FHLB Membership and Funding and the Level of Bank and Thrift

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					FHLB Membership and Funding and the Level of Bank and
          Thrift Holding Company Risk
                                       September 20, 2010

Abstract:
The purpose of this study is to investigate the influence of Federal Home Loan Bank (FHLB)
membership and dependence on FHLB funding on the level of risk of bank and thrift holding
companies (BHCs and THCs). To this end, portfolios of holding company (HC) stock are formed
according to both HCs’ FHLB membership status and HCs’ reliance on advances. With daily
data from 2001 to 2009, total risk, market risk, and interest rate risk are estimated using bivariate
GARCH models of returns on pairs of portfolios that have opposing characteristics related to
FHLB membership and reliance on advances. Throughout the period studied, FHLB membership
is associated with lower total risk and market risk, contrary to arguments put forth by some
researchers and regulators ((Flannery and Frame 2006), (Nickerson and Phillips 2004),
(Stojanovic, Vaughan, and Yeager 2008)). This inverse relationship becomes stronger during the
subprime mortgage crisis of 2007-2009. Similarly, greater reliance on FHLB advances is
associated with lower total risk in some years, particularly 2008 and 2009. In all years greater
reliance on FHLB advances is associated with lower market risk. No consistent relationship is
found between FHLB membership and interest rate risk or between reliance on advances and
interest rate risk. The results are consistent with the view that FHLBs restrict advances to risky
members and that FHLB policies and services have some risk-reducing effects Scott and Hein
(2009). They also support the idea that FHLBs stabilize the stream of funding to banks and
thrifts during credit crunches. In addition, portfolios of THC stocks are found to have had lower
total risk than portfolios of BHC stocks from 2001 to 2009, suggesting that, outside of several
major failed THCs, regulation by the soon-to-be defunct OTS was at least as effective as that of
the Federal Reserve.




                                                 1
FHLB Membership and Funding and the Level of Bank and Thrift Holding Company Risk

1. Introduction

Federal Home Loan Banks (FHLBs) are an important source of funding and liquidity to the U.S.

mortgage market. Ashcraft, Bech, and Frame (2009) document that, during the early stages of the

credit crunch that culminated in the recent recession in the U.S. and world economies, the

FHLBs provided emergency funding to financial institutions (FIs) before the Federal Reserve

and the Treasury Department intervened through the Troubled Asset Relief Program (TARP). In

the second half of 2007, after the three major credit rating agencies downgraded securities

backed by subprime mortgages, the total outstanding value of FHLB loans to members, called

“advances,” grew 36.7%, from $640 billion to $875 billion. Ashcraft, Bech, and Frame (2009)

call the FHLB system “the lender of next to the last resort,” because the Federal Reserve started

opening crisis-related lending facilities in December 2007, after FHLBs had stepped in to help

the banks and thrifts.

    Some authors (Nickerson and Phillips (2004), Stojanovic, Vaughan, and Yeager (2008),

Flannery and Frame (2006)), however, argue that FHLBs may contribute to financial system risk

by enabling members to make riskier loans than they would in their absence. This could occur,

e.g., if proper controls are not in place to limit advances to FHLB members that make risky

loans, or if there are insufficient incentives to limit FHLBs that make advances to risky

members. Other authors (Scott and Hein (2009)) counter that FHLB membership actually

reduces FI risk. Regulatory oversight of FHLBs, collateral requirements on advances, rationing

of advances, and FHLB-provided risk management services are some of the channels through

which FHLBs can reduce member risk.




                                               2
       According to FHLB system reports, FHLB member FIs had $631 billion in advances

outstanding on Dec. 31, 2009, about 5.4% of the $11.7 trillion in residential mortgage debt that

the Federal Reserve Board of Governors reported was outstanding in the U.S. at that time. By

comparison, fellow housing-related government-sponsored enterprises (GSEs) Fannie Mae and

Freddie Mac reported total liabilities at that time of $884 billion and $837 billion, respectively,

according to their forms 10-K filed with Securities and Exchange Commission. 1 The financial

crisis of 2007-2009 made it plainly evident that the U.S. mortgage market’s behavior

considerably influences both the U.S. and world financial systems. It follows that, as a

significant player in the U.S. mortgage market, FHLBs can influence the U.S. and, consequently,

the world economies.

       The objective of this paper is to examine the influence of both FHLB membership and

dependence on FHLB funding on the riskiness of bank and thrift holding companies (BHCs and

THCs). Stock market data are used to test the hypotheses that HC control of FHLB members is

associated with lower levels of total risk, market risk, and interest rate risk. Additionally, the data

are used to test hypotheses that greater HC reliance on FHLB advances is associated with lower

levels of those three risks. The results of these tests could help guide FHLB directors in

choosing the extent to which they offer advances to their membership and also help the

policymakers to determine whether and how to change the structure and regulation of the

FHLBs.

       Further, by including data from both Federal Reserve-regulated BHCs and Office of Thrift

Supervision (OTS)-regulated THCs, tests may be conducted of the hypothesis that markets


1
    The figure on FHLB total liabilities comes from http://www.fhlb-
of.com/specialinterest/finreportframe2.html. The figure on U.S. mortgage debt outstanding comes from
http://www.federalreserve.gov/econresdata/releases/mortoutstand/current.htm.

                                                        3
viewed OTS regulation as weaker than that of the Federal Reserve regulation. This issue is

interesting because the OTS oversaw some of the largest FIs to nearly collapse or fail in the

recent crisis. Examples include AIG, which was rescued by the government shortly before

collapsing, Lehman Brothers, which filed for bankruptcy protection, and Washington Mutual,

which went into FDIC receivership. The July 2010 Dodd-Frank Wall Street Reform and

Consumer Protection Act eliminates the OTS and divides thrift and thrift holding company

regulation among FDIC, the Office of the Comptroller of the Currency (OCC), and the Federal

Reserve. 2

     This study employs data on HC stock returns from the Center for Research on Security

Prices (CRSP). This is the first time stock market data have been used in the academic literature

to study the relationship between FHLB membership and funding and FHLB member risk.

Previous research on theses relationships has relied on accounting-based risk measures, which

have several disadvantages. They are backwards looking, reporting the past behavior of FIs, and

they fail to incorporate information about systemic or macroeconomic risk. Accounting data are

also subject to managers “window dressing” through the discretion allowed by accounting rules

and timing the reporting of bad news. Market data incorporate investors’ knowledge of

economy-wide conditions, their expectations for future HC performance, and information that

HC managers do not release in financial statements. HC stocks are assembled into portfolios

according to FHLB membership, dependence on FHLB advances, and regulator. Using portfolios

condenses information from hundreds of HCs into a few relatively easy-to-compare assets.

Portfolios also smooth out noise from short-term shocks to individual HCs while allowing

examination of differences in behavior among different classes of HCs.

2
  H.R. 4173--111th Congress: Dodd-Frank Wall Street Reform and Consumer Protection Act. (2010). In GovTrack.us
(database of federal legislation). Retrieved July 27, 2010, from http://www.govtrack.us/congress/bill.xpd?bill=h111-
4173

                                                         4
    The data used in this study contribute to the study of the FHLBs in two other ways. First,

recent research on the relationship between FHLBs and the performance of their members has

focused on commercial banks alone. In this study, bank data are complemented by thrift data,

widening the sample under consideration and allowing tests of differences between the two

groups, which until recently were guided by separate regulators. Second, variables in this study

are measured at the HC-level. Previous research on FHLBs has employed subsidiary-level data,

which may lead to under- or overestimates of bank risk because parent HCs can shift risk among

subsidiaries. For example, a bank that uses FHLB advances to fund risky loans will appear less

risky if its parent shifts the bank’s riskiest assets to healthier subsidiaries. HC accounting data

also have the advantage of matching stock market data, which are available for HCs rather than

subsidiaries.

    The main finding is that, throughout the period studied, FHLB membership is associated

with lower total risk as measured by GARCH estimates of the conditional variance of returns. A

similar relationship is found with market risk as measured by the market beta from a two-factor

model of portfolio returns. Using Value at Risk (VaR) as a metric, the difference in total risk is

found to be economically significant throughout the study and greatest during the middle- and

late-subprime mortgage crisis years of 2008 and 2009. Using market beta as a metric, the

difference in market risk is found to be economically significant. For most of the study, FHLB

membership does not have a significant positive or negative association with interest rate risk.

When it does, the degree of association is not economically significant.

    In addition, greater reliance on FHLB advances is associated with lower total risk during

2008 and 2009, and the risk reduction is economically significant. Greater reliance on FHLB

advances is also associated with an economically significant reduction in market risk throughout



                                                5
the study, with the largest reduction occurring in 2008 and 2009. For most of the study, reliance

on FHLB advances has neither a positive nor a negative relationship with interest rate risk. When

it does, the relationship is not economically significant.

       These results indicate that the risk-reducing effects of FHLB membership and FHLB

policies regarding advances outweigh the effects of other policies that might encourage risky

behavior. The results are consistent with FHLBs restricting advances to risky members,

increasing collateral requirements for risky advance takers, and limiting advance-taking in

general with capital-purchase requirements. They also support the notion that FHLBs provide

back-up funding to banks, thrifts, and the mortgage market during credit crunches.

    Portfolios of stocks issued by OTS-regulated THCs consistently had lower total risk than

portfolios of Federal Reserve-regulated BHCs from 2001 to 2009. The differences were

economically significant, with the largest differences in 2008 and 2009. With the exception of

2001, THC market risk is either less than or not significantly different from that of HC

portfolios. With the exception of 2009, THC portfolio interest rate risk is either less than or not

significantly different from that of BHC portfolios. The results indicate that outside of several

major failed FIs, regulation of other FIs by the soon-to-be defunct OTS was not worse than and

may have been better than that of the Federal Reserve.

    This essay proceeds as follows. Section 2 reviews the literature on the relationship between

FHLB lending and member risk as well as a theory of the relationship between FI reliance on

FHLB funding and FI risk. Section 3 describes the econometric model and estimation

techniques. Section 4 describes data sources and portfolio construction. Section 5 reports

empirical results. Section 6 concludes.




                                                  6
2. Literature Review and Theory

          Congress and President Herbert Hoover created the FHLB system in 1932, during the

Great Depression, to ensure liquidity in the mortgage market.3 The system includes 12 FHLBs,

each one owned nearly entirely by private FIs, governed by its own board of directors, and

serving a district comprised of two or more states. Following changes in membership rules

enacted by Congress in the 1980s and 1990s, membership is now available to all U.S. depository

institutions (DIs) with more than 10 percent of their portfolios in residential mortgage-related

assets. In addition, commercial banks with total assets less than $1 billion, public housing

authorities, and life insurance companies (LICs) are allowed to join FHLBs. According to data

provided by the Federal Housing Finance Agency (FHFA), system membership rose from about

3,200 institutions at the end of 1989 to about 8,100 in the fourth quarter of 2009. The 8,100

members include nearly all U.S. thrifts and about 80% of U.S. commercial banks. Though

FHLBs have some discretion over their policies, they have always been federally regulated, first

by the Federal Home Loan Bank Board (FHLBB) from their creation in 1932 until 1989, next by

the Federal Housing Finance Board (FHFB) from 1989 until 2008, and then by the FHFA since

2008.

