### Discussion Paper

No. 2017-103 |
November 23, 2017

Do institutions behave rationally in distressed markets?

## Abstract

The authors theoretically analyze the efficiency of liquidity flows in stabilizing distressed markets. Their analysis focuses on the incentives for financial institutions; specifically, they focus on arbitrage profit as an incentive and liquidity risk as a disincentive. The authors show that even with a major negative market shock, a financial institution can increase its market investment if it has sufficient funding liquidity. In addition, their model reveals a positive relationship between funding liquidity and liquidity flows. Thus, a distressed market might stabilize more quickly when financial institutions, acting as liquidity providers, have sufficient funding to bear the market’s liquidity risk.

## Comments and Questions

Corresponding Author,Doojin Ryu is a Tenured Associate Professor at College of Economics, Sungkyunkwan University (SKKU), Seoul, Korea. Ryu worked at the National Pension Service, Hankuk University of Foreign Studies, and Chung-Ang University. Ryu is the Editor of Investment Analysts Journal (SSCI) and the associate editor of Emerging Markets Review (SSCI). ...[more]

... Ryu has published numerous articles in Quantitative Finance, Economics Letters, Journal of Business Ethics, Journal of Banking & Finance, International Review of Economics & Finance, Journal of Real Estate Finance & Economics, Finance Research Letters, Pacific-Basin Finance Journal, Journal of Futures Markets, Applied Economics, and Journal of Derivatives.

https://sites.google.com/site/doojinryu/home/info

https://sites.google.com/site/doojinryu/home/papers

This is a good paper that provides important model on behavior of institution in distressed market. There are some empirical paper about institutional investors and market crash, but I have rarely seen the model about them. This paper shows why institution behave differently in case of market crush, using simple ...[more]

... and easy example: if they have enough money then they invest more and market become stable, but if they do not hold enough money, then institutions amplify the crisis. I, however, have a questions about the paper. In the page 5, Authors suppose that both short sales and borrowing are prohibited; but, in general, institutional investor often use short sales. Under this constraints, the result seems only natural: if institutions do not have enough money, then they sell their asset. So I'm curious about the results without this constraint.

(Also there is a small typo-error in page 3 line 18 : henceforth, ... -> (henceforth, ...)

This paper analyzes about the funding behavior of financial institutions in terms of funding liquidity and drive the role of financial institution. The model settings are general and simple so it is not difficult to follow, however, the result is interesting. I saw variety studies about the role of financial ...[more]

... institution, but the distinguish point is that the paper suggest the proposition theoretically, not empirically. Therefore, the researchers who want to figure out relationship between funding liquidity and financial institution can develop based on this paper.

see attached file

Dear anonymous referee,

Thank you very much for giving us the chance of revision. As you suggest, we believe that this paper has a potential and contributes to the existing literature. Temporarily, we answer for the comments. After the editor makes a revision decision, we will fully reflect all of ...[more]

... your comments in our revised version.

Comments 1

The paper sheds light on the role of funding liquidity of financial institutions in a distressed market and provides a valuable alternative in explaining the investment behavior of financial institutions in a distressed market. The idea in the present paper is similar to the one in DeLong et al. (1990). Namely, an informed investor might be forced to liquidate at disadvantageous prices - that is before prices recover from some shock - and uninformed investors (noise traders) potentially further depress the price.

Answer 1

DeLong et al. (1990) analyzed the effects of uninformed noise traders on informed traders' behavior and financial markets. However, in addition to the uninformed trader, this paper studies the price destabilizing of the financial market by analyzing the effects of market liquidity risk and funding liquidity risk.

Comments 2

In Finance, an arbitrage opportunity does not require any net investment. This stands in sharp contrast to the financial institution's investment policy in the present paper. I suggest to talk about an informational rent instead of arbitrage profits as the financial institution knows that the depressed price will recover to the fundamental value for sure. Note that the greater the negative shock to the price is the higher is the informational rent to be earned.

Answer 2

Shleifer and Vishny (1997) refer to arbitrage as follows.

“Textbook arbitrage in financial markets requires no capital and entails no risk. In reality, almost all arbitrage requires capital, and is typically risky… professional arbitrage has a number of interesting implications for security pricing, including the possibility that arbitrage becomes ineffective in extreme circumstances, when prices diverge far from fundamental values.”

This paper introduces the concept of arbitrage in the above context, and other studies (Liu and Longstaff (2004), Liu and Mello (2011), Lewellen (2011)) also use the same concept of arbitrage.

As Referee mentions, I agree that the driver of arbitrage profit in this paper is the informational advantage and therefore arbitrage profit can be regarded as informational rent. However, we believe that it is appropriate to use arbitrage because we developed the analysis with focus on arbitrage opportunities and price destabilization.

Comments 3

In my view, the relevant driver of the results is not liquidity risk per se but the restriction that the financial institution is unable to borrow funds upon realizing the cash outflow \theta.

Answer 3

As Referee pointed out, some may have access to resources and may be able to invest more when prices diverge further from fundamentals. In general, however, institutional investors are difficult to borrow by credit rationing in situations of market decline or large fund outflows. Brunnermeier and Pedersen (2009) state that, in extreme situations, liquidity spirals could arise when marginal calls forced to sell assets held by financial institutions. As we have witnessed in 2008, the government has eventually bail out financial institutions by credit crunch.

This paper attempted to analyze the situation of market decline such as the financial crisis, so borrowing was as not considered. However, as Diamond and Dybvig (1983) describe the cause of credit rationing as liquidity risk, liquidity risk can be thought of in a broad sense including credit rationing. Accordingly, if we look at funding liquidity as net fund flows (= fund inflows - fund outflows), we can also include the concept of borrowing (fund inflows). However, as our research focuses on liquidity risk due to fund outflows, extension of the existing model will be required for credit rationing analysis.

