December 11, 2011

Fed's Term Auction Facility: Analysis of an Unconventional Lending Facility


The purpose of this exercise is to analyze and describe conventional and unconventional lending facilities used by the Federal Reserve to support the financial sector during the crisis.

In particular, among the various facilities used by the Fed, the present exercise focuses on the Term Auction Facility (TAF). Where it is not differently specified, the following information was obtained from Fed’s website. The data are also available at the same website, and they are provided here.

(a) Goals of the program and intended beneficiaries.

The TAF is a temporary program managed by the Fed designed to "address elevated pressures in short-term funding markets." Under the program the Fed auctions collateralized loans with various maturities (up to 84 days) to depository institutions that are "in generally sound financial condition" and "are expected to remain so over the terms of TAF loans." All depository institutions that are eligible to borrow under the primary credit program are eligible to participate in TAF auctions. All TAF loans must be fully collateralized. Eligible collateral is the same as that accepted for discount window loans and includes a wide range of financial assets. Each TAF auction is for a fixed amount, with the rate determined by the auction process (subject to a minimum bid rate).

The program was first instituted in December 2007 in coordination with simultaneous and similar initiatives undertaken by the Bank of Canada, the Bank of England, the European Central Bank and the Swiss National Bank. The final Term Auction Facility auction was conducted on March 8, 2010.

Purpose

The TAF was a response to problems associated with the subprime mortgage crisis. Because of widespread concerns about the condition of many financial institutions, investors became very reluctant to lend, especially at maturities beyond the very shortest terms.

Hence, the main purpose of this program was to provide depository institutions with liquidity in an alternative way with respect to the discount window. Many banks were reluctant to borrow at the discount window out of fear that their borrowing would become known and would be erroneously taken as a sign of financial weakness. On the other hand, by offering loans at rates that are below-market (LIBOR), the TAF discreetly provides relatively cheap short-term funding to ailing institutions. In other words, the goal of the TAF was to reduce the incentive for banks to hoard cash, i.e. to reduce the liquidity premium.

(b) Time series of aggregate borrowing under the facility.




(c) List of the top 10 users of the facility.

Borrower
Loan amount ($mn)
BANK OF AMERICA NA
212,167.00
BARCLAYS BK PLC NY BR
188,326.00
BANK OF SCOTLAND PLC NY BR
180,920.00
WELLS FARGO BK NA
153,953.20
WACHOVIA BK NA
147,025.00
SOCIETE GENERALE NY BR
124,377.20
DRESDNER BK AG NY BR
123,328.20
RBS CITIZENS NA
117,150.00
BAYERISCHE LANDESBANK NY BR
108,190.00
DEXIA CREDIT LOCAL NY BR
105,166.80

(d) Analysis of the effectiveness of the program.

When the TAF was dismissed, on March 2010, the total credit extended to banks added up to $3,818 billion. Also, the Fed points out that all loans made under the facility were completely refunded together with interest, in compliance with the terms of the facility.

Now, the Federal Reserve claimed that “by increasing the access of depository institutions to funding, the TAF has supported the ability of such institutions to meet the credit needs of their customers.” So, the program enabled the Federal Reserve to provide term funds to a broader range of counterparties and against a broader range of collateral than it could through open market operations. As a result, the TAF helped promote the distribution of liquidity when unsecured bank funding markets were under stress.

On the other hand, as Thornton (2010) observes, “rather than reducing the liquidity premium in LIBOR rates, the announcement of the TAF increased the risk premium in financial and other bond rates because market participants interpreted the announcement by the Fed and other central banks as a sign that the financial crisis was worse than previously thought”. Thornton provides some empirical evidence, too.

As a conclusion, the TAF had an ambiguous overall effect as for its ability to effectively decrease the propensity of institutions to hoard liquidity and provide short-term funding to the financial system.

(e) Description of an analogous program at the ECB.

As reported in December 12th, 2007 Press Release by the European Central Bank (ECB), “The Governing Council of the ECB has decided to take joint action with the Federal Reserve by offering US dollar funding to Eurosystem counterparties.
The Eurosystem shall conduct two US dollar liquidity-providing operations, in connection with the US dollar Term Auction Facility, against ECB-eligible collateral for a maturity of 28 and 35 days. The submission of bids will take place on 17 and 20 December 2007 for settlement on 20 and 27 December 2007, respectively. The US dollars will be provided by the Federal Reserve to the ECB, up to $20 billion, by means of a temporary reciprocal currency arrangement (swap line).”
So, the ECB implemented a program similar to Fed’s TAF by borrowing US dollars through a foreign-exchange swap line. Foreign-exchange swaps are one of the various instruments used by the ECB in order to carry out its fine-tuning operations (i.e. ad hoc actions with the aim of managing the liquidity situation in the market and steering interest rates, in particular in order to smooth the effects on interest rates caused by unexpected liquidity fluctuations in the market). In particular, FX swaps consist of simultaneous spot and forward transactions in euro against a foreign currency. Basically, the Eurosystem buys (or sells) euro spot against a foreign currency and, at the same time, sells (or buys) it back in a forward transaction on a specified repurchase date.

Other references:
Wikipedia - Term Auction Facility
European Central Bank, The Implementation of Monetary Policy in the Euro Area, 2011

November 24, 2011

VAR estimation and cumulative response to shocks for the Hasbrouck model with different specifications

The aim of this project is the estimation of a VAR process molded on the Hasbrouck model. In particular, the model considered has the following reduced form (RF) specification:



and the following structural form (SF) representation:



where yt = [ rt  xt ]’, and rt  represents returns from a stock and obtained as the log difference of the mid-quotes in two subsequent periods, i.e.



and xt = {1,-1}, depending on whether a transaction is initiated by the buyer or the seller, respectively (i.e. whether the realized price is above or below the mid-quote).

The data set includes trades and quotes from the ITCH feed for Amgen (AMGN) and from TAQ for John Deere (DE). The files containing this information are provided below:

The results discussed below are obtained by running the following Matlab code:



Note that the estimated coefficients refer to the matrix of coefficients generated by the product 


for the lags of the two variables rt and xt in the SF representation of the VAR model, whereas they refer to the entry A12 in the matrix of coefficients A for the contemporaneous effect of xt on rt again in the SF representation.

(a) Estimation of the Hasbrouck VAR:



Stock: AMGN

Equation: rt

R2

1.4050E-01

Variable
lag
coefficient
t-statistic
constant

1.4872E-06
2.3930E+00
r
1
-1.0112E-01
-1.4629E+01

2
3.4773E-03
-1.1039E+00

3
1.9697E-02
1.2987E+00

4
3.9301E-03
-6.4438E-01

5
3.9358E-02
4.1271E+00
x
0
-1.3247E-08
-2.7536E+01

1
3.9012E-08
3.0929E+01

2
2.6534E-08
6.7267E+00

3
1.5311E-08
2.8532E+00

4
3.7657E-09
-9.7301E-01

5
2.7018E-09
2.0719E-01

Equation: xt

R2

5.5220E-01

Variable
lag
coefficient
t-statistic
constant

-1.9380E-02
-3.3940E+00
r
1
-1.9325E+02
-2.8418E+00

2
-1.3483E+02
-1.9670E+00

3
-1.3676E+02
-1.9956E+00

4
-3.1328E+01
-4.5879E-01

5
7.7282E+01
1.2155E+00
x
1
6.1244E-01
7.0156E+01

2
7.6485E-02
7.2777E+00

3
5.9862E-02
5.6831E+00

4
2.8602E-02
2.7174E+00

5
3.7386E-02
4.1068E+00

Stock: DE

Equation: rt

R2

2.5751E-02

Variable
lag
coefficient
t-statistic
constant

3.1689E-06
1.0511E+01
r
1
-4.6338E-03
-7.8262E-01

2
8.6860E-03
1.4647E+00

3
8.7373E-03
1.4731E+00

4
2.2391E-02
3.7789E+00

5
5.5227E-03
9.3799E-01
x
0
4.8916E-06
8.9877E+00

1
3.5896E-06
5.7774E+00

2
1.4471E-06
2.3093E+00

3
1.0292E-07
1.6421E-01

4
-4.5744E-08
-7.3548E-02

5
-1.4585E-06
-2.6497E+00

Equation: xt

R2

6.9150E-01

Variable
lag
coefficient
t-statistic
constant

-2.4893E-02
-7.7720E+00
r
1
-2.2958E+03
-3.7301E+01

2
-7.0211E+02
-1.1156E+01

3
-2.8913E+02
-4.5852E+00

4
-1.7222E+02
-2.7334E+00

5
8.8098E+00
1.4070E-01
x
1
5.5359E-01
9.5800E+01

2
1.5162E-01
2.2951E+01

3
9.3421E-02
1.4062E+01

4
4.4952E-02
6.8013E+00

5
7.3822E-02
1.2645E+01


(b) Re-estimation of the VAR using signed volumes (xVt):