       Through a central Office of Finance, the FHLBs issue debt for which they bear joint and

several liability. Joint and several liability within a cooperative borrowing unit means that

individual members of the cooperative are each responsible for repaying the debt incurred by

another member if that member defaults. Several privileges afforded by legislation lower default

risk and increase the liquidity of FHLB debt, leading investors to demand lower interest rates on

it than on debt issued by other private FIs. First, the FHLBs have a line of credit at the Treasury
3
    Hoffmann (2001) summarizes the legislative history of the FHLBs.

                                                        7
allowing them to borrow in emergencies. Second, FHLB debt is included among the securities

eligible for purchase by the Federal Reserve in its open market operations. Third, because of the

previously perceived, now actual, federal guarantee of the government sponsored agencies

(GSEs), FHLB debt is unlikely to encounter low demand associated with general credit crunches.

Fourth, the Competitive Equality Banking Act (CEBA) of 1987 grants FHLBs a “super lien” that

gives them priority over other creditors in the event of the failure of a member institution. The

lower interest rates these privileges confer have been documented by Ambrose and Warga

(2002) and Nothaft, Pearce, and Stevanovic (2002). These low interest rates are then passed on to

FHLB members in the form of relatively low interest rates on FHLB advances.

    Several authors have argued that weaknesses in FHLB regulations and policies allow FHLB

members to use advances to make risky loans. These authors write that this is possible because

1) FHLB members have little incentive to monitor behavior by fellow members within their

FHLBs, 2) FHLB managers have little incentive to monitor behavior across FHLBs, and 3)

interest rates on advances do not vary according to borrower risk. Studying data from the 1980s,

the time of the thrift crisis, Ashley, Brewer, and Vincent (1998) show that advances, as a percent

of total assets, were higher at thrifts that were insolvent, reorganized, or closed, than those that

were not.

    Legislation following the thrift crisis, including the Financial Institutions Reform Recovery

and Investment Act, reformed the regulation and governance of FHLBs and thrifts. But

Nickerson and Phillips (2004) find other causes for concern about the FHLB system. Among

them are similarities between the FHLB system and the U.S. farm credit system, which the

federal government bailed out in the 1980s. Like the FHLBs, the institutions comprising the farm

credit system bore joint and several liability for their system’s debt, and both systems share



                                                 8
similar rules on member stock ownership. Citing a theory of group borrowing presented in Che

(2002), Nickerson and Phillips (2004) argue that because individual FHLBs may obtain new debt

without direct permission from the other FHLBs, the FHLB system does not enjoy the risk

reduction associated with joint liability found in the theories of cooperative borrowing proposed

by Stiglitz (1990) and Ghatak and Guinnane (1999). They add that the federal guarantee on

FHLB system debt further reduces monitoring incentives for individual FHLBs. Flannery and

Frame (2006) argue that member ownership of individual FHLBs does not reduce risk-taking

incentives because shares of FHLBs are not tradable and require six months to five years

advance notice to sell. This makes it difficult for FHLB members to exercise the sort of equity

market discipline exercised by shareholders of publicly-traded corporations. Providing empirical

support to these arguments is a study by Bennett, Vaughan, and Yeager (2005) in which the

authors find that advances to total assets ratios are positively, though modestly, correlated with

the likelihood of an FDIC supervisory rating downgrade.

    Stojanovic, Vaughan, and Yeager (2008) propose a model of FHLB funding that implies

member reliance on FHLB funding is positively associated with member risk. The model is

concerned with the choices managers of FHLB member FIs make regarding their sources of

funding. Figure 1 (adapted from Stojanovic, Vaughan, and Yeager (2008)) illustrates the model.

A hypothetical FI manager chooses a quantity of loans (Q), shown on the horizontal axis, that

sets the marginal cost of funds equal to the marginal revenue from loans. Cost and revenue are

measured as interest rates, which appear on the vertical axis. The upward sloping line represents

the marginal cost of insured deposits (MC-id), which is assumed to increase with quantity. The

downward sloping line represents the marginal revenue from lending (MR-l), which declines

with quantity either because of capital regulations, declining monitoring expertise, or both.



                                                 9
    Uninsured deposits, such as jumbo CDs, are assumed to be available in effectively unlimited

quantities and to be priced in a national market for which individual FIs are price takers. The two

horizontal lines represent the marginal cost of uninsured deposits (MC-ud) in two situations. In

the first, the FI’s default risk is so low that the interest rates on uninsured deposits are

comparable to those on FHLB advances. Hence, MC-ud is equal to the marginal cost of advances

(MC-adv). Under those assumptions, the bank’s marginal cost of funding curve will be the

darkened line ABCD. After the FI reaches the quantity Q-id in insured deposits, it switches to

uninsured deposits, which are cheaper. The FI maximizes profit at loan quantity Q* and

uninsured deposit cost r*, where marginal revenue from lending equals the marginal cost of

borrowing.

    Figure 1 – Model of Financial Institution (FI) Funding Decision




    In the second situation, the FI manager undertakes risky activities that increase failure

probability. The interest rate on uninsured deposits increases in response to the FI’s increased

credit risk. If FHLB advances continue to be available at interest rate r*, the FI will borrow from


                                                10
the FHLBs and continue lending a quantity Q*. In that case there is a positive relationship

between reliance on advances and risk. If, however, FHLBs restrict advances, the FI’s marginal

cost curve becomes the line AEFG, leading to a lower loan quantity, Q’ and higher interest rate

r’. In that case a negative relationship exists between the FI’s reliance on advances and risk.

    Empirically, Stojanovic, Vaughan, and Yeager (2008) find that reliance on advances is

associated with an economically significant increase in bank risk for only a few accounting-

based risk measures out of many studied. They find no economically significant relationship

between banks’ advances to total assets ratios and two measures of credit risk, the ratio of non-

performing loans to total loans and the ratio of commercial real estate loans to total assets. They

find a negative relationship between reliance on advances and interest rate risk, with interest rate

risk measured with both a regulatory measure and the ratio of assets and liabilities that reprice in

one year to total assets. They find no difference between members’ and non-members’

probability of failure according to the Federal Reserve’s System to Estimate Examination

Ratings (SEER) score. Stojanovic, Vaughan, and Yeager (2008) find, however, that after banks

become FHLB members they exhibit economically significant increases in liquidity risk,

measured by the non-core funding to total assets ratio, and leverage risk, measured by the equity

to total assets ratio. The sample used in Stojanovic, Vaughan, and Yeager (2008) includes banks

rather than BHCs, and the time period covered is 1992 to 2005, a relatively quiet period for the

U.S. banking sector.

       The empirical findings of Stojanovic, Vaughan, and Yeager (2008) as well as arguments

in Scott and Hein (2009) suggest that several factors contribute to negative relationships between

FI risk and FHLB membership and FI risk and FHLB advance-taking. First, as mentioned in

Section 1, FHLBs have always been required to meet federal regulations. These regulations were



                                                 11
enforced by the FHLBB from the FHLBs’ creation in 1932 until 1989, by the FHFB from 1989

until 2008, and by the FHFA from 2008 to the present. An example of these regulations is that

under the Gramm-Leach-Bliley Act (GLBA) of 1999, all FHLBs must submit capital plans

meeting minimal requirements to the regulator. These capital plans generally require FHLB

members to purchase more stock as they borrow more advances. As a result, the opportunity cost

of advances is greater than their interest rate alone. 4

     Second, FHLBs officers may read confidential regulatory examination reports, enhancing

their knowledge of member risk, Scott and Hein (2009) write. Third, Scott and Hein (2009)

write, and FHLB officials confirmed in interviews, FHLBs require members to post collateral in

proportion to their advances. When FHLB members show signs of default risk, instead of

increasing interest rates on advances, FHLBs halt new advances and take “physical possession”

of the collateral through a custodial service. FHLB members know they could suffer a reduction

or cessation in advances if they appear too risky to their FHLBs. Thus, FHLB membership

comes with incentives to reduce risky lending. Fourth, as Scott and Hein (2009) argue, FHLBs

provide small member institutions with risk management resources, such as interest rate swaps,

that they otherwise could not afford. Fifth, FHLBs offer advances with maturities as long as 30

years and emergency funding in credit crunches, both of which lower members’ liquidity risk.

     Scott and Hein (2009) compare risk-related accounting ratios for banks before and after they

join FHLBs. They find that membership was not followed by significant declines in member

equity to total assets ratios or significant increases in total assets, real estate loans, or loan loss

provisions. In summary, previous research on FHLBs shows that opposing forces drive the

4
 Federal Home Loan Office of Finance (2010). Discussion of the FHLBanks’ Capital Structure and Regulatory
Capital Requirements. Retrieved Aug. 10, 2010 from
http://www.fhlb-of.com/ofweb_userWeb/resources/capitalqanda.pdf. See also Federal Home Loan Bank of
Pittsburgh (2010). Capital Plan of the Federal Home Loan Bank of Pittsburgh. Retrieved Aug. 10, 2010 from
http://www.fhlb-pgh.com/pdfs/capitalplan/capplanpgh.pdf.

                                                     12
relationship between BHC and THC membership and risk as well as BHC and THC reliance on

advances and risk. Which of these forces prevails is an empirical question. In this paper, data on

HC stocks are employed to study these relationships. HC stocks are formed into portfolios of

stocks issued by HCs that control FHLB members and stocks issued by HCs that do not. If

FHLBs have policies that discourage risky lending by members and provide risk-reducing

products and services not available elsewhere, then a portfolio of FHLB member stocks can be

expected to exhibit lower conditional variance of returns than a portfolio of non-member stocks.

The following hypothesis is therefore tested:

    H1A: HC control of FHLB-member subsidiaries is associated with lower total risk as

measured by the conditional variance of returns.

    Beginning around the middle of 2007, investors became more sensitive to the downside

risks associated with securities backed by mortgages. This sensitivity spread to most assets

issued by financial institutions, leading to a credit shortage for many FIs. If FHLB membership

provides access to liquidity during credit crunches that is not otherwise available, FHLB

members can be expected to demonstrate smaller increases in risk during this period. The

following hypothesis is therefore tested:

    H1B: HC control of FHLB-member subsidiaries is associated with a smaller increase in total

risk during the subprime mortgage crisis.

    Stock market data provides a means to estimate portfolio market risk and interest rate risk

by employing two-factor stock return models that include the returns on a market portfolio and a

measure of long-term interest rates. If FHLBs membership brings incentives to reduce total risk,

it is likely that HC members will better diversify their asset portfolios, thus lowering their market

risk as well. If FHLBs offer products that help lower interest rate risk, it is likely that HC



                                                 13
members will have lower interest rate risk as well. The following two additional hypotheses are

therefore tested:

     H1C: HC control of FHLB-member subsidiaries is associated with lower market risk as

measured by the market beta from a two-factor model.

     H1D: HC control of FHLB-member subsidiaries is associated with lower interest rate risk as

measured by the interest rate beta from a two-factor model.

     To test hypotheses regarding the relationship between reliance on FHLB funding and risk,

additional stock portfolios are formed according to HCs’ advances to total liabilities ratios. If

FHLBs restrict advances to risky members, one can expect the risk of a portfolio of HCs that are

most reliant on FHLB advances to be lower than the risk of a portfolio of HCs that are least

reliant on them. The following hypotheses are therefore tested.

     H2A: Greater HC reliance on advances is associated with lower total risk.

     If FHLB advances were issued on risk-reducing terms to members, and if FHLBs provided

additional advances to relatively low-risk institutions during the recent credit crunch, the

negative relationship between reliance on advances and risk that is hypothesized to have existed

before mid-2007 is expected to strengthen afterward. Therefore, the following hypothesis is

tested:

     H2B: Greater HC reliance on advances is associated with smaller spikes in total risk (the

conditional variance of returns) during the subprime crisis.

     If FHLBs restrict advances to risky members, it is likely that HCs that better diversify their

portfolios will be able to obtain more advances. If FHLBs advances with long maturities help

lower interest rate risk, it is likely that HC members will have lower interest rate risk as well as




                                                14
their reliance on advances increases. The following two additional hypotheses are therefore

tested:

     H2C: Greater HC reliance on advances is associated with lower market risk.

     H2D: Greater reliance on advances is associated with lower interest rate risk.

     As mentioned earlier, the federal governments’ thrift and THC regulator, the OTS, was

eliminated by the Dodd-Frank Act of 2010. The agency’s demise followed a number of

criticisms of its regulation of large FIs that failed or nearly failed during the subprime mortgage

crisis. For instance, the Treasury department and the FDIC’s inspectors general reported in April

2010, “a number of weaknesses in OTS oversight of Washington Mutual,” including failures to

ensure what was the nation’s largest S&L corrected problems with loan underwriting, weakness

in management, and inadequate internal controls.5 In contrast, the federal government’s other

BHC regulator, the Federal Reserve, obtained greater regulatory powers from the Dodd-Frank

Act even though many of the BHCs it oversaw were troubled as well, as evidenced by the many

BHCs that received substantial bailout funds through the TARP program. While a few large

THCs regulated by OTS caused systemic problems, it is possible that most THCs were relatively

less risky than BHCs. The presence of thrift and THC data in the sample enable tests of

differences in the risk of BHCs and THCs. The following hypotheses, parallel to the hypotheses

presented above, are also tested:

     H3A: OTS regulation is associated with lower total risk.

     H3B: OTS regulation is associated with smaller increases in total risk during the subprime

mortgage crisis.


5
 Department of the Treasury and Federal Deposit Insurance Corporation (2010). Evaluation of Federal Regulatory
Oversight of Washington Mutual Bank. Retrieved Aug. 10, 2010 from http://www.ustreas.gov/inspector-
general/audit-reports/2010/10-002EV.pdf.


                                                     15
     H3C: OTS regulation is associated with lower market risk.

     H3D: OTS regulation is associated with lower interest rate risk.

     Hypotheses are summarized in Table 1.

3. Model

        This section presents the econometric approach used to test the hypotheses listed above.

It includes a description of the GARCH approach to modeling asset returns, specification of the

mean and variance equations, an explanation of the estimation approach, and a discussion of how

the model estimates will be used to test the hypotheses and interpret results

        Since their introduction in the 1980s, generalized autoregressive conditional

heteroscedasticity (GARCH) models have frequently been used to study the behavior of asset

returns. Surveys of the literature on GARCH models include Bollerslev, Chou, and Kroner

(1992), Engle (2001), and Bauwens, Laurent, and Rombouts (2006). GARCH models assume

that the period t conditional variance of an asset’s return can be modeled using the period t-1

return’s squared deviation from the estimated data generating process (the ARCH term) and the

t-1 conditional variance estimate (called the GARCH term). In this study, these conditional

variance estimates reflect the volatility of HC stock returns and proxy for the HCs’ expected total

risk. GARCH models offer advantages over basic mean regression models because they do not

assume the variance of the regression error term is constant over time, they allow researchers to

model the dynamics of conditional variance, and they need not assume that stock returns are

distributed normally. In the context of stock returns, this framework enables one to model a stock

or a portfolio’s total risk as it changes over time.

        GARCH studies related to the stock returns of FIs include Song (1994), who studies the

interest rate risk and systemic risk of portfolios of DI stocks, Elyasiani and Mansur (1998), who



                                                  16
use GARCH-in-mean (GARCH-M) models to study the impact of return volatility and interest

rate volatility on BHC portfolio returns, Elyasiani, Mansur, and Pagano (2007), who use

multivariate GARCH models to study inter-industry spillovers of risk on the stock returns of

several types of FIs, and Elyasiani, Mansur, and Wetmore (2010), who use multivariate GARCH

models to study the equity returns and return volatilities of real estate investment trusts (REITs),

BHCs, S&L holding companies, and LICs.

       In this study, bivariate GARCH models are employed to describe the conditional means

and conditional variances of pairs of portfolio return series. For portfolios indexed by i = 1,2, the

conditional means of returns (Ri,t) are modeled using two factors, the market return (RMt) and the

change in the level of long-term interest rates (∆IR10t). Akella and Chen (1990), Bae (1990),

Browne, Carson, and Hoyt (1999), Elyasiani and Mansur (2003), Elyasiani and Mansur (2004),

and Elyasiani, Mansur, and Pagano (2007) find that market returns and long-term interest rates

have significant effects on BHC stock returns. Due to the non-stationarity of the long-term

interest rate series, the differenced series is used here, as in Elyasiani, Mansur, and Pagano

(2007). The two-factor model enables the estimation and comparison of each portfolio’s market

risk and interest rate risk, represented by the market and interest rate betas. Simultaneous

estimation of the two-return models allows Wald tests of cross-equation equality of market and

interest rate betas as well as parameters in the conditional variance equation.

       The conditional variance terms (hii,t) are modeled using a GARCH (1,1) model

augmented by dummy variables (D1, D2, and D3) representing three phases (described below) of

the subprime mortgage crisis. Charts of portfolio return series indicate that return volatility was

substantially higher during these three periods than at other times. The charts also indicate that

there were substantial differences in the level of volatility between these three periods. For one



                                                 17
example, see Chart 1, which displays the returns on HIGHADV, a portfolio, described in more

detail in Section 4.2, of HCs in the sample that were most reliant on FHLB advances.

       Dummy variable D1 takes the value of one from the start of 2007:3 to the end of 2008:2.

This period begins shortly before the downgrades of credit ratings on subprime mortgage-backed

securities and the collapse of hedge funds that were heavily invested in such securities. It ends

about two months before the near-collapse of Bear Stearns and the Lehman Brothers bankruptcy.

It was during this time period that the FHLBs increased advances to members to improve

liquidity in the mortgage market. Dummy variable D2 takes the value of one from the start of

2008:3 to 2009:2. This time frame includes the collapse of Lehman Brothers, which set off a

severe credit crunch and one of the most volatile periods in the history of U.S. stock markets.

During this period, the Treasury Department bought equity stakes in FIs to prevent a collapse of

the financial system, and the FHFA took Fannie Mae and Freddie Mac into conservatorship. By

the end of this period, the price of many FI stocks had partially rebounded, the financial system

had begun to stabilize,and FHLBs began reducing advances to members. Dummy variable D3

takes the value of one from the start of 2009:3 to the end of the study at the end of 2009:4. This

was a period of heightened volatility relative to 2001:1 to 2007:2, though the volatility was not

as great as it was during other periods of the subprime crisis.

       When simultaneously estimating GARCH models of systems of multiple asset returns,

one must either assume that the correlation of returns is fixed or time-varying. Based on

estimation results discussed in Section 5, and because it seems unlikely that the portfolios

studied here would have the same correlation for nine years, the model estimates presented in

Section 5 are computed using the dynamic conditional correlation (DCC) approach proposed by

Engle (2002). Empirical results concerning this assumption are in Section 5.1. In the context of a



                                                 18
two-return system, the DCC approach models the conditional correlation of returns, ρ12, as a

GARCH(1,1) process involving the unconditional correlation of returns, the product of the

previous period’s shocks, and the previous period’s conditional correlation. The estimated

systems include five equations written as follows:




       The systems are estimated using a two-step process. In the first step, univariate models of

the conditional variances, hii,t, are estimated using the method of maximum likelihood. The

conditional mean models are nested in the conditional variance models through the residuals, εi,t.

In the second step, the parameters of the conditional correlation series are estimated by

maximum likelihood using the estimated residuals from the first step as data.

       In the system specified above, R1,t and R2,t vary according to the pair of portfolios under

study. The first pair includes a portfolio of FHLB members (MEMBER) and a portfolio of FHLB

non-members (NONMEMBER). The second pair includes a portfolio (HIGHADV) of firms that

are most reliant on FHLB advances and a portfolio (LOWADV) of HCs that are least reliant on

advances. The third pair includes a portfolio of THCs (THC) and a portfolio of BHCs (BHC).

Portfolio construction is described in more detail in Section 4.2.

       The period t conditional variances of the portfolios, h11,t and h22,t, are interpreted as the

portfolios’ total risk. Mean daily total risk is calculated for each portfolio, and t-statistics are


                                                 19
computed to test for differences in the mean between the portfolios. Depending on the pair of

portfolios under consideration, these tests provide evidence regarding hypotheses H1A, FHLB

membership is associated with lower total risk; H2A, greater reliance on advances is associated

with lower total risk, and H3A, OTS regulation is associated with lower total risk.

        To put the differences in mean daily total risk in economic terms, mean daily 1%, one-

day VaRs are calculated to compare potential losses on investments in the portfolios on

unexpectedly bad days. The portfolio’s one-percent, one-day VaR is the change in the value of

an investment in the portfolio if the portfolio’s realized return is equal to the first percentile of its

expected return distribution. The portfolio’s expected return distribution is calculated under the

assumption it is normally distributed with the mean equal to the estimated model’s predicted

return for that day. The distribution’s variance is equal to the estimated conditional variance, or

total risk, for that day. A portfolio with greater total risk has a lower first percentile of its

expected return distribution and is thus subject to greater losses on surprisingly “bad” days. VaR

is calculated here as if the investment in the portfolio were $1 million.

        The difference in mean one-day, 1% VaR is the difference in the values the portfolios

would lose on an unusually bad day, a day that could be expected to occur two or three times in a

trading year of 250 days. The threshold for economic significance is set at a mean difference in

one-day, 1% VaR of $1,000, or 0.1% of the hypothetical $1 million investment. This is assumed

to be an amount that for a hypothetical investor might justify the transaction cost of switching

from the higher VaR portfolio to the lower VaR portfolio, given equal mean expected returns.

        The coefficients on the conditional variance equations’ dummy variables, ϕi1, ϕi2, and ϕi3,

represent the change in portfolio i’s (i =1,2) total risk during the three phases of the subprime

crisis described above relative to the 2001:1 to 2007:2 base period. Wald statistics are calculated



                                                   20
to test the hypothesis of equality of these parameters across portfolios. Depending on the pair of

portfolios under consideration these tests provide evidence regarding hypotheses H1B, FHLB

membership is associated with a smaller increase in total risk during the subprime mortgage

crisis; H2B, greater reliance on advances is associated with a smaller increase in total risk during

the crisis; and H3B, OTS regulation is associated with a smaller increase in total risk during the

crisis.

