Assessing the credit risk of money market funds during the eurozone crisis

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Assessing the credit risk of money market funds during the eurozone crisis夽 Sean Collinsa,1 , Emily Gallaghera,b,∗ a b

Investment Company Institute (ICI), 1401 H St. NW, Suite 1200, Washington, DC 20005, USA Paris School of Economics, Centre d’Economie de la Sorbonne, 106-112 Boulevard de l’Hôpital, 75647 Paris cedex 13, France

a r t i c l e

i n f o

Article history: Received 9 December 2014 Received in revised form 7 June 2015 Accepted 9 December 2015 Available online xxx JEL classification: G01 Keywords: Money market mutual fund Credit risk Copula Default probability Break-the-buck

a b s t r a c t This paper measures credit risk in prime money market funds (MMFs) and studies how such credit risk evolved during the eurozone crisis of 2011–2012. To accomplish this, we estimate the annualized expected loss on each fund’s portfolio. We also calculate by Monte Carlo the cost of insuring a fund against losses amounting to over 50 basis points. We find that credit risk of prime MMFs, though small, doubled from 12 basis points in June 2011 to 23 basis points in December 2011 before receding in 2012. Contrary to common perceptions, this did not primarily reflect funds’ credit exposure to eurozone banks because funds took measures to reduce this exposure. Instead, credit risk in prime MMFs rose because of the deteriorating credit outlook of banks in the Asia/Pacific region. We conclude that the increase in the credit risk of prime MMFs in the second half of 2011 reflected contagion in the worldwide banking system coupled with slowing global economic growth, not actions taken by MMFs. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In the five business days following the default of Lehman Brothers in September 2008, money market funds experienced redemptions totaling over $300 billion. Unlike banks, money market funds (MMFs) do not hold capital against credit losses, nor are they insured by the federal government. Instead, credit risks in money market funds are mitigated by liquidity, maturity, credit rating, and concentration limits on funds’ portfolios, as mandated by the Securities and Exchange Commission (SEC). In the aftermath of the Lehman Brothers default, the SEC significantly tightened money market fund regulations. Regulators, press reports and some

夽 For helpful comments, we thank Iftekhar Hasan (editor), two anonymous referees, special guest editors, Russ Wermers, Laura Starks, Bertrand Maillet (head of research at ABN Amro), credit risk experts at Fidelity, participants at the 2014 International Conference on Credit Analysis and Risk Management, participants at the 2014 Oxford University FRAP conference, and seminar participants at the University of Maryland. A special thanks to James Duvall of the ICI for his research assistance. The views expressed here are those of the authors only; as such, they do not represent those of ICI, its staff, or ICI member firms. ∗ Corresponding author at: Investment Company Institute (ICI), 1401 H St. NW, Suite 1200, Washington, DC 20005, USA. Tel.: +1 202 371 5428. E-mail addresses: [email protected] (S. Collins), [email protected] (E. Gallagher). 1 Tel.: +1 202 326 5800.

academic studies (e.g., Chernenko et al., 2014; Rosengren, 2012) have questioned whether the new, tighter regulations were sufficient to constrain credit risks in MMF portfolios during periods of market stress. These studies cite the rapidly deteriorating credit quality during 2011–2012 of certain European banks, in which MMFs held substantial investments. Based on the scale of their investments in European banks, these studies suggest that credit risk in prime MMFs rose markedly during the second half of 2011.2 If true, this could indicate that the SEC’s 2010 reforms to MMFs were insufficient to prevent a replay of September 2008. This paper offers a detailed analysis of the scale and sources of credit risk in MMF portfolios during the eurozone crisis. We begin by developing a method for assessing credit risks in MMF portfolios. This is necessary because MMFs price their portfolio holdings at amortized cost, such that fund yields (and yield spreads) do not immediately reflect changes in the credit quality of their

2 We focus only on the credit risk in prime MMF portfolios in this paper. Prime MMFs are money market funds that invest in a range of money market securities, including commercial paper, bank CDs, medium-term and floating-rate notes, repurchase agreements (repos) and Treasury and agency securities. Government money market funds typically invest only in Treasury or agency securities or repos backed by Treasuries and agencies and therefore should be default-risk-free.

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portfolios securities.3 Furthermore, current market yields on MMFs’ outstanding portfolio securities are frequently unavailable since secondary markets for short-term securities, like certificates of deposit and commercial paper, are notoriously thin (Covitz and Downing, 2007). Thus, to study credit risk in MMFs, we must first develop a measure that evolves with market conditions. Next, we use this measure to study the evolution of MMF portfolio credit risks during the eurozone crisis of 2011–2012. The goal is to understand (a) how much credit risk was in MMF portfolios over this period and (b) whether increases in MMFs’ credit risks were attributable to their investments in European banks or other factors. In theory, CDS premiums could be used to measure the credit risk in MMF portfolios. Numerous recent studies have sought either to assess the credit risk or capital adequacy of banks using CDS premiums. For example, Segoviano and Goodhart (2009) treat the entire banking system as a portfolio, the riskiness of which is based on the CDS premiums of individual banks. Other studies have used 5-year CDS premiums to assess systemic risk in bank portfolios at a fixed horizon, such as over the next quarter or the coming year (Avesani et al., 2006,Huang et al., 2009). Money market funds pose a unique problem, though, in that the bulk of their assets are very short-term, typically maturing in 3 months or less while CDS premiums are not generally quoted at maturities of less than 6 months. Furthermore, market participants indicate that CDS are often thinly traded at 6- and 12-month horizons. To deal with this, we use default probabilities obtained from the Risk Management Institute (RMI) at the National University of Singapore. RMI generates forward-looking default probabilities for issuers on a daily basis for maturities of 1, 3, 6, 9, 12, 18, and 24 months ahead for about 34,000 firms for 106 economies around the world. RMI publishes default probabilities even in some cases (such as Canadian banks) for which CDS are not generally traded. We match these default probabilities using characteristics of the securities money market funds hold (such as a security’s issuer, maturity, and security type) collected from SEC form N-MFP. For example, if a fund holds a Ford Motor medium-term note that has a remaining maturity of 3 months, that note is matched with Ford Motor’s annualized 3-month cumulative default probability. This default probability is multiplied by the presumed default loss rate on Ford Motor to generate an annualized expected loss on the security. Aggregating (on an asset-weighted basis) across all of a fund’s holdings provides an estimate of the “expected loss-to-maturity” (ELM) of the fund’s portfolio under the assumption that the fund holds each security until it matures (or defaults). Because the term structure of CDS premiums is normally upward sloping for high quality issuers (Agrawal and Bohn, 2006; Han and Zhou, 2011), we expect ELM to be lowest for those MMFs with the shortest portfolio maturities.4 While ELM is useful for measuring a fund’s overall credit risk, it may overstate the risk of a September 2008-like event. A money market fund may offer a per-share price of $1.00 if its mark-tomarket value remains within 12 cent (50 basis points) of $1.00. If its mark-to-market value drops below $.995, the fund must lower its per-share price to $.99. This is colloquially known as “breaking

3 At first glance, the most obvious way to estimate the credit risk on an MMF is by the difference between the yield on a prime MMF and the yield on a comparable government-only MMF. If a fund holds a security and that security’s credit quality declines, the security’s market price should also decline, boosting the security’s market yield. But because funds use amortized cost accounting, the rise in the security’s yield would not be immediately reflected in the fund’s yield. Generally speaking, only if that security matures and the fund rolls over its holding of that security, would the fund’s yield then rise to reflect the increased credit risk. 4 Data sources and code used to produce the results in this paper are available on request.

the buck.” Policymakers and other experts have expressed concerns that if one fund breaks the buck, this could lead to a run on other MMFs.5 Following the default of Lehman Brothers on September 15, 2008, the Reserve Primary Fund broke the buck on September 16, 2008. Over the 5 days ending September 19, prime MMFs met historic redemptions. Prime money funds with exposure to Lehman Brothers’ debt experienced outflows. However, several MMFs with no direct exposure to Lehman Brothers or other distressed issuers also incurred heavy outflows in September-October 2008 (McCabe, 2010). These redemptions are reported to have contributed to a freezing of commercial paper markets, threatening the mechanism through which business make payrolls and finance their daily operations (Schapiro and Mary, 2012). Therefore, investors, fund managers, and policymakers may be interested in the risk premium associated with a fund breaking the buck. We therefore compute an alternative measure of MMF risk, namely the cost of insuring against a fund breaking the buck, which we call BBI(l, ). We allow for a insurance deductible, l, of 50 basis points of a fund’s assets and a maximum coverage amount, , of 300 basis points of a fund’s assets. We select l and u to be consistent with the structure of the U.S. Treasury’s 2008–2009 temporary guarantee program for MMFs. BBI(l, ) is more difficult to calculate than ELM because defaults may be correlated across issuers. For example, MMFs hold (U.S. dollar-denominated) commercial paper and other short-term debt issued by large global banks. The failure of a large global bank could threaten the solvency of other large banks if, for instance, surviving banks hold debt issued by the failing bank. To correctly assess the probability that a fund might break-the-buck, default correlations need to be taken into account. We do this using a copula (Li, 2000) implemented by Monte Carlo simulation. ELM and BBI(l, ) have elements in common with measures of systemic risk and stress indicators for banks (Tarashev and Jackel, 2008; Huang et al., 2009; Segoviano and Goodhart, 2009). They also have similarities to Bank for International Settlement (BIS) guidelines for assessing Incremental Risk Charge (IRC). Under Basel II, a bank may face a capital surcharge (the IRC) on its “trading book,” those securities a bank intends to actively trade and hold for less than one year. Under BIS guidelines, to determine the capital surcharge, the bank models the credit risk in its trading book under three assumptions: (a) the horizon for measuring credit risk (“credit horizon”) is one year; (b) the capital surcharge takes into account a security’s “liquidity horizon,” which is the point at which the bank can dispose of trading book securities (generally, the shorter the liquidity horizon, the lower is the IRC); (c) the bank maintains a “constant-risk” trading book, periodically rebalancing its trading book to maintain a constant level of credit quality (for example, if the credit rating of a trading book security declines from AAA to AA, the bank is assumed to replace that security with a AAArated security). Studies by regulators (Dunn et al., 2006) indicate that the IRC is 30 percent lower for a hypothetical bank with a liquidity horizon of 1-month compared to a bank with a liquidity horizon of 1 year. Given that we measure a fund’s credit risk from annualized expected losses derived from annualized cumulative default probabilities on portfolio securities, we are implicitly setting a fund’s “credit horizon” to one year. In addition, our approach sets a fund’s “liquidity horizon” to the remaining maturity of its securities holding.6 Finally, we assume that a fund maintains a

