swing pricing for mutual funds - nus · there exists a critical threshold z for the market shock...

Swing Pricing for Mutual FundsBreaking the Feedback Loop

Between Fire Sales and Fund Redemptions

Marko Weber

Department of MathematicsNational University of Singapore

[email protected]

Asset Pricing and Risk Management

August 30, 2019

joint work with Agostino Capponi and Paul Glasserman

Marko Weber Swing Pricing and Mutual Fund Runs 1 / 33

Woodford Equity Income Fund



The fund blocked redemptions on June 3rd.



• The fund shrunk from £10 billion at its peak to £3.7 billion.

• Woodford didn’t have enough liquid assets to meet redemptions andsuspended withdrawals on June 3rd.

• Withdrawals are still suspended (management fees are not...).

• EU liquidity requirements failed (circumvented illegally?)



Mark Carney to a Treasury committee on June 26th:

This is a big deal. You can see something that could be systemic...These funds are built on a lie, which is that you can have daily liq-uidity for assets that fundamentally aren’t liquid. And that leads to anexpectation of individuals that it’s not that different to having money ina bank.



Large-scale redemptions from funds could test markets’ ability to ab-sorb asset sales, amplifying price moves, transmitting stress to otherparts of the financial system, and disrupting the availability of financein the real economy. Although to date these vulnerabilities have notcreated financial instability, they could do so under severe stress andare likely to become more important if more funds expand into lessliquid assets.

Financial Stability Report, Financial Policy Committee (FPC), July 2019.


Mutual Funds’ Share of Corporate Bond Market

0%

4%

8%

12%

16%

20%

1990 1995 2000 2005 2010 2015

Proportion of outstanding corporate bonds held in the US that are owned by mutual funds


Third Avenue Focused Credit

The Third Avenue Focused Credit Fund invested in low grade corporate debt.• 2009 to mid-2014, total return ≈ 80%.• 2015: portfolio losses and heavy outflows, fund shrinks from $2 billion to

$789 million.• December 16, 2015: the fund requests SEC approval to block further

redemptions:

If the relief is not granted, and the Fund is unable to suspend re-demptions, the institutional investors would likely be best positionedto take advantage of any redemption opportunity, to the detriment ofthose investors – most likely, retail investors – who remain in the Fund.These remaining investors would suffer a rapidly declining net assetvalue and an even further diminished liquidity of the Fund’s securitiesportfolio. The relief would help avoid such an outcome.


Summary

• When prices are falling, investors who exit a mutual fund first get out atbetter prices

• The transaction costs they impose on the fund are borne by investors whostay in the fund longer

• This first-mover advantage creates a positive feedback loop betweenfalling prices and asset sales, particularly in less liquid markets —potentially destabilizing

• Swing pricing can break the cycle, internalize transaction costs, reducetransaction costs, and enhance financial stability


Institutional Structure of Open-end Mutual Funds

• The fund is obliged to repay investors at the first NAV determined after thesubmission of the redemption order.• It may take several days to liquidate enough assets to raise the required

amount of cash.Marko Weber Swing Pricing and Mutual Fund Runs 11 / 33

Institutional Structure of Open-end Mutual Funds

Liquidity MismatchFunds offer same-day liquidity to their investors (redeemed shares are paid atthe end-of-day net asset value), but the assets they hold may not be as easy tosell on short notice and funds may be forced to sell assets at reduced prices insubsequent days.

First-mover AdvantageThe liquidity mismatch creates an incentive for investors to redeem theirshares early, because they anticipate that the cost of other investors’redemptions will be reflected in the future NAV of the fund.


Redemptions and Mutual Fund Performance

• Conditional on low past performance, funds that hold illiquid assetsexperience more outflows than funds that hold liquid assets.• The impact of outflows on fund returns is larger for illiquid funds.


Model Description

Feedback effect: outflow increases selling pressure, reducing fund’s NAV,leading to more outflow.• Outflow is linear in performance: ∆R︸︷︷︸

redemptions

= − β︸︷︷︸sensitivity

× ∆S︸︷︷︸fund’s performance

• Asset price impact is linear: ∆P︸︷︷︸price change

= γ︸︷︷︸illiquidity

× ∆Q︸︷︷︸traded assets


Model Description

Early

Redemptions

Fund's

NAV

Further

Redemptions

• Alert investors (first movers) anticipate the feedback effect. Instead ofwaiting and redeeming when the fund effectively hits their performancethreshold (at a lower NAV), they redeem immediately (at a higher NAV).

