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____________ Rev iew _____________
Vol. 69, No. 5
M av 1987
5 Do the New Exchange Rate Indexes
Offer Better Answers to Old
Questions?
18 Has Programmed Trading Made Stock
Prices More Volatile?
30 Agricultural Banks: Causes of Failures
and the Condition of Survivors
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Federal Reserve Bank of St. Louis
Review
M ay 1987
In This Issue • • .
The sluggish response of the U.S. trade and current account balances to the
decline of the dollar’s foreign exchange value against the currencies of the major
industrialized countries since early 1985 has led many analysts to question the
traditional construction of exchange rate indexes. Criticism that the coverage of
traditional indexes are too narrow to reflect accurately the current pattern o f U.S.
trade, has led to new, more inclusive aggregate exchange rate measures in recent
years. In the first article of this Review, “Do The New Exchange Rate Indexes Offer
Better Answers to Old Questions?”, Dallas S. Batten and Michael T. Belongia
examine several of these recently introduced exchange rate indexes.
They find that the newer indexes performed no better than the older measures
in explaining U.S. trade flows during the floating rate period. In fact, the tradi
tional, narrower indexes outperformed the newer indexes in explaining the flow
of U.S. non-petroleum imports. Hence, the authors conclude that the new ex
change rate indexes do not solve the current puzzle surrounding the persistence
of the U.S. external deficit.
*
*
*
Numerous commentators have claimed that the recent application of com
puter techniques to monitor price differences and trigger trades between the
spot, futures and options markets for stocks (called programmed trading) has
increased the volatility of stock prices. The alleged increase in volatility is
important because it has led to closer scrutiny of the stock market by the
Securities and Exchange Commission and periodical calls for legislative action.
G.
J. Santoni examines this issue in the second article in this Review, “Has
Programmed Trading Made Stock Prices More Volatile?” Santoni discusses the
theory that underlies programmed trading and examines various measures of
stock price variation. These results suggest that programmed trading has not
increased price volatility in the spot market for stocks.
*
*
*
Financial stress in agriculture is evident among farmers and their creditors as
well. One example of the impact of financial stress among agricultural creditors is
the 168 agricultural banks that failed between 1984 and 1986. Nonetheless, not all
farm lenders have experienced significant financial difficulty in the course of the
post-1980 downturn in the farm sector. Thus, an examination of the puzzle of why
some banks failed while others survived is the focus of the third article in this
Review, “Agricultural Banks: Causes of Failures and the Condition of Survivors.”
In this article, Michael T. Belongia and R. Alton Gilbert analyze a sample of farm
banks to isolate the likely causes of failures. By looking at 1981 data, they rule out
weaker balance sheets or lower earnings prior to the farm sector downturn as
potential causes of farm bank troubles: banks that failed and those that survived
were similarly capitalized and profitable in 1981. However, the banks that failed
held somewhat riskier portfolios than those who did not. For example, the failed
3
In This Issue . . .
banks invested more of their assets in loans generally, and farm loans particularly,
than did the surviving banks. The failed banks also held fewer federal government
securities, which are free of default risk. Of the surviving banks in 1986, Belongia
and Gilbert find that about 70 percent are in sound financial condition. Finally,
they find that most counties in the sample still are served by at least one healthy
agricultural bank.
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Do the New Exchange Rate
Indexes Offer Better Answers
to Old Questions?
Dallas S. Batten and Michael T. Belongia
T
■M. HE persistent U.S. trade and current account
deficits appear somewhat paradoxical in light of the
dramatic decline of the dollar’s foreign exchange value
against the currencies of industrialized countries
since early 1985. Some analysts have argued that the
dollar’s decline has been overstated. The traditional
dollar exchange rate indexes, which include primarily
industrial countries’ currencies, have been criticized
as too narrow to reflect the movement of the dollar
accurately. In response to this argument, new, more
inclusive aggregate exchange rate measures have been
developed.1The new broader indexes are alleged to be
better measures of the dollar’s foreign exchange value
and hence, they should better explain U.S. trade flows.
Although the notion that indexes with a broader
range of currencies will contain more information has
intuitive appeal, neither economic nor index number
theory can be used to determine whether a particular
exchange rate index is superior to another.2 In this
article we assess the performance of the new indexes
empirically. Specifically, we investigate whether one
or more of the new indexes is related more closely to
U.S. merchandise exports and U.S. non-petroleum im
ports than three more established and more tradi
tional exchange rate measures. The performance of
the alternative exchange rate indexes is evaluated in
terms of their in-sample and out-of-sample statistics.
