The Behavior of an Institutional Investor with Arbitrage Opportunities and Liquidity Risk

ABSTRACT

This study analyzes the efficiency of liquidity flows in stabilizing distressed markets from a theoretical perspective. We show that even in the event of a major negative market shock, a financial institution can increase its investment in the market when there is a strong incentive for arbitrage profit. However, the institution may choose to reduce its investment if the fear from liquidity risk exceeds the arbitrage incentive. In addition, our model reveals a positive relationship between funding liquidity and market liquidity. Our findings help to explain several financial issues in distressed markets, including the flight to quality, liquidity dry-ups, asset fire sales, and market shock amplifications.

KEY WORDS:

• arbitrage profit
• distressed market
• flight to quality
• liquidity risk
• market efficiency

JEL CLASSIFICATION:

• G14
• G18
• G21

Notes

1. The findings of empirical studies on market microstructures support the superiority of institutional investors in terms of information (Ahn, Kang, and Ryu 2008; Ryu 2015; Webb et al. 2016; Yang, Choi, and Ryu 2017).

2. Many studies adopt a restricted setting to investigate the effect of investors’ incentives on the collapse of a banking system (Diamond and Dybvig, 1983; Goldstein and Pauzner 2005), funds market (Liu and Mello 2011), currency market (Morris and Shin 1998), or risky asset market (Bernardo and Welch 2004).

3. Regardless of the price we choose at time 0, the result of the model does not change. For convenience, we set the price at time 0 to the price at time 3 (i.e., $R$). However, unlike the price at time 0, the price at time 3 is known in advance to the institution only.

4. We add time 0 to the model because we need a price at time 0 to account for the trading strategy of the trend followers, who follow market trends such that their aggregate demand is proportional to past market returns.

5. The institution does not have private information of a negative shock.

6. We use the price at time 1 as the numeraire because the institutional investor makes an investment at time 1. In addition, asset returns are frequently used in model development.

7. In the interval $v\le \theta \le f$, $r\left(\theta \right)=\frac{\alpha /R}{\left(1+\mu \right)}$ is induced by $r\left(\theta \right)=\frac{\alpha }{R}-\mu r\left(\theta \right)$.

8. In the model, the market price begins at $R$ at time 0, drops at time 1 and time 2, and then converges again to $R$ at time 3. For convenience, we set the prices of both time 0 and time 3 to $R$. However, unlike the price at time 0, the price at time 3 is not known to the trend followers in advance. Therefore, the demand $\alpha /R$ of the trend followers at time 2 is determined after observing the price at time 0 and at time 1, rather than the value determined by the price at time 3. The institution knows the price at time 3 at time 1 and, thus, determines θ to maximize its asset value at time 3.

9. Symmetry is not valid for the area where neither are defined.

10. The institution may have access to other resources and may be able to invest more when prices diverge further from the fundamentals. However, because we analyze the case of a market decline, such as a financial crisis, we do not consider borrowing. In general, institutional investors find it difficult to borrow during a market decline (owing to credit rationing) or in the event of large fund outflows.

Additional information

Funding

This work was supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea: [Grant Number NRF-2017S1A5A2A01025583].