Price impact and liquidity mismatch provide an incentive to front run.


Model Description

Redeeming investors are either first movers (who exploit the liquiditymismatch) or second movers (who don’t exploit the liquidity mismatch)• Forward-looking vs. Mechanical.• Fast vs. Slow.

Exogenous

shock

First movers'

redemptions

Asset

liquidation to

repay first

movers

1st round of

second movers'

redemptions and

corresponding asset

liquidation

2nd round of

second movers'

redemptions and

corresponding asset

liquidation


Direct Ownership

Benchmark: Investors hold the asset directly, without the intermediation of themutual fund.

• Investors subject to the same financial constraints: ∆Q = β∆P.• Sales drive down the price: ∆P = γ∆Q.

The aggregate price change is ∆Ptot = ∆Z1−γβ .


Mechanics of Redemptions: First Movers

• Consider a single asset that represents the fund’s portfolio• A proportion π of investors in the fund are first movers• An initial market shock ∆Z hits the asset• The redemption procedure is:

∆Rfmtot = −πβ∆Stot , (First movers redeem)

−∆Qfmtot × (P0 + ∆Z + γ∆Qfm

tot ) = ∆Rfmtot × (S0 + ∆Z ),(Fund sells asset shares)

∆Sfmtot =

(Q0 + ∆Qfmtot )× (P0 + ∆Z + γ∆Qfm

tot )

N0 −∆Rfmtot

− S0

(Funds’ NAV changes)


Mechanics of Redemptions: Second Movers

• Second movers start redeeming after all first movers’ redemptions• Their redemption behavior may be described as:

∆Ssm0 = ∆Sfm

tot , Psm0 = P0 + ∆Z + γ∆Qfm

tot , Nsm0 = N0 −∆Rfm

tot ,

∆Rsmn+1 = −(1− π)β∆Ssm

n , (Second Movers redeem)

−∆Qsmn+1 × (Psm

n + ∆Psmn+1) = ∆Rsm

n+1 × (Ssmn + ∆Ssm

n+1),(Fund sells asset shares)

∆Ssmn+1 =

(Qsmn + ∆Qsm

n+1)(Psmn + ∆Psm

n+1)

Nsmn −∆Rsm

n+1− Ssm

n

(Fund’s NAV changes)


Impact of First-mover advantage

Aggregate change in value of a fund share is ∆Stot =∑∞

n=0 ∆Ssmn .

Aggregate price change of the asset is ∆Ptot = ∆Z + γ∆Qfmtot +

∑∞n=0 ∆Psm

n .Liquidity mismatch has a nonlinear impact on asset price and value of a fundshare.

PropositionIf π = 0, changes in the price of the asset and in the value of a fund sharedepend linearly on ∆Z, and both are equal to the price change of the asset inthe direct ownership model.

PropositionIf π > 0, the price change depends nonlinearly on ∆Z. The nonlinearity is“increasing” in γ.



Low Γ

10% 20% 30% 40% 50% 60%-DZ

10%

20%

30%

40%

50%

60%

70%

-DPtot

High Γ

2% 4% 6% 8% 10%-DZ

5%

10%

15%

20%

25%

-DPtot



The first-mover advantage may lead to the fund’s failure.

PropositionThere exists a critical threshold ∆Z ∗ for the market shock beyond which priceimpact and outflows lead to the fund’s failure. The critical threshold ∆Z ∗ ismonotone in γ.

0.5% 1% 1.5% 2% 2.5% 3%Γ ´ 10

6

20%

40%

60%

80%

100%

-DZ*


Contrast with bank deleveraging

• Following a shock to assets, a bank sells assets to restore a capital ratio• asset sale pushes down prices (fire sale). . .• . . . which leads to a successive round of deleveraging

• The aggregate impact of deleveraging on asset prices is linear (as inCapponi and Larsson (2015)):

∆Ptot = (I − S)−1∆Z ,

where S is the systemicness matrix

• The presence of first movers introduces a crucial structural differencebetween fire sales triggered by leverage targeting and fire sales triggeredby mutual fund redemptions


Swing Pricing

October 2016: SEC announces amendments to Rule 22c-1 to promoteliquidity risk management in the open-end investment company industry.

From November 19, 2018, open-end funds are allowed to use swing pricing:funds will be allowed to adjust (“swing”) their net asset value per share toeffectively pass on the costs stemming from redemption activity to theshareholders associated with that activity.