THE CONSTRUCTION OF EXCHANGE
RATE INDEXES
Constructing a multilateral exchange rate index re
quires addressing a number of theoretical and statisti
cal issues.3The primary issue in this paper is whether
the number of currencies in the index matters — a
question for which theory offers no guidance. An in
dex also requires a base year for the trade (or other)
weights that will be applied to the constituent curren
cies. It generally is not possible, however, to find a year
that satisfies the necessary criteria.4 Other practical
problems associated with constructing an exchange
rate index include the choice of weighting schemes
(multilateral or bilateral) and alternative mathematical
formulas (geometric or arithmetic).5
Characteristics o f the Traditional
Indexes
Among the best-known exchange rate indexes are
those produced by the Federal Reserve Board (FRB),
Morgan Guaranty (MG-15) and the International Mon-
Dallas S. Batten, a former research officer at the Federal Reserve Bank
of St. Louis, is currently deputy assistant secretary for policy coordina
tion at the U. S. Department of the Treasury, and Michael T. Belongia is
a senior economist at the Federal Reserve Bank of St. Louis. Anne M.
Grubish provided research assistance.
3See Dutton and Grennes (1985) for a detailed discussion of theoreti
cal and statistical issues concerning the construction of exchange
rate indexes.
'See Cox (1986), Rosensweig (1986), Hervey and Strauss (1987)
and Morgan Guaranty (1986). Rosensweig’s index is nominal, not
real, as this analysis requires. Hence, it is not included in the
empirical investigation.
4ln theory, absolute purchasing power parity should hold in the base
year and the constituent countries should consume identical com
modity bundles. Absolute purchasing power requires an exchange
rate that equates the price levels between nations.
2ln fact, contrary to the intuitive argument, Belongia (1986) found that
certain indexes especially designed for specific purposes performed
poorly in their designed role relative to other, more general indexes.
5See Dutton and Grennes (1985), pp. 20-27. Also, see Belongia
(1986), p. 7, for a numerical example and further discussion of the
distinction between arithmetic and geometric weights.
5
MAY 1987
FED ERAL RESERVE BAN K OF ST. LOUIS
Table 1
Characteristics of Alternative Exchange Rate Indexes
Index
Averaging
Procedure
SDR
Deflator
(to convert
nominal to real)
Weights
Coverage
Arithmetic
Multilateral
exports plus imports
fixed at 1980-84 level
5 major industrial countries
(U.S., Germany, Japan, France,
United Kingdom)
CPI
FRB
Geometric
Multilateral
exports plus imports
fixed at 1972-76
level
10 major industrial U.S.
trading partners (G-10 plus
Switzerland)
CPI
MG-15
Geometric
Bilateral exports
plus imports of only
manufactures fixed
at 1980 level
15 major industrial U.S.
trading partners (the 10
countries in FRB plus
Australia, Austria,
Denmark, Norway, Spain)
WPI
7-Gr
Geometric
Bilateral exports
plus imports;
12-quarter moving
average changing
quarterly
16 major U.S. trading
partners (the 10 countries
in FRB plus Australia,
Hong Kong, Singapore, Spain,
South Korea, Taiwan)
CPI
MG-40
Geometric
Bilateral exports
plus imports of only
manufactures fixed
at 1980 level
40 major U.S. trading
partners including 22
LDCs (including the 15
countries in MG-15)
WPI
X-101
Geometric
Bilateral exports
plus imports; 3-year
moving average
changing annually
101 U.S. trading partners
(essentially all)
CPI
etary Fund for the Special Drawing Right (SDR). Their
basic characteristics, along with those for the newer
indexes — the Federal Reserve Bank of Chicago’s 7-Gr,
Morgan Guaranty’s 40-currency index (MG-40), and
the Federal Reserve Bank of Dallas’ X-101 — which will
be discussed later, are presented in table 1. Table 2
reports the weights that each of these indexes assigns
to different foreign currencies. The narrowest index is
the SDR index, which assigns weights based on the
four other currencies (besides the U.S. dollar) that
make up the SDR.6
6The SDR is the International Monetary Fund’s official unit of account
and serves as an international reserve asset often used in place of
gold for making international payments. Since the SDR is denomi
nated in terms of only the U.S. and four other nations’ currencies,
however, a dollar exchange rate based on SDR weights reflects
changes in the dollar against only four other currencies.
6
The FRB and MG-15 indexes base their weights
primarily on trade with the G-10 countries and Switz
erland.7These indexes reflect trade among developed,
industrialized economies but do not include the cur
rencies of less-developed countries (LDCs).8The MG15 index is somewhat more broadly based than the
FRB index in that it includes Australia, Spain and
several other countries.