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See, for example, FSOC (2012) and Squam Lake (2011, 2013). Our approach is in some sense more conservative than the BIS guidelines under which banks compute IRC. BIS guidelines allow banks to treat a security’s liquidity horizon as the date by which the bank can reasonably expect to dispose of the security in the market with little price pressure. Thus, if a bank holds a 10-year corporate bond and believes it could dispose of it in, say, 6 months with little or no 6

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“constant risk portfolio” throughout the year. In effect, this means that as a fund’s securities mature, it is assumed that the fund rolls the assets into identical securities. It is important to note that these measures address only the credit risk in MMFs, namely the risk to a money fund of one or more of its securities defaulting. MMFs also face risks from changes in interest rates and shareholder redemptions. For example, a Treasury-only MMF has little if any credit risk, but its portfolio can decline in value if interest rates rise. Pressures on a fund’s portfolio from both credit and interest rate risk can be heightened if the fund at the same time experiences redemptions, which could raise the chances of the fund breaking the buck. Since our methodology does not take into account interest rate or redemption risk, it should not be taken as a general methodology such as would be necessary for stress testing MMFs. Our results indicate that credit risk in prime MMFs, as measured by ELM, is small, averaging just 15 basis points from January 2011 to December 2012 on an asset-weighted basis. By comparison the 6-month and 5-year CDS premium on JPMorgan Chase, a relatively higher credit-quality large U.S. bank, averaged 36 and 112 basis points, respectively, over this same period. Nonetheless, the credit risk exposure of prime funds doubled during the peak of the eurozone crisis. ELM rose from 12 basis points in January 2011 to 23 basis points in December 2011 before receding to 10 basis points in December 2012. As we show, over 2011–2012, the levels of credit risk varied across prime MMFs, reflecting differences in funds’ exposures to U.S. and foreign banks, U.S. Treasuries, municipalities and nonfinancial companies. The standard deviation of credit risk across MMFs (as measured by ELM) was 4 basis points in January 2011. This rose to 11 basis points in December 2011. The maximum credit risk in any individual prime MMF was 47 basis points in December 2011, while the minimum was slightly above zero. The cost of break-the-buck insurance, BBI(50, 300), should be less than ELM for two reasons. First, break-the-buck insurance would kick in only if a fund actually breaks the buck, in other words if its mark-to-market value drops below $.995 per share. Second, like conventional insurance policies, the deductible and maximum coverage amount limit the insurance provider’s exposure and thus the cost of purchasing the insurance. As we show, BBI(50, 300) is indeed less than ELM. We estimate that the cost of break-the-buck insurance over the period January 2011 to December 2012 averaged 8 basis points (weighted by assets), roughly half the 15 basis point average level of ELM over the 24-month period. Interestingly, this 8 basis point estimate is quite close to the range of fees the U.S. Treasury assessed under its 2008–2009 temporary program that provided break-the-buck insurance for money market funds. Although less than ELM, BBI(50, 300) follows a similar pattern, rising in late 2011 to a peak of 12 basis points. The common perception is that the credit risk of prime MMFs increased in mid-to-late 2011 because these funds held, or even increased, their holdings of securities issued by eurozone banks in order to boost fund yields (e.g., Chernenko et al., 2014; Rosengren, 2012). Our results present a rather different picture. Our key finding is that MMF holdings of eurozone or other European banks did not contribute importantly to the increase in the average credit risk of prime MMFs in the second half of 2011. Instead, the rise was primarily due to an increased contribution from prime fund investments in banks domiciled in the Asia-Pacific

price pressure, Basel II standards allow the bank to treat the bond’s liquidity horizon as 6 months. Suppose, in contrast, that a money market fund holds a medium term note with a remaining maturity of 6 months. Even if the fund could sell the note with no price pressure within, say, 7 days, our ELM and BBI(l, ) concept implicitly sets the note’s liquidity horizon to the remaining maturity of 6 months.

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region. As credit conditions deteriorated for eurozone banks in the fall of 2011, MMFs drastically reduced their holdings of eurozone bank debt and shortened the maturities of their remaining eurozone holdings. This offset to a great extent an increase in the credit risk attributable to eurozone banks. At the same time, prime funds increased their holdings of bank debt in Canada, Norway, Australia/New Zealand, and Japan. In the fall of 2011, however, as the economic outlook deteriorated in the eurozone, CDS premiums rose on banks across the world, including through the Asia/Pacific region. Some of this likely reflected concerns that the failure of a large eurozone bank would reverberate across the world financial system. More generally, slowing global economic growth might also have lowered the credit quality of banks in the Asia/Pacific region and other export-driven economies. Standard and Poor’s August 5th, 2011 downgrade of the U.S. sovereign debt credit rating may also have contributed to the rise in CDS premiums among large global banks. Finally, the credit quality of Japanese banks might have suffered from the lingering impact of the March 2011 tsunami (including Japan’s nuclear power plant issues). This growth in global credit risk, combined with the increased holdings of MMFs in regions outside the eurozone, largely explains why prime MMFs experienced a rise in measured credit risk in the second half of 2011. Given that eurozone developments only indirectly affected banks in the Asia/Pacific region, we conclude that the increase in the credit risk of prime MMFs in the second half of 2011 reflected contagion in the worldwide banking system, not actions taken by MMFs. The rest of this paper proceeds as follows. In Section 2, we document the method used to generate estimates of funds’ expected losses, ELM, and break-the-buck insurance costs, BBI(50, 300). In Section 3, we describe the unique dataset employed. We proceed to the results in Section 4. We begin this section with an analysis of the distributions of ELM and BBI(50, 300) over time. Next, we present our main results – an analysis of the sources credit risks in prime MMFs during late 2011. Before concluding, we examine other factors, such as fund liquidity and average maturity, that influence credit risk in MMFs. In doing so, we assess whether provisions in the SEC’s 2010 reforms had the potential to lessen the risk of a fund breaking the buck from a credit shock. 2. Method This section describes our approach to estimating the credit risk of prime money market funds. For exposition, we introduce the following notation: I J Tj Di wij Ri pi (Tj )

= = = = = = =

total number of issuers in a fund’s portfolio total number of securities in a fund’s portfolio remaining days to maturity on security j remaining days to a default by issuer i proportion of a fund’s assets invested in security j issued by issuer i recovery rate on an issuer i’s securities in the event of a default cumulative probability up to time Tj that issuer i defaults; i.e., P(Di < Tj )  

pi (Tj ) = 1 − YiTj

1 − pi (Tj )

360/Tj

, the annualized counterpart of pi (Tj )





= equal to 1 if Di < Tj and zero otherwise such that P YiTj = 1 =  pi (Tj )

Define expected loss-to-maturity (ELM) for a given fund at a given moment in time to be: ELM =

J I  

wij (1 − Ri )pi (Tj )

(1)

i=1 j=1

To make Eq. (1) operational, we use default probabilities provided by RMI. As the next section discusses, RMI creates forward-looking default probabilities for a large number of issuers worldwide for maturities of 1, 3, 6, 9, 12, 18, and 24 months. We interpolate these to obtain pi (Tj ) for any intervening maturity. Given the RMI default probabilities (or interpolated values), the annualized expected loss

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on each security j issued by issuer i is simply (1 − Ri )pi (Tj ). ELM approximates the expected loss on a fund’s portfolio, where each security is multiplied by its portfolio weight, wij . It also may be useful for financial stability purposes to measure the cost of insuring against a fund “breaking the buck.” As noted in Section 1, a fund is said to break-the-buck if its mark-tomarket value falls below $.995. Under the assumption that the fund maintains a “constant risk” portfolio, the cost of insuring against this event depends on expected losses as well as any first-loss (deductible) provision and the maximum amount of the coverage. For example, one could envision designing a “break-the-buck” insurance policy with a deductible and a cap on total losses incurred by the insurer. Define any first-loss provision as l and the insurer’s cap as . Then, break-the-buck (BBI) insurance is:



BBI(l, ) = E min [max (Loss − l, 0) , u] where Loss =



I i=1

J j=1





(2)

wij (1 − Ri )YiTj , (1 − Ri ) is the loss rate if

issuer i defaults, and E { • } is the expectations operator. This is the annualized cost of providing “break-the-buck” insurance (BBI) against a “constant risk” money market fund portfolio. Calculating ELM is straightforward, requiring only multiplication and addition. If defaults were independent events, calculating BBI(l, ) would also be straightforward. Things get more challenging when we assume defaults are correlated across issuers. In that case, calculating BBI(l, ) requires computation of an I-dimensional integral (where I ≤ J). This is a well-known problem in the banking literature on calculating value-at-risk (VaR) and required regulatory capital such as IRC. That literature generally assumes that defaults of banks and other financial institutions are correlated. Many of the securities that money market funds hold are issued by banks or other financial intermediaries. Thus, we assume defaults are correlated across issuers. The challenge of calculating expected losses like Eq. (2) when defaults are correlated is often solved by Monte Carlo. We calculate Eq. (2) using a copula approach (Li, 2000) implemented by Monte Carlo. Appendix A provides details on the method. Briefly, the approach involves simulating random default times for each issuer i a large number of times (n=1 to N trials). Default probabilities, and hence the random default times, are correlated across issuers with correlations calibrated to historical movements in default probabilities from January 2011 to December 2012.7 To allow for fat tails, following Hull and White (2004), we use a t-copula with 5 degrees of freedom.8 Research (e.g., Glasserman et al., 2007; Jin and Nadal De Simone, 2014; Diks et al., 2014) finds that, compared to a normal copula, a t-copula is better suited for modeling positive dependence in the tails and, therefore, systemic risk. If a given simulation indicates that issuer i defaults before time Tj , a fund experiences a loss on security j equal to wij (1 − Ri ). Losses across all of a fund’s