Comments 4

The authors assume some deterministic price process.

Answer 4

The price process is not deterministic because theta is assumed a uniform distribution. So, the asset price at time2 is stochastically determined by theta. Even if institution chooses mu at time1 to maximize the expected value of profit, the realized profit is stochastically determined.

Comments 5

The authors discuss market stability in section 3.2. I disagree strongly. Nothing is said about whether the price recovers more quickly due to the financial institution's investment. The resiliency of the price is exogenous to the model. After the negative shock at date t=1 the financial institution knows that the price will recover at date t=3. This is independent of the financial institution's investment.

Answer 5

If there are multiple institutional investors in the market and only a few institutions experience liquidity risk, other institutions will increase the size of investments and market prices will not diverge from the fundamental. However, if many institutional investors invest in a direction opposite to the fundamental price and many suffer from lack of liquidity, the price at time2 will fall sharply. We hypothesize that only one institutional investor exists and we consider market destabilization as the situation in which prices deviate from fundamental value. Referee sees market stability as a concept of time, but this paper defines market stability as the degree of destabilization in fundamentals. The concept is also used in other papers (Brunnermeier and Pedersen (2009), Shleifer and Vishny (1994), and De Long et al. (1990)). Among them, Brunnermeier and Pedersen (2009) describe the relationship between speculator and market destabilization as follows.

“The system is also destabilized if speculators lose money on their previous position as prices move away from fundamentals.”

Comments 6

The authors argue along (7) that the funding liquidity f and the shock s are symmetric. Mathematically, this is true. However, as can be seen from figure 4, there are values of s which do not yield an equilibrium for the corresponding f value. Thus, economically both variables definitely are not symmetric.

Answer 6

As referee mentions, there are areas that are not defined in a particular s, and s and f are not 'perfectly' symmetric. But the reason we have referred to it as symmetric is because s and f have a similar effect on institutional investors' decisions.

Reference

Brunnermeier, M. K., & Pedersen, L. H. (2009). Market liquidity and funding liquidity, Review of Financial Studies, 22(6), 2201-2238.

De Long, J. B., Shleifer, A., Summers, L. H., & Waldmann, R. J. (1990). Noise trader risk in financial markets. Journal of Political Economy, 98(4), 703-738.

Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91(3), 401-419.

Liu, J., & Longstaff, F. A. (2004). Losing money on arbitrage: Optimal dynamic portfolio choice in markets with arbitrage opportunities. Review of Financial Studies, 17(3), 611-641.

Lewellen, J. (2011). Institutional investors and the limits of arbitrage. Journal of Financial Economics, 102(1), 62-80.

Liu, X., & Mello, A. S. (2011). The fragile capital structure of hedge funds and the limits to arbitrage. Journal of Financial Economics, 102(3), 491-506.

Shleifer, A., & Vishny, R. W. (1997). The limits of arbitrage. Journal of Finance, 52(1), 35-55.

The paper examines the behavior of a rational risk neutral informed institutional investor in the presences of trend following traders and the possibility of a withdrawal of funds by its backers. Investment takes place over a finite horizon with institutional traders acting first in period 1 based on private information, ...[more]

... trend following traders trade in period 2, and then the private information is revealed in period 3. Also during period 2, the institutional investor’s backers withdraw a randomly determined portion of their funds, possibly requiring the institutional to liquidate some of its position.

I wish this paper was written in a more traditional manner; an asset with a terminal value, four markets with prices in each market, and clearly articulated investor demand. The model would be considerably easier to read. As it is, I struggled to interpret throughout, from equation (1) onwards. I do not recognize the framework upon which the model is built. If it is original, it is inadequately developed. If it is developed based an existing model, the source is not referenced. The presentation reads as a collection of seemingly ad hoc, assertions regarding price, return, and actions. I am left with a number of unresolved questions that either point to problems in the model or, more favorably, a benign inadequate development. Take equation (1), the market clearing condition for the t=1 market. Demand is R-s+mu. On what basis is this demand? With mu as the demand from the institutional traders, where does R-s come from? Equation (3) is return, but it is just a re-expression of (1). It is unclear what is being asserted and what is derived.

The market is described as being populated by the institutional investors and the trend followers. That leaves the market without noise traders. Who is the counter-party to the trades in the t=1 market? If the t=1 market is only the institutional investors, then it seems to me that the market clearing condition is 1=mu. Who holds the asset in t=0?

I do not understand the trading activity by the institutional investors. The market is hit by a negative shock. “The institution occasionally trades the risky asset to exploit an arbitrage opportunity.” Private information of a negative shock would presumably induce the institutional traders to enter the market with negative position. This does not seem to be the case since, in Section 3 (p5), the reader is informed that short selling is prohibited. Also, the price coincides with returns, suggesting a positive holding. The alternative I can think of is that the institutional investor enters t=1 with a positive holding that they reduce in light of the negative information. In this case, the loss is already realized from the t=0 holding. The institutional investor is not exploiting the information except to get out at a price above the new fundamental. Additionally, assets are being converted to cash, reducing exposure. In this setting, mu is the remaining exposer and not the trade. All this, I believe, would change the institutional investor's optimization problem from the problem solved in Section 3.

“At time 0, before the negative shock distresses the market, the price of the risky asset is equal to its fundamental value, and the (normalized) fundamental return is denoted R.” (p2) This, to me, suggests an R that is established prior to the realization of s and the subsequent trading activities, in contrast to eqn (3).

The t=2 price (and return) is alpha/R. On what basis do the backwards looking trend followers, looking at p0 and p1, come up with demand proportional to forward looking event such as R? Since, according to (3), R depends on s and mu, it seems unlikely they should know it. Also, the more aggressively the informed traders trade on their knowledge of s, the smaller the positon taken by the trend followers, which seems counterintuitive.

