Using Agent-Based Modeling to Assess Liquidity Mismatch in Open-End Bond Funds

In this paper, we introduce a small-scale heterogeneous agent-based model of the US corporate bond market. The model includes a realistic micro-grounded ecology of investors that trade a set of bonds through dealers. Using the model, we simulate market dynamics that emerge from agent behaviors in response to basic exogenous factors (such as interest rate shocks) and the introduction of regulatory policies and constraints. A first experiment focuses on the liquidity transformation provided by mutual funds and investigates the conditions under which redemption-driven bond sales may trigger market instability. We simulate the effects of increasing mutual fund market shares in the presence of market-wide repricing of risk (in the form of a 100 basis point increase in the expected returns). The simulations highlight robust-yet-fragile aspects of the growing liquidity transformation provided by mutual funds, with an inflection point beyond which redemption-driven negative feedback loops trigger market instability.

conditions under which a run on mutual funds can lead to instability. In this paper, we seek to assess 48 the significance of the price feedback loop associated with mutual fund redemption behavior. We use 49 agent-based modeling (ABM) and simulation to better understand the endogenous price dynamics 50 following a market-wide reassessment of risk (using a 100 basis point increase in expected bond 51 yields). We analyze the impact of redemption driven feedback loops under increasing mutual fund 52 participation levels (using market shares of 15%, 25% and 35%).  The expansion of the bond market coincided with decreasing risk premiums and increasing 61 price risks. In the current low yield environment, bond prices (which behave inversely to yields) are 62 very sensitive to changes in expected returns, with small increases in interest rates or credit spreads 63 triggering significant drops in bond prices (a feature known as convexity). Figure 2 highlights the 64 remarkable secular decline in the 10-year Treasury yield, often used as a benchmark for evaluating 65 relative yields on corporate bonds. In addition to convexity, price risk in the overall market has further increased due to a 67 lengthening of the maturity of the outstanding bonds (a longer maturity implies higher price 68 sensitivity) and a decline in overall credit quality. Faced with historically low yields, issuers have 69 been eager to lock in "low rates for longer" through the issuance of bonds with longer maturities, 70 see Figure 3. Overall credit quality has declined as well. Table 1   accounted for roughly 1.7% of the corporate bond market at the beginning of 1981 (see Figure 4).

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By the end of Q3 2016 (see Figure 5), the mutual fund market share had increased to around 17% (this 96 excludes holdings of exchange traded funds which account for an additional 2.8% of the market).   some interesting applications to currency and housing markets), we aim to analyze the liquidity 148 conundrum in the corporate bond market (as outlined in Section 2 above).

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Our work draws heavily on the strong foundation of prior agent-based models, including advice 150 on how to pursue this type of research [16]. Our focus is squarely on crisis dynamics following some 151 of the prior work cited. However, our work is marked by several important differences.

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• Most prior agent-based models focus on central limit order book market structures (as in most 153 equity markets).

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• Our corporate bond market model is a decentralized dealer-based quote-driven market, selected   buy-side agents based on insurance companies, hedge funds, and mutual funds (as asset managers).

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The non-dealer banks represent less than 4% of the US corporate bond market, so we left that agent 272 class out for now.    The hedge fund agent acts as a short-term tactical trader who follows a relative value trading 295 strategy. As such, the hedge fund maintains both long and short positions and makes active use of 296 leverage. In the real world, fixed income relative value hedge funds have historically been among the 297 most leveraged market participants.

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The hedge fund agent is not subject to external inflows (basically a closed end fund) or 299 redemptions (assume investor lock up); its trading capacity is constrained only by the availability 300 of secured financing (leverage) from broker-dealer agents. We assume the hedge fund finances 301 all positions on margin through prime-brokerage style arrangements with some of the dealers.

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Broker-dealers limit leverage using security-specific haircuts that can be dynamically adjusted 303 depending on market conditions.   behavior is limited through regulatory constraints and market discipline, the latter expressed through 315 a constraint on value-at-risk (VaR) relative to capital.

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In order to assess the significance of a negative price feedback loop caused by mutual fund 318 redemption behavior, we run agent-based simulations using a simplified model which includes only 319 two agent types: mutual funds and dealers. We model dynamics in the asset layer of the model, concave shape, which implies that the sensitivity of outflows (to bad performance) is greater than the 327 sensitivity of inflows (to good performance). We specify the daily flow for a given fund at simulation 328 tick t as a percentage of the fund's prior daily wealth (NAV) as: Where R d t−1 is the daily return lagged by a day (at the end of the prior simulation tick), R w t−1 is 330 the weekly return lagged by a day, found. However, selling is a bit more aggressive in that the agent attempts to raise the necessary cash 345 using any bonds that can be traded.

