ساختار سرمایه شکننده از صندوق های تامینی و محدودیت های آربیتراژ

During a financial crisis, when investors are most in need of liquidity and accurate prices, hedge funds cut their arbitrage positions and hoard cash. The paper explains this phenomenon. We argue that the fragile nature of the capital structure of hedge funds, combined with low market liquidity, creates a risk of coordination in redemptions among hedge fund investors that severely limits hedge funds' arbitrage capabilities. We present a model of hedge funds' optimal asset allocation in the presence of coordination risk among investors. We show that hedge fund managers behave conservatively and even abstain from participating in the market once coordination risk is factored into their investment decisions. The model suggests a new source of limits to arbitrage.

In the financial crisis of 2007–2009, hedge funds reduced their exposures to risky investments and increased their cash holdings very quickly. The Economist estimates that between July and August 2008 alone, the industry's cash holdings rose from $156 billion to a record $184 billion, equivalent to 11% of assets under management. 1 The reallocation toward cash seemed to be in anticipation of unprecedented pressure for redemptions from investors. In fact, the hedge fund industry experienced record levels of redemptions during the third and fourth quarters of 2008. In the first half of 2009, investors continued to pull money out of hedge funds. Ironically, redemptions appear to have been self-reinforcing. A report titled Hedge Funds 2009 by the International Financial Services London Research (IFSL) says: Hedge funds faced unprecedented pressure for redemptions in the latter part of 2008, with investors withdrawing funds due to dissatisfaction with the performance or to cover for even greater losses or cash calls elsewhere. This in turn led to forced selling and closures of positions by hedge funds causing a cycle of further losses and redemptions. Some funds were not able to meet withdrawal requests so were forced to suspend redemptions, as selling illiquid assets would have damaged the investors that remained. In this paper we ask why hedge funds, with a reputation for being aggressive investors seeking high returns, hold significant amounts of cash in their balance sheets. And, why do they quickly increase their cash holdings (hoard liquidity) when a crisis strikes? One would think that it is precisely during times of high uncertainty and high volatility that arbitrage opportunities are greater.2 Why then do hedge funds become much less aggressive in exploiting price distortions and pass up profit opportunities? In their quest for arbitrage gains, hedge funds also perform the important social role of enforcing market efficiency. From a social welfare point of view, it is not optimal that hedge funds allocate large fractions of their portfolios to riskless securities, instead of pursuing arbitrage opportunities in risky assets. Holding cash is synonymous with imposing limits on arbitrage. With insufficient arbitrage trading, financial markets can wander off erratically and risk falling into a vicious cycle that goes from lower price informativeness to less liquidity and back, a process of continued deterioration that can prolong a financial crisis. Thus, to analyze a modern financial crisis it is necessary to understand the reasons that hedge funds limit their arbitrage activities. So far the finance literature has associated the limits to arbitrage with investor uncertainty about the fundamental value of the assets held by arbitrageurs. According to Shleifer and Vishny (1997), when investors do not understand or observe perfectly arbitrageurs' trading positions, they can react with their feet after observing poor performance. Understanding that poor performance can cause redemptions, hedge fund managers refrain from making investments that might lose money in the short term, even if a profit could be realized in the long run.3 In this paper, we offer an alternative explanation for the limits of arbitrage. We highlight investors' concerns about coordination risk (i.e., the uncertainty about what other investors might decide to do), instead of about fundamental risk. One key feature of the capital structure of hedge funds is the fragile nature of their equity. Equity capital in hedge funds can be redeemed at investors' discretion, a feature somewhat similar to demand deposit-debt in banks.4 The fragile equity capital in hedge funds introduces the risk of coordination among hedge fund investors. The coordination risk arises because investors suspect that other investors might redeem, and to meet redemptions the hedge fund may be forced to liquidate positions at a loss. If investors suspect that, after liquidating positions to satisfy early redemptions, the hedge fund would be left with insufficient equity, a clear advantage exists to being a first mover. Then, even long-horizon investors could decide to withdraw, resulting in a vicious cycle of redemptions and asset sales that can trigger a disorderly collapse of the hedge fund. This risk of coordination must be taken into account by prudent hedge fund managers, who limit their arbitrage activities and hoard cash both to honor redemptions at little cost and to reassure concerned investors. We use global game methods to model the asset allocation decision of a hedge fund that is subject to the risk of a run by its investors. We start by considering the benchmark case with no coordination problem. A random number of investors is assumed to redeem early for exogenous reasons. The random amount of the early redemptions requires the hedge fund to decide how much cash it needs to hold ex ante. The hedge fund's trade-off is between lower potential liquidation costs if it holds more cash, and a higher return if it invests more in risky assets. This trade-off gives an optimal level of cash holdings. In the presence of coordination risk, however, we show that hedge funds choose to hold more (i.e., excess) cash. Coordination risk affects the optimal level of cash in a fund in two ways. First, the fear of a possible