According to eqn (3), R=1+s-mu. It would seem that market efficiency is achieved by mu=s, but then there would be no returns. Even in the absence concerns over the withdrawal of funds, the institutional investor should not trade to achieve the efficient price but rather, Kyle (1985) like, induce only partial adjustment through their position.

I find the use t=1 price as numeraire counterintuitive and confusing. It implies, among other things, that the p0 price changes based on s. Readers would benefit from clear articulation the activities and positions of all market participants in each period, including t=0. I could follow better if each period were priced based on the terminal value, maybe; p0=F (or is that F/R), p1 =p1(F,s,mu), p2=p2(F,s,mu,alpha,theta), p3=F+s, where F = pre-shock fundamental value and s~random with E(s)=0.

Minor issues:

The institutional traders are assumed “fully rational,” thus rendering the question in the title moot. As a theoretical analysis, this paper is unable to offer an answer. Rather, it answers the question as to how a rational institutional investor will behave.

The description of the institutional investors in the first paragraph of the model section mixes assumed attributes with findings.

Eqn (2), the third line should be alpha/R-mu*r(v) since theta>v does not change the market.

Comments and Referee Report on “Do institutions behave rationally in distressed markets?”

This theoretical paper examines important market microstructure issues. This study models the mechanism by which institutional investor moves away from fundamental value due to liquidity risk. Institutional investor is not actively investing in market because it is ...[more]

... afraid of fund outflows, and the gap between fundamental value and price is complexly determined by the size of market shock, funding liquidity, and the tendency of trend follower. In particular, this study derives the optimal decision of institutional investor as a closed form solution, and the contribution is high by analyzing the relationship between the three factors (S, f, and alpha) and market price. The paper is well-written and well-organized and I believe that it contains significant academic contributions. I recommend the acceptance of this paper conditional upon satisfactorily addressing or explaining the following issues.

1. The model assumes a single institutional investor, and at time 2, the market would be unstable if institutional investor withdraws its investment. However, in the real market, there are multiple investors, and even if one investor fails to arbitrage due to liquidity risk, other investors will capture arbitrage opportunities and price will converge to fundamental value at time 2. Assuming multiple heterogeneous institutional investors, how do you expect the results of the model to change?

2. This study assumes that fund outflows (theta) occur randomly at time 2, but it does not explain why fund outflow occurs. Shleifer and Vishny (1997), a major study on limit to arbitrage, have interpreted the reason for the decrease in asset under management (AUM) as the poor performance of the fund, which considers it (performance-based-arbitrage) as the main reason for limit to arbitrage.

3. In this model, institutional investor has a risk neutral incentive. However, a general economic model assumes a risk averse agent. Is there a particular reason for assuming a risk neutral investor? If you introduce a risk averse investor, what do you expect the results to be?

4. The last is a minor question. In Equation (1), the author sets the market price at time 1 to unity. I wonder if there is a particular reason for normalizing to 1 without using ‘p1’, which is generally used notation in the time discrete model.

Dear anonymous referees and invited readers,

Thank you very much for giving us the chance of revision. As you pointed out, we believe that this paper has a potential and contributes to the existing literature. Because of the revision based on your comments, the quality of this paper has been ...[more]

... improved. We answer for the comments of the referees and reflect the comments in the revised paper as follows.

Referee Report 1

Comments 1

The paper sheds light on the role of funding liquidity of financial institutions in a distressed market and provides a valuable alternative in explaining the investment behavior of financial institutions in a distressed market. The idea in the present paper is similar to the one in DeLong et al. (1990). Namely, an informed investor might be forced to liquidate at disadvantageous prices - that is before prices recover from some shock - and uninformed investors (noise traders) potentially further depress the price.

Answer 1

DeLong et al. (1990) analyzed the effects of uninformed noise traders on informed traders' behavior and financial markets. It shows the situation where informed traders have to sell at an unfavorable price. However, this paper focuses not only on the uninformed traders’ price depression, but also on funding liquidity risk due to early withdrawal of fund investors. If there is no funding liquidity risk, informed trader will not sell even if uninformed traders depress the price, because informed trader can maximize profits (without fund inflows) if it holds positions up to time 3.

Comments 2

In Finance, an arbitrage opportunity does not require any net investment. This stands in sharp contrast to the financial institution's investment policy in the present paper. I suggest to talk about an informational rent instead of arbitrage profits as the financial institution knows that the depressed price will recover to the fundamental value for sure. Note that the greater the negative shock to the price is the higher is the informational rent to be earned.

Answer 2

Shleifer and Vishny (1997) refer to arbitrage as follows:

“Textbook arbitrage in financial markets requires no capital and entails no risk. In reality, almost all arbitrage requires capital, and is typically risky… professional arbitrage has a number of interesting implications for security pricing, including the possibility that arbitrage becomes ineffective in extreme circumstances, when prices diverge far from fundamental values.”

Other studies - Liu and Longstaff (2004), Liu and Mello (2011), Lewellen (2011) - also use the above concept of arbitrage. This paper also introduces the same concept of arbitrage mentioning as follows:

“The financial market, which is subject to a negative shock, diverges from fundamental values in the short term but converges to fundamental values in the long term. This context provides arbitrage opportunities, allowing a large institution to trade against temporary price deviations.”

As Referee notices, we agree that the driver of profit in this paper is the informational advantage and therefore the profit can be regarded as informational rent. However, we believe that it is appropriate to use the term “arbitrage” because we developed the analysis with focus on arbitrage opportunities and temporary price deviations.

Comments 3

In my view, the relevant driver of the results is not liquidity risk per se but the restriction that the financial institution is unable to borrow funds upon realizing the cash outflow \theta.

