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Research Statement

In the equity market, if “the price is right,” then there should be “no free lunch.” While free lunches are rare—or virtually nonexistent once standard frictions are taken into account—can we really take this as evidence that prices are approximately right, and that in the absence of those frictions they would be exactly right? My answer is no. The ultimate friction is indeterminacy: the investor’s inability to distinguish rationality from irrationality.

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Working Papers

Lost In Transmission (Job Market Paper) –
Publicly traded companies sometimes own shares in other publicly traded companies, while also holding other non-traded assets. I refer to the owning company as the parent, and the held company as the subsidiary. These situations offer a rare opportunity to test a fundamental idea in rational equilibrium pricing: valuation consistency — the principle that identical payoff streams should have the same price, even when bundled with other assets.

In other words, the stake in the subsidiary should have the same value whether it stands alone or is combined with the parent’s other assets. However, because those other assets are not traded, there is no perfect redundancy among tradable assets. This breaks the clean logic of textbook Law of One Price settings — where all components are tradable — and is instead analogous to the broader question of consistency among equity prices in general, where idiosyncratic components make most equity payoffs non-redundant.

Under valuation consistency, if the value of a parent company's stake in a subsidiary increases by $1 million, the parent company's market value should also increase by $1 million, assuming the rest of the parent's assets and liabilities remain constant. If the changes in the market value of the stake in the subsidiary and the parent’s other assets were uncorrelated, one could estimate a transmission rate between the subsidiary and the parent by regressing the changes in the parent’s market value on the changes in the value of the stake and a constant. If consistency holds, the transmission rate should be equal to one.

However, in practice, changes in the value of the parent’s other assets are often correlated with those of the stake in the subsidiary — in many cases strongly positively, as both often operate in the same sector and the same geographic area — which would tend to inflate the estimated transmission rate. It is therefore crucial to account for common movements unrelated to ownership.

Assuming these can be captured by closely related stock price movements, I find that, among a panel of parent–subsidiary pairs, a $1 million weekly increase (or decrease) in the value of a parent company’s stake in a subsidiary results, on average, in only a $550,000 weekly increase (or decrease) in the parent company’s market value.

This suggests that consistency does not hold. Standard explanations, such as capital gains taxes or liquidity concerns, do not account for the general tendency to underreact. However, when no other assets are present—for example, when the parent holds only liabilities at the parent level—the transmission rate is indistinguishable from one.
Indeterminacy: The Ultimate Limit to Arbitrage –
Publicly traded parent companies are found to underreact significantly to changes in the value of their publicly traded subsidiaries. This paper resolves the puzzle by introducing the notion of price indeterminacy: arbitrageurs do not know the fundamental value with certainty and must rely on publicly available prices to guide their trades. Under this assumption, the observed underreaction becomes compatible with the absence of excess returns—that is, with no (near-)arbitrage opportunities—even for risk-neutral arbitrageurs with no capital and no short-selling constraints.

Suppose that the stock price of the subsidiary contains some noise—fluctuations driven either by inattentive traders or by factors unrelated to fundamentals—that, in the absence of arbitrage, would not transmit to the parent. If the parent also holds other assets that are not independently tradable, any movement in the subsidiary’s value that fails to transmit can just as plausibly be attributed to an offsetting change in the value of the parent’s other, unobservable assets. This ambiguity limits arbitrage, as it becomes impossible to determine with precision, on the spot, whether the discrepancy reflects a mispricing or a revaluation of the rest of the parent’s portfolio.

As a result, while the inconsistency between the subsidiary’s value and the parent’s market valuation is not directly observable at the time of trading, it can be estimated across many states of the world by an econometrician—as I do in Lost in Transmission. However, arbitrage activity eliminates any clearly exploitable inconsistency—any gap that would otherwise generate excess returns—thereby limiting the remaining degree of underreaction.

For example, when an event occurs that forces a correction—such as an equity carve-out—risk-neutral arbitrageurs will trade until the expected correction is fully priced in. If they are risk-averse, they trade only up to the point where the expected return compensates for the risk of being wrong about the size or direction of the correction. In both cases, the underreaction persists, although risk-neutrality substantially limits its magnitude.
Valuation Consistency in the Equity Market: When It Tends to Hold and When It Might Not –
This paper investigates a subtle but pervasive limit to arbitrage: ambiguity. I focus on Negative Stub Values (NSVs)—situations in which a publicly traded parent company is worth less than its stake in a publicly traded subsidiary. While NSVs are often viewed as signs of mispricing, this is not always justified. The analysis distinguishes between verifiable and non-verifiable NSVs, depending on whether the value of the parent’s other assets can be inferred.

In the verifiable cases, where the parent holds few or no other assets, I find that valuation consistency holds to a satisfactory degree. In contrast, non-verifiable NSVs appear more suspicious: large discrepancies are observed, and in several cases, multibillion-dollar corrections follow events such as equity carve-outs. These corrections suggest that arbitrage was limited not by capital or short-selling constraints, but by uncertainty about whether mispricing truly existed.

The findings provide empirical support for the conjecture of Brav and Heaton: when rationality and irrationality are hard to distinguish, mispricing can persist—not because arbitrage is impossible, but because arbitrageurs cannot be certain it is warranted.