy. In general, the mapping from individual agent beliefs to market beliefs is complex and nonlinear, suggesting that several puzzles that arise in the representative agent setting may in fact be due to disagreement, and limiting the possibility of drawing inferences about the pricing kernel and beliefs from asset prices alone. Nevertheless, market beliefs are often highly informative about objective probabilities. We analyze the properties of the market belief process, viewed as an estimator, and show that it satisfies several remarkable properties, nesting Bayesian updating, frequentist estimators, and allowing for shrinkage estimation. We relate these properties to the literature on market selection and to the adaptive market hypothesis.  

• Distorted Risk Incentives from Size Threshold-Based Regulations (joint with Burton Hollifield, Shane Johnson, and Yan Liu). April 2022.
  
  Abstract. Many regulations are based on size thresholds. We develop a model that shows that such regulations distort risk-taking incentives, providing above-threshold firms with greater incentives to take risk and below-threshold firms the opposite. Risk distortion varies nonlinearly as a function of the distance from the size threshold, and is increasing in the magnitude of the regulatory costs. We test our model by examining changes in risk around the Dodd-Frank Act, a major regulation with size thresholds. We provide empirical evidence that is consistent with the main predictions of the model.
  
  

• “Long Term Investing in Fully Collateralized Futures Contracts” (with Christoph Meinerding and Christian Schlag), first draft posted soon.
  
  This paper studies the long-term performance of fully collateralized, marked-to-market futures investments typically employed by commodity ETFs. Under a constant investment opportunity set, we derive closed-form expressions for the expected holding-period return as a function of the risk-free rate, the futures risk premium, and the investment horizon, and benchmark the results to a prepaid forward. Daily margining and collateralization reduce effective futures exposure between rebalancing dates, so the expected holding-period return lies between the risk-free rate and the expected return of the underlying when the risk premium is positive, and is, on average, below the expected growth rate of the futures price. More frequent rolling lowers the wedge between the futures and prepaid-forward returns. Finally, we analyze how the term premium affects the futures investment’s return relative to the benchmark, emphasizing a trade-off between convexity and the term premium.

Work in Progress

• “The Risk- and Ambiguity-Adjusted Probability Distribution” (with Hagen Kim)

• “Portfolio Choice with Commodity ETFs” (with Christoph Meinerding and Christian Schlag)

• “Efficient methods for solving large scale equilibrium models with disagreement” (with Paul Ehling, Christian Heyerdahl-Larsen and Junjie Guo)

• Applied Stochastic Portfolio Theory (joint with Johannes Ruf)