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Finding the Model That Captures Investment Risks, but Not Mispricing of Assets

Apr 4, 2023 | Public | 0 comments


Trying to accurately project the return on your investment has never been easy, which of course explains why some win big, and some lose, in the stock markets. As the stakes get bigger, investors use a variety of models to analyze various pieces of information they have gathered on a security, such as on its competitors and its business outlook, in attempts to predict its future price. A big challenge in that exercise is to weigh two aspects: the various types of risks that a security has, and the role of potential mispricing.

A research paper titled “Pricing Without Mispricing” tests the ability of five prominent models to predict future returns by evaluating only risks, assuming that there is no mispricing. The paper was selected as the “Best Paper” by Wharton’s Jacobs Levy Equity Management Center for Quantitative Financial Research in its 2022 list of winners of research papers.

“A lot of the recent work in asset pricing is devoted to coming up with the ‘correct’ asset pricing model that describes expected returns, wherever they come from,” said Robert F. Stambaugh, the Miller Anderson & Sherrerd Professor of Finance at Wharton, who co-authored the paper with Jianan Liu, currently with Qube Research and Technologies, and Tobias J. Moskowitz, the Dean Takahashi Professor of Finance at Yale School of Management. “We’re interested in figuring out what model would describe expected returns if they came only from risk and not from mispricing.”

“Having that model allows you to have a benchmark against which you can measure expected return in the actual pricing of stocks and to gauge how much expected return is due to mispricing and how much is due to risk,” Stambaugh continued. “What would the price of a security be in the absence of mispricing? By having a model that can correctly represent that, you can then use that model to gauge how much mispricing there is in actual prices.” Mispricing could occur because of a failure to incorporate relevant information about the fundamental value of a security.

“Would you pay the same fee to a manager who’s giving you high expected returns by exposing you to more risk, versus a manager who’s giving you high expected returns by buying underpriced securities?”— Robert F. Stambaugh

Genesis and Scope of the Study

The authors motivate their study by quoting Nobel laureate and Chicago Booth economics professor Eugene Fama, who is considered the father of modern finance, on the challenge in studying market efficiency: “We can only test whether information is properly reflected in prices in the context of a pricing model that defines the meaning of “properly.” The authors set out to ask which pricing model best defines “properly” as Fama put it. In other words, Fama spoke of a model that would describe expected returns that come only from risk and not also from mispricing, Stambaugh explained.

The paper assumes that mispricing would get corrected over a 10-year period. “The market might be incorrectly incorporating current information, but that information will get correctly reflected in the price eventually. We assume that 10 years is a sufficiently long time for any information that’s relevant to the price to have gotten into the price.” That said, the assumption is not that all mispricing will go away after 10 years, he clarified. “There’s always new mispricing that arises. We’re just saying that mispricing associated with a given piece of information will be corrected within 10 years.”

Stambaugh pointed out that after mispricing is removed from the equation, risks should be the only predictors of returns, especially risks investors cannot eliminate by diversifying their holdings. “So, in a rational and efficient market, prices should depend only on so-called systematic or non-diversifiable risks that somebody has to bear,” he said. “And then prices would reflect compensation for whoever bears that risk.”

If the return on a security exceeds that of a benchmark — say, an index — after adjusting for volatility in prices, it is said to have a positive alpha. In the absence of mispricing, the proper benchmark asset pricing model should deliver zero alpha for any investment strategy, the paper notes.

The authors construct strategies based on 10-year-old information and studied popular asset pricing models to see which of those failed to assign zero alpha to those strategies. “If an asset pricing model fails to assign a zero alpha to a strategy that uses only 10-year-old data, then we conclude that that pricing model can’t be the one that would describe prices in a world without mispricing,” he said. Put another way, the right pricing model for an efficient market without mispricing would not assign a “positive alpha” to strategies using information that’s at least 10 years old.

“[The no-mispricing model] allows you to have a benchmark against which you can measure expected return in the actual pricing of stocks and to gauge how much expected return is due to mispricing and how much is due to risk.”— Robert F. Stambaugh

Capital Asset Pricing Model (CAPM) Scores in a World Without Mispricing

The authors studied five commonly used models to predict returns from stock investing: the traditional CAPM of Sharpe and Lintner, the three-factor model of Fama and French, the four-factor model of Hou-Xue-Zhang, the five-factor model of Fama and French, and the CAPM augmented by the betting-against-beta factor of Frazzini and Pedersen.

The study discovers that the CAPM, which uses a single market factor (or just the return on the stock market), assigns zero alphas to such strategies, but the other four models, which are “multifactor” models that include additional factors, do not. Multifactor models may weigh additional factors such as firm size, value, and momentum. Prominent multifactor models distort expected returns in the absence of mispricing even for the largest and the most liquid stocks, the paper adds.

That is not to say that the CAPM is superior to the other models, Stambaugh clarified. “The other models may very well do a good job at describing expected returns — remember, the actual expected returns can come from either mispricing or risk,” he said. “If you were a portfolio manager trying to construct strategies with high alpha, or high expected returns, these various other pricing models could be very good at telling you which securities have high expected returns. But those high expected returns could come from either risk compensation or mispricing.”

Their study also finds that large stocks are likely to provide their test with the greatest power, given those stocks’ more persistent multifactor betas. “We expect larger stocks to have more stable betas,” the paper states. “By virtue of their size, large firms are likely to have greater inertia, taking longer to change course in ways that would significantly impact their characteristics relevant to factor exposures.”

Takeaways for Investors, Fund Managers

Stambaugh pointed out that for fund managers, the main utility of the paper is in identifying “the model that can tell whether the higher returns they’re offering clients are coming from mispricing or from risk compensation.” The utility for investors is transparency in what precisely they are paying their fees for. “Would you pay the same fee to a manager who’s giving you high expected returns by exposing you to more risk, versus a manager who’s giving you high expected returns by buying underpriced securities?” Stambaugh asked. “To which manager would you pay a higher fee? The latter, clearly.”

More broadly, Stambaugh said the challenge of distinguishing between risks and mispricing has been a central problem in determining asset pricing for many decades. The novel aspect of their study is in trying to determine the correct benchmark model. “In that sense, we believe our study addresses a longstanding question of primary importance in asset pricing,” he added.

The Road Ahead

According to the authors, further research is required to build on the findings of their paper. “In an initial attempt to compare the abilities of pricing models to serve as the no-mispricing benchmark, we believe the models we consider present a horserace with interesting entrants,” they stated in their paper. “We certainly acknowledge that there could be speedier horses out there.”

At the same time, future research in asset pricing should “continue building models that better describe actual expected returns, whether or not the prices determining those expected returns include mispricing,” the paper adds. Even if such models offer limited utility in gauging the extent of market inefficiencies or understanding risk premia, they can be useful in other ways, such as in designing investment strategies, it noted.


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