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Dealers are the essential price setters in the initial model. Given the intent to trade, asset owners 348 make a request-for-quote (RFQ) to all dealers. Dealers must respond with "no quote" or a full quote 349 for the requested order size (no partial order fills are allowed for now).

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The market universe consists of five tradable bonds (see Table 4 for details). The bonds are 377 identical with respect to structure, form and major covenants including issuer, redemption (bullet 378 redemption at maturity without optionality clauses) and rate provisions (fixed coupon). The bonds 379 differ along only three dimensions:  3. Coupon rates range from 1.75% to 4.00%. At any point in time, all asset owners perceive the same fundamental value for a specific bond.

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That is, all asset owners use the same valuation model and observe the same input prices. The value 385 for the above five bonds is fully reflected in five data points (a par yield curve with five rates) and a 386 simple calculation of a bond's price given its par yield.

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The starting conditions for the agent-based simulation include: • Bond index composition with weights based on nominal amount (Table 4, Index Weights).

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• Initial par yield curve and bond prices (Table 2, Yield and Price).

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• Starting bond holdings are allocated to two buy-side agents: mutual fund and insurance agent.

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The mutual fund holds either 15%, 25% or 35% of the outstanding nominal in the market, with 392 the remaining nominal held by the insurance agent. The mutual fund is invested across all 393 bonds in the index based on the index weights. All dealers start with square (zero) inventory 394 positions.

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In addition, initial endowments for the buy-side agents include:

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• Mutual fund: In addition to its bond holdings, the fund has an opening cash position reflecting 397 a 5% cash-to-assets ratio.

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• Insurance company: Initial portfolio allocation includes a 60/40 split between fixed income and 399 equity markets (assumed to be invested in a broad market index like the S&P 500).   prices (see Table 5), as well as for prices at the bottom of the market (see Table 6). The dynamics of the redemption-driven feedback loop and recovery are outlined in Table 7,  before (see Figure 9). These shock-induced drops are followed by further drops in prices for the next 453 10 to 20 ticks due to the redemption-driven feedback loop. As above, the rate hike impacts increase 454 with maturity, showing price drops in the 1% to 14% range. The larger mutual fund market share 455 increases the effects of the feedback loop, with secondary price decreases now in the 1.7% to 2.7% 456 range (see Table 8). This is a definite increase over the first simulation, but the feedback loop still has 457 much less of an effect as compared to the interest rate shock. Once the market stabilizes and normal 458 trading activity returns, there is a somewhat better recovery in prices.  The final simulations use a market share of 35%, a substantial increase over the current situation.

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Again, the simulations are run for 252 ticks and a 100 basis point interest rate shock is delivered at 462 tick 50. The interest rate hike causes the expected price drops across all five bonds as before (see 463   Table 5). However, after that the simulations take a different path. After these shock-induced drops, 464 the prices fall of a cliff. For the next 50 clicks the redemption-driven feedback loop causes a spiral 465 of decreasing prices (see Figure 10). In fact the concave curve means that the price drops accelerate 466 with correspondingly dramatic wealth destruction. The price drops are more pronounced from the 467 outset, but reach an inflection point followed by precipitous price drops until all the dealer capacity is 468 consumed (and the market flatlines). In these simulations, the redemption-driven price drops dwarf 469 the initial interest rate shock effects. The feedback loop causes price drops in the 35% to 44% range, 470 as compared to the shock-induced drops of roughly 1% to 14%, see Table 9.  In actuality, the instability and all out market crashes start to occur at approximately a 30% 472 mutual fund market share (see Figure 11). Though notice that the feedback look is not as severe and 473 overall it takes roughly 50 more trading days (or ticks) to completely crash. We should not read too 474 much into this exact market share level since we aim to use our model to evaluate regulatory policies 475 or re-create market behaviors, not predict specific thresholds. We are much more interested in the 476 emergent behaviors and relative comparisons that can provide useful guidance. Figure 11. Bond price trends for a 30% mutual fund market share.

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In this paper, we introduce an agent-based model of the corporate bond market and obtain response to an interest rate shock, with secondary redemption-driven feedback loops causing further 488 declines in price, followed by gradual stabilization and recovery. However at a 35% market share, 489 the model becomes unstable, with the initial shock-induced price drops followed by an accelerating 490 feedback loop that overwhelms the sell-side broker dealers and freezes the market. This is exactly 491 the behavior that concerns both regulators and practitioners. We believe that this agent-based model   The following abbreviations are used in this manuscript: