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ECONOMY

D ECONOMY

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TITLE

THESIS

AUTH. 1ST

8

1988

7

NO. 1468-1485

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47

001247981

Table

3

Consistency of Bank Loss Reserve Decisions for the years 1982-1985 Number of Banks

Consistently Conservative Consistently Aggressive Not Consistent

Sample size = 82

1

>

K0/K1




'l

(4a)

+ e

'

(4b)

t

where

the Bid price on a 2-year or 5-year swap on day

t;

A is the Ask price on a 2-year or 5-year swap on day

t;

B

is

TBILL TNOTE

Z

is )

t

tv >

t

I K.

JI

the rate on 2-year T Bills on day t;

is the rate on 5-year T-Notes on day t.

The positive relationship between the size of the Bid-Ask spread and the level of interest rates implies that

8,

and

3.

are positive.

The daily percentage change of the Bid-Ask Spread and Interest

Rates was calculated by Equations 5a and 5b.

(A-B) %A Spread =

" (A-B) t+1 , (A-B)

t

(T Bill Rate)

%i T

B1U

(5a)

>

RatSS "

- (T Bill Rate)

~ (T Bill Rate)

(5b)

t

If

the result of Equation 5b was greater than zero,

that day was

classified as an up day for interest rates as well as for %A Spread, if

the results were less than or equal to zero,

fied as

a

down day.

thac day was classi-

Looking at the data for down days revealed that

during the crash of October 1987 (October 19 to November 4) not only did the T Bill and T-Note rate fall as a result of the flight to

quality, but the Bid-Ask spread more than doubled as

a

result of the

Hence the regressions run to test

uncertainties in the market place.

the down change relationships (6b and 6d) were run two ways.

First,

all down days were included and then those down days associated with the October 1987 crash were omitted for the data set.

The regression

equations run to test the change relationships are:

%A Spread = a + r OVD 2YR,t,up %A Spread r 0VD

„ 2YR,t,down .

%A T Bill

8

2

= a +

6-

2

= a + %A Spread, r VD 5YR,t,up

+ e„

t,up

%A T Bill

,

t,down

%A T Note t t,down

8-,

3

(6a)

t

=

+ e„

(6b)

t

et

(6c)

t

t

%A Spread,...,

5YR,t,down

For 6a and 6c,

= a +

Q 3

%A T Note t + e t,down t

the expected sign of the beta is positive.

(6d)

And for

the hypothesized sign for the beta is negative indicating

6b and 6d,

an inverse relationship between a downward change in the interest rate

and a widening of the spread.

Results

Table 4b.

1

gives the results of the regression for Equations 4a and

As expected,

the significantly positive beta indicates that as

the level of interest rates is high, the Bid-Ask spread is wider than

when the level of interest rates is low. 2-year T Bill and the 5-year T-Note.

This is true for both the

-9-

Table

1

Regression Results for Interest Rate Levels and Spreads

(A - B)

Q

=

1.41

=

.45

=

.16

=

2YR,t

° +

e

a+

3

TBILL i

2YR,t

+ S i

i

Standard Error R

2

ft

=

241

(A - B)

s|

=

1.23

Standard Error

=

.26

=

.19

R

2

to

Table 6b,

6c,

2

=

=

5YR,t

TN ° TE 1

5YR,t

+ 6 i

241

contains the results of the regressions for Equations 6a, For positive changes

and 6d.

interest there

is

in the T Bill and T-Note rate of

no statistically significant

relationship between

increases in the 3id Ask Spread and increases in the interest rate. However, for downward changes in the T Bill and T-Note rates there is a

significantly positive relationship between interest rate decreases

and

a

narrowing spread.

As

can be seen from a comparison of the two

regressions with or without the impact of the October 87 Crash, there is

a

statistically negative relationship between downward changes in

-10-

rate and a widening spread.

the interest

However, for the entire

sample (October Crash included) the relationship is much more significant

.

Table

2

Regression Results for Percentage Changes in Interest Rates and Spreads

%A Spread r 0VD

2YR,t,up

=

a +

O

2

%A TBILL

t,up

+ e t

All Data =

5.48

Standard error =

16.07

6

R

2

2

to

= =

144

%A Spread cvn *

5YR,t,up

All Data =

18.24

Standard error =

12.74

6

3

2

R

=

& = 136

.03

=

a +

%A TNOTE

6

3

t,up

+ e t

-11-

Table

%A Spread

2YR>t)d own

2

(continued)

= a +

B

2

%A TBILL

+ e,

,

t

,down

t

Crash Data Excluded

All Data = -

77.86

= -21.68

8 2

Standard error R

2

=

19.65

=

.18

m =

Standard error = R

2

=

m =

96

= a + %A Spread, VD * 5YR,t,down

6.

%A TNOTE^

8.91 .12

88

+ e^

t.down

3

,

t

Crash Data Excluded

All Data = -114.53

8

Standard error = R

2

=

m =

8^

Standard error

16.49

R

.41

2

= -39.53

=

19.27

=

.16

m =

104

96

Conclusions In pricing interest

rate swaps of a given maturity,

participants consider many factors such as credit

the market

risk, of

the counter-

parties, transaction costs, the level of interest rates, changes in

interest rates, and the supply and demand for interest rate swaps. The results of this research indicate that the level of interest rates are significant in determining the Bid and

market.

Ask.

spread in the swap

Further, downward movement in interest rates has an inverse

relationship with the Bid and Ask spread, as interest rates fall the

-12-

Bid Ask spread widens.

ments,

In a period of extreme interest rate move-

for example the October 87 Crash,

this relationship is intensi-

fied.

For upward movements in the interest rates,

there does not seem to

be a statistically identifiable relationship between increases in the

interest rates and the Bid and Ask spread.

This would imply that some

of the other factors as mentioned above play a more important -role in

spread determination when rates are rising.

Further work

needed in

is

quantifying and gathering data on the other factors so that

a

more

complete explanation can be offered for the pricing of interest rate swaps.

-13-

Ref erences

"An Economic Analysis of Interest Bicksler, James and Andrew H. Chen. Rate Swaps." Journal of Finance July 1986, pp. 645-655. ,

Use, Risk, and Prices." "Interest Rate Swaps: Felgran, Steven D. New England Economic Review November/December 1987, pp. 22-32. ,

C. W. Smithson, and L. M. Wakeraan. "The Evolving Market Smith, C. W. Finance Journal Winter 1986, pp. Midland Corporate for Swaps." 20-23. ,

,

Evaluating the Credit Exposure of and K. W. Fung. Wall, Larry D. Federal Reserve Bank of Atlanta Interest Rate Swap Portfolio . Working Paper 87-8, December 1987. ,

Whittaker, Gregg J. "Pricing Interest Rate Swaps in an Options Pricing Framework." Federal Reserve Bank of Kansas City. RWP 87-02, May 1987.

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