7 Note, as an anonymous referee has pointed out, there are a number of ways to simulate correlated defaults. While a detailed review of these various approaches is beyond the scope of this paper, one prominent alternative has been to introduce correlation through a two-factor model, where one factor is idiosyncratic to the firm and a second picks up default correlation across all firms in one’s sample (Glasserman and Li, 2005). This reduces the dimension of the correlation matrix one must evaluate, which can be quite important when dealing with hundreds or thousands of issuers. Others have used multi-factor models, for example, letting defaults be correlated across firms in an industry but independent across industries. Similar approaches could be applied in our context, such as modeling default correlations through a multi-factor model with U.S. banks as one group, European banks as another, and industrials as a third. As detailed in Appendix A, our approach follows that of Tarashev and Jackel (2008), which, rather than using a factor model to simulate default probabilities, simulates directly on the basis of the entire correlation matrix of default probabilities. In their case and ours, this approach works because the number of issuers (in our case about 100) is relatively small. 8 Experiments with df = 1 and df = 10 indicate marginal differences from those based on df = 5 .

securities are accumulated during a particular simulation n. If a fund’s losses in simulation n accumulate to more than the deductible (i.e., 50 basis points of the fund’s assets), the fund is counted as having broken the buck (i.e., Loss > l). Monte Carlo calculates Eq. (2) by sampling uniform random variates  witha probability of success (“success” meaning default) of P YiTj = 1 =  pi (Tj ), where  pi (Tj ) are correlated across issuers. This, however, may require a large numbers of simulated random draws because credit defaults are “rare events” (Glasserman and Li, 2005). Consequently, researchers often use variance reduction techniques such as importance sampling (Rubenstein and Kroese, 2007) to improve simulation efficiency. However, as others have noted (e.g., Zhao et al., 2013), there is importance sampling is a relatively new tool in the pricing of financial derivatives. We opt to reduce standard errors through the brute force method of running a large number of simulations (N = 50, 000).9 The resulting estimates of BBI(l, ) are in the expected range (when compared to ELM) and the standard errors of BBI(l, ) are small, generally in the range of 1 basis point or less. We present BBI(50, 300). Setting l = 50 implies that there is a 50-basis-point deductible, which could be assumed either by the fund’s adviser or by fund shareholders. We set  = 300 basis points. Under this assumption, the maximum insurable loss, after the 50basis-point deductible is incurred, would be 300 basis points of fund assets. If a fund’s losses from defaults totaled more than 350 basis points, the insurance would pay out, and the fund would close. Any losses greater than 350 basis points would accrue to fund investors. We selected these choices for l and , in part, because they are roughly in line with the parameters of the U.S. Treasury’s 2008–2009 guarantee program for money market funds. Under that program, the Treasury temporarily provided break-the-buck insurance for money market funds. The insurance kicked in if a fund’s market-to-market price per share fell below $.995, in other words, if the fund broke the buck. If a fund broke the buck and used the Treasury’s insurance, the fund was required to close and liquidate. Consequently, Treasury’s losses would have been limited to the difference between a fund’s $1.00 NAV and the market value of the fund’s assets. The Treasury’s program was backed by, and limited to, balances in the Treasury’s Exchange Stabilization Fund (ESF). When the Treasury introduced the money market fund guarantee program in September 2008, the balance in the ESF was about $50 billion, which implies that the Treasury’s potential exposure was limited to about 3 percent of the total assets of prime money market funds.10 In addition, some regulators and academics argue for requiring money market fund advisers to commit capital to support losses their money market funds might experience. Regulators in Europe argue for a capital buffer of 300 basis points of fund assets. Some academics (Squam Lake, 2013,Hanson et al., 2013) have suggested that U.S. fund advisers be required to hold a capital buffer in the range of 3–4 percent of risk-weighted assets. On the basis of these considerations, we set  = 300 basis points. The Treasury’s guarantee program did not impose an explicit deductible, which, on one hand, suggests setting l = 0 . On the other hand, the guarantee program required a fund using the Treasury

9 Experiments with simulation sizes of up to 200,000 reveal little difference in results (except for a reduction in the standard errors of the estimates) but increase very substantially required computing times. 10 It has occasionally been suggested that the Treasury Department guaranteed trillions of dollars in money market fund assets (e.g., Bair, 2013). The Treasury’s exposure, however, was limited to the roughly $50 billion available to it through the ESF. Also, the Treasury guarantee only applied to, at most, the assets in funds as of September 19, 2008. On that date, prime money market funds had assets of $1728 billion, according to iMoneyNet.com. Thus, the total exposure of the Treasury Department was limited to 289 basis points of prime fund assets, based on the calculation 10,000 ×$50 billion/$1728 billion.

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insurance to demand payment on any capital support agreement provided by the fund’s adviser. For various reasons, fund advisers sometimes voluntarily entered into capital support agreements with their money market funds. In such an arrangement, the adviser would typically agree to buy, guarantee to buy, or provide insurance on the value of, one or more fund securities at par value. In effect, this would provide a deductible to the Treasury on its insurance. It is unclear how much this deductible would have been worth to the Treasury Department because no money market fund ever drew on the Treasury’s insurance program. Consequently, we rather arbitrarily set l = 50 basis points. 3. Data To undertake the analysis, we create a unique dataset comprising a complete record of the individual holdings of prime money market funds over the period January 2011 to December 2012.11 We match those individual holdings by issuer and maturity with their annualized expected loss (via Eq. (1)). We obtain the complete record of the portfolio holdings of all prime MMFs from the SEC’s Form N-MFP. We categorize these holdings by the parent of the issuer. For example, Honda Auto Receivables Owner Trust, which issues commercial paper in the U.S. to help finance auto loans to U.S. residents, is affiliated with Honda Motor Company Ltd., which we take to be its “parent.” Parent companies are often global firms that may for any number of reasons need dollar funding from MMFs and other financial market participants. For instance, prime MMFs lend dollars on a short-term basis to large global banks (including those with headquarters in Europe, Japan, Australia and elsewhere) to make loans to subsidiaries of foreign companies that do business in the United States, to make consumer or car loans to U.S. residents, or to invest in U.S. Treasury and agency securities. Eurozone banks may also borrow dollars to make dollar loans to subsidiaries of U.S. companies that do business in Europe. Unlike U.S. banks, large foreign banks do not have significant retail U.S. dollar deposits to fund their global dollar-based operations and thus may seek to borrow dollars elsewhere, such as from MMFs. We assign each parent firm to a particular region of the world based on the parent firm’s headquarters. For example, BNP Paribas SA is headquartered in France and thus assigned a region of “Europe.” Similarly, JPMorgan Chase & Co, although having worldwide operations, is assigned a region of “U.S.” Table 1 provides summary statistics on the holdings of prime MMFs. As can be seen, prime MMFs invest in a range of money market instruments, including commercial paper, bank CDs, Eurodollar deposits, medium term- and floating-rate notes, Treasury and agency securities, and repurchase agreements. In May 2011, commercial paper constituted 30.1 percent of prime fund assets, bank CDs 42.8 percent, Treasury and agency securities 14.5 percent, repurchase agreements 18.5 percent, and other securities 4.6 percent. Table 2 tabulates these holdings by the issuer’s region of the world, either Americas, Europe, Asia/Pacific, or Other. In May 2011, over one-third (37.2 percent) of prime funds’ assets was invested in issuers headquartered in the Americas, mostly in the United States; about 8 percent of funds’ assets were invested in Canadian issuers

11 It has been suggested that we extend this analysis to the years before eurozone crisis to develop a stronger baseline and/or repeat this analysis during the 2008–2009 financial crisis. However, monthly portfolio holdings data on MMFs did not become available until November 2010. In fact, these monthly disclosures were part of the SEC’s 2010 reforms. Before November 2010, MMFs, like long-term mutual funds, disclosed information about the fund in their prospectuses and provided the SEC with portfolio holdings detail on a quarterly basis, which for various reasons is not easily compiled.

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Table 1 Aggregate prime MMF holdings of different security-types, May 2011. Security type category

Assets (billions of $)

% Of prime fund assets

Total Commercial paper (CP) and Other Notes Financial CP Asset-backed CP Other CP Variable rate demand notes Other notes

1700.7 578.7 241.1 130.2 48.1 76.4 82.9

100.0% 41.5% 17.3% 9.3% 3.4% 5.5% 5.9%

Bank CDs

597.6

42.8%

Treasury and agencies Agency securities Treasuries

202.4 117.7 84.7

14.5% 8.4% 6.1%

Repurchase Agreements Treasury and agency repo Other repo

258.0 170.2 87.8

18.5% 12.2% 6.3%

64.1 58.1 6.0

4.6% 4.2% 0.4%

Other Other instruments Municipal securities

Table 2 Securities held by prime money market funds by region and country, May 2011. This table measures aggregate prime MMF holdings of securities issued by companies, by headquarter country, as of May 2011. Other includes supranational securities and securities from countries accounting for less than 0.1 percent of total prime MMF assets. Region/country

Assets (billions of $)

% Of prime fund assets

Total

$1700.7

100.0%

Americas USA Canada

632.6 502.4 130.3

37.2% 29.5% 7.7%

Europe France UK Germany Netherlands Switzerland Sweden Norway Belgium Spain Denmark Italy Austria Luxembourg