Answer 3

As Referee pointed out, some may have access to resources and may be able to invest more when prices diverge further from fundamentals. In general, however, institutional investors are difficult to borrow by credit rationing in situations of market decline or large fund outflows. Brunnermeier and Pedersen (2009) state that, in extreme situations, liquidity spirals could arise when marginal calls forced to sell assets held by financial institutions. As we have witnessed in 2008, the government has eventually bail out financial institutions by credit crunch.

This paper attempted to analyze the situation of market decline such as the financial crisis, so borrowing was as not considered. However, as Diamond and Dybvig (1983) describe the cause of credit rationing as liquidity risk, liquidity risk can be thought of in a broad sense including credit rationing. Accordingly, if we look at funding liquidity as net fund flows (= fund inflows - fund outflows), we can also include the concept of borrowing (fund inflows). However, as our research focuses on liquidity risk due to fund outflows, extension of the existing model will be required for credit rationing analysis.

Comments 4

The authors assume some deterministic price process.

Answer 4

The price process is not deterministic because theta is assumed a uniform distribution. So, the asset price at time 2 is stochastically determined by theta. Even if institution chooses mu at time 1 to maximize the expected value of profit, the realized profit is stochastically determined.

Someone might wonder why we use uniform distribution. In this study, we are interested in how an institution behaves when there is uncertainty in theta (i.e., funding liquidity risk) and how it affects market prices. It is not our interest that the size of institution’s trading volume and the size of price deviation. If someone uses a different distribution, trading volume and the price will change. However, it should be careful that the distribution is truncated at 0 and at f (theta should be in the interval [0, f]) and the optimal mu may not be obtained in closed form. Once optimal mu is obtained, the price at time 2 is determined same as equation (2). We will mention the reason for choosing a uniform distribution in the paper.

Comments 5

The authors discuss market stability in section 3.2. I disagree strongly. Nothing is said about whether the price recovers more quickly due to the financial institution's investment. The resiliency of the price is exogenous to the model. After the negative shock at date t=1 the financial institution knows that the price will recover at date t=3. This is independent of the financial institution's investment.

Answer 5

If there are multiple institutional investors in the market and only a few institutions experience liquidity risk, other institutions will increase the size of investments and market prices will not diverge from the fundamental. However, if many institutional investors invest in a direction opposite to the fundamental price and many suffer from lack of liquidity, the price at time2 will fall sharply. We hypothesize that only one institutional investor exists and we consider market destabilization as the situation in which prices temporarily deviate from fundamental value. Referee sees market stability as a concept of time, but this paper defines market instability as the degree of price deviation from fundamentals. This concept is also used in other papers -Brunnermeier and Pedersen (2009), Shleifer and Vishny (1994), and De Long et al. (1990). Among them, Brunnermeier and Pedersen (2009) describe the relationship between speculator and market destabilization as follows.

“The system is also destabilized if speculators lose money on their previous position as prices move away from fundamentals.”

Comments 6

The authors argue along (7) that the funding liquidity f and the shock s are symmetric. Mathematically, this is true. However, as can be seen from figure 4, there are values of s which do not yield an equilibrium for the corresponding f value. Thus, economically both variables definitely are not symmetric.

Answer 6

As referee mentions, there are areas that are not defined in a particular s, and s and f are not 'perfectly' symmetric. But the reason we have referred to it as symmetric is because s and f have a similar effect on institutional investors' decisions. We will reflect referee’s comment in a footnote.

Referee Report 2

Comments 7

If it is original, it is inadequately developed. If it is developed based an existing model, the source is not referenced.

Answer 7

The model of this paper has a structure similar to that of Shleifer and Vishny(1997) and extends the Shleifer and Vishny(1997) to explain the limit of arbitrage caused by funding liquidity risk. We will mention the above facts in the paper.

Comments 8

Take equation (1), the market clearing condition for the t=1 market. Demand is R-s+mu. On what basis is this demand? With mu as the demand from the institutional traders, where does R-s come from?

The market is described as being populated by the institutional investors and the trend followers. That leaves the market without noise traders. Who is the counter-party to the trades in the t=1 market? If the t=1 market is only the institutional investors, then it seems to me that the market clearing condition is 1=mu. Who holds the asset in t=0

Answer 8

There are one institutional investor and many trend followers in the model. However, the explanation of the trend follower that is necessary for the concrete model development is omitted. At time 1, trend followers act as noise traders. That is, they experience a negative shock and generate the demand of R-s. At time 2, the trend followers observe past prices and do market trend following trading. We will add a detailed explanation of trend followers to the paper.

Comments 9

Private information of a negative shock would presumably induce the institutional traders to enter the market with negative position. This does not seem to be the case since, in Section 3 (p5), the reader is informed that short selling is prohibited. Also, the price coincides with returns, suggesting a positive holding. The alternative I can think of is that the institutional investor enters t=1 with a positive holding that they reduce in light of the negative information. In this case, the loss is already realized from the t=0 holding.

Answer 9

The institution doesn’t have private information of a negative shock. Rather than, it invests mu in the risky asset at time 1 after observing the impact of the negative shock. Changes in the prices of time0 and time1 indirectly affect mu by changing demand of uninformed traders. Except that, the price change of time0 and time1 is irrelevant to the choice of mu.

Comments 10

Equation (3) is return, but it is just a re-expression of (1). It is unclear what is being asserted and what is derived.

This, to me, suggests an R that is established prior to the realization of s and the subsequent trading activities, in contrast to eqn (3).

On what basis do the backwards looking trend followers, looking at p0 and p1, come up with demand proportional to forward looking event such as R? Since, according to (3), R depends on s and mu, it seems unlikely they should know it.