Stock: AMGN

Equation: rt

R2

3.9045E-02

Variable
lag
coefficient
t-statistic
constant

1.4872E-06
1.9603E+00
r
1
-1.0112E-01
-1.1902E+01

2
3.4773E-03
4.0721E-01

3
1.9697E-02
2.3098E+00

4
3.9301E-03
4.6273E-01

5
3.9358E-02
4.6970E+00
xV
0
-1.3247E-08
-4.4139E+00

1
3.9012E-08
1.2884E+01

2
2.6534E-08
8.6614E+00

3
1.5311E-08
4.9825E+00

4
3.7657E-09
1.2271E+00

5
2.7018E-09
8.8587E-01

Equation: xt

R2

1.2657E-01

Variable
lag
coefficient
t-statistic
constant

-1.1615E+01
-5.4069E+00
r
1
-3.4625E+04
-1.4378E+00

2
-1.9473E+04
-8.0455E-01

3
-3.2947E+04
-1.3631E+00

4
3.9506E+04
1.6412E+00

5
3.8296E+04
1.6125E+00
xV
1
1.4283E-01
1.6812E+01

2
1.4354E-01
1.6696E+01

3
1.2109E-01
1.4000E+01

4
9.4511E-02
1.0912E+01

5
6.2098E-02
7.1966E+00

Stock: DE

Equation: rt

R2

3.8311E-03

Variable
lag
coefficient
t-statistic
constant

7.9210E-07
2.7816E+00
r
1
5.0775E-03
8.7730E-01

2
1.0051E-02
1.7380E+00

3
7.5085E-03
1.2985E+00

4
2.1588E-02
3.7348E+00

5
5.4057E-03
9.3608E-01
xV
0
1.2569E-09
3.2170E+00

1
1.8315E-09
4.6824E+00

2
1.5372E-09
3.9278E+00

3
1.1583E-09
2.9587E+00

4
1.2367E-09
3.1589E+00

5
9.0419E-10
2.3111E+00

Equation: xt

R2

9.2510E-03

Variable
lag
coefficient
t-statistic
constant

-3.6456E+01
-8.6528E+00
r
1
-2.9853E+04
-3.4819E-01

2
-3.7331E+04
-4.3574E-01

3
-4.2116E+04
-4.9167E-01

4
2.3718E+04
2.7699E-01

5
1.4167E+05
1.6560E+00
xV
1
5.6051E-02
9.6884E+00

2
3.6705E-02
6.3351E+00

3
3.2688E-02
5.6393E+00

4
3.1312E-02
5.4016E+00

5
3.4526E-02
5.9605E+00


(c ) Re-estimation of the VAR one last time using inside depth (idt):



