Abstract
The (volume-synchronized) probability of informed trading (PIN) is a relative proxy for adverse selection (flow toxicity) in securities trading. We find that (V)PIN puzzlingly explains the discount of U.S. exchange-listed funds. While (V)PIN can unintentionally represent behavioral biases, we suggest the “proportion measure of purchased futures losers or sold future winners” as a more direct proxy for behavioral biases. While the proportion measure is positively and significantly correlated with (V)PIN and the value-weighted discount of closed-end funds, it is unrelated with the price impact parameter, the adverse selection component of the bid-ask spread, and the illiquidity measure. A risk factor defined as the highest-over-lowest excess return of sorted portfolios in terms of the proportion measure, well explains the return of listed funds along with the well-known factors. Lastly, the co-movement of closed-end and exchange-traded fund pairs is pronounced for developed markets and is influenced by the proportion measure.
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Notes
- 1.
The four-part CEF puzzle is as follows: (1) CEFs are usually initial-public offered (IPO’ed) at premiums; (2) after issuance, CEFs trade at discounted prices; (3) discounts are very volatile, and their fluctuation varies across time and funds; and (4) when a CEF is acquired, liquidated, or “open-ended,” its price closes at the NAV [25]. Ross [26] finds that 6–7% discounts in CEFs fairly reflect future fund expenses. De Long et al. [27] theoretically argue that the CEF discount can persist in the absence of arbitrageurs due to unhedgeable noise trader risk.
- 2.
According to Baker and Wurgler [33] (p. 138): “Corporate executives have better information about the true value of their firms than outside investors. Thus, legalities aside, executives’ portfolios decisions may also reveal their views about the mispricing of their firm. If sentiment leads to correlated mispricings across firms, insider trading patterns may contain a systematic sentiment component. See Seyhun [34] for evidence on the ability of insider trading activity to predict stock returns… … rules out data that do not go back as far as stock returns data (that is, to the 1960s), which would exclude, for example, data on insider trading; micro-level data on trading behavior, and implied volatility series.”
- 3.
We find fault with neither PIN nor VPIN. Rather, we focus on a facet in the financial market where an adverse selection proxy can reflect behavioral biases especially when an asset is heavily weighed by sentiment.
- 4.
Similarly extending the same model of Grossman and Stiglitz [41], Chen and Choi [18] predict that, for the cross-listed pairs of Canadian firms listed on both the Toronto Stock Exchange (TSX) and the NYSE, a higher proportion of informed traders on the original listing on the TSX than on the cross-listing on the NYSE leads to the relative premium on the latter stock on the NYSE under certain conditions. Besides, see Chan et al. [17] for another application of Grossman and Stiglitz [41] to the segmentation of A- and B-shares in China.
- 5.
If the listed fund (\(F\)) is a CEF, then a comparable ETF can represent the underlying assets (\(N\)). The proportion of behaviorally biased trades for fund \(i\) (\(\pi_{i}\)) can be empirically estimated as the proportion of purchased future losers or sold future winners (proportion measure) introduced in Sect. 3.1.
- 6.
See Tuckman and Vila [42] for modeling arbitrageurs who face holding costs.
- 7.
This is a static model, and the choice of asset for the both groups of traders is exogenous. If we allow the traders to freely switch between the fund and the underlying assets, then the fund will almost always trade at its NAV.
- 8.
It can be shown that given \(\omega_{i} \equiv \omega_{i}^{B} + \omega_{i}^{R} = \pi_{i} \eta \left( {\phi_{i} - 1} \right)\tau_{S} + \eta \left( {\tau_{S} + \tau_{\upsilon } } \right)\), a direct partial derivative can be \(\partial \omega_{i} /\partial \pi_{i} = \eta \left( {\phi_{i} - 1} \right)\tau_{S} < 0\) since \(\phi_{i} \equiv \tau_{i} /\left( {\tau_{i} + h_{i}^{2} \tau_{S} } \right) \in \left( {0,1} \right).\) Consequently, for a sufficiently small difference of the proportion of behaviorally driven trades on the fund (\(\pi_{F}\)) over that on the underlyings (\(\pi_{N}\)) such that \(\Delta \pi_{i} \equiv \pi_{F} - \pi_{N} \searrow 0^{ + }\), \(\pi_{F} > \pi_{N}\) implies \(\omega_{F} < \omega_{N}\), thus \(\omega_{N} /\omega_{F} > 1\).
- 9.
Depending on the magnitudes of parameters, the fund can also trade with a premium against its NAV.
- 10.
There can be alternative measures of return to fund trading: Pairs trading return. In the spirit of Gatev et al. [43], for a given listed fund, by longing the shares of the discounted fund while shorting the stocks of the relatively overpriced underlying assets (NAV), the implied excess return to this pairs trading over month \(t\) is
\({\text{ReturnArb}}_{t} \equiv {\text{Return}}_{t}^{\text{fund}} {-}{\text{Return}}_{t}^{\text{NAV}} .\)
Alternative measure of pairs trading return. Relative to the market index (S&P 500 depository receipts, SPY), one can long and short sell a pair of relatively underpriced and overpriced funds as
\({\text{ReturnAbs}}_{t} \equiv \left| {Return_{t}^{\text{fund}} {-}{\text{Return}}_{t}^{\text{SPY}} } \right|.\)
- 11.
See Sect. 2 for the proportion of behaviorally biased trades which theoretically determines the discount of listed funds against their NAVs.
- 12.
Whether the proportion measure is defined in terms of the number of trades or traded shares (trading volume), the actual estimates are mutually proximate and their impacts on the discount of listed funds qualitatively equivalent in Table 1.
- 13.
- 14.
We do not use Petersen’s [49] clustering robust standard errors because PIN and VPIN are by nature the measures of informed trading, or flow toxicity, that tends to cluster around information events.
- 15.
- 16.
From the perspective of financial technology (fintech), a robo-advisor with a trading algorithm based on the proportion measure can be suggested.
- 17.
We thank Jungsuk Han for these intuitions.
- 18.
See Bekaert and Urias [68] for an early discussion of emerging market closed-end funds.
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Acknowledgements
Special thanks are due to Warren Bailey (de facto co-author), David Easley, Andrew Karolyi, and Maureen O’Hara for their teachings. We also thank Yong-Ho Cheon, Jungsuk Han, Soeren Hvidkjaer, Byoung Uk Kang, Gi Hyun Kim, Alok Kumar, Albert S. Kyle, Jaehoon Lee, Albert Menkveld, and Yinggang Zhou for invaluable discussion and feedback. The authors conducted part of this research as visiting scholars at the Johnson Graduate School of Management, Cornell University, and P.M.S. Choi as a doctoral student under Warren Bailey’s advisory. P.M.S. Choi is grateful for the grants provided by the Fulbright Scholarship Program and Ewha Womans University. This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (NRF-2019S1A5A2A03053680). Jaysang Ahn, Ethan Jaesuh Kim, Sabin Kim, SaMin Kim, Young Jin Kim, Hyun Jun Lee, and Jaehyun Rhee provided excellent research assistance. We also appreciate technical help from Mancang Dong and Mike Leiter. Standard disclaimer rules apply, and all errors are of our own.
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Choi, P.M.S., Choi, J.H. (2021). Informed or Biased? Some Evidence from Listed Fund Trading. In: Choi, P.M.S., Huang, S.H. (eds) Fintech with Artificial Intelligence, Big Data, and Blockchain. Blockchain Technologies. Springer, Singapore. https://doi.org/10.1007/978-981-33-6137-9_11
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