Answer 10

In the model, the market price begins at R(>1) at time 0, and drops at time 1 and time 2. After then it converges to R again at time 3. For convenience, we set the prices of time 0 and time 3 to R equally. However, unlike time 0 price, time 3 price 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 of time 0 and time 1 rather than the value determined by time 3 price. The institutional investor knows the price of time 3 at time 1, so it determines theta to maximize the asset value of time 3.

The addition of time 0 in the model is due to the need of time 0 price to account for the trading strategy of the trend followers (they follow market trends such that their aggregate demand is proportional to past prices), and the reason why time 0 price is set equal to terminal price R is because it is most appropriate price at time 0 among various values.

Comments 11

Also, the more aggressively the informed traders trade on their knowledge of s, the smaller the positon taken by the trend followers, which seems counterintuitive.

Answer 11

According to a study on amplification trading, an informed trader initially performs divergence trading in a direction opposite to the fundamental value, and then when the uninformed traders amplify the market price, it maximizes profit by investing again in the direction of fundamental value. However, in order to implement the amplification trading strategy on the downside, short selling should be allowed and funding liquidity risk should be low enough.

Comments 12

According to eqn (3), R=1+s-mu. It would seem that market efficiency is achieved by mu=s, but then there would be no returns.

Answer 12

According to R> 1 condition, s> mu is established. Therefore, arbitrage opportunities exist in this model.

Comments 13

I find the use t=1 price as numeraire counterintuitive and confusing. It implies, among other things, that the p0 price changes based on s. Readers would benefit from clear articulation the activities and positions of all market participants in each period, including t=0. I could follow better if each period were priced based on the terminal value, maybe; p0=F (or is that F/R), p1 =p1(F,s,mu), p2=p2(F,s,mu,alpha,theta), p3=F+s, where F = pre-shock fundamental value and s~random with E(s)=0.

Answer 13

The reason why the price of time 1 is used as numeraire is because the investment of institutional investor occurs at time 1 and asset returns are frequently used in model development such as optimization problem. Of course, pt (p1, p2, p3) can be a more intuitive notation, but in optimization problems, this notation can make the problem more complex because asset returns at each time should be expressed as “pt/p1”. Diamond and Dybvig (1983) also set a final return to R for the initial technology investment of 1 to present a model in terms of return on investment. Nevertheless, we admit that it can be confusing to use both price and return together. So, we will unify the term with price. Then, the prices of time 0, time 1, time 2 and time 3 are denoted respectively R, 1, r and R.

Since we are focusing on funding liquidity risk, we assume that theta follows stochastic process. Even if s can be a random value, this assumption will blur the points of this paper.

Comments 14

The institutional traders are assumed “fully rational,” thus rendering the question in the title moot. As a theoretical analysis, this paper is unable to offer an answer. Rather, it answers the question as to how a rational institutional investor will behave.

Answer 14

As referee pointed out, we will change the title as follows: The behavior of an institutional investor with arbitrage opportunity and liquidity risk.

Comments 15

The description of the institutional investors in the first paragraph of the model section mixes assumed attributes with findings.

Answer 15

As mentioned above, we will delete the findings in the model section.

Comments 16

Eqn (2), the third line should be alpha/R-mu*r(v) since theta>v does not change the market.

Answer 16

The third line in eq(2) contains r(theta) in the right-hand side to help the reader understand, but we will explicitly modify it as follows: r(theta) = (alpha / R) / (1 + mu).

Invited Reader Comments

Comments 16

In the page 5, Authors suppose that both short sales and borrowing are prohibited; but, in general, institutional investor often use short sales. Under this constraints, the result seems only natural: if institutions do not have enough money, then they sell their asset. So I'm curious about the results without this constraint.

Answer 16

In Comments 9 we answered as follows: “If short selling is possible, there is an incentive for the institutional investor to do amplification trading, further reducing the market price. However, this is not the focus of this paper, so short selling condition is excluded.”

Even if short selling is possible, funding liquidity risk still exists. Institutional investors therefore will not fully exploit arbitrage opportunities and the intensity of amplification trading is expected to be weaker than assuming no liquidity risk.

Comments 17

1. The model assumes a single institutional investor, and at time 2, the market would be unstable if institutional investor withdraws its investment. However, in the real market, there are multiple investors, and even if one investor fails to arbitrage due to liquidity risk, other investors will capture arbitrage opportunities and price will converge to fundamental value at time 2. Assuming multiple heterogeneous institutional investors, how do you expect the results of the model to change?

2. This study assumes that fund outflows (theta) occur randomly at time 2, but it does not explain why fund outflow occurs. Shleifer and Vishny (1997), a major study on limit to arbitrage, have interpreted the reason for the decrease in asset under management (AUM) as the poor performance of the fund, which considers it (performance-based-arbitrage) as the main reason for limit to arbitrage.

3. In this model, institutional investor has a risk neutral incentive. However, a general economic model assumes a risk averse agent. Is there a particular reason for assuming a risk neutral investor? If you introduce a risk averse investor, what do you expect the results to be?

4. The last is a minor question. In Equation (1), the author sets the market price at time 1 to unity. I wonder if there is a particular reason for normalizing to 1 without using ‘p1’, which is generally used notation in the time discrete model.

Answers 17

1. If there are multiple institutional investors, the optimal decision of an investor depends on the decision of other investors. Assuming homogeneous investors, all investors in the equilibrium will choose the same optimal theta. However, the value of the optimal decision will vary depending on whether investors are aware of each other's decisions.

In the absence of information asymmetry between institutional investors, they know that collusion is the most profitable and, if any, they can see who the betrayer is. As a result, the optimal theta will be the same as that of this paper.

However, if there is information asymmetry, investors cannot collude because they do not observe others’ decision. Then, as the number of investors increases, their market power decreases. As a result, the optimal theta in the equilibrium will be bigger than that of monopolistic case.