          Portfolio i’s market beta, βi1, has an economic interpretation as the portfolio’s market

risk, the premium investors demand for the portfolio’s inability to hedge against fluctuations in

the general market. Wald statistics are calculated to test the hypothesis of equality of market

betas across portfolios, providing evidence regarding hypotheses H 1C, FHLB membership is

associated with lower market risk; H2C, greater reliance on advances is associated with lower

market risk; and H3C, OTS regulation is associated with lower market risk. Portfolio i’s interest

rate beta, βi2, has an economic interpretation as the portfolio’s interest rate risk, the premium

investors demand for the portfolio’s inability to hedge against fluctuations in long-term interest

rates. Wald statistics are calculated to test the hypothesis of equality of interest rate betas across

portfolios, providing evidence regarding hypotheses H1D, FHLB membership is associated with

lower interest rate risk; H2D, greater reliance on advances is associated with lower interest rate

risk; and H3D, OTS regulation is associated with lower interest rate risk. A difference greater than

0.1, or 10 basis points, is considered economically significant for both the market risk betas and

interest rate betas. This is conjectured to be a difference in risk premium great enough to warrant

switching from the lower beta portfolio to the higher beta portfolio.

          To study whether the estimated relationships vary over time, the five-equation system

specified above was estimated on subsamples of the data from each individual year from 2001 to



                                                 21
2009. Each yearly subset had between 246 and 251 observations. Difference of means tests were

conducted on each yearly subsample’s estimated conditional variance series. Wald tests were

conducted to test for differences in each year’s market betas and interest rate betas.

4. Data

This section describes the sources of data and the methods used to form the portfolios.

4.1 Data sources

           All data on stocks come from the Center for Research on Security Prices (CRSP). The

return on the market portfolio (RMt) is the return on the CRSP value-weighted market portfolio

excluding dividends. The long term interest rate (10YT) is the yield on the 10-year constant

maturity Treasury, data for which come from the Federal Reserve Board of Governors Web site.

For BHCs, accounting data come from call reports and BHC (Y-9C) reports supplied by the

Federal Reserve Bank of Chicago. These accounting data are used to calculate advances to

liabilities ratios. For THCs, the corresponding data come from Thrift Financial Reports (TFRs)

supplied by the OTS and from tables in Standard & Poor’s Compustat database.6 FHLB

membership information comes from the FHFA.

           The study covers the period from the start of 2001, when advances data are first available

in the call reports, to the end of 2009. HC accounting data were matched to HC stock market data

in several ways. For the years 2001 to 2007, BHC accounting data were matched to stock market

data using a listing of BHCs’ Federal Reserve ID numbers and CRSP ID numbers provided by

the Federal Reserve Bank of New York. In 2008, BHCs began reporting their Committee on

Uniform Security Identification Procedures (CUSIP) numbers in BHC reports. Those CUSIP

numbers were used to match accounting data to CRSP data for 2008 and 2009. For all years,

THC accounting data was matched to CRSP stock return data using ticker symbols supplied by
6
    The OTS does not make public THC accounting data. Hence, the need to obtain this data from Compustat.

                                                        22
the OTS. In any given time period, HCs are included in the sample if stock market data and

accounting data are both available for them. HCs that control FHLB-member insurance

companies are excluded because data on insurance company advances are not readily available

for the time period studied.

       HCs in the sample reported total assets between $63 million (University Bank of Ann

Arbor, Michigan in the first quarter of 2006) to $2.3 trillion (Bank of America in the first quarter

of 2009). In terms of size, the HCs represent a broad range of U.S. BHCs and THCs. Mid-sized

and large HCs are disproportionately represented, given their greater likelihood of issuing stock.

Aggregate advances held by HCs in the sample range from $232 billion to $497 billion,

depending on the quarter of the observation. Given that system-wide FHLB advances

outstanding ranged from $473 billion to $928 billion during this time, the sample includes firms

that were using 40 to 60% of all advances outstanding, depending on the date.

4.2 Portfolio formation

    Six portfolios of HC stocks are formed and grouped into three pairs for comparison. See

Table 1 for brief portfolio descriptions. Portfolios combine data from hundreds of HCs into a few

assets that are relatively easy to compare. In addition, portfolios smooth out sudden fluctuations

in returns from short-term shocks to individual HCs while allowing examination of differences in

behavior among different categories of HCs.

    The first two portfolios are formed according to HC control of FHLB-member subsidiaries.

The HCs that control at least one FHLB-member subsidiary enter a portfolio called “MEMBER”

while the HCs that do not are placed in a portfolio called “NONMEMBER.” These portfolios

allow tests of the hypotheses regarding the relationship between FHLB membership and the

various types of risk (H2A, H2B, H2C, and H2D).



                                                  23
     The second pair of portfolios is formed according to HC reliance on advances. The HCs

that rely most on advances are placed in a portfolio called “HIGHADV” while the HCs that rely

on them least are placed in a portfolio called “LOWADV.” The HIGHADV portfolio contains the

HCs that are above the top quartile of advances to liabilities ratio. The LOWADV portfolio

contains the HCs that are below lowest quartile of advances to liabilities ratio. The advances-to-

total liabilities ratio rankings are recomputed each quarter. The composition of the portfolios

changes accordingly. These portfolios allow tests of the hypotheses regarding the relationship

between reliance on advances and the various types of risk (H2A, H2B, H2C, and H2D).

    The third pair of portfolios is formed according to HC regulator. HCs that are THCs

regulated by the OTS are included in a portfolio called THC. Those that are BHCs regulated by

the Federal Reserve are included in a portfolio called BHC. These portfolios allow tests of the

hypotheses regarding the relationship between OTS regulation and the various types of risk (H3A,

H3B, H3C, and H3D).

    HCs are excluded from portfolios on days when data are not available on the price of their

stocks. The portfolio construction method implies that portfolio membership varies over time. It

eliminates survivorship bias and ensures that the portfolios include the largest number of firms

possible.

5. Empirical Results

       This section presents the empirical analysis. Descriptive statistics and model diagnostics

are reported first. They are followed by analyses of the bivariate GARCH model estimates

concerning the relationship between reliance on advances and total risk, FHLB membership and

risk, and regulator and risk. The presented results include model parameter estimates (presented

in Table 4) and tests of risk equality (Table 5) for observations taken from the entire sample



                                               24
period of 2001 to 2009 as well as tests of risk equality for annual subsamples of the data (tables 6

to 8), The discussion includes economic interpretations in terms of VaR and risk premia, the

background for which is in Section 3.

5.1 Descriptive Statistics and Model Diagnostics

       This section presents descriptive statistics, which are also presented in tables 2 and 3. The

sample contains 2245 daily observations taken between the first day of 2001 and the last day of

2009. The HIGHADV portfolio contains between 119 and 150 stocks, depending on the quarter,

with a mean of 139 stocks. The LOWADV portfolio contains a minimum of 119 stocks, a

maximum of 151 stocks, and a mean of 139.7. The MEMBER portfolio contains between 464

and 587 stocks with a mean of 541.3. The NONMEMBER portfolio contains between 13 and 31

and has a mean of 22.2. The THC portfolio contains between 117 and 156 stocks and has a mean

of 138.1. The BHC portfolio contains between 362 and 459 stocks and has a mean of 428.6.

       Ljung-Box Q statistics were computed for the return and squared return series at 10, 20,

and 30 lags (Table 3). All support rejection of the hypothesis of no autocorrelation in the return

and squared return series, supporting the use of GARCH models. Jarque-Bera tests for normality

as well as tests of skewness and kurtosis indicate the return series are non-normal and skewed,

further supporting GARCH modeling of the return series. (Dickey and Fuller 1979) and (Phillips

and Perron 1988) unit root tests were conducted on all portfolio return series, the market return

series (RMt), and the series of undifferenced 10-year Treasury rates. The null hypothesis of a unit

root is rejected for all series except the 10-year Treasury rates. Once differenced, the null of a

unit root is rejected for the 10-year Treasury rates. This supports the use of the first difference of

10-year Treasury rates in the models.




                                                 25
       The models were estimated using both the DCC-GARCH and constant correlation

GARCH approaches. Comparison of Ljung-Box statistics for the squared residuals indicates that

the DCC estimates fit the data better for all three models. The conditional correlation equation

(Equation (5)) parameters are significant for all three models (Table 4). A test of the hypothesis

of conditional correlation proposed by Tse (2000), however, leads to rejection of the hypothesis

of constant correlation for only two of the three models estimated here (see Table 4). The

exception is the model of MEMBER and NONMEMBER returns. The DCC results are presented

here for three reasons, first for consistency, second because the DCC approach performed better

in terms of goodness of fit, and third because the conditional correlation equation parameters are

significant for all three models. The parameter estimates and standard errors obtained from the

two approaches are close, and the conclusions regarding the hypotheses do not change if the

constant correlation approach is used.

5.2 FHLB membership and risk

       In this section, results are presented regarding H 1A, H1B, H1C, and H1D, the hypotheses

regarding the relationships between FHLB membership and several types of risk. The analysis

focuses on estimates of the bivariate GARCH model, given in equations (1) to (5), of returns on

the MEMBER and NONMEMBER portfolios. The MEMBER portfolio contains stocks issued by

HCs that control an FHLB member subsidiary. The NONMEMBER portfolio contains stocks

issued by HCs that do not.

       First, results based on data from 2001 to 2009 are presented regarding H1A, FHLB

membership is associated with lower total risk (conditional variance of returns). As Table 5,

Panel 1 shows, the difference in mean daily total risk (MEMBER mean daily total risk minus

NONMEMBER mean daily total risk) is -4.941×10-5. The difference is significant at the one



                                               26
percent level. In economic terms, the average one-day, 1% VaR on a $1 million investment in

MEMBER is $4,927 less than the same investment in NONMEMBER, a figure that is above the

$1,000 threshold for economic significance. This evidence favors H1A, FHLB membership is

associated with lower total risk. This difference in risk may be explained in part by risk

management services provided by FHLBs. It may also be explained by risk-reducing FHLB

policies related to advance-taking. Relatively risky HCs that do not intend to meet the

requirements of these policies may not choose FHLB membership, which carries the opportunity

cost of a FHLB stock purchase.

    Next, results based on 2001-2009 data are discussed in regards to H1B, HC control of FHLB-

member subsidiaries is associated with a smaller increase in total risk during the subprime

mortgage crisis. The coefficients on the dummy variables D1, D2, and D3 (ϕi1, ϕi2, and ϕi3 for

portfolios i=1,2) may be interpreted as increases in total risk during three phases of the subprime

crisis. Table 4, Panel 1 presents these coefficient estimates. Table 5, Panel 1 presents the

differences in the coefficient estimates (MEMBER equation coefficients minus NONMEMBER

equation coefficients) along with Wald tests of cross-equation equality of the coefficients. The

only pair of coefficients for which the Wald test leads to rejection of equality is ϕ12 and ϕ22.

