Mu Hat Mu Hat Capital Management

We inherited a chaotic universe and made it precise.

Mu Hat begins with the same beliefs any fundamental investor would recognize — a firm’s future cashflows, size, earnings quality, profitability, and momentum contribute to its valuation. We then apply these ideas systematically across the U.S. equity universe. The practical challenge is not simply finding a factor that worked in the past. It is determining which signals are meaningful today, how they interact, and whether they can be owned after trading costs, liquidity, risk, and portfolio concentration are taken seriously.

The evolution of empirical asset pricing

1964 · CAPM

The market becomes the first benchmark.

Sharpe’s CAPM gave investors a disciplined starting point: expected excess returns should be related to exposure to broad market risk. The model remains useful because it separates risk that can be diversified away from risk that should be compensated. Its limitation was also clear: one market exposure cannot explain every persistent difference among stocks.

William Sharpe

William Sharpe

1976 · APT

More than one systematic force

Ross’s arbitrage pricing theory opened the door to a broader view. If stock returns are driven by several systematic forces, then expected returns can be described by exposure to multiple priced sources of risk. That insight is the bridge from one market beta to a broader factor framework.

Stephen Ross

Stephen Ross

1993–2015 · Fama-French

Factors become measurable.

Fama and French made the multi-factor idea empirically useful. Size, value, profitability, and investment patterns gave practitioners a common language for measuring exposures and evaluating performance. The lesson was not that any named factor should always be owned; it was that fundamentals can be organized, measured, and tested.

Eugene Fama
Eugene Fama
Kenneth French
Ken French
2011 onward · The Factor Zoo

The problem becomes selection.

Success bred excess. The literature produced hundreds of proposed signals, not all of which are economically distinct, durable, or investable. John Cochrane, in his presidential address to the American Finance Association, named the result a factor zoo. The question shifted from whether factors exist to which signals deserve capital after replication, out-of-sample testing, and implementation costs.

John Cochrane

John Cochrane

Today · Mu Hat

The real-world application

Mu Hat starts with the premise that expected returns cannot be observed directly. They have to be estimated.

Any model of asset prices must address three questions: what factors should be in the model, what is the functional form, and how do we estimate the model. Nearly everything we do is an attempt to address one of these problems. We treat the academic literature as the research library, not the portfolio. New results enter the process only after they have been replicated, tested out of sample, and combined with attention to risk, liquidity, and trading costs.

The Mu Hat Model

Influential Papers

The research library

  1. Asness, C. S., Moskowitz, T. J., and Pedersen, L. H. (2013). “Value and Momentum Everywhere.” Journal of Finance 68:929–985.
  2. Breeden, D. T. (1979). “An Intertemporal Asset Pricing Model with Stochastic Consumption and Investment Opportunities.” Journal of Financial Economics 7:265–296.
  3. Carhart, M. M. (1997). “On Persistence in Mutual Fund Performance.” Journal of Finance 52:57–82.
  4. Cochrane, J. H. (2011). “Presidential Address: Discount Rates.” Journal of Finance 66:1047–1108.
  5. Fama, E. F., and French, K. R. (1992). “The Cross-Section of Expected Stock Returns.” Journal of Finance 47:427–465.
  6. Fama, E. F., and French, K. R. (1993). “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33:3–56.
  7. Fama, E. F., and French, K. R. (1996). “Multifactor Explanations of Asset Pricing Anomalies.” Journal of Finance 51:55–84.
  8. Fama, E. F., and French, K. R. (2015). “A Five-Factor Asset Pricing Model.” Journal of Financial Economics 116:1–22.
  9. Fama, E. F., and MacBeth, J. D. (1973). “Risk, Return, and Equilibrium: Empirical Tests.” Journal of Political Economy 81:607–636.
  10. Feng, G., Giglio, S., and Xiu, D. (2020). “Taming the Factor Zoo: A Test of New Factors.” Journal of Finance 75:1327–1370.
  11. Gibbons, M. R., Ross, S. A., and Shanken, J. (1989). “A Test of the Efficiency of a Given Portfolio.” Econometrica 57:1121–1152.
  12. Hansen, L. P., and Jagannathan, R. (1991). “Implications of Security Market Data for Models of Dynamic Economies.” Journal of Political Economy 99:225–262.
  13. Harvey, C. R., Liu, Y., and Zhu, H. (2016). “…and the Cross-Section of Expected Returns.” Review of Financial Studies 29:5–68.
  14. Hou, K., Xue, C., and Zhang, L. (2015). “Digesting Anomalies: An Investment Approach.” Review of Financial Studies 28:650–705.
  15. Jegadeesh, N., and Titman, S. (1993). “Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency.” Journal of Finance 48:65–91.
  16. Lintner, J. (1965). “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets.” Review of Economics and Statistics 47:13–37.
  17. Mehra, R., and Prescott, E. C. (1985). “The Equity Premium: A Puzzle.” Journal of Monetary Economics 15:145–161.
  18. Merton, R. C. (1973). “An Intertemporal Capital Asset Pricing Model.” Econometrica 41:867–887.
  19. Novy-Marx, R. (2013). “The Other Side of Value: The Gross Profitability Premium.” Journal of Financial Economics 108:1–28.
  20. Novy-Marx, R., and Velikov, M. (2016). “A Taxonomy of Anomalies and Their Trading Costs.” Review of Financial Studies 29:104–147.
  21. Novy-Marx, R., and Velikov, M. (2024). “Assaying Anomalies.” SSRN working paper.
  22. Pástor, L., and Stambaugh, R. F. (2003). “Liquidity Risk and Expected Stock Returns.” Journal of Political Economy 111:642–685.
  23. Roll, R. (1977). “A Critique of the Asset Pricing Theory’s Tests Part I: On Past and Potential Testability of the Theory.” Journal of Financial Economics 4:129–176.
  24. Ross, S. A. (1976). “The Arbitrage Theory of Capital Asset Pricing.” Journal of Economic Theory 13:341–360.
  25. Sharpe, W. F. (1964). “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk.” Journal of Finance 19:425–442.
Mu Hat

Read the research.

The firm’s research memos document the process in practice: signed by the partner who wrote them, cited in the convention of the literature, with public summaries.

Read the Research