The difficulty of choosing among the traditional
exchange rate measures to represent the dollar’s value
is perhaps best illustrated by the relationships in chart
The Group of Ten, or G-10, countries are Belgium, Canada, France,
West Germany, Italy, Japan, the Netherlands, Sweden, the United
Kingdom and the United States.
8A less-developed country typically is defined as one in which per
capita income is less than one-fifth of U.S. per capita income.
FEDERAL RESERVE BAN K OF ST. LOUIS
MAY 1987
Table 2
Percentage Weights Assigned to Major Currencies in Six U.S.
Dollar Exchange Rate Indexes
Exchange Rate Index
Country
United States
Germany
Japan
France
United Kingdom
Canada
Italy
Netherlands
Belgium
Sweden
Switzerland
Australia
Mexico
Spain
South Korea
Taiwan
Singapore
Hong Kong
All other
TOTAL
SDR'
FRB
42.0
19.0
15.0
12.0
12.0
—
—
—
—
—
—
20.8
13.6
13.1
11.9
9.1
9.0
8.3
6.4
4.2
3.6
—
___
MG-15
___
—
10.9
23.2
5.9
9.2
30.3
4.1
3.0
3.5
1.7
2.8
2.4
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
—
1.4
7-Gr2
___
7.2
21.5
4.0
7.5
29.8
3.3
3.4
2.4
1.3
1.6
2.1
—
0.0
0.0
1.6
1.4
4.2
5.2
2.1
3.0
0.0
100.0
100.0
100.0
100.0
—
MG-40
—
X-1012
___
9.9
18.5
5.1
8.2
20.7
3.7
2.0
2.2
1.5
1.8
1.7
4.6
1.3
2.1
3.1
0.9
2.0
10.7
5.4
17.1
2.9
4.8
21.0
2.7
2.1
1.5
1.1
1.1
0.2
5.9
1.0
3.0
4.0
1.4
2.1
22.7
100.0
100.0
'Weights are for $/SDR. The reciprocal of this, SDR/$, was used in the empirical analysis.
21985 weights are shown. Actual weights are three-year moving averages, and hence, vary over time.
1 and table 3. Using measures of the real exchange
rate, which are the nominal exchange rate indexes
adjusted for differences in price levels between the
United States and foreign countries, the chart shows
that, between 1973 and 1980, the real value of the
dollar fell by as little as 3 percent based on the MG-15
measure, or by as much as 14 percent based on the
FRB measure.9 Similarly, the chart indicates that the
real value of the dollar rose by as much as 57 percent
(FRB) or as little as 32 percent (MG-15) between 1980
9A geometric, real trade-weighted exchange rate index can be con
structed by the formula:
n ( Pus,
100
it
1= 1 Pm
Elt )w,
•
~
E,.o
where Pus and Pi are the price levels in the U.S. and the foreign
country, respectively, E, is the nominal exchange rate in foreign
currency units per dollar, t denotes time period with base period at
zero, n denotes number of currencies in the index and w( is the
weight associated with trade between the United States and foreign
country i.
and 1984. Finally, the range of values for the dollar’s
decline since the September 1985 Plaza Accord is
between —15 percent (SDR) and —22 percent (FRB).
The divergent behavior of these indexes also is evi
dent in table 3. As the top portion of the table indi
cates, the SDR index has the smallest average quarterly
change, the smallest standard deviation, and narrow
est range for quarterly changes; these statistics indi
cate its relative stability over time. The FRB and MG-15
indexes have slightly wider ranges for quarterly
changes over time. The bottom portion of the table,
which reports simple correlation coefficients between
different pairs of real exchange rates, shows that per
centage changes in each index are quite highly cor
related.10Overall, the data in chart 1 and table 3 indi
cate that, although movements in the indexes are
,0Each correlation coefficient is significant at the 0.001 level or higher.
Percentage changes in variables are used to eliminate the effects of
any common trend in the data.
7
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
C h a rt 1
Selected Real Effective Exchange Rates Expressed
as V a lu e of D o lla r
positively correlated, there are substantial quantita
tive differences in their movements over time.
The New Indexes
Some economists have viewed these three tradi
tional indexes as deficient not only because they have
failed to produce a consensus about the dollar’s “true”
value, but because they have significant problems of
error by omission. The primary criticism is that these
indexes ignore the importance of LDCs and NewlyIndustrialized Countries (NICs), especially Pacific-rim
countries, to U.S. trade. Thus, although the degree of
broader coverage differs, the new indexes expand con
siderably the number of countries represented rela
tive to the more traditional measures.