2. Fund outflows generally occur when fund returns are bad. However, it can also happen when the market situation is not good or when the liquidity of the fund investors becomes insufficient due to other factors.

3. Many economics studies often assume risk neutral agents. Nevertheless if we assume a risk averse institutional investor in this paper, institution will be more likely to avoid liquidity risk and consequently the optimal theta is expected to be further reduced comparing to that of risk neutral model.

4. See Answer 13.

Reference

Brunnermeier, M. K., & Pedersen, L. H. (2009). Market liquidity and funding liquidity, Review of Financial Studies, 22(6), 2201-2238.

De Long, J. B., Shleifer, A., Summers, L. H., & Waldmann, R. J. (1990). Noise trader risk in financial markets. Journal of Political Economy, 98(4), 703-738.

Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91(3), 401-419.

Liu, J., & Longstaff, F. A. (2004). Losing money on arbitrage: Optimal dynamic portfolio choice in markets with arbitrage opportunities. Review of Financial Studies, 17(3), 611-641.

Lewellen, J. (2011). Institutional investors and the limits of arbitrage. Journal of Financial Economics, 102(1), 62-80.

Liu, X., & Mello, A. S. (2011). The fragile capital structure of hedge funds and the limits to arbitrage. Journal of Financial Economics, 102(3), 491-506.

Shleifer, A., & Vishny, R. W. (1997). The limits of arbitrage. Journal of Finance, 52(1), 35-55.

Dear anonymous referees and invited readers,

Thank you very much for giving us the chance of revision. As you pointed out, we believe that this paper has a potential and contributes to the existing literature. Because of the revision based on your comments, the quality of this paper has been ...[more]

... improved. We answer for the comments of the referees and reflect the comments in the revised paper as follows.

Referee Report 1

Comments 1

The paper sheds light on the role of funding liquidity of financial institutions in a distressed market and provides a valuable alternative in explaining the investment behavior of financial institutions in a distressed market. The idea in the present paper is similar to the one in DeLong et al. (1990). Namely, an informed investor might be forced to liquidate at disadvantageous prices - that is before prices recover from some shock - and uninformed investors (noise traders) potentially further depress the price.

Answer 1

DeLong et al. (1990) analyzed the effects of uninformed noise traders on informed traders' behavior and financial markets. It shows the situation where informed traders have to sell at an unfavorable price. However, this paper focuses not only on the uninformed traders’ price depression, but also on funding liquidity risk due to early withdrawal of fund investors. If there is no funding liquidity risk, informed trader will not sell even if uninformed traders depress the price, because informed trader can maximize profits (without fund inflows) if it holds positions up to time 3.

Comments 2

In Finance, an arbitrage opportunity does not require any net investment. This stands in sharp contrast to the financial institution's investment policy in the present paper. I suggest to talk about an informational rent instead of arbitrage profits as the financial institution knows that the depressed price will recover to the fundamental value for sure. Note that the greater the negative shock to the price is the higher is the informational rent to be earned.

Answer 2

Shleifer and Vishny (1997) refer to arbitrage as follows:

“Textbook arbitrage in financial markets requires no capital and entails no risk. In reality, almost all arbitrage requires capital, and is typically risky… professional arbitrage has a number of interesting implications for security pricing, including the possibility that arbitrage becomes ineffective in extreme circumstances, when prices diverge far from fundamental values.”

Other studies - Liu and Longstaff (2004), Liu and Mello (2011), Lewellen (2011) - also use the above concept of arbitrage. This paper also introduces the same concept of arbitrage mentioning as follows:

“The financial market, which is subject to a negative shock, diverges from fundamental values in the short term but converges to fundamental values in the long term. This context provides arbitrage opportunities, allowing a large institution to trade against temporary price deviations.”

As Referee notices, we agree that the driver of profit in this paper is the informational advantage and therefore the profit can be regarded as informational rent. However, we believe that it is appropriate to use the term “arbitrage” because we developed the analysis with focus on arbitrage opportunities and temporary price deviations.

Comments 3

In my view, the relevant driver of the results is not liquidity risk per se but the restriction that the financial institution is unable to borrow funds upon realizing the cash outflow \theta.

Answer 3

As Referee pointed out, some may have access to resources and may be able to invest more when prices diverge further from fundamentals. In general, however, institutional investors are difficult to borrow by credit rationing in situations of market decline or large fund outflows. Brunnermeier and Pedersen (2009) state that, in extreme situations, liquidity spirals could arise when marginal calls forced to sell assets held by financial institutions. As we have witnessed in 2008, the government has eventually bail out financial institutions by credit crunch.

This paper attempted to analyze the situation of market decline such as the financial crisis, so borrowing was as not considered. However, as Diamond and Dybvig (1983) describe the cause of credit rationing as liquidity risk, liquidity risk can be thought of in a broad sense including credit rationing. Accordingly, if we look at funding liquidity as net fund flows (= fund inflows - fund outflows), we can also include the concept of borrowing (fund inflows). However, as our research focuses on liquidity risk due to fund outflows, extension of the existing model will be required for credit rationing analysis.

Comments 4

The authors assume some deterministic price process.

Answer 4

The price process is not deterministic because theta is assumed a uniform distribution. So, the asset price at time 2 is stochastically determined by theta. Even if institution chooses mu at time 1 to maximize the expected value of profit, the realized profit is stochastically determined.

Someone might wonder why we use uniform distribution. In this study, we are interested in how an institution behaves when there is uncertainty in theta (i.e., funding liquidity risk) and how it affects market prices. It is not our interest that the size of institution’s trading volume and the size of price deviation. If someone uses a different distribution, trading volume and the price will change. However, it should be careful that the distribution is truncated at 0 and at f (theta should be in the interval [0, f]) and the optimal mu may not be obtained in closed form. Once optimal mu is obtained, the price at time 2 is determined same as equation (2). We will mention the reason for choosing a uniform distribution in the paper.

Comments 5

The authors discuss market stability in section 3.2. I disagree strongly. Nothing is said about whether the price recovers more quickly due to the financial institution's investment. The resiliency of the price is exogenous to the model. After the negative shock at date t=1 the financial institution knows that the price will recover at date t=3. This is independent of the financial institution's investment.

Answer 5

If there are multiple institutional investors in the market and only a few institutions experience liquidity risk, other institutions will increase the size of investments and market prices will not diverge from the fundamental. However, if many institutional investors invest in a direction opposite to the fundamental price and many suffer from lack of liquidity, the price at time2 will fall sharply. We hypothesize that only one institutional investor exists and we consider market destabilization as the situation in which prices temporarily deviate from fundamental value. Referee sees market stability as a concept of time, but this paper defines market instability as the degree of price deviation from fundamentals. This concept is also used in other papers -Brunnermeier and Pedersen (2009), Shleifer and Vishny (1994), and De Long et al. (1990). Among them, Brunnermeier and Pedersen (2009) describe the relationship between speculator and market destabilization as follows.

“The system is also destabilized if speculators lose money on their previous position as prices move away from fundamentals.”

Comments 6

The authors argue along (7) that the funding liquidity f and the shock s are symmetric. Mathematically, this is true. However, as can be seen from figure 4, there are values of s which do not yield an equilibrium for the corresponding f value. Thus, economically both variables definitely are not symmetric.

Answer 6

As referee mentions, there are areas that are not defined in a particular s, and s and f are not 'perfectly' symmetric. But the reason we have referred to it as symmetric is because s and f have a similar effect on institutional investors' decisions. We will reflect referee’s comment in a footnote.

Referee Report 2

Comments 7

If it is original, it is inadequately developed. If it is developed based an existing model, the source is not referenced.

Answer 7

The model of this paper has a structure similar to that of Shleifer and Vishny(1997) and extends the Shleifer and Vishny(1997) to explain the limit of arbitrage caused by funding liquidity risk. We will mention the above facts in the paper.

Comments 8

Take equation (1), the market clearing condition for the t=1 market. Demand is R-s+mu. On what basis is this demand? With mu as the demand from the institutional traders, where does R-s come from?

The market is described as being populated by the institutional investors and the trend followers. That leaves the market without noise traders. Who is the counter-party to the trades in the t=1 market? If the t=1 market is only the institutional investors, then it seems to me that the market clearing condition is 1=mu. Who holds the asset in t=0

Answer 8

There are one institutional investor and many trend followers in the model. However, the explanation of the trend follower that is necessary for the concrete model development is omitted. At time 1, trend followers act as noise traders. That is, they experience a negative shock and generate the demand of R-s. At time 2, the trend followers observe past prices and do market trend following trading. We will add a detailed explanation of trend followers to the paper.

Comments 9

Private information of a negative shock would presumably induce the institutional traders to enter the market with negative position. This does not seem to be the case since, in Section 3 (p5), the reader is informed that short selling is prohibited. Also, the price coincides with returns, suggesting a positive holding. The alternative I can think of is that the institutional investor enters t=1 with a positive holding that they reduce in light of the negative information. In this case, the loss is already realized from the t=0 holding.

Answer 9

The institution doesn’t have private information of a negative shock. Rather than, it invests mu in the risky asset at time 1 after observing the impact of the negative shock. Changes in the prices of time0 and time1 indirectly affect mu by changing demand of uninformed traders. Except that, the price change of time0 and time1 is irrelevant to the choice of mu.

Comments 10

Equation (3) is return, but it is just a re-expression of (1). It is unclear what is being asserted and what is derived.

This, to me, suggests an R that is established prior to the realization of s and the subsequent trading activities, in contrast to eqn (3).

On what basis do the backwards looking trend followers, looking at p0 and p1, come up with demand proportional to forward looking event such as R? Since, according to (3), R depends on s and mu, it seems unlikely they should know it.

Answer 10

In the model, the market price begins at R(>1) at time 0, and drops at time 1 and time 2. After then it converges to R again at time 3. For convenience, we set the prices of time 0 and time 3 to R equally. However, unlike time 0 price, time 3 price 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 of time 0 and time 1 rather than the value determined by time 3 price. The institutional investor knows the price of time 3 at time 1, so it determines theta to maximize the asset value of time 3.

The addition of time 0 in the model is due to the need of time 0 price to account for the trading strategy of the trend followers (they follow market trends such that their aggregate demand is proportional to past prices), and the reason why time 0 price is set equal to terminal price R is because it is most appropriate price at time 0 among various values.

Comments 11

Also, the more aggressively the informed traders trade on their knowledge of s, the smaller the positon taken by the trend followers, which seems counterintuitive.

Answer 11

According to a study on amplification trading, an informed trader initially performs divergence trading in a direction opposite to the fundamental value, and then when the uninformed traders amplify the market price, it maximizes profit by investing again in the direction of fundamental value. However, in order to implement the amplification trading strategy on the downside, short selling should be allowed and funding liquidity risk should be low enough.

Comments 12

According to eqn (3), R=1+s-mu. It would seem that market efficiency is achieved by mu=s, but then there would be no returns.

Answer 12

According to R> 1 condition, s> mu is established. Therefore, arbitrage opportunities exist in this model.

Comments 13

I find the use t=1 price as numeraire counterintuitive and confusing. It implies, among other things, that the p0 price changes based on s. Readers would benefit from clear articulation the activities and positions of all market participants in each period, including t=0. I could follow better if each period were priced based on the terminal value, maybe; p0=F (or is that F/R), p1 =p1(F,s,mu), p2=p2(F,s,mu,alpha,theta), p3=F+s, where F = pre-shock fundamental value and s~random with E(s)=0.