875.8 254.3 192.4 117.6 93.1 71.7 70.7 21.0 13.5 13.5 12.6 10.4 3.5 1.5

51.5% 15.0% 11.3% 6.9% 5.5% 4.2% 4.2% 1.2% 0.8% 0.8% 0.7% 0.6% 0.2% 0.1%

Asia/Pacific Australia/New Zealand Japan

186.2 109.3 77.0

11.0% 6.4% 4.5%

6.0

0.4%

Other

(primarily banks). Of the portion invested in the United States, over half was invested in U.S. Treasury, agency, or municipal securities. A bit more than 50 percent of prime funds assets were attributable to issuers domiciled in Europe, the bulk of which was invested in issuers domiciled in three countries (France, 15 percent; U.K., 11 percent, and Germany, 7 percent). Another 11 percent of prime fund assets was invested in issuers domiciled in the Asia/Pacific region, split between Japan and Australia/New Zealand. To calculate ELM and BBI(50, 300) we need default probabilities that match the remaining maturity of each security a fund holds. The default probabilities used to generate expected losses are collected from the Risk Management Institute (RMI) of the National University of Singapore. RMI generates forward-looking default probabilities for issuers on a daily basis for maturities of 1, 3, 6, 9, 12, 18, and 24 months ahead. These probabilities are

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generated using the reduced form forward intensity model of Duan et al. (2012), published in the Journal of Econometrics. RMI covers around 60,400 listed firms (some of which are no longer active) in 106 economies around the world and releases default probabilities for 34,000 firms. In fact, RMI publishes default probabilities for a number of firms which are important for our analysis but for which CDS are simply not traded, notably for Canadian banks. Covariates include macroeconomic factors (e.g., trailing 1-year returns on the S&P 500), a firm’s “distance-to-default” based on Merton (1974), as well as firm-specific capital structure, liquidity, and volatility metrics from 1990 to the present. RMI’s default probabilities have a good track record, especially for issuers in developed countries, at maturities of 6 months or less, which is the horizon we are most concerned with in this paper. In particular, Duan et al. (2012) reports out-of-sample accuracy ratios exceed 90% at horizons of 1–3 months. As of RMI’s most recent technical report, 1-month accuracy ratios for the U.S., French, and Japanese firms were 0.94, 0.87, and 0.91, respectively (RMI, 2014). By hand, we match the month-end portfolio holdings of prime MMFs issuer-by-issuer and maturity-by-maturity with default probabilities obtained from RMI.12 Without some assumptions, we would be unable to match most of the securities that prime funds hold with RMI-supplied default probabilities (e.g., for a security with a remaining maturity of 67 days). We deal with this by linearly interpolating default probabilities for every day between the maturities that RMI provides. Because some of the securities that prime funds hold mature within 1–7 days (e.g., overnight repurchase agreements), we also need estimates of default probabilities for maturities of less than 1 month. We solve this problem by imposing the condition that for any random variable x whose support is in the range [0, ∞), if x has a continuous cumulative probability distribution, then P[x ≤ 0] = 0. This condition implies that  pi (Tj = 0) = 0, allowing us to linearly interpolate between that 30 value and  pi (Tj ) = 360 . Next, we match cumulative default probabilities (either actual or interpolated values) by hand with the list of parent firms collected from the holdings of MMFs as reported in the N-MFP reports. We are able to match default probabilities with parent firms for over 90 percent of the assets of prime MMFs. To calculate ELM and BBI(50, 300) we also need recovery rates, Ri , for each issuer. Consistent with market practice, we use a recovery rate of 0.40 for all private sector issuers except Japanese banks. For Japanese banks, we follow market convention and use a recovery rate of 0.35.13 Our analysis could be extended by randomizing recovery rates. However, evidence in Tarashev and Jackel (2008) suggests that the added complexity may not offer much additional insight in terms of results; they indicate, based on data collected from Markit for 136 entities, that the recovery rate market participants expect varies in a narrow range around 40 percent for daily data from late 2003 to early 2005.14 Consequently, we simply fix

12 In measuring a fund’s credit risk, we use the final legal maturity date (e.g., 271 days) as reported to the SEC in form N-MFP. The final legal maturity includes any “demand feature” a security may have, which allows a fund to demand its return of capital within a prespecified number of days. This is in contrast to the security’s maturity date, which a fund may use to determine its weighted average maturity (WAM). Consider, for example, a floating rate note that matures in 271 days but has a yield that resets weekly. Consistent with the security’s weekly interest rate reset, the fund may use a maturity of 7 days in calculating its WAM. But the fund must use the final legal maturity date of 271 days in calculating the fund’s weighted average life (WAL). 13 For example, on its CDSW page, Bloomberg uses a recovery rate of 0.4 to estimate implied default probabilities for private sector issuers from CDS premiums. The only exception appears to be that Bloomberg uses a recovery rate of 0.35 for Japanese banks. 14 Jokivuolle and Viren (2013) indicate that there is strong correlation between default probabilities and losses given default (i.e., 1 − Ri ). Using a sample of Finnish

our recovery rates at either 0.35 or 0.4 depending on the parent company. Given the RMI default probabilities, the expected loss on a security from a given issuer with a given remaining maturity is the relevant default probability times the expected loss given default. From expected losses on individual portfolio securities, we can calculate the expected losses on individual prime MMFs, as in Eq. (1), and on prime MMFs as a group (i.e., asset-weighted average ELM). Additionally, from RMI default probabilities, we can simulate a fund’s break-the-buck insurance cost, BBI(50, 300), as in Eq. (2). Our analysis could overstate ELM and BBI(l, u) for a number of reasons. First, the fixed income securities prime funds hold sometimes have credit enhancements, such as a guarantee, letter of credit, or other provision that guarantees return of principal and interest. Although such enhancements reduce the risk of holding a security, we do not take them into account except in cases where the guarantee is provided by the U.S. government or other sovereign nation. Second, MMFs sometimes hold asset-backed securities. All else equal, asset-backed commercial paper (ABCP) have less credit risk than securities that are not asset-backed. For example, recovery rates on asset-backed securities that defaulted during the 2007–2008 crisis are generally reported to have been much higher (in the range of 80 percent or more) compared with a recovery rate of about 40 percent on unsecured Lehman Brothers debt. We ignore this fact and simply treat ABCP as senior unsecured debt. Third, repurchase agreements (repo) are more than fully collateralized by securities that a fund’s repo counterparty (the borrower) must place with a third-party custodian. The fund may seize this collateral if the repo counterparty fails to unwind the repo (i.e., fails to return the fund’s cash) when the repo expires. All else equal, this makes repo less risky than other senior unsecured debt. Nevertheless, we ignore this, treating repo as uncollateralized (i.e., the credit risk is the full credit risk of the repo counterparty) unless the repos are fully collateralized by Treasury and agency securities, in which case we treat repos as having the default risk of the U.S. government.15 Fourth, some of the roughly 10 percent of assets that we cannot match with default probabilities are securities issued by non-financial companies. Generally speaking, when available, CDS premiums on non-financial corporations have tended to be lower than those on financial companies.16 Another portion of the unmatched securities are issued by municipalities. These are most often in the form of variable rate demand notes (VRDNs), which typically have 1-day or 7-day demand features. These securities are generally considered to be of high credit quality since the fund can tender the securities to the demand feature provider (usually a financial institution).17 To ensure that panel data results are not

bank loans for one year, they develop an endogenous loss model and simulate losses, finding that losses are likely to be considerably higher during downturns. During simulated shocks, their expected losses remain less than or equal to 60% (i.e., Ri = 0.40). 15 For a money market fund, there may be liquidity risk (which is not the subject of this paper) in a repo backed by Treasury and agency collateral but there is arguably no credit risk (which is the subject of this paper). If a fund’s repo counterparty fails to return the fund’s cash when the repo matures, the fund would seize the Treasury and agency collateral pledged by the repo counterparty. A fund might need to liquidate some of the Treasury and agency collateral to meet shareholder redemptions, but that is case of liquidity risk, not credit risk. Put differently, we assume that if the fund were to hold the Treasury and agency collateral to maturity, it would all mature at par. 16 We are able to match most publicly-traded non-financial companies, particularly large companies (e.g., PepsiCo, General Electric, Hewlett-Packard). CDS premiums on these companies tend to be low. For example, on January 31, 2011, then 1-year CDS premium on PepsiCo was quoted at 11 basis points, compared to 50 basis points for BNP Paribas SA, a large European bank. 17 Enhancements and demand features necessarily lower the probability of default on a security since the joint probability of both the issuer and the provider defaulting will always be lower than the probability of just the issuer defaulting. The one

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skewed by a number of small funds for which we were unable to match the majority of portfolio securities to default probabilities, we remove funds for which less than 70 percent of fund assets could be matched to default probabilities in any given month. These omitted funds tend to be small, representing 10 percent of industry assets in total. On the other hand, our analysis could understate ELM and BBI(50, 300) because of how we treat sovereign debt. RMI does not publish default probabilities for sovereigns. Consequently, we simply assume that the default probabilities for U.S. Treasury and agency securities are zero at all maturities. We doubt many readers would object to this treatment for Treasury securities. With respect to agency securities, we note that over our sample shortterm agency securities have yielded only a few basis points more than Treasury securities, indicating that market participants view short-term agency debt as about as risky as Treasury debt, consistent with the federal government’s takeover of Fannie Mae and Freddie Mac in September 2008. Nevertheless, market participants do not necessarily view Treasury and agency securities as risk free. For example, CDS premiums on Treasury securities are low but not zero. It is unclear whether this arises because the CDS market for Treasury securities is thin (Austin and Miller, 2011) or because market participants now view Treasury securities as having some, albeit still very small, default risk. If it is the latter, our analysis might understate ELM and BBI(50, 300) by some, presumably small, margin.18 We run two robustness checks to ensure that alternative treatments do not significantly alter our estimation of a fund’s credit risk. First, rather than omit VRDNs – which, in effect, gives VRDNs the average credit risk of the remainder of the fund – we match each VRDN with the default probability of the demand feature provider. For example, if Snohomish County, Washington issues a VRDN with a demand feature provided by Bank of America, we would apply Bank of America’s probability of default before maturity (with the maturity set to the next put date rather than the final maturity date). Results, displayed in Appendix B, Fig. B8, signal that, not only does this alternative treatment of VRDNs have almost no impact on a fund’s overall credit risk as measured by ELM, but our original choice to simply omit VRDNs results in slightly more conservative estimates. For example, the average difference between our original measure and this alternative measure is 0.5 basis points with a standard deviation of 1.1 basis points. Second, rather than treat ABCP and repos (not fully collateralized by Treasury/agency securities) as senior unsecured debt, we assume a recovery rate of 80% on these securities. The difference between our original ELM and the ELM calculated from this much less conservative treatment of ABCP and repos is small – averaging just 1.8 basis points with a standard deviation of 2.2 basis points. In summary, these checks indicate that ELM is a conservative, yet reasonable, estimate of a fund’s credit risk. In results not shown, we also verify that the main results of this study hold under these alternative treatments of VRDNs, ABCP, and repos.

One might ask whether we can use the yield and/or CUSIP detail available for each security on Form N-MFP to infer a fund’s credit risk. If so, we could avoid the laborious process described above of joining each funds’ portfolio holdings with default probabilities. Also, we could avoid making simplifying assumptions about the true counterparty risk of more complex securities, such as those with letters of credit. For various reasons, however, using the yields and/or CUSIPs on Form N-MFP would result in lower quality estimates. The yields on individual securities are usually reported as of the date of purchase, not the date of filing. Thus, an aggregate credit risk measure based on reported security-level yields would lag behind the current market.19 This issue cannot generally be overcome by using the CUSIPs listed on Form N-MFP and linking those with current market yields from an outside data provider. The majority of prime MMF assets are commercial paper (CP) and CDs, for which in many cases price quotes are not readily available from data services such as Bloomberg.2021 Therefore, current market yields are unavailable for the majority of holdings. Our ELM and BBI(50, 300) measures overcome these deficiencies.22

Fig. 1 plots the asset-weighted average across all prime funds of expected loss-to-maturity, ELM, and break-the-buck insurance, BBI(50, 300), for the period January 2011 to December 2012. This figure indicates that the aggregate credit risk of prime funds is low. ELM and BBI(50, 300) averaged just 15 and 8 basis points, respectively, on an asset-weighted basis from January 2011 to December 2012. By comparison the 6-month CDS premium on BNP Paribas averaged 106 basis points over this same period. This low level is consistent with these facts: (a) money market funds hold very short-term securities; (b) these securities are investment grade and virtually all are of the highest short-term credit rating; (c) the term structure of credit default swap spreads is generally upward sloping. Together, these characteristics limit the credit risk of prime MMFs. To demonstrate the value in using a metric like ELM to measure a fund’s credit risk, Fig. 1 also plots the prime-to-government money market fund yield spread. This is the most commonly used indicator

exception would be if the defaults are perfectly correlated. But enhancements and demand features are costly. It seems unlikely that a fund (or other market participant) would willingly bear such costs if they were valueless. 18 The SEC’s N-MFP data indicate that money market funds hold very little, if any, sovereign debt of other countries. This reflects the fact that MMFs may only hold U.S. dollar denominated securities in combination with an apparent lack of issuance by non-U.S. sovereigns of money market instruments denominated in U.S. dollars. In our N-MFP data, a very small number of securities are linked to a sovereigns other than the U.S. federal government. These limited cases arise: (a) because a sovereign has guaranteed the money market instrument of a private or quasi-private sector issuer; (b) a sovereign has taken over the liabilities of a private sector company. Virtually all of these cases arise from Germany, France, Belgium, Norway, or Japan. We assume that the default probabilities of these securities are zero.

19 Furthermore, security yields are missing or entered with error on a substantial portion of securities in Form N-MFP. These yields must also be text-mined from the security titles listed on Form N-MFP, introducing further potential issues. 20 This may in part be because many of these securities are thinly traded. For example, according to Covitz and Downing (2007), “CP is an illiquid buy-and-hold instrument” since secondary market offerings of commercial paper account for only about 8% of the total face amount traded, or about 16% of the total transaction volume. Also see Krishnamurthy (2002), Squam Lake (2013), Rosengren (2013). 21 Even if secondary markets were deeper, 24% of prime MMF assets do not have a CUSIPs reported on Form N-MFP as of May 2011. Even more troublesome, funds often enter their own internal CUSIPs on the Form, introducing matching error. 22 It is worth noting in passing that an alternative approach of measuring MMF credit risk based on yield spreads may be possible in the future because the SEC plans to revise the N-MFP form.

4. Results This section begins with an overview of the cross-sectional and intertemporal distribution of ELM and BBI(50, 300) in Section 4.1, followed by the main results of the paper in Section 4.2. We offer a detailed analysis of the contributions of funds’ regional bank investments to their overall credit risk during the eurozone crisis. The goal is to determine whether a marked increase in prime MMFs’ credit risk in late 2011 is primarily attributable to funds’ European investments. Finally, Section 4.3 documents portfolio characteristics, such as longer portfolio maturities, that are associated with higher credit risk in prime MMFs. 4.1. The distribution of ELM and BBI(50, 300)

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of a prime fund’s credit risk. It is simple to calculate, but as noted in the introduction, the use of amortized cost accounting weakens the value of this metric. This is because if the credit quality of a fund’s security declines, the security’s market price should also decline, boosting the security’s market yield. But because funds use amortized cost accounting, this increase is not reflected in the fund’s yield until that security matures and the fund rolls over its holding. Consequently, a fund’ s yield spread should lag behind and be less variable than a fund’s true credit risk. This is exactly what we find. Although the two metrics are close on average, in some months, ELM and yield spread diverge by as much as 8 basis points, primarily because of month-to-month variation in ELM. Additionally, yield spread lags about 2 months behind ELM, which coincides neatly with the maturity of prime fund holdings (e.g., funds’ weighted average final legal maturity, WAL, is 60 days for securities issued by banks during 2011–2012). As would be expected, BBI(50, 300), which better measures the risk of a 2008-like event, is lower than ELM. Nevertheless, since the two metrics are both generated from default probabilities, they follow a similar pattern over time. For example, in December 2011, ELM hit a peak of 23 basis points compared to 12 basis points for BBI(50, 300). Interestingly, the estimates for BBI(50, 300) are about in the range of fees the U.S. Treasury assessed under its 2008–2009 temporary guarantee program. The Treasury Department initially set the cost to funds for this insurance at 4 basis points at an annual rate for funds with a mark-to-market value of $0.9975 or above and 6 basis points for funds with a mark-to-market value of less than $0.9975 but greater than $0.9950 (insurance was not available to money market funds with a mark-to-market value of less than $0.9950).23 The Treasury raised the cost to 6–8.8 basis points at an annual rate (again depending on whether a fund’s mark-to-market was above or below $0.9975) when it first renewed the insurance program; this is about in line with our estimate of 8 basis points for BBI(50, 300) over the period 2011–2012. Asset-weighted averages of ELM and BDI(50, 300) across time, however, mask cross-sectional variation in funds’ credit risks (Fig. 2). The standard deviation of ELM was 4 basis points in January 2011. This rose to 11 basis points in December 2011. The maximum expected loss in any individual prime MMF was 47 basis points in December 2011, while the minimum was just slightly above zero. The maximum simulated break-the-buck insurance premium, BBI(50, 300), for any fund was 18.5 basis points in November 2011, while the minimum was 1 basis point. This reflects heterogeneity in funds’ portfolio holdings, some concentrating a larger portion of their assets in U.S. Treasury and agency securities and others more invested in bank-issued debt. Credit risk in prime MMFs evolves considerably over the period 2011 through 2012. On an asset-weighted basis, ELM rises from 12 basis points in June 2011 to a maximum of 23 basis points in December 2011. That rise is consistent with the market’s intensifying concerns about eurozone banks, a deteriorating outlook for the U.S. economy, and the looming U.S. federal government debt ceiling crisis. Still, the rise was small compared to the increases in CDS premiums on global banks over the same period. By March 2012, ELM had receded to 14 basis points, little different from its level in July 2011. ELM and BBI(50, 300) fell, on average, over the remainder of 2012, likely in response to the challenges of eurozone policy makers to find an all-encompassing economic and political solution to the eurozone’s problems and the risks that the lack of a solution posed for global financial markets.

23 See U.S. Treasury Department, “Treasury Announces Temporary Guarantee Program for Money Market Funds,” September 29, 2008.

Fig. 1. Expected loss-to-maturity, ELM, and expected cost of break-the-buck insurance, BBI(50, 300). This figure plots prime MMFs’ asset-weighted average ELM, Yield spread, and BBI(50, 300). Estimates are annualized costs. For each fund, ELM is the expected loss on portfolio securities, Yield spread is the yield on each prime money market fund minus the average yield on all government-only money market funds, and BBI(50, 300) is the estimated break-the-buck insurance premium, taking into account default correlations (as calculated in Appendix A).

4.2. The contribution of funds’ European bank investments to credit risk In the second half of 2011, prime fund managers acted to reduce their exposure to the eurozone crisis. However, it is unclear what, if any, effect these efforts had on the aggregate credit risk of their portfolios. It has been assumed that these efforts were, in some sense, ‘too little too late’. For example, Chernenko et al. (2014) contend that “risk taking” by MMFs, in the form of lending to eurozone banks, drove large investor redemptions in the summer of 2011. This leaves the impression that MMFs did not divest of their eurozone exposure early enough. Consequently, as the credit conditions of eurozone banks deteriorated over the summer and fall of 2011, the credit risk in funds’ portfolios expanded, driving investors to redeem their shares. We use our measures of portfolio credit risk, ELM andBBI(50, 300), to evaluate whether an increase in the credit risk of prime MMFs during the second half of 2011 is primarily attributable to holdings of eurozone bank debt. 4.2.1. Anecdotal evidence from flows, maturities, and CDS premiums First, however, we look at this question with simple descriptive statistics. As Fig. 3 demonstrates, prime funds sharply reduced their non-repo investments in European banks.24 Most notably, prime MMFs reduced the portion of their bank holdings issued by French-domiciled banks from 20 percent in May 2011 to

24 In Figs. 3 and 4, we study bank-issued securities excluding Treasury/agencybacked repurchase agreements. This is because when estimating a security’s expected loss, we assume securities that are fully collateralized by U.S. government debt have zero credit risk (see Section 3). Therefore, we exclude these Treasury/agency-backed repurchase agreements from these figures to avoid diluting our understanding of regional contributions to credit risk.