Stock: AMGN

Equation: rt

R2

5.3874E-02

Variable
lag
coefficient
t-statistic
constant

-3.7280E-07
-4.8430E-01
r
1
-9.8169E-02
-1.1035E+01

2
1.4969E-02
1.6748E+00

3
3.1517E-02
3.5299E+00

4
1.1959E-02
1.3455E+00

5
3.8592E-02
4.6378E+00
xV
0
-1.0346E-08
-3.4599E+00

1
4.2370E-08
1.4023E+01

2
2.7035E-08
8.7679E+00

3
1.3838E-08
4.4729E+00

4
1.9472E-09
6.3012E-01

5
9.0100E-10
2.9333E-01
id
1
5.4164E-07
6.1803E+00

2
2.7731E-07
2.4696E+00

3
-2.0101E-09
-1.7868E-02

4
-1.0524E-07
-9.3551E-01

5
-2.6622E-07
-3.0039E+00

Equation: xt

R2

1.3345E-01

Variable
lag
coefficient
t-statistic
constant

-8.1477E+00
-3.7218E+00
r
1
-1.2791E+04
-5.0533E-01

2
-3.0477E+04
-1.1985E+00

3
-7.7233E+04
-3.0411E+00

4
6.5406E+04
2.5868E+00

5
3.8298E+04
1.6177E+00
xV
1
1.3959E-01
1.6393E+01

2
1.3816E-01
1.5891E+01

3
1.1763E-01
1.3450E+01

4
1.0258E-01
1.1725E+01

5
5.7986E-02
6.6453E+00
id
1
-7.0185E-02
-2.8145E-01

2
-9.6914E-01
-3.0343E+00

3
-1.0054E+00
-3.1421E+00

4
2.0109E+00
6.2915E+00

5
-8.2450E-01
-3.2708E+00

Equation: idt

R2

7.9614E-01

Variable
lag
coefficient
t-statistic
constant

4.0629E-01
5.2063E+00
r
1
3.0637E+02
3.3953E-01

2
-3.6986E+02
-4.0802E-01

3
-1.6861E+03
-1.8624E+00

4
-3.4692E+03
-3.8490E+00

5
-1.6520E+03
-1.9575E+00
xV
1
3.1328E-03
1.0321E+01

2
1.3425E-04
4.3314E-01

3
-4.0323E-04
-1.2933E+00

4
-9.0015E-05
-2.8861E-01

5
3.4966E-04
1.1241E+00
id
1
7.7963E-01
8.7703E+01

2
5.8936E-02
5.1763E+00

3
-5.0136E-03
-4.3956E-01

4
-4.2211E-03
-3.7048E-01

5
9.6309E-02
1.0718E+01

Stock: DE

Equation: rt

R2

4.0524E-03

Variable
lag
coefficient
t-statistic
constant

8.1449E-07
2.8587E+00
r
1
4.9502E-03
8.5525E-01

2
9.9163E-03
1.7146E+00

3
7.4213E-03
1.2834E+00

4
2.1481E-02
3.7161E+00

5
5.3622E-03
9.2855E-01
xV
0
1.3139E-09
3.3366E+00

1
1.9066E-09
4.8369E+00

2
1.6040E-09
4.0666E+00

3
1.2605E-09
3.1951E+00

4
1.2906E-09
3.2913E+00

5
9.5463E-10
2.4362E+00
id
1
2.6491E-08
7.2184E-01

2
-1.0909E-08
-2.1662E-01

3
1.0118E-08
2.0092E-01

4
-3.3625E-08
-6.6768E-01

5
4.4848E-08
1.2182E+00

Equation: xt

R2

2.4651E-02

Variable
lag
coefficient
t-statistic
constant

-3.7961E+01
-9.0763E+00
r
1
-3.9029E+03
-4.5871E-02

2
-2.5239E+04
-2.9686E-01

3
-3.2797E+04
-3.8583E-01

4
3.3468E+04
3.9386E-01

5
1.3998E+05
1.6490E+00
xV
1
4.9589E-02
8.5686E+00

2
3.1439E-02
5.4250E+00

3
2.8598E-02
4.9330E+00

4
2.6752E-02
4.6428E+00

5
2.8875E-02
5.0151E+00
id
1
7.4783E+00
1.3907E+01

2
-8.9044E+00
-1.2057E+01

3
-6.0254E-01
-8.1396E-01

4
-1.4352E+00
-1.9387E+00

5
5.5825E-01
1.0316E+00

Equation: idt

R2

8.5838E-01

Variable
lag
coefficient
t-statistic
constant

-3.2536E-02
-7.2264E-01
r
1
8.0694E+01
8.8102E-02

2
9.2587E+01
1.0117E-01

3
-5.9768E+02
-6.5317E-01

4
4.2327E+02
4.6272E-01

5
-1.8022E+01
-1.9723E-02
xV
1
-1.9007E-04
-3.0509E+00

2
-1.4832E-04
-2.3776E+00

3
-1.3555E-04
-2.1721E+00

4
3.5928E-06
5.7921E-02

5
-6.4841E-05
-1.0461E+00
id
1
9.3718E-01
1.6190E+02

2
1.0236E-02
1.2875E+00

3
7.9848E-03
1.0020E+00

4
-2.6881E-02
-3.3733E+00

5
-1.0150E-02
-1.7423E+00


For each of the specifications, we compute and plot the cumulative impulse response


or

for the specifications with volume.

Figure 1 - VAR as in (a) - AMGN

Figure 2 - VAR as in (a) - DE

Figure 3 - VAR as in (b) - AMGN

Figure 4 - VAR as in (b) - DE

Figure 5 - VAR as in (c) - AMGN

Figure 6 - VAR as in (c) - DE