run makes a greater number of investors redeem even if they do not face liquidity shocks. To satisfy redemptions at minimum cost, hedge funds optimally choose to hold more cash. Second, cash holdings have a direct impact on investors' decision to withdraw and, consequently, on the probability of a run. Naturally, the probability of a run is decreasing in the cash holdings. In sum, the source of the limits to arbitrage in our paper is market illiquidity and the unstable nature of the equity capital in hedge funds. We emphasize the friction of investors' uncertainty about the actions of other investors in the fund, i.e., the liability side of the balance sheet, while in Shleifer and Vishny (1997) investors are uncertain about the asset side of the balance sheet, i.e., asset quality. Limits to arbitrage due to coordination risk are particularly likely in financial crises, when market liquidity is low and coordination problems are severe. We believe that a fuller explanation for the limits to arbitrage requires that the two motives triggering investors' redemptions be taken together. It is interesting to contrast the behavior of hedge funds with that of banks before and during the financial crisis of 2007–2009. Before the crisis, on average, hedge funds operated with much lower leverage ratios than banks.5 During the crisis, hedge funds also reduced their exposures to illiquid assets more quickly and more drastically. Fig. 1 shows that banks switched systematically to cash holdings only after the collapse of Lehman Brothers in September 2008, much later than hedge funds. We argue that the different investment and financing policies are due in part to differences in the nature of the capital structures of the two types of institutions. Equity in hedge funds is fragile, because it can be redeemed at the request of investors, while equity in banks is locked in permanently, because it cannot be tendered back to the bank for redemption. The fragile nature of the equity (and debt) in hedge funds creates an effective market-disciplining mechanism. It induces hedge funds to behave conservatively, by holding less risky portfolios and operating with less leverage. This difference may help to explain why hedge funds survived much better than banks when the initial mortgage default crisis produced unexpectedly large dislocations and turmoil in financial markets in 2007–2009. Many observers were surprised by the fact that hedge funds, typically regarded as the riskiest segment of the financial markets, were much more resilient than banks. Our paper helps to explain this phenomenon: The fragile capital structure of hedge funds encourages micro-prudence, but it also curtails arbitrage trading, leading to macro-unsoundness.Our work relates to a large literature on bank runs. Gorton and Winton (2003) provide an excellent survey. Gorton (2008) discusses in detail the panic runs in the recent crisis. The setup in our model is similar to that in Diamond and Dybvig (1983). The difference is that we assume that the size of early withdrawals is ex ante random, and this allows us to study the optimal cash holding problem of a hedge fund. In general, a bank-run game has multiple equilibria, but we resort to global game methods to solve for the unique equilibrium. In this respect, our paper is close to the work of Goldstein and Pauzner (2005), but the purpose and the scope of the two papers differ.6 We study the optimal cash holdings in the balance sheets of hedge funds, while Goldstein and Pauzner study the optimal liquidity provision of banks. A panic run can be driven by liquidity concerns or by concerns about solvency (see the discussion in Brunnermeier, 2009). In our model, the realization of large early withdrawals forces a hedge fund to liquidate positions in illiquid markets at reduced prices, and this triggers a run. In contrast, the run can be driven by fundamentals, as in Goldstein and Pauzner (2005). Bad fundamentals leave little asset value for investors who withdraw late, and this causes an immediate run. In the recent financial crisis, capital markets experienced many runs triggered for liquidity reasons, rather than for fundamental reasons. There were runs on many financial institutions that appeared to have adequate regulatory capital before they collapsed. Even so, investors ran, worried that the financial institutions had insufficient liquidity to meet massive early withdrawals and that assets would have to be liquidated at a deep discount. Our work also relates to Chen, Goldstein, and Jiang (2010). They find that mutual fund outflows are significantly more sensitive to poor performance for funds that invest in illiquid assets. This insight is similar to our result that market illiquidity potentially generates a panic run on high-end financial intermediaries, such as hedge funds and mutual funds. Compared with their work, we explicitly model how hedge fund managers factor into their ex ante investment and financing decisions the ex post panic run. In the same vein as Shleifer and Vishny (1997), Stein (2005) argues that open-ended funds, as a result of competition, could be suboptimal, because their investments are limited by the occurrence of early withdrawals in response to poor performance. Our emphasis is on the mechanisms that curtail arbitrage. Our focus on coordination risk differs from the arguments presented in these papers. In a banking context, Morris and Shin (2008) also argue that cash held by a debtor bank can lower the threshold of coordination among creditors to not withdraw. They do not formalize the argument, however, which we develop further by studying the ex ante optimal asset allocation decision of hedge funds and the limits to arbitrage. The paper is organized as follows. In Section 2, we first describe the model setup. Next, we solve the optimal asset allocation for a hedge fund, without and with the coordination problem facing the fund's investors. After that we analyze the model's implications and predictions. In Section 3, we generalize the model and discuss some broader issues of relevance to financial markets. In Section 4, we provide remarks and conclusions.