The countries and weights used to construct the
new exchange rate indexes are shown in the last three
columns of table 2. Again, refer to table 1 for the
characteristics of these indexes. Two of the indexes
(MG-40 and 7-Gr) expand the number of countries
http://fraser.stlouisfed.org/
8
Federal Reserve Bank of St. Louis
primarily to emphasize trade with Pacific-rim coun
tries. The X-101 index covers U.S. trade with all coun
tries for which data are available. (There actually is a
broader nominal index, based on 131 countries, but
gaps in the data on foreign price levels narrow the
coverage for the real index.) These newer indexes,
because they recognize the increasing importance of
U.S. trade with LDCs and NICs over time, are intui
tively appealing; it would seem that they should pro
vide a more accurate assessment of the dollar’s value.
As a first comparison, chart 2 and table 3 can be
examined to investigate relationships between the
new and the old indexes. In the table’s upper half,
percentage changes in each of the new indexes appear
to be less variable than the traditional indexes. In the
table’s lower portion, however, percentage changes in
the new indexes are shown to be significantly cor
related with each other and the traditional indexes.
Thus, the new indexes appear to reflect much o f the
information contained in the narrower, traditional
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
vant. Thus, one would expect that lagged adjustment
exists and that differentials in real income growth play
important roles.
Table 3
Summary Statistics for Alternative Real
Exchange Rate Measures, 1/1975-111/1986
Index
SDR
FRB
M G -1 5
7 -G r
o
I
O
2
X -101
Mean
-0.0002
0.0005
0.0008
0.0004
0.0019
0.0024
Standard
Deviation
Minimum
Maximum
0.027
0.041
0.032
0.026
0.027
-0.051
-0.082
-0.064
-0.052
-0.054
0.058
0.084
0.064
0.022
-0.036
0.051
0.059
0.049
Correlation Coefficients
Index
FRB
MG-15
7-Gr
MG-40
X-101
SDR
FRB
MG-15
7-Gr
0.988
0.922
0.921
0.947
0.963
0.908
0.923
0.914
0.990
0.902
0.910
0.915
0.844
MG-40
0.950
0.862
NOTE: All calculations are based on first differences of
logarithms.
indexes and vice versa. Chart 2, however, which shows
the SDR index plotted against the three new indexes,
however, indicates that judgments about how much
the dollar’s value has changed still depend crucially
on the measure chosen.
THE SENSITIVITY OF TRADE FLOWS
TO CHANGES IN EXCHANGE RATES
AND INCOME
The dollar has been depreciating since February
1985. One major puzzle that has accompanied this
decline is why the trade and current account balances
have not responded more. When analyzed in nominal
terms, the standard J-curve phenomenon typically is
used to explain the slow adjustment of the current
account balance to a change in the foreign currency
value of the dollar. For example, because of prior
commitments and contracts, import prices will rise
and export prices will fall before the volume of exports
and imports responds to a decline in the foreign
exchange value of the dollar. When analyzed in real
terms, however, only the volume adjustment is rele
To investigate the sensitivity of real tr ade flows to
changes in real incomes and the real exchange rate,
simple reduced-form models were constructed for U.S
real exports and U.S. real non-petroleum imports.11
Before presenting the models, three caveats must be
recognized. First, these are highly simplified, aggre
gated models and are not meant to capture all the
specifics and nuances of trade flows. Their sole pur
pose is to provide a general, quantitative indication of
the income and exchange rate elasticities of trade
flows to enable a comparison of the various exchange
rate indexes. Second, because these models are highly
aggregated, they ignore the special problems of LDCs
and their efforts to generate increased trade surpluses
to better service their external debt. Third, all of the
statistical results presented are specific to the models
estimated and may vary if alternative models or sam
ple periods are applied to the problem. As the refer
ences in footnote 11 suggest, however, the models
estimated certainly follow an established tradition in
the empirical literature.
The Export Model
The model of U.S. real exports emphasizes the
forces that affect the world demand for and the U.S.
supply of U.S. exports. The world demand for U.S.
exports is assumed to depend on two factors: the level
of foreign real economic activity (income) and the
price of U.S. goods relative to those of other countries.
The higher the level of foreign real income, ceteris
paribus, the larger the foreign demand for U.S. exports.
The higher the price of U.S. goods relative to those
abroad, ceteris paribus, the lower the demand for U.S.
exports.