Swing pricing has been applied for over 15 years in Luxembourg and otherEuropean countries


Swing Pricing: Our Version

DefinitionThe adjustment ∆Ssw is a swing price if the aggregate change in value of afund share ∆Stot is equal to the change in value of a fund share in the absenceof first movers (that is, with π = 0).

PropositionThe swing price is

∆Ssw = γπβ∆Z1− βγ

.

Equivalently,∆Ssw = −γ∆Rfm

tot .


Properties of Swing Pricing

• The swing price is linear in the total number of redemptions (from firstmovers) and the slope is determined by the illiquidity of the asset

• Swing pricing removes the incentive to redeem immediately

• Swing pricing doesn’t just transfer liquidation costs to redeeming investors— it reduces these costs and the first-sale impact

• For the swing price to be effective:• the swing price should account for the shape of the market impact function• investors should be informed about a fund’s swing pricing mechanism (to

reduce number of redemptions).


Swing Pricing in Practice

• Usually specified by two numbers, a threshold and a cap• If net outflows exceed 5% of the fund, the NAV will be swung by up to 2%• Also for net inflows

• Our analysis argues for a larger swing factor at larger outflows• Our swing price is proportional to first-mover redemptions• Fixed factor may be inadequate

• Threshold is typically secret• Investors don’t know if NAV was swung (or how much) even after the fact


Swing Pricing in Practice

Swing pricing and fragility in open-end mutual funds (D. Jin, M. Kacperczyk, B.Kahraman, F. Suntheim).

• The swing pricing adjustment is larger when portfolio illiquidity is higherand during periods of market stress.• Investors are less likely to redeem shares during market stress in funds

that adopt swing pricing.• Negative impact of outflow on fund’s performance is reduced if swing

pricing is adopted.• Funds with swing pricing attract fewer new investors.


Multiple Funds

The reinforcing feedback mechanism, and hence the first-mover advantage, isexacerbated if multiple funds have overlapping portfolios.

∆Ptot ≈ ∆Z + (Impact from Fund 1) + (Impact from Fund 2)

+ (Cross-impact).

PropositionAssume both funds apply swing pricing. The swing price is

∆Sswboth = −γ(∆Rfm

tot,1 + ∆Rfmtot,2).

• Swing pricing should also account for the externalities imposed by firstmovers of the other fund.• A fund’s swing price is lower if the other fund also applies swing pricing.


Cooperative Swing PriceLet ∆Ssw

loc be the NAV adjustment that makes a fund’s first movers internalizeonly their liquidation costs. Let ∆Ssw

glob be the swing price that offsets the effectof first movers at both funds.

PropositionSuppose π1, π2 > 0, and fund 2 applies swing pricing. We have

|∆Sswboth| ≤ |∆Ssw

loc | ≤ |∆Sswglob|.

1% 2% 3% 4% 5% 6% 7%Γ ´ 10

6

2%

4%

6%

8%

10%

-DSsw

DSbothsw

DSlocsw

DSglobsw


Operational Problems

• Difficult to estimate the liquidity of the underlying portfolio.• Information on redemptions at other funds not readily available.• U.S. funds usually accept orders up to 4:00pm and seek to value fund

shares at approximately the same time• In Europe, funds may stop accepting orders at noon or 2:00pm, giving

them more time to observe order flow before striking the day’s NAV• Some intermediaries wait until the end of the day to submit orders for

multiple accounts — fund has limited intraday flow data• “Know your flow:” Need for funds to understand their investor base and

timing of trade flows. (This need is arguably greater without swing pricing)


Transparency?

Transparency: The fund does not have to agree on an exact swing pricingrule with its investors. In fact, some jurisdictions explicitly recommend funds tolimit the information they share with investors to avoid strategic redemptionsaimed at gaming the swing pricing mechanism.

Information Sharing: Funds need to share information on their investor baseto account for fire-sale externalities at other funds


Conclusions

• There exists a critical threshold for the market shock beyond which theliquidation costs are no longer sustainable and the fund fails to repayshares at the promised NAV.• Swing pricing transfers the cost of liquidation from the fund to the

redeeming investors, and – importantly – reduces this cost by removingthe first-mover advantage.• The presence of multiple funds holding the same portfolio exacerbates fire

sales losses, and therefore increases the benefit of swing pricing.• Cooperative swing pricing is the most efficient solution for reducing total

liquidation costs


swing pricing for mutual funds - nus · there exists a critical threshold z for the market shock...

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