These are the coefficients on D2, which represents the period from 2008:3 to 2009:2, the time

during which major FIs collapsed or nearly collapsed from subprime-mortgage related losses.

The coefficient ϕ12, associated with the MEMBER portfolio, is less than ϕ22, associated with the

NONMEMBER portfolio. The results provide partial support for H1B, FHLB membership is

associated with smaller spikes in total risk during the subprime crisis. Stocks of HCs that

controlled FHLB-member subsidiaries experienced a significantly smaller jump in volatility

during the most severe phase of the credit crunch. This is consistent with FHLBs serving as



                                                27
backup funding sources for their members during the credit crunch. It is also consistent with

relatively risky firms, whose problems began to be acknowledged by investors in the subprime

mortgage crisis, choosing not to join FHLBs.

    The discussion now turns to H1C, FHLB membership is associated with lower market risk.

Estimates here are based on data from 2001 to 2009. The market betas, β11 and β21, may be

interpreted as the premia demanded by investors for each portfolio’s non-diversifiable, or

market, risk. Table 4, Panel 1 presents the market beta estimates. Table 5, Panel 1 presents the

differences in the market beta estimates (MEMBER market beta minus NONMEMBER market

beta) along with Wald tests of cross-equation equality of the market betas. The MEMBER market

beta is 0.362, or 36.2 basis points, less than the NONMEMBER market beta. Equality of market

betas is rejected at the one percent level of significance. The difference is above the 10 basis

point threshold for economic significance. This result is consistent with H1C, FHLB membership

is associated with lower market risk. HCs with FHLB members may seek to lower total risk

through activities such as asset diversification that also reduce market risk.

    Next, results using data from 2001 to 2009 are examined with regards to H1D, FHLB

membership is associated with lower interest rate risk. The interest rate betas, β12 and β22, may be

interpreted as the premia demanded by investors for each portfolio’s sensitivity to fluctuations in

long-term interest rates. Table 4, Panel 1 presents the interest rate beta estimates. The interest

rate beta of the MEMBER portfolio is .0049, or 0.49 basis points, less than that of the

NONMEMBER portfolio. Equality of interest rate betas is rejected at the one percent level of

significance (Table 5, Panel 1). The difference in interest rate betas, however, is below the 10

basis point threshold for economic significance. The result supports H1D, FHLB membership is

associated with lower interest rate risk. FHLB membership brings access to some interest rate



                                                 28
risk management tools, such as interest rate swaps. These benefits may help lower interest rate

risk among HCs that control FHLB members. However, the advantages are not economically

significant.

        To examine whether the results obtained above vary over time, bivariate GARCH models

of the returns on MEMBER and NONMEMBER were estimated on yearly subsamples of the data.

Table 6 shows the results of tests of the annual differences in mean total risk (MEMBER total

risk minus NONMEMBER total risk). In all years, MEMBER had greater total risk, and equality

of differences is rejected at high levels of significance each year. The results support H1A, FHLB

membership is associated with lower total risk. The sizes of the differences are particularly large

in 2008 and 2009, when they reach -0.845 and -2.222, respectively. The differences range from -

0.080 to -0.377 in the other years. The difference in risk during the subprime mortgage crisis can

also be seen in the VaR differences. A $1 million investment in MEMBER would lose, on

average, $6,969 less on a bad day than a $1 million investment in NONMEMBER in 2008. For

2009 the figure jumps to $20,357. The only other comparable VaR difference comes in 2001,

when it is $7,899. In all years, the difference in VaR is above the $1,000 threshold for economic

significance, indicating that throughout the study, FHLB membership was associated with

substantial differences in HC risk. This evidence supports both H1A, FHLB membership is

associated with lower total risk, and H1B, FHLB membership is associated with lower increases

in total risk during the subprime crisis.

        Table 6 shows the annual differences in market betas (MEMBER market beta minus

NONMEMBER market beta) and the results of tests of equality of annual market betas. The

MEMBER portfolio’s market betas are consistently less than those of the NONMEMBER

portfolio, with differences ranging from 16.4 basis points to 53.5 basis points. Equality of



                                                29
parameters is rejected each year at the one percent level of significance, and the differences are

economically significant. The results support H1C, FHLB membership is associated with lower

market risk.

        Table 6 shows the annual differences in interest rate betas (MEMBER interest rate beta

minus NONMEMBER interest rate beta) and the results of tests of equality of annual interest rate

betas. As with the results drawn from the entire sample, the magnitude of differences in interest

rate betas is three orders of magnitude smaller than the differences in market beta, indicating any

differences have relatively little economic significance. From 2002 to 2006 and in 2008 and

2009, the hypothesis of equal interest rate betas cannot be rejected. In 2001 and 2007, the

MEMBER interest rate beta is greater than the NONMEMBER interest rate beta. In no year is the

difference economically significant. As with the results drawn from the entire sample, these

findings do not support H1D, FHLB membership is associated with lower interest rate risk.

        In summary, FHLB membership is associated with lower total risk throughout the period

studied. The difference in risk between a portfolio of HCs that control FHLB members and a

portfolio of HCs that do not is found to be economically significant. The difference is largest in

2001, 2008, and 2009. That result, along other evidence, indicates FHLB membership is

associated with a smaller increase in total risk during the subprime mortgage crisis. Additionally,

FHLB membership is found to have a economically significant negative relationship with market

risk. FHLB membership is not found to have a positive or negative relationship with interest rate

risk.

5.3 Reliance on FHLB advances and risk

        This section presents results concerning the hypotheses regarding the relationships

between HC reliance on advances and risk (H2A, H2B, H2C, and H2D). The analysis focuses on



                                                30
estimates of the bivariate GARCH model, given in equations (1) to (5), of returns on the

HIGHADV and LOWADV portfolios. The HIGHADV portfolio contains stocks issued by HCs in

the top quartile of advances to liabilities ratio. The LOWADV portfolio contains stocks issued by

HCs in the bottom quartile.

       First, results using data from 2001 to 2009 are discussed regarding H2A, greater HC

reliance on advances is associated with lower total risk (the conditional variance of returns). As

Table 5, Panel 2 shows, when the bivariate GARCH results for the entire period of the study are

used, the difference in mean daily total risk (HIGHADV mean daily total risk minus LOWADV

mean daily total risk) is -2.158×10-5. The difference is significant at the one percent level. In

economic terms, the HIGHADV portfolio’s mean one-day, 1% VaR for a $1 million investment

was $1,162 less than that of the LOWADV portfolio. This is above the $1,000 threshold of

economic significance. The results provide evidence in favor of H2A, greater HC reliance on

advances is associated with lower total risk, although the difference is not economically

significant. This finding indicates that FHLBs restrict advances to risky members and provide

additional advances to low-risk members that request them.

       Next, results are discussed regarding H2B, greater HC reliance on advances is associated

with smaller increases in total risk during the subprime crisis. These results are based on 2001 to

2009 data. The coefficients on the dummy variables D1, D2, and D3 (ϕi1, ϕi2, and ϕi3 for portfolios

i=1,2) are interpreted as increases in total risk during three phases of the subprime crisis relative

to the first six-and-a-half years of the study. Table 4, Panel 2 presents these coefficient estimates,

and Table 5, Panel 2 presents their differences (HIGHADV coefficients minus LOWADV

coefficients) along with Wald tests of cross-equation coefficient equality. The only pair of

coefficients for which the Wald test leads to rejection of equality is ϕ12 and ϕ22. These are the



                                                 31
coefficients on D2, which represents the period from 2008:3 to 2009:2. This was the period

during which major FIs, such as Bear Stearns, AIG, and Lehman Brothers collapsed or nearly

collapsed from exposure to losses on subprime mortgage-backed securities. The coefficient ϕ12,

associated with the HIGHADV portfolio, is less than ϕ22, associated with the LOWADV portfolio.

The results indicate that stocks of HCs that relied most on advances experienced a significantly

smaller jump in volatility during the most severe phase of the credit crunch. This is consistent

with FHLBs serving as backup funding sources for their members during the credit crunch. It is

also consistent with FHLBs directing relatively more advances to safer members rather than to

risky members. The results provide partial support for H 2B, greater HC reliance on advances is

associated with smaller increases in total risk during the subprime crisis.

       The discussion now turns to H2C, greater HC reliance on advances is associated with

lower market risk. The market betas, β11 and β21, are interpreted as the premia demanded by

investors for each portfolio’s non-diversifiable, or market, risk. Table 4, Panel 2 presents the

market beta estimates. Table 5, Panel 2 presents the differences in the market beta estimates

(market beta from the HIGHADV equation minus the market beta from the LOWADV equation)

along with Wald tests of cross-equation equality of the market betas. The HIGHADV market beta

is 0.237, or 23.7 basis points, less than the LOWADV market beta. Equality of market betas is

rejected at the one percent level of significance. The difference is greater than the 10 basis point

threshold of economic significance. This result is consistent with H2C, greater HC reliance on

advances is associated with lower market risk. This may occur because HC’s that diversify their

portfolios and hedge better against macroeconomic fluctuations are likely to obtain more

advances from FHLBs.




                                                 32
       Next, results using 2001 to 2009 data are examined with regards to H2D, greater HC

reliance on advances is associated with lower interest rate risk. The interest rate betas, β12 and

β22, may be interpreted as the premia demanded by investors for each portfolio’s sensitivity to

fluctuations in long-term interest rates. Table 4, Panel 2 presents the interest rate beta estimates.

Table 5, Panel 2 presents the differences in the interest rate beta estimates (HIGHADV interest

rate beta minus LOWADV interest rate beta) along with Wald tests of cross-equation equality of

the interest rate betas. The Wald test leads to non-rejection of the hypothesis of equal interest

rate betas. This result is not consistent with H2D, greater HC reliance on advances is associated

with lower interest rate risk. Advances are available in maturities of up to 30 years, giving FIs

that use them greater ability to reduce interest rate risk on long-term loans. But using more

advances does translate into reduced interest rate risk. That said, neither is evidence found that

greater reliance on advances is associated with higher interest rate risk.

       To examine whether the results obtained above are consistent over time, bivariate

GARCH models of the returns on HIGHADV and LOWADV were estimated on yearly

subsamples of the data. Table 7 presents the results of annual tests of difference in mean total

risk, annual tests of differences in market and interest rate betas, and annual differences in VaR.

       In 2002, 2004, 2005, and 2007, HIGHADV had greater mean daily total risk. In 2001,

2003, 2006, 2008, and 2009, HIGHADV had lower total risk. The results indicate that before

2008, the total risk measures of the two portfolios were relatively close. In 2008 and 2009,

however, the risk reduction associated with reliance on advances is more economically

meaningful. This can be observed in the annual differences in the average one-day, 1% VaR on

$1 million invested in each of the two portfolios. A $1 million investment in LOWADV would

lose $2,113 more on average from an extreme negative event than a $1 million investment in



                                                 33
HIGHADV in 2008 and $5,314 in 2009. In other years, the differences in average VaR range

from $230 more on HIGHADV to $1,080 more on LOWADV. In relatively calm periods, the

negative relationship between total risk and advances is inconsistent and relatively small. During

the credit crunch, however, the HCs that relied more on advances have a relatively large total

risk advantage. These results supports H2A, greater HC reliance on advances is associated with

lower total risk, and H2B, greater HC reliance on advances is associated with smaller increases in

total risk during the subprime mortgage crisis.