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Fig. 2. Distribution of ELM and BBI(50, 300). This figure shows box-and-whisker plots of ELM and BBI(50, 300), respectively, across funds by month (January 2011–December 2012). Rectangles represents the interquartile range (IQR), which extends from the 25th to 75th percentile, and the median is the horizontal line in the middle of the rectangle. The ends in the lines extending from below and above the rectangle represent the minimum and maximum values in the ranges from Q1 − 1.5 * IQR to Q1 and from Q3 to Q3 + 1.5 * IQR, respectively. If observations exist outside of this range (i.e., in the top or bottom 0.35 percentiles of a normal distribution), they are considered to be outliers and are denoted with a dot.

Fig. 3. Prime MMFs’ holdings of bank-issued securities by region and country, 2011. This figure shows MMF assets held in bank-issued securities by the domicile of the bank as a percentage of total MMF assets held in bank-issued securities, excluding securities fully collateralized by U.S. Treasury or Agency securities (i.e. Treasury/Agency-backed repo).

just 3 percent by December 2011. As prime funds pulled back from the eurozone, they reallocated their investments to regions presumably more insulated from the eurozone crisis, including the U.S., Canada, certain Northern European countries, and, most notably, the Asia/Pacific region. Prime funds’ assets attributable to Asia/Pacific-domiciled banks rose by $55 billion and went from 15 to 26 percent of prime MMF bank-issued investments. This increase went primarily to banks headquartered in Japan. From, May to December 2011 the portion of prime funds’ bank assets issued by Japanese banks doubled. By December 2011, prime funds had more assets invested in Asia/Pacific banks than they did in France, Germany, and the UK combined, representing a sharp reversal from earlier in the year. In addition, prime funds attempted to mitigate credit risks from European issuers by lowering the WAL (final legal maturity) of their remaining holdings in European-domiciled banks. As Fig. 4 shows,

the WAL for prime funds’ French, German, and UK bank holdings fell from around 70 days in May 2011 to below 30 days in December 2011. At the same time, the maturities of funds’ U.S. and Canadian bank holdings remained roughly constant. Although funds’ Canadian bank investments were much longer-dated, Canadian banks were known to be of particularly high credit quality over the period.25 Funds’ investments in Aus/NZ bank securities were also longer-dated (although the maturities trended downward over the period). In contrast, MMFs’ holdings of Japanese banks – which nearly doubled between May and January 2011 – were comparatively short-dated. Presumably, this reallocation toward Japanese banks should have lowered funds’ overall credit risks.

25 See, for example, Greenwood (2011): “...Canadian banks boast some of the lowest risk levels in the industry.”

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150 130 110 90 70 50 30

France Japan Canada

Germany Aus/NZ

DEC

NOV

OCT

SEP

AUG

JUL

JUN

APR

MAY

MAR

FEB

JAN

10

UK USA

Fig. 4. Weighted average life (WAL) of prime MMFs’ bank-issued securities by country, 2011. This is the value-weighted average final legal maturity in days (WAL) of prime MMF holdings by country. Only securities issued by banks, excluding those fully collateralized by U.S. Treasury and Agency securities, are included.

Fig. 5. 5-Year CDS premiums for banks or different regions, 2011. The CDS premium for European financials is the iTraxx senior financial index for Europe. The CDS premiums for large Japanese, Australia/New Zealand, and U.S. banks is the average of 5-year CDS premiums for (Sumitomo Bank and Mizuho Bank), (National Australia Bank, Westpac, and ANZ), and (Bank of America, JPMorgan Chase, Citi, Wells Fargo, and Goldman Sachs), respectively. Canadian banks are excluded because their CDS is thinly traded.

However, financial conditions deteriorated outside the eurozone, obfuscating our understanding of the sources of funds’ credit risks. Fig. 5 plots the index of 5-year CDS premiums for large European financial institutions (i.e., the Markit iTraxx senior financial index). The figure also plots the averages of 5-year CDS premiums for selected large Japanese, Australia/New Zealand (Aus/NZ), and U.S. banks. This figure highlights that U.S. banks were not much safer than many foreign banks over this period. In fact, Bank of America, with a 5-year CDS premium of 457 basis point as of November 2011, was one of the riskiest major banks in the world. The CDS premiums on Japanese and Aus/NZ banks are almost

always lower than the European CDS index. Thus, all else equal, by shifting their portfolios toward banks in Japan and Aus/NZ, prime MMFs expected to reduce risk. But, as shown here, the three series are correlated. Notably, the 5-year CDS premiums for the Japanese and Aus/NZ banks rose from low levels (100 basis points or less) in January 2011 to over 250 basis points on October 4, the same day the 5-year CDS index for European financials hit its highest level (296 basis points) up to that point in 2011. CDS premiums on Japanese banks, and to a lesser extent on Aus/NZ banks, spiked again in late November when the CDS index on European financials hit its highest point ever (355 basis points). This correlation between the CDS indexes of European banks and Asia/Pacific banks is not perfect, however. For example, in mid-September, CDS premiums on Japanese and Aus/NZ banks fell somewhat while those on European banks continued to climb, indicating that non-eurozone factors also influenced the perceived credit quality of Japanese and Aus/NZ banks. Notably, Standard & Poor’s August 5th downgrade of the U.S. sovereign credit rating likely reverberated internationally. Furthermore, export-driven Japanese and Aus/NZ economies were likely especially vulnerable to what appeared to be slowing global economic growth. Finally, the lingering effects of the tsunami and the resulting nuclear disaster may also have stoked anxieties about the health of Japanese banks. To summarize, while there is strong evidence that fund managers took actions to insulate their funds from the eurozone crisis, the net effect of those actions on portfolio credit risks remains unclear. Summary statistics appear insufficient to determine the sources of credit risk in fund portfolios. In the next section, we evaluate the security types that contributed to each fund’s credit risk (as measured by ELM and BBI) using regression analysis and by constructing counterfactual portfolios. 4.2.2. Regression evidence Regression evidence indicates that prime funds were, at least to some extent, passive recipients of contagion from eurozone banks to the global banking system. Table 3 shows regression results across a panel of fund-months over 2011–2012. The dependent variable is BBI(50, 300). We choose this metric because it allows for correlated defaults and is arguably more applicable to financial stability concerns. However, the same patterns emerge when we use ELM as the dependent variable. Explanatory variables include various permutations of a fund’s bank exposure as well as average 5-year CDS premiums on European, Asia/Pacific, and U.S. banks. In columns (1) and (2), the explanatory variables are the percentage of fund assets invested in the banks of different countries or regions. We control for movements in global credit risk through time fixed effects. The coefficients on funds’ French, other European, and total European bank exposures are all positive and significant. According to the model in column (2), a one standard deviation (17.2 percentage point) reduction in a fund’s allocation to European banks is predicted to reduce the fund’s required insurance premium by 0.9 basis points (roughly 11 percent of the 8 basis point average BBI(50, 300)). Thus, funds could expect to insulate themselves from the eurozone crisis by reducing their allocation to European banks. However, coefficients in these two models also suggest that even a small reallocation of fund assets into Asia/Pacific banks, particularly Japanese banks, more than offsets the effect of a reduction in European bank holdings on a fund’s credit risk. For example, the coefficient on ASIAPAC in column (2) indicates that a one standard deviation (7.4 percentage point) increase in a fund’s allocation to Asia/Pacific banks results in a 1.7 basis point increase in BBI(50, 300). Thus, the affect of a one standard deviation change in exposure to Asia/Pacific banks is nearly twice that of a change in exposure to European banks.

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S. Collins, E. Gallagher / Journal of Financial Stability xxx (2015) xxx–xxx Table 3 Regressions of BBI(50, 300) on prime MMF’s bank exposures and CDS indexes. These are panel regressions across fund-months over the period 2011–2012. The dependent variable is BBI(50, 300). The goal is to parse the regional/country investments that contributed most to a fund’s credit risk during the eurozone crisis. The exposure variables measure the percentage of a prime fund’s assets invested in banks of a given country or region, regardless of the type of security (i.e. Treasury and agency-backed repo securities are included). In columns (1) and (2), the intercept is allowed to vary by time to control for changes in global credit risk. In column (3), time-fixed effects are replaced with 5 year CDS variables, CDS EUROPE, CDS ASIAPAC, and CDS USA (not shown). These CDS variables measure the average CDS premiums of large banks in the specified region or country. We do not control for Canadian CDS because it is thinly traded. The regression in column (4) employs no intercept or fixed effects in order to force the model to explain BBI(50, 300) through the interaction of regional exposure and CDS variables alone. In this regression, a fund with zero bank exposure is assumed to have zero credit risk. Standard errors are clustered by fund. BBI(50, 300) Independent variables

(1)

(2)

FRANCE OTHER EUROPE AUS/NZ JAPAN USA CANADA

0.05879*** (0.01590) 0.03944*** (0.00769) 0.14380*** (0.02414) 0.30167*** (0.02275) 0.03674*** (0.01230) −0.03230** (0.01594) 0.05185*** (0.00731) 0.22378*** (0.01717) 0.01210 (0.01037)

EUROPE ASIAPAC NORTHAMERICA EUROPE × CDS EUROPE ASIAPAC × CDS ASIAPAC USA × CDS USA Time control (not shown) R2 N * ** ***

(3)

(4)

−0.64791 (0.49839)

Intercept

−0.01860 (0.01737) −0.05976*** (0.01737) 0.03459*** (0.00975) 0.01720 (0.02960)

−0.01745 (0.01568)

0.00011* (0.00007) 0.00140*** (0.00021) 0.00027** (0.00013)

0.00039*** (0.00003) 0.00170*** (0.00012) 0.00048*** (0.00006)

Time F.E.

Time F.E.