Answer 13

The reason why the price of time 1 is used as numeraire is because the investment of institutional investor occurs at time 1 and asset returns are frequently used in model development such as optimization problem. Of course, pt (p1, p2, p3) can be a more intuitive notation, but in optimization problems, this notation can make the problem more complex because asset returns at each time should be expressed as “pt/p1”. Diamond and Dybvig (1983) also set a final return to R for the initial technology investment of 1 to present a model in terms of return on investment. Nevertheless, we admit that it can be confusing to use both price and return together. So, we will unify the term with price. Then, the prices of time 0, time 1, time 2 and time 3 are denoted respectively R, 1, r and R.

Since we are focusing on funding liquidity risk, we assume that theta follows stochastic process. Even if s can be a random value, this assumption will blur the points of this paper.

Comments 14

The institutional traders are assumed “fully rational,” thus rendering the question in the title moot. As a theoretical analysis, this paper is unable to offer an answer. Rather, it answers the question as to how a rational institutional investor will behave.

Answer 14

As referee pointed out, we will change the title as follows: The behavior of an institutional investor with arbitrage opportunity and liquidity risk.

Comments 15

The description of the institutional investors in the first paragraph of the model section mixes assumed attributes with findings.

Answer 15

As mentioned above, we will delete the findings in the model section.

Comments 16

Eqn (2), the third line should be alpha/R-mu*r(v) since theta>v does not change the market.

Answer 16

The third line in eq(2) contains r(theta) in the right-hand side to help the reader understand, but we will explicitly modify it as follows: r(theta) = (alpha / R) / (1 + mu).

Invited Reader Comments

Comments 16

In the page 5, Authors suppose that both short sales and borrowing are prohibited; but, in general, institutional investor often use short sales. Under this constraints, the result seems only natural: if institutions do not have enough money, then they sell their asset. So I'm curious about the results without this constraint.

Answer 16

In Comments 9 we answered as follows: “If short selling is possible, there is an incentive for the institutional investor to do amplification trading, further reducing the market price. However, this is not the focus of this paper, so short selling condition is excluded.”

Even if short selling is possible, funding liquidity risk still exists. Institutional investors therefore will not fully exploit arbitrage opportunities and the intensity of amplification trading is expected to be weaker than assuming no liquidity risk.

Comments 17

1. The model assumes a single institutional investor, and at time 2, the market would be unstable if institutional investor withdraws its investment. However, in the real market, there are multiple investors, and even if one investor fails to arbitrage due to liquidity risk, other investors will capture arbitrage opportunities and price will converge to fundamental value at time 2. Assuming multiple heterogeneous institutional investors, how do you expect the results of the model to change?

2. This study assumes that fund outflows (theta) occur randomly at time 2, but it does not explain why fund outflow occurs. Shleifer and Vishny (1997), a major study on limit to arbitrage, have interpreted the reason for the decrease in asset under management (AUM) as the poor performance of the fund, which considers it (performance-based-arbitrage) as the main reason for limit to arbitrage.

3. In this model, institutional investor has a risk neutral incentive. However, a general economic model assumes a risk averse agent. Is there a particular reason for assuming a risk neutral investor? If you introduce a risk averse investor, what do you expect the results to be?

4. The last is a minor question. In Equation (1), the author sets the market price at time 1 to unity. I wonder if there is a particular reason for normalizing to 1 without using ‘p1’, which is generally used notation in the time discrete model.

Answers 17

1. If there are multiple institutional investors, the optimal decision of an investor depends on the decision of other investors. Assuming homogeneous investors, all investors in the equilibrium will choose the same optimal theta. However, the value of the optimal decision will vary depending on whether investors are aware of each other's decisions.

In the absence of information asymmetry between institutional investors, they know that collusion is the most profitable and, if any, they can see who the betrayer is. As a result, the optimal theta will be the same as that of this paper.

However, if there is information asymmetry, investors cannot collude because they do not observe others’ decision. Then, as the number of investors increases, their market power decreases. As a result, the optimal theta in the equilibrium will be bigger than that of monopolistic case.

2. Fund outflows generally occur when fund returns are bad. However, it can also happen when the market situation is not good or when the liquidity of the fund investors becomes insufficient due to other factors.

3. Many economics studies often assume risk neutral agents. Nevertheless if we assume a risk averse institutional investor in this paper, institution will be more likely to avoid liquidity risk and consequently the optimal theta is expected to be further reduced comparing to that of risk neutral model.

4. See Answer 13.

Reference

Brunnermeier, M. K., & Pedersen, L. H. (2009). Market liquidity and funding liquidity, Review of Financial Studies, 22(6), 2201-2238.

De Long, J. B., Shleifer, A., Summers, L. H., & Waldmann, R. J. (1990). Noise trader risk in financial markets. Journal of Political Economy, 98(4), 703-738.

Diamond, D. W., & Dybvig, P. H. (1983). Bank runs, deposit insurance, and liquidity. Journal of Political Economy, 91(3), 401-419.

Liu, J., & Longstaff, F. A. (2004). Losing money on arbitrage: Optimal dynamic portfolio choice in markets with arbitrage opportunities. Review of Financial Studies, 17(3), 611-641.

Lewellen, J. (2011). Institutional investors and the limits of arbitrage. Journal of Financial Economics, 102(1), 62-80.

Liu, X., & Mello, A. S. (2011). The fragile capital structure of hedge funds and the limits to arbitrage. Journal of Financial Economics, 102(3), 491-506.

Shleifer, A., & Vishny, R. W. (1997). The limits of arbitrage. Journal of Finance, 52(1), 35-55.