       Table 7 shows the annual differences in market betas (HIGHADV market beta minus

LOWADV market beta) and the results of tests of equality of annual market betas. The

HIGHADV portfolio’s market betas are consistently less than those of the LOWADV portfolio.

Equality of parameters is rejected each year at the one percent level of significance. During 2008

and 2009, the differences in market betas become substantially larger than from 2001 to 2007. In

2008 and 2009 the differences are -0.382 and -0.468. From 2001 to 2007, their range is from -

0.168 to -0.262. In all years, the differences are above the 10 basis point threshold of economic

significance. The results support H2C, greater HC reliance on advances is associated with lower

market risk.

       Table 7 shows the annual differences in interest rate betas (HIGHADV interest rate beta

minus LOWADV interest rate beta) and the results of tests of equality of annual interest rate

betas. As with the results drawn from the entire sample, the magnitude of differences in interest

rate betas is three orders of magnitude smaller than the differences in market beta, indicating any

differences have relatively little economic significance. In 2001, 2002, 2003, 2005, 2006, and

2009, the hypothesis of equal interest rate betas cannot be rejected. In 2004, the HIGHADV

interest rate beta is smaller than the LOWADV interest rate beta, but it is larger in 2008 and 2009.



                                                  34
As with the results drawn from the entire sample, these findings do not support H2D, greater

reliance on advances is associated with lower interest rate risk.

       To summarize the results, over the period from 2001 to 2009 a positive, economically

significant relationship is found between HC reliance on FHLB advances and total risk. When

the relationship is examined on an annual basis, the positive relationship does not consistently

hold. However, the largest difference in total risk occurs during the middle and late parts of the

subprime mortgage crisis, 2008 and 2009, when greater reliance on FHLB advances is associated

with an economically significant reduction in total risk. Market risk is consistently lower for HCs

that rely more on advances, and the difference is economically significant. In general, no

relationship in either direction is found between FHLB advances and interest rate risk.

5.4 OTS regulation and risk

       In this section, results are presented regarding H 3A, H3B, H3C, and H3D, the hypotheses

regarding the relationships between OTS regulation and several types of risk. The analysis

focuses on estimates of the bivariate GARCH model, given in equations (1) to (5), of returns on

the THC and BHC portfolios. The THC portfolio contains stocks issued by HCs regulated by the

OTS. The BHC portfolio contains stocks issued by HCs regulated by the Federal Reserve.

       First, results are discussed regarding H3A, OTS regulation is associated with lower total

risk (conditional variance of returns) using data from 2001 to 2009. As Table 5, Panel 3 shows,

the difference in mean daily total risk (THC mean daily total risk minus BHC mean daily total

risk) is -2.232×10-5. Equality of means is rejected at the one percent level of significance. In

economic terms, the THC portfolio’s mean one-day, 1% VaR was $2,581 less than that of the

BHC portfolio, an economically significant difference. This is evidence in favor of H3A, OTS

regulation is associated with lower total risk. One explanation of this finding is that although



                                                 35
OTS regulated some of the most notable failed or near-failed BHCs (Washington Mutual,

Lehman Brothers, AIG), many BHCs regulated by the Federal Reserve were in poor enough

condition to warrant emergency government capitalization under TARP. The poor condition of

these BHCs could explain the greater volatility of the BHC portfolio.

       Next, results are discussed regarding H3B, OTS regulation of THCs is associated with a

smaller increase in total risk during the subprime mortgage crisis. The coefficients on the dummy

variables D1, D2, and D3 (ϕi1, ϕi2, and ϕi3 for portfolios i=1,2) may be interpreted as increases in

total risk during three phases of the subprime crisis. Table 4, Panel 3 presents these coefficient

estimates. Table 5, Panel 3 presents the differences in the coefficient estimates (coefficients from

the THC equation minus the coefficients for the BHC equation) along with Wald tests of cross-

equation equality of the coefficients. For all three pairs of coefficients, the hypothesis of equality

cannot be rejected. This contradicts H3B, OTS regulation of THCs is associated with a smaller

increase in total risk during the subprime mortgage crisis. It is also the case, however, that OTS

regulation is not associated with a greater increase in total risk during the subprime mortgage

crisis either. In spite of the problems at several very large THCs, when most all publicly-traded

THCs and BHCs are taken into account, the increase in volatility during the subprime mortgage

crisis was not greater for THCs than BHCs.

       The discussion now turns to H3C, OTS regulation is associated with lower market risk.

The data studied here cover the period from 2001 to 2009. The market betas, β11 and β21, may be

interpreted as the premia demanded by investors for each portfolio’s non-diversifiable, or

market, risk. Table 4, Panel 3 presents the market beta estimates. Table 4, Panel 3 presents the

differences in the market beta estimates (THC market beta minus BHC market beta) and the

Wald tests of cross-equation equality. The THC market beta is 0.012, or 1.2 basis points, less



                                                 36
than the NONMEMBER market beta. Equality of market betas is rejected at the one percent level

of significance. In economic terms, the premium investors demanded as result of market risk is

below the threshold of economic significance. This result is consistent with H1C, OTS regulation

is associated with lower market risk. It indicates that, on the whole, THCs were slightly better

hedged against fluctuations in the broader market than BHCs.

       Next, results are examined using 2001 to 2009 data with regards to H3D, OTS regulation

is associated with lower interest rate risk. The interest rate betas, β12 and β22, may be interpreted

as the premia demanded by investors for each portfolio’s sensitivity to fluctuations in long-term

interest rates. Table 4, Panel 3 presents the interest rate beta estimates. For both portfolios, the

interest rate beta estimates are two orders of magnitude smaller than the market betas, indicating

the economic significance of the results is small. As shown in Table 5, Panel 3, the interest rate

beta of the THC portfolio is .0022, or 0.22 basis points less than that of the BHC portfolio.

Equality of interest rate betas is rejected at the one percent level of significance. The difference

in interest rate betas, however, is below the 10 basis point threshold of economic significance.

The result supports H3D, OTS regulation is associated with lower interest rate risk. Interest rate

risk does not appear to be significant for either type of HC, but THCs appear to have hedged

themselves against it better than BHCs.

       To examine whether the results obtained above are consistent over time, bivariate

GARCH models of the returns on THC and BHC were estimated on yearly subsamples of the

data. Table 8 shows the results of tests of the annual differences in mean total risk (THC total

risk minus BHC total risk). In all years, THC had lower total risk, and equality of differences is

rejected at high levels of significance each year. The sizes of the differences increase

substantially 2008 and 2009. In economic terms, during 2008 a hypothetical $1 million invested



                                                 37
in THC would lose, on average, $6,021 less of its value on an unexpectedly bad day than $1

million invested in BHC. In 2009, this figure is $10,160. In other years, the differences in VaR

range from $289 to $1,635. The differences in 2003, 2006, 2008 and 2009 are economically

significant. The results support H3A, OTS regulation is associated with lower total risk and for

H3B, OTS regulation is associated with a smaller increase in total risk during the subprime

mortgage crisis. Although several THCs experienced disastrous losses during this period, when

all THCs and BHCs with publicly traded stock are examined, THCs experienced a smaller

increase in total risk. Perhaps the OTS was poorly-equipped to oversee large HCs in comparison

to the Federal Reserve but better able to regulate small and mid-sized HCs.

        Table 8 shows the annual differences in market betas (THC market beta minus BHC

market beta) and the results of tests of equality of annual market betas. The THC portfolio’s

market betas are less than those of the BHC portfolio from 2004 to 2006 and in 2009, with the

differences economically significant in 2005 and 2009. The THC market beta is greater in 2001.

In all other years, the hypothesis of equal market betas is not rejected. The results are consistent

with the slight difference in market betas in the estimate using the entire sample. They provide

weak support for H1C, OTS regulation is associated with lower market risk. Over two time

periods of the study, market risk for THCs is either slightly greater than for BHCs, or not

significantly different.

        Table 8 shows the annual differences in interest rate betas (THC interest rate beta minus

BHC interest rate beta) and the results of tests of equality of annual interest rate betas. From

2001 to 2008, the hypothesis of equal interest rate betas cannot be rejected. In 2009, however,

the THC portfolio is significantly less sensitive to interest rate risk in the statistical but not the




                                                 38
economic sense. The results indicate that H3D, OTS regulation is associated with lower interest

rate risk, does not hold for most of the study.

        To summarize the results in this section, the portfolio of THCs consistently exhibits

lower total risk than the portfolio of BHCs. The difference in total risk is frequently

economically significant, particularly in the subprime crisis years of 2008 and 2009. The THC

portfolio shows a slightly lower level of market risk when all data from 2001 to 2009 are used.

When the data are divided annually, the THC portfolio has lower market risk that is

economically significant in 2005 and 2009. For most of the study, OTS regulation is neither

associated with lower interest rate risk nor higher interest rate risk.

6. Conclusions

Bivariate GARCH models of HC stock portfolios are used to study the relationship of FHLB

membership and FHLB advances with several types of risk from 2001 to 2009. The main finding

is that, throughout the time period studied, HC control of FHLB member subsidiaries is

associated with lower total risk, as measured by GARCH estimates of the conditional variance

of returns, and market risk, as measured by the market beta from a two-factor model of portfolio

returns. Using VaR as a metric, the difference in total risk is found to be economically significant

throughout the study and greatest during the middle- and late-subprime mortgage crisis years of

2008 and 2009. Using market beta as a metric, the same finding applies to market risk.

        In addition, a negative, economically significant relationship between greater reliance on

FHLB advances and total risk is present during 2008 and 2009. Greater reliance on FHLB

advances is also associated with lower market risk throughout the study. The strength of the

association is greatest during 2008 and 2009.




                                                  39
       These results indicate that the risk-reducing effects of FHLB membership and FHLB

policies regarding advances outweigh the effects of other policies that do not provide incentives

to monitor risk. FHLBs restrict funding to riskier members, increasing collateral requirements for

risky advance takers, and limit advance-taking by requiring capital purchases that increase with

advances. The results also support the notion that FHLBs provide backup funds to banks and the

mortgage market during credit crunches. These results do not apply to the behavior of the FHLBs

themselves. A fruitful avenue for future research might be to examine the balance sheet and risk

management policies of the FHLB themselves.

       Additionally, the data are used to study the relationship between regulator and risk.

Portfolios of stocks issued by OTS-regulated THCs consistently had lower total risk than

portfolios of Federal Reserve-regulated BHCs from 2001 to 2009. The differences were

economically significant, particularly in 2008 and 2009. With the exception of 2001, THC

market risk is less than or not significantly different from that of HC portfolios. With the

exception of 2009, THC portfolio interest rate risk is less than or not significantly different from

that of BHC portfolios. The results indicate that outside of several major failed FIs, regulation of

other FIs by the soon-to-be defunct OTS was not worse than and may have been better than that

of the Federal Reserve.