CDS

–

0.79 3131

0.70 3131

0.68 3131

N.A. 3131

Estimates with a p-value below 0.10. Estimates with a p-value below 0.05. Estimates with a p-value below 0.01.

In contrast, funds’ allocations to banks in the U.S. and Canada have a comparatively smaller effect on their credit risk. The effect of a marginal increase in a fund’s exposure to U.S. banks on its breakthe-buck insurance cost is nearly equivalent to that of exposure to other European banks. Meanwhile, the coefficient on CANADA in column (1) is negative and significant, suggesting that the average fund could reduce its credit risk by allocating more assets to Canadian banks. In column (3) we seek to understand whether allocations to certain countries/regions are independently important or only important when CDS premiums are rising. Explanatory variables include the average 5-year CDS premiums on banks in Europe, Asia/Pacific, and the US (taken from Fig. 5) as well as an interaction between these CDS variables and the exposure variables from columns (1) and (2).26 The same basic patterns from

26 Since CDS premiums are not consistently available for Canadian banks, we only control for funds’ exposures to Canadian banks and not their CDS premiums.

11

columns (1) and (2) hold, only now we see that a fund’s Asia/Pacific and U.S. bank exposures only significantly affect its credit risks when CDS premiums are high. In contrast, a fund’s European exposure has an independently significant effect on BBI(50, 300). This is consistent with average CDS on European banks being higher than that on other banks throughout 2011–2012. One interpretation is that funds shifted assets into the Asia/Pacific in an effort to lower their eurozone-related credit risk only for global CDS premiums to rise markedly. In reality, a fund with zero bank exposure is assumed to have very low credit risk (see Section 3), therefore a no-intercept model may be more appropriate. The regression in column (4) of Table 3 includes no intercept or fixed effects in order to force the model to explain BBI(50, 300) through the interaction of a fund’s regional bank exposures and average regional 5-year CDS premiums alone. Again, the regression signals that the primary factor pushing up credit risk over the period appears to be exposure to Asia/Pacific banks at a time when CDS premiums were rising. Fig. 6 shows results of a counterfactual comparing BBI(50, 300) to the BBI(50, 300) that would have occurred had prime funds continued throughout the remainder of 2011 to hold the portfolios they held in May 2011 (in other words, had they not taken steps to insulate their portfolios from the eurozone crisis). This figure is constructed using predicted values from the regression in column (4) of Table 3. Actual BBI(50, 300) (i.e., the dependent variable in Table 3) is also shown (top left panel, gray line with circular markers). Plotted values are measured as fund asset-weighted averages across months. As seen in the upper-left panel, predicted BBI(50, 300) rose by 4.4 basis points from May to December 2011. According to the counterfactual, credit risk would have been similar had prime funds continued to hold their May-level portfolio allocations throughout the rest of 2011. Throughout 2011, the contribution from North America remained low and stable (top right panel), in part reflecting the fact that much of prime funds’ exposure to North American banks includes holdings of Canadian banks with below average credit risks (Greenwood, 2011). The lower-left panel shows the contribution of Europe to predicted BBI(50, 300). The solid black line shows that the actual contribution from Europe rose only slightly (0.6 basis points) from May to December 2011, consistent with prime funds’ actions to limit exposure to eurozone issuers. Moreover, the counterfactual predicted BBI(50, 300) – the dashed line in the that panel – indicates that the contribution from Europe would have risen substantially (2.3 basis points rather than 0.6) had funds not acted to limit their exposure to the eurozone. Thus, as the lower right panel indicates, most of the rise in BBI(50, 300) from May to December 2011 reflected contributions from countries outside Europe, notably those in the Asia/Pacific region (3.1 basis points). The Asia/Pacific region contributed more than Europe to the credit exposure of prime funds in the second half of 2011. The same patterns hold when we study ELM instead of BBI(50, 300) and when we restrict the sample to only the riskiest prime MMFs. One might question whether error in the regression model used to generate Fig. 6 influences the results. Another concern is that the findings apply only to the average fund and not to those funds with the riskiest portfolios going into the eurozone crisis. To resolve these concerns we turn to our other credit risk measure, ELM. As discussed in Section 2, a fund’s ELM is just the weighted sum of the expected losses on the fund’s portfolio securities. Therefore, to determine the regional contributions to the credit risk of a group of funds, we simply calculate a weighted sum of the expected losses on these funds’ portfolio securities by the region of the issuer. We restrict our sample to only those funds with top quartile credit risk (as measured by ELM) as of May 2011, just before the worsening of the eurozone crisis. These funds tended to have higher European bank exposure and were arguably least prepared for the coming

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Fig. 6. Predicted and predicted counterfactual BBI(50, 300), 2011. This figure shows actual, predicted and a predicted counterfactual values for BBI(50, 300) (upper left panel) in basis points. Counterfactual values are constructed on the assumption that prime funds continued to hold throughout 2011 the portfolios they held in May 2011. The other panels in the chart show the contributions of the three regions (North America, Europe, and Asia/Pacific) to predicted BBI(50, 300) or to predicted counterfactual BBI(50, 300), respectively. The contributions of the three regions total to the predicted and predicted counterfactual BBI(50, 300) measures in the upper-left panel. Predicted and predicted counterfactuals values are generated from the panel regression model in column (4) of Table 3. Plotted values are measured as fund asset-weighted averages across months.

shock. Fig. 7 displays the results. It confirms that funds made significant efforts to lower their credit exposure to European banks. Among this group of funds, the actual contribution from Europe to ELM increased by 4 basis points from May to December. This is small compared to counterfactual increase of 14 basis points had these funds not acted to reduce their European credit exposure. It also confirms that, even among the riskiest funds, the Asia/Pacific region contributed more than Europe to funds’ credit risk during the eurozone crisis. This is true both in absolute terms and in relative changes. These factors, not funds’ European investments, appear to be the primary reasons the credit risks of prime MMFs rose in the second half of 2011. We conclude that the increase in prime fund credit risk in the second half of 2011 reflected worsening global economic conditions and contagion in the worldwide banking system, rather than MMFs’ exposure to the eurozone. 4.3. The influence of maturities and liquidity on credit risk We expect the cost of break-the-buck insurance to be lowest for those MMFs with the shortest portfolio maturities since the term structure of CDS premiums is normally upward sloping for high quality issuers (Agrawal and Bohn, 2006; Han and Zhou, 2011). If this is the case, then the SEC’s decision to impose a minimum

liquidity standard and a maximum weighted average life (WAL) on MMFs in January 2010 potentially reduced the credit risk of some prime funds. In Table 4, we assess the degree to which a fund’s portfolio maturity and liquidity influences its risk of breaking the buck. We begin with maturities. In column (1), the explanatory variable is the WAL of a fund’s portfolio securities. It is measured as the value-weighted final maturity on a fund’s securities. The coefficient is positive and statistically significant. It is also moderately economically significant. To lower BBI(50, 300) by one basis point (i.e., 13 percent of the average of 8 basis points) would require a cut in WAL of 55 days – about two standard deviations.27 The 2010 reforms capped a money market fund’s WAL at 120 days. Before the 2010 reforms, WAL limits did not exist, funds did not publish WALs, and hence, the reduction in fund WALs as a result of the SEC’s 2010 reforms is unknown. However, before and after 2010, money market funds were generally prohibited from holding securities with a remaining life of more than 397 days. Thus, we judge the current 120 day WAL limit against a hypothetical fund with a WAL of 260 days (about half way between 120 and 397 days). Before the SEC’s

27 The weighted average WAL over 2011–2012 was 78 days. This metric includes U.S. Treasury securities.

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Fig. 7. Actual and counterfactual ELM, 2011. Using a restricted sample of funds with top quartile credit risk (as measured by ELM) as of May 2011, this figure shows actual and counterfactual values for ELM (upper left panel) in basis points. ELM is the value-weighted sum of the expected losses on portfolio securities. Counterfactual values are constructed on the assumption that prime funds continued to hold throughout 2011 the portfolios they held in May 2011. The other panels in the chart show the contributions of the three regions (North America, Europe, and Asia/Pacific) to ELM or to counterfactual ELM, respectively. The contributions of the three regions total to the actual and counterfactual ELM measures in the upper-left panel.

2010 reforms, a fund could have held such a portfolio if the securities were floating rate instruments with a weekly interest rate reset. The regression indicates that the SEC’s imposition of a WAL limit in 2010 would have reduced the risk of this hypothetical fund breaking the buck by 2.6 basis points (. 018 × (120 −−260)), or 32 percent of the average BBI(50, 300) over 2011–2012. We do not know if this is an extreme example. But it does suggest that a WAL limit can help mitigate the risk of a fund with an outlying average maturity breaking the buck. In column (2) explanatory variables measure the WAL of a fund’s securities issued by the banks of different countries. The sample is restricted to funds that had at least some investments in the banks of each country studied. In any given month, funds with longer-dated investments in European and North American banks appear to have had higher credit risk, while the maturities of investments in Asia/Pacific banks is insignificant. This could be related to the fact that the Japanese bank with the lowest default risk (Bank of Tokyo-Mitsubishi) issued comparatively longer-dated securities to MMFs (e.g., 40 days in December 2011) while the Japanese bank with the greatest default risk (Mizuho Bank) issued the shortest maturing securities (e.g., 20 days in December 2011). Nonetheless, it appears that the rise in credit risk coming from the Asia/Pacific is primarily attributable to asset growth coupled with

rising CDS premiums in that region, rather than the maturities of those assets. More liquid funds have lower credit risk. However, the economic effect is only moderate. In column (3), the explanatory variables include a fund’s weekly liquidity as a percentage of assets (LIQUIDITY), the percentage of fund assets held in institutional share classes (INSTITUTIONAL), and the natural log of fund assets (FUNDASSETS).28 We include these latter two controls because it has been said that large, institutional prime funds take on more credit risk to attract investor flows (Chernenko et al., 2014) and, according to Gallagher et al. (2015), these same types of funds maintain higher liquidity ratios. The coefficient on LIQUIDITY indicates that a one standard deviation (10 percentage point) increase in a fund’s weekly liquidity results in a 0.5 basis point (i.e., 6 percent of the average of 8 basis points) decline in BBI(50, 300). According to iMoneyNet’s definition of weekly liquidity, prime funds’ (simple) average weekly liquidity rose by about 17 percentage points after the reforms, signaling a

28 This is the percentage of fund assets invested in securities maturing within 5 business days, U.S. Treasury securities, and U.S. agency securities maturing within 60 days.