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                                           42
 Tables

 Table 1
 Hypotheses and Portfolio Descriptions
 Abbreviation                 Statement of Hypothesis
 H1A                          HC control of FHLB-member subsidiaries is associated with lower total risk.
 H1B                          HC control of FHLB-member subsidiaries is associated with a smaller increase in total risk during the subprime mortgage crisis.
 H1C                          HC control of FHLB-member subsidiaries is associated with lower market risk.
 H1D                          HC control of FHLB-member subsidiaries is associated with lower interest rate risk.
 H2A                          Greater HC reliance on advances is associated with lower total risk.
 H2B                          Greater HC reliance on advances is associated with a smaller increase in total risk during the subprime mortgage crisis.
 H2C                          Greater HC reliance on advances is associated with lower market risk.
 H2D                          Greater HC reliance on advances is associated with lower interest rate risk.
 H3A                          OTS regulation is associated with lower total risk.
 H3B                          OTS regulation is associated with a smaller increase in total risk during the subprime mortgage crisis.
 H3C                          OTS regulation is associated with lower market risk.
 H3D                          OTS regulation is associated with lower interest rate risk.
 Portfolio Name               Description
 HIGHADV                      Stocks issued by HCs in the highest quartile of advances to total liabilities ratio.
 LOWADV                       Stocks issued by HCs in the lowest quartile of advances to total liabilities ratio.
 MEMBER                       Stocks issued by HCs that control FHLB members.
 NONMEMBER                    Stocks issued by HCs that do not control FHLB members.
 THC                          Stocks issued by THCs.
 BHC                          Stocks issued by BHCs.


Table 2
Number of stocks in portfolios
                                                                         Mean                                       minimum                                     maximum
HIGHADV                                                                  139.0                                        119                                         150
LOWADV                                                                   139.7                                        119                                         151
MEMBER                                                                   541.3                                        464                                         587
NONMEMBER                                                                22.15                                         13                                          31
THC                                                                      138.1                                        117                                         156
BHC                                                                      428.6                                        362                                         459
 This table gives the mean, minimum, and maximum number of stocks in the portfolios examined in this study. HIGHADV is a portfolio of stocks issued by HCs above the highest
 quartile of advances to total liabilities ratio. LOWADV is a portfolio of stocks issued by HCs below the lowest quartile of advances to total liabilities ratio. MEMBER is a portfolio
 of stocks issued by HCs that control FHLB members. NONMEMBER is a portfolio of stocks issued by HCs that do not control FHLB members. THC is a portfolio of stocks issued
 by THCs. BHC is a portfolio of stocks issued by BHCs.



                                                                                          43
Table 3
Descriptive Statistics (2001-2009)
                          HIGHADV            LOWADV              MEMBER                NONMEMBER           THC                 BHC                  RM                    ∆IR10
No. of observations       2245               2245                2245                  2245                2245                2245                 2245                  2245
Mean                      0.00040            0.00051             0.00044               0.00061             0.00050             0.00043              0.00005               -0.00049
Standard Deviation        0.00948            0.01378             0.01087               0.01706             0.01010             0.01147              0.01370               0.06580
Minimum                   0.06832            0.11322             0.08859               0.11506             0.08055             0.09169              0.09540               0.25000
Maximum                   -0.05958           -0.10891            -0.07479              -0.12710            -0.06503            -0.08099             -0.09001              -0.51000
Median                    0.00068            0.00068             0.00059               0.00060             0.00072             0.00058              0.00061               0.00000
J-B (MSL)                 0.00000            0.00000             0.00000               0.00000             0.00000             0.00000              0.00000               0.00000
Skewness                  0.31286            0.31438             0.47656               0.23218             0.20335             0.53003              -0.25617              -0.03954
Kurtosis                  9.42168            12.96439            12.64031              10.72132            9.54653             13.20897             6.56726               2.72291
Q(10)                     35.992***          34.612***           30.897***             25.547***           26.615***           32.570***            40.785***             20.310***
Q(20)                     66.665***          64.559***           56.641***             52.336***           40.233***           62.448***            66.557***             30.778*
Q(30)                     77.579***            88.649***          76.446***           83.822***             61.575***          81.779***             86.866***            41.708*
  2
Q (10)                    1596.08***           1659.93***         1431.232***         1364.383***           1852.959***        1327.716***           2188.969***          184.509***
Q2(20)                    2616.01***           3074.49***         2528.055***         2497.503***           2991.734***        2420.401***           4004.083***          298.577***
Q2(30)                    3378.90***           4197.93***         3344.124***         3414.964***           3890.379***        3222.306***           5090.351***          428.000***
This table presents descriptive statistics for the variables used in this study. HIGHADV is the daily returns on a portfolio of stocks issued by HCs above the top quartile of the sample
in reliance upon advances, measured by the advances-to-liabilities ratio. LOWADV is the daily returns on a portfolio of stocks issued by HCs below the bottom quartile of the sample
in reliance upon advances. MEMBER is the daily returns on a portfolio of stocks issued by HCs that control FHLB member subsidiaries, while NONMEMBER is the daily returns on
a portfolio of stocks issued by HCs that do not. THC is the daily returns on a portfolio of THC stocks, and BHC is the daily returns on a portfolio of BHC stocks. RM is the return on
the CRSP value-weighted market portfolio. ∆IR10 is the change in the yield on a constant maturity 10-year Treasury bond. J-B is the Jarque-Bera joint normality test statistic. MSL
stands for marginal significance level. Q(n) and Q2(n) are the Ljung-Box test statistics for the 10th, 20th, and 30th order autocorrelation in return and squared return series. The critical
values at the 5% level for 10, 20, and 30 degrees of freedom are 18.30, 31.41, and 43.77, respectively.
***, **, and * represent significance at the 1%, 5%, and 10% levels, respectively.




                                                                                           44
Table 4
Bivariate GARCH Model Estimates (2001-2009)
                                           Panel 1                                        Panel 2                                        Panel 3
Coefficients                               MEMBER                  NONMEMBER              HIGHADV                 LOWADV                 THC                    BHC
βi0               Intercept                0.473×10-3***           0.421×10-3***          0.461×10-3***           0.482×10-3***          0.515×10-3***          0.463×10-3***
                                           (6.306                  (4.392)                (5.886)                 (6.615)                (7.487)                (5.633)
βi1               Market                   0.513***                0.876***               0.424***                0.661***               0.521***               0.532***
                                           (51.910)                (79.371)               (41.822)                (68.397)               (55.652)               (47.489)
βi2               ΔIR10                    -3.153×10-3***          1.781×10-3             -2.552×10-3*            -3.026×10-3**          -1.548×10-3            -3.781×10-3***
                                           (-2.725)                (1.113)                (-1.900)                (-2.357)               (-1.285)               (-2.651)
νi1               Intercept                0.554×10-6***           0.998×10-6***          0.327×10-6***           0.245×10-6***          0.276×10-6***          0.253×10-6***
                                           (3.790×10-7)            (4.423×10-7)           (3.499×10-7)            (4.365×10-7)           (4.011×10-7)           (3.669×10-7)
λi1               ARCH                     0.076***                0.086***               0.047***                0.049***               0.069***               0.053***
                                           (5.984)                 (6.771)                (6.344)                 (6.533)                (7.545)                (7.490)
αi1               GARCH                    0.875***                0.867***               0.928***                0.929***               0.905***               0.929***
                                           (40.735)                (46.710)               (79.207)                (100.647)              (68.691)               (95.754)
ϕi1               2007:3-2008:2            2.791×10-6***           3.497×10-6***          1.998×10-6***           1.480×10-6***          1.473×10-6***          1.503×10-6***
                                           (3.453)                 (3.966)                (4.078)                 (4.444)                (3.783)                (3.921)
ϕi2               2008:3-2009:2            15.521×10-6***          36.058×10-6***         4.995×10-6***           9.931×10-6***          4.819×10-6***          6.969×10-6***
                                           (3.789)                 (4.391)                (2.896)                 (4.036)                (3.323)                (3.332)
ϕi3               2009:3–2009:4            1.194×10-6              1.833×10-6             1.112×10-6***           0.813×10-6             0.604×10-6*            0.663×10-6
                                           (1.592)                 (1.546)                (2.037)                 (1.370)                (1.748)                (1.332)
η                 DCC ARCH                 0.034***                                       0.029***                                       0.039***
                                           (11.804)                                       (6.124)                                        (8.163)
δ                 DCC GARCH                0.965***                                       0.970***                                       0.961***
                                           (328.808)                                      (197.447)                                      (198.915)
Panel F: Model Diagnostics
Tse (2000) test    Constant Correlation     -0.187                                        -6.566***                                       -5.174***
                                          2
Ljung-Box statistics based on
Q(10)              No Autocorrelation       38.310                                        53.498*                                         43.702
Q(20)              No Autocorrelation       82.396                                        81.988                                          74.753
Q(30)              No Autocorrelation       113.083                                       128.867                                         124.466
This table presents parameter estimates and diagnostic statistics for bivariate GARCH models of the daily returns on portfolios of BHC and THC stocks. The model estimated is:




HIGHADV is the daily returns on a portfolio of stocks issued by HCs above the top quartile of the sample advances to liabilities ratio. LOWADV is the daily returns on a portfolio
of stocks issued by HCs below the bottom quartile of the sample in advances to liabilities ratio. MEMBER is the daily returns on a portfolio of stocks issued by HCs that control
FHLB member subsidiaries, while NONMEMBER is the daily returns on a portfolio of stocks issued by HCs that do not. THC is the daily returns on a portfolio of THC stocks, and
BHC is the daily returns on a portfolio of BHC stocks. t-values are in parentheses. Q(n) are the Ljung-Box test statistics for the 10th, 20th, and 30th order autocorrelation for
standardized and squared standardized residuals. The critical values at the 5% level for 10, 20, and 30 degrees of freedom are 18.30, 31.41, and 43.77, respectively. ***, **, *
represent significance at the 1%, 5%, and 10% levels, respectively.