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Table 4 Regressions of BBI(50, 300) on prime MMF’s portfolio maturities. These are panel regressions across fund-months over the period 2011–2012. The dependent variable is BBI(50, 300). Researchers may be interested to know how a fund’s portfolio maturity and liquidity influence the cost of its break-the-buck insurance. In columns (1) and (2), explanatory variables include various permutations of a fund’s weighted average life (WAL). WAL measures the average final legal maturity of a fund’s securities, weighted by the value of each security in the portfolio. In column (2), the observation sample consists only of funds with non-zero assets in banks from France, Other Europe, Aus/NZ, Japan, U.S., and Canada. In this column, WAL is measured for a fund’s investments in banks only and is aggregated by the bank’s country. For example, WAL (FRANCE) measures the value-weighted average final maturity of a fund’s investments in BNP Paribas and other banks headquartered in France. In columns (3) and (4), the key explanatory variable is LIQUIDITY. This is the percentage of fund assets invested in securities maturing within 5 business days, U.S. Treasury securities, and U.S. agency securities maturing within 60 days. Other explanatory variables include the percentage of fund assets held in institutional share classes, INSTITUTIONAL, measured from Investment Company Institute (ICI) data and the natural log of fund assets, FUNDASSETS. In column (4) we also include (but do not show) the percentage of fund assets invested in European, Asia/Pacific, and North American banks, separately. In all regressions, the intercept is allowed to vary by time to control for changes in global credit risk. Standard errors are clustered by fund. BBI(50, 300) Independent variables

(1)

WAL

0.01836** (0.00840)

(2)

(3)

(4)

−0.05156*** (0.01394) 0.01218*** (0.00429) 0.18845* (0.11243)

−0.03784*** (0.01108) 0.00042 (0.00324) −0.03145 (0.07671) Time F.E. Region Exp. 0.72 3054

0.01022* (0.00541) 0.02107** (0.00874) 0.00145 (0.00180) −0.00129 (0.00722) 0.01776*** (0.00357) 0.00631*** (0.00167)

WAL (FRANCE) WAL (OTHER EUROPE) WAL (AUS/NZ) WAL (JAPAN) WAL (USA) WAL (CANADA) LIQUIDITY INSTITUTIONAL FUNDASSETS Control (not shown)

Time F.E.

Time F.E.

Time F.E.

R2 N

0.39 3131

0.62 1586

0.48 3054

* ** ***

Estimates with a p-value below 0.10. Estimates with a p-value below 0.05. Estimates with a p-value below 0.01.

0.9 basis point reduction in the average fund’s risk of breaking the buck from correlated issuer defaults.29 According to the model, large, institutional funds would face higher insurance costs; however, this is due to these funds’ higher allocations to international banks – possibly reflecting economies of scale in the costs of researching international credits. As evidence, coefficients on INSTITUTIONAL and FUNDASSETS are no longer significant when we control for (not shown) the percentage of fund

29 The SEC Form N-MFP portfolio holdings data used throughout this study became available in November 2010. Thus, we must use iMoneyNet data to estimate funds’ weekly liquidity before the 2010 reforms. Due to data limitations, the iMoneyNet measure is indicative of, but not identical to, the SEC’s definition of weekly liquidity (LIQUIDITY). iMoneyNet measure excludes all U.S. agency securities maturing within 60 days and double counts U.S. Treasury securities maturing within 7 days. Despite these differences, the iMoneyNet measure is usually within 2 percentage points of the SEC’s definition. According to iMoneyNet data, liquidity rises from 31 percent of assets over 2006–2007 (before the crisis and the 2010 reforms) to 48 percent of assets over 2011–2012.

assets invested in global banks in column (4). At the same time, a fund’s weekly liquidity remains statistically important. In sum, these results indicate that liquidity, maturity, and credit risk are closely tied. A fund with average credit risk can lower its break-the-buck insurance premium by over 10 percent simply by both lowering its WAL and increasing its weekly liquidity by one standard deviation. It follows that the liquidity requirements and WAL limits imposed under the SEC’s 2010 reforms both likely reduced the credit risk in some MMFs, lessening the likelihood of another 2008-like event. 5. Conclusion This paper measures credit risk in prime money market funds. This is done in a way that accounts for the maturity of each portfolio security, which is of considerable importance. Using the approach documented in this paper, we generate two measures for evaluating credit risk in prime MMFs. The first is the expected loss-to-maturity on fund’s portfolio, or ELM, which is simply the (asset-weighted average) expected loss on the fund’s holdings. While ELM is useful for measuring a fund’s overall credit risk, it may overstate the risk of a September 2008-like event. Therefore, we create a second measure – the break-the-buck insurance cost on the fund, BBI(50, 300). This is an estimate of the annualized insurance premium needed to insure a fund against breaking the buck, taking into account default correlations. We use these metrics to study the evolution of credit risks through the turbulent markets of 2011–2012. Contrary to perceptions, our results suggest that an increase in prime funds’ average credit risk in 2011 is not primarily attributable to funds’ European bank exposure. Beginning in June 2011, prime funds’ efforts to reduce both the size and maturity of their investments in European banks largely counteracted the effect of rising European bank credit risks. At the same time, prime funds’ shifted assets toward banks in the Asia/Pacific region, which, although presumably safer, also had sharply rising CDS premiums as fears of eurozone contagion and global economic conditions worsened. This shift is primarily responsible for the jump in prime funds’ average credit risk over late-2011. Thus, our results lend more support to the view that prime funds were passive recipients of an increase in credit risk outside the eurozone. Finally, we analyze a number of portfolio characteristics that are associated with higher levels of credit risk. Our results suggest that regulators and fund managers can influence the credit risk of fund portfolios by altering portfolio maturities and liquidity. Therefore, the SEC’s 2010 liquidity and weighted average life (WAL) requirements likely improved the ability of some MMFs to withstand severe credit shocks. Appendix A. Monte Carlo simulation of BBI(50, 300) 1. Using default probabilities collected from RMI, for each issuer i in the fund’s portfolio and for provided maturities T of 30, 90, 180, 270, 360, 540, and 720 days ahead: (a) Set pi (0) = 0 (b) Linearly interpolate pi (T) for maturities of Tj days, where j is a security in a fund’s portfolio, Tj ∈ {1, 2, . . ., 720) and T ∈ / {30, 90, 180, 270, 360, 540, 720} (c) Calculate the annualized default probability  pi (Tj ) = 1 −





1 − pi (Tj ) 360/Tj 2. Create the correlation matrix  to be used in the copula. Following Tarashev and Jackel (2008), we approximate the correlation matrix  as corr(lnDi , lnDj ) where lnDi , is the (log) distance-to-default. They show that corr(lnDi , lnDj ) ≈corr[−1 ( pi (T )), −1 ( pj (T ))] where −1 (•) is the

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Fig. B8. Alternative treatments of VRDNs, ABCP, and repos. We run two robustness checks to ensure that alternative treatments of securities do not substantively alter our estimation of a fund’s expected loss, ELM. In the first figure, rather than omit VRDNs, we match each VRDN with the default probability of the demand feature provider with the maturity set to the next put date. In the second figure, rather than treat ABCP and repos (not fully collateralized by Treasury/agency securities) as senior unsecured debt, we assume a recovery rate of 80% on these securities. ELMf,t is the expected loss on fund f at time t under the corresponding treatment. On the graphs,  and  represent the mean and the standard deviation of (Orig . ELMf,t − Alt . ELMf,t ), respectively. The dashed black lines represent the 45 degree line.

inverse cumulative normal distribution, and −1 ( pi (T )) is pi (T )). As described in Section month-to-month change in −1 ( 3, we have 24 months of data, 7 different provided maturities, and about 100 unique “high level” issuers. Without some restrictions,  would be very large. Consequently, we assume that  is constant across time and maturities. We also set to zero any correlation with a p-value >0.10; in effect, we are assuming that if a correlation is not statistically significant at the 10 percent level, it is zero. 3. For each issuer i, draw a vector of n = 1, 2, . . . N (where N = 50, 000) random variates zi,n from a multivariate t-distribution t (0, ), which has a mean vector of zero, a correlation matrix of  and  degrees of freedom. To do this, we must use a Cholesky decomposition of , which requires  to be positive definite. To ensure that  is indeed positive definite, we follow Rebonato and Jackel (1999) adjusting the eigenvalues of  as necessary by very small amounts. 4. Calculate ui,n = t−1 (zi,n ) where t−1 (•) is the inverse cumulative tdistribution. Issuer i’s random uniform variates (ui,n ) are reused across funds and months. 5. For each of the 24 months: (a) By issuer, merge the random variates (ui,n ) with the fund portfolio holdings dataset for that month. (b) For each security j in the holdings dataset and for each of the N trials, set: Tj = 0 if Yi,n ui,n >  pi (Tj ) Tj = 1 if Yi,n ui,n ≤  pi (Tj ) Tj = 1 in trial n, issuer i is assumed to have defaulted If Yi,n before security j matures. (c) For each fund f: (i) Calculate

the aggregate portfolio loss in each of the N trials, Lossn =

I J i=1

j=1

Tj . wij (1 − Ri )Yi,n

(ii) Calculate the insurance payout in each of the N trials: n = min [max (Lossn − l, 0) , ]...where l is the insurance deductible and  is the maximum coverage (assumed in this paper to equal 50 basis points and 300 basis points, respectively).   N (iii) Calculate BBI(l, ) = E n = N1  and the standard n=1 n



N

error of the BBI(l, ) estimate,

n=1

[n −E(n )] N(N−1)

2

.

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