                                                                                       45
Table 5
Tests of risk equality (all observations from 2001-2009)
                                                                                     Panel 1:                            Panel 2:                             Panel 3:
                                                                                     MEMBER and NONMEMBER                HIGHADV and LOWADV                   THC and BHC
Hypothesis                                                                           Difference  Test statistic          Difference    Test statistic         Difference        Test statistic
Difference in means test
Equal mean daily total risk:                                                         -4.941×10-5      -20.779***         -2.158×10-5         -13.813***       -2.232×10-5       -21.335***
Mean difference in daily VaR on $1 million investment                                $4,927           N.A.               $1,162              N.A.             $2,581            N.A.
Wald tests
Equal total risk increase from 2007:3 to 2008:2:                                    -0.706×10-6       0.397              0.519×10-6         1.263           -0.030×10-6        0.007
Equal total risk increase from 2008:3 to 2009:2:                                    -20.538×10-6 6.554***                -4.936×10-6        5.022***        -2.150×10-6        1.376
Equal total risk increase from 2009:3 to 2009:4:                                    -0.639×10-6       0.220              0.299×10-6         0.188           -0.059×10-6        0.012
Equal market risk:                                                                  -0.362            1011.784***        -0.237             1247.87***      -0.012             3.856***
Equal interest rate risk:                                                           -4.935×10-3       6.660***           0.474×10-3         0.184           2.233×10-3         3.996***
For the portfolios examined in this study, this table shows the results of tests of equality of total risk, calculations of differences in mean daily VaR, and tests of equality of total
risk increases during the subprime mortgage crisis, equality of market risk, and equality of interest rate risk. The tests of equal mean daily total risk are performed using t-statistics.
VaR is the portfolio’s one-day, 1% value at risk, the change in the value of a $1 million investment in the portfolio if the portfolio’s realized return is equal to the first percentile of
its expected return distribution. The remaining tests of equal risk are performed using Wald statistics. Estimates from the following bivariate GARCH model are used to calculate
the test statistics and VaR figures:




For portfolio i (i = 1,2), hii,t is the conditional variance, interpreted as total risk, βi1 is the market beta, interpreted as market risk, and βi2 is the interest rate beta, interpreted as
interest rate risk. In Panel 1, MEMBER is a portfolio of stocks issued by HCs that control FHLB-member subsidiaries, while NONMEMBER is a portfolio of stocks issued by HCs
that do not. Values in the “Difference” column are the MEMBER values minus the NONMEMBER values. Panel 2 contains results for HIGHADV, a portfolio of stocks issued by
HCs in the top quartile of the sample in advances-to-liabilities ratio and LOWADV, a portfolio of stocks issued by HCs in the bottom quartile of the sample in reliance upon
advances. Values in the “Difference” column are the HIGHADV values minus the LOWADV values. In Panel 3, THC is a portfolio of THC stocks, and BHC is a portfolio of BHC
stocks. Values in the “Difference” column are the THC values minus the BHC values. Values in the “Difference” column are the MEMBER value minus the NONMEMBER value.
***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.




                                                                                             46
Table 6
Annual equality of risk tests and VaR differences -- MEMBER and NONMEMBER portfolios
Year      n          Mean Total Risk          t               MSL        Mean VaR      Market Risk      χ2                MSL         Interest Rate Risk     χ2               MSL
                     Difference                                          Difference    Difference                                     Difference
2001        246      -0.377×10-5              -60.195***      0.000      -7899         -0.426           1838.675***       0.000       0.004×10-3             6.196***         0.013
2002        251      -0.236×10-5              -14.265***      0.000      -4988         -0.517           619.119***        0.000       -0.005×10-3            0.844            0.358
2003        250      -0.084×10-5              -106.455*** 0.000          -2866         -0.453           200.972***        0.000       -0.003×10-3            0.281            0.596
2004        250      -0.088×10-5              -69.344***      0.000      -3355         -0.372           77.680***         0.000       0.003×10-3             0.319            0.572
2005        250      -0.080×10-5              -130.682*** 0.000          -3374         -0.164           44.683***         0.000       -0.004×10-3            0.548            0.459
2006        250      -0.068×10-5              -55.055***      0.000      -2804         -0.165           20.954***         0.000       0.006×10-3             0.745            0.388
2007        249      -0.181×10-5              -5.414***       0.000      -3609         -0.216           63.032***         0.000       0.010×10-3             2.742*           0.098
2008        251      -0.845×10-5              -6.990***       0.000      -6969         -0.441           289.117***        0.000       0.005×10-3             0.442            0.506
2009        249      -2.222×10-5              -7.125***       0.000      -20357        -0.535           161.270***        0.000       -0.003×10-3            0.082            0.775
For the MEMBER and NONMEMBER portfolios, this table shows the results of annual tests of equality of total risk, calculations of differences in mean daily VaR, and tests of
equality of market risk and interest rate risk. MEMBER is a portfolio of stocks issued by HCs in the top quartile of the sample in advances-to-liabilities ratio. NONMEMBER is a
portfolio of stocks issued by HCs in the bottom quartile of the sample in reliance upon advances. The tests of equal mean daily total risk are performed using t-statistics. VaR is the
portfolio’s one-day, 1% value at risk, the change in the value of a $1 million investment in the portfolio if the portfolio’s realized return is equal to the first percentile of its
expected return distribution. The remaining tests of equal risk are performed using Wald statistics. Estimates from the following bivariate GARCH model are used to calculate the
test statistics and VaR figures:




For portfolio i (i = 1,2), hii,t is the conditional variance, interpreted as total risk, βi1 is the market beta, interpreted as market risk, and βi2 is the interest rate beta, interpreted as
interest rate risk. The column headed “Year” gives the year of data from which the model was estimated. Column “n” gives the number of observat ions in the corresponding year.
Values in all “Difference” columns are the MEMBER values minus the NONMEMBER values. The column labeled “t” gives the t-statistic for the null hypothesis that the two mean
conditional variances are equal. All columns labeled “MSL” give their corresponding test statistic’s Marginal Significance Level. The columns labeled χ2 gives the Wald test
statistic for the null hypothesis that β11= β21 or β12= β22 . ***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.




                                                                                             47
Table 7
Annual equality of risk tests and VaR differences -- HIGHADV and LOWADV portfolios
Year     n       Mean Conditional          t              MSL         Mean VaR        Market Beta      χ2                 MSL        Interest Rate        χ2              MSL
                 Variance Difference                                  difference      Difference                                     Beta Difference
2001      246    -0.016×10-5               -2.797***      0.006       -230            -0.220           138.647***         0.000      -0.001×10-3          0.026           0.871
2002      251    0.016×10-5                4.753***       0.000       850             -0.237           215.886***         0.000      -0.000×10-3          0.000           0.986
2003      250    -0.004×10-5               -10.884*** 0.000           -188            -0.262           203.512***         0.000      0.001×10-3           0.193           0.661
2004      250    0.021×10-5                19.656***      0.000       828             -0.229           119.893***         0.000      -0.002×10-3          512.188*** 0.000
2005      250    0.010×10-5                15.601***      0.000       6               -0.168           40.946***          0.000      -0.003×10-3          0.382           0.537
                            -5
2006      250    -0.001×10                 -0.692         0.490       -193            -0.184           52.811***          0.000      0.005×10-3           1.218           0.270
2007      249    0.055×10-5                12.736***      0.000       1080            -0.218           208.366***         0.000      0.008×10-3           8.350***        0.004
2008      251    -0.442×10-5               -5.381***      0.000       -2113           -0.382           558.253***         0.000      0.017×10-3           13.264***       0.000
2009      249    -0.750×10-5               -9.719***      0.000       -5314           -0.468           16674.131*** 0.000            0.002×10-3           0.168           0.682
For the HIGHADV and LOWADV portfolios, this table shows the results of annual tests of equality of total risk, calculations of differences in mean daily VaR, and tests
of equality of market risk and interest rate risk. HIGHADV is a portfolio of stocks issued by HCs that control FHLB-member subsidiaries, while NONMEMBER is a
portfolio of stocks issued by HCs that do not. The tests of equal mean daily total risk are performed using t-statistics. VaR is the portfolio’s one-day, 1% value at risk,
the change in the value of a $1 million investment in the portfolio if the portfolio’s realized return is equal to the first percentile of its expected return distribution. The
remaining tests of equal risk are performed using Wald statistics. Estimates from the following bivariate GARCH model are used to calculate the test statistics and VaR
figures:




For portfolio i (i = 1,2), hii,t is the conditional variance, interpreted as total risk, βi1 is the market beta, interpreted as market risk, and βi2 is the interest rate beta,
interpreted as interest rate risk. The column headed “Year” gives the year of data from which the model was estimated. Column “n” gives the number of observations in
the corresponding year. Values in all “Difference” columns are the HIGHADV values minus the NONMEMBER values. The column labeled “t” gives the t-statistic for
the null hypothesis that the two mean conditional variances are equal. All columns labeled “MSL” give their corresponding test statistic’s Marginal Significance Level.
The columns labeled χ2 gives the Wald test statistic for the null hypothesis that β11= β21 or β12= β22 . ***, **, * represent significance at the 1%, 5%, and 10% levels,
respectively.




                                                                                           48
Table 8
Annual equality of risk tests and VaR differences -- THC and BHC portfolios
Year      n         Mean Conditional         t                VaR               MSL         Market Beta     χ2                MSL         Interest Rate Beta    χ2           MSL
                    Variance Difference                                                     Difference                                    Difference
2001      246       -0.007×10-5              -2.307***        -442              0.022       0.041           10.871***         0.001       -0.001×10-3           0.057        0.811
2002      251       -0.015×10-5              -4.014***        -824              0.000       0.007           0.297             0.586       0.004×10-3            2.125        0.145
2003      250       -0.042×10-5              -219.360***      -1635             0.000       0.007           0.163             0.687       0.001×10-3            0.151        0.698
2004      250       -0.004×10-5              -11.740***       -289              0.000       -0.078          16.852***         0.000       0.000×10-3            0.188        0.665
2005      250       -0.012×10-5              -33.671***       -538              0.000       -0.103          24.608***         0.000       -0.000×10-3           0.007        0.934
2006      250       -0.026×10-5              -18.444***       -1025             0.000       -0.068          12.509***         0.000       -0.002×10-3           0.349        0.554
2007      249       -0.051×10-5              -5.885***        -906              0.000       -0.023          2.030             0.154       0.002×10-3            0.225        0.635
2008      251       -0.635×10-5              -14.051***       -6021             0.000       -0.026          1.616             0.204       -0.000×10-3           0.000        0.995
2009      249       -1.179×10-5              -42.386***       -10160            0.000       -0.191          123.792***        0.000       0.008×10-3            7.783***     0.005
For the THC and BHC portfolios, this table shows the results of annual tests of equality of total risk, calculations of differences in mean daily VaR, and tests of equality of market
risk and interest rate risk. THC is a portfolio of stocks issued by HCs that control FHLB-member subsidiaries, while BHC is a portfolio of stocks issued by HCs that do not. The
tests of equal mean daily total risk are performed using t-statistics. VaR is the portfolio’s one-day, 1% value at risk, the change in the value of a $1 million investment in the
portfolio if the portfolio’s realized return is equal to the first percentile of its expected return distribution. The remaining tests of equal risk are performed using Wald statistics.
Estimates from the following bivariate GARCH model are used to calculate the test statistics and VaR figures:




For portfolio i (i = 1,2), hii,t is the conditional variance, interpreted as total risk, βi1 is the market beta, interpreted as market risk, and βi2 is the interest rate beta, interpreted as
interest rate risk. The column headed “Year” gives the year of data from which the model was estimated. Column “n” gives the number of observations in the corresponding year.
Values in all “Difference” columns are the THC values minus the BHC values. The column labeled “t” gives the t-statistic for the null hypothesis that the two mean conditional
variances are equal. All columns labeled “MSL” give their corresponding test statistic’s Marginal Significance Level. The col umns labeled χ2 gives the Wald test statistic for the
null hypothesis that β11= β21 or β12= β22 . ***, **, * represent significance at the 1%, 5%, and 10% levels, respectively.




                                                                                             49
                  Chart 1 - HIGHADV Portfolio Daily Returns, 2001-2009
          0.08

          0.06

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Returns




          0.00

          -0.02

          -0.04

          -0.06
                  2002   2003    2004    2005    2006   2007   2008      2009
                                          Year




                                           50

				
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