The supply of U.S. exports is expressed as a function
of the price of U.S. exports relative to the prices of
other goods and services produced in the United
States and the utilization of productive capacity in the
United States. The higher the price of U.S. exports
relative to the prices of other goods or the higher the
level of capacity utilization, ceteris paribus, the larger
the production of U.S. goods for export.
To generate an estimating equation, a dynamic rep
resentation is assumed. Because the demand for or
"These models are fashioned after those of Batten and Belongia
(1986), Clark (1974), Goldstein and Khan (1978), and Spitaller
(1980).
9
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
C h a rt 2
Selected Real Effective Exchange Rates Expressed as
V a lu e of D ollar
i n d e x , 1975.01 = 100
145
In d e x , 1975.01 = 1 00
145
*\
/
130
/
/
115
/ v
•A
MG40
\
/
v -\
J ///
100
X-101
^ A
//
*
\
4\V
rA\
v \
* \ \%
/ \
\
130
\\11 <i
\ 1
\ 1
\\ %1
\\ \1
i
i
i
/
/
i
*
/ /
4
\
\\ \ 7-GR
115
\\\ \
\X
\\
100
7
SN//
XN».
SDR
85
85
1975
76
77
78
79
80
the supply of exports may not adjust instantaneously
to changes in the explanatory variables, each explana
tory variable is expressed as a distributed lag. Then, a
market equilibrium was assumed and a reduced form
was obtained; this reduced form is expressed in gen
eral terms as:
P
(1) In EX, = a +
q
+
2
2 P,ln FGNP,_,
i= 0
7 i In (USXP/GNPDEF),_|
j= l
+
r
2
8kIn RER,_k +
k= l
s
2
0mIn CAP,_m + e,,
m= 0
where:
EX
FGNP
USXP
= U.S. real exports,
= index o f foreign real GNP,
= U.S. export unit value index,
http://fraser.stlouisfed.org/
10
Federal Reserve Bank of St. Louis
81
82
83
84
85
1986
GNPDEF = U.S. GNP deflator,
RER
CAP
= real trade-w eighted exchange rate
currency/$), and
= rate o f U.S. capacity utilization.12
(foreign
The real exchange rate was included to measure
U.S. prices relative to those in the rest of the world
(expressed in dollars), taking into account price-level
differences across countries.
Results from least squares estimation of equation 1
over the period 1/1975 to III/1986 using each o f the six
exchange rate indexes are given in table 4.13Each set of
results differs only by the real exchange rate measure
used in the estimation. The regression results in table
4 indicate how well the alternative real exchange rate
indexes explain movements in real U.S. exports.
,2Lag lengths were selected using techniques presented in Batten
and Thornton (1984).
13The sample period actually begins in 1/1973; eight observations are
lost in the lag-length selection process.
MAY 1987
FED ERAL RESERVE BA N K OF ST. LOUIS
Table 4
Results for U.S. Merchandise Export Equations
Exchange Rate
IlnFGNP
iln(USXP/GNPDEF)
SlnRER
InCAP
R2/SE
DW
P
SDR
1.416*
(13.88)
0-3
0.425
(1.23)
1-8
-0.706*
(5.30)
1-5
0.016
(0.08)
0
0.970
0.019
1.59
0.497
(3.93)
FRB
1.592*
(15.95)
0-3
-0.370
(0.76)
1-8
-0.712*
(5.33)
1-8
-0.180
(0.88)
0
0.971
0.019
1.68
0.397
(2.97)
MG-15
2.002*
(12.96)
0-3
-0.789
(1.65)
1-8
-1.363*
(5.96)
1-8
-0.061
(0.32)
0
0.973
0.018
1.83
0.458
(3.54)
7-Gr
1.697*
(17.00)
0-3
-0.289
(0.88)
1-8
-1.158*
(7.30)
1-8
-0.281
(1.40)
0
0.971
0.019
1.72
0.313
(2.26)
MG-40
2.071*
(12.00)
0-3
-1.192*
(2.12)
1-8
-1.534*
(5.69)
1-8
0.022
(0.11)
0
0.973
0.018
1.77
0.485
(3.81)
X-101
1.750*
(10.59)
0-4
0.089
(0.23)
1-8
-0.794*
(4.76)
1-5
-0.271
(0.90)
0
0.963
0.021
1.54
0.524
(4.22)
NOTE: The items listed under coefficient column headings are, in order: coefficient estimate, absolute value of t-statistic (in parentheses),
and lags estimated.
'Statistically significant at the 5 percent level.
On the basis of the summary statistics and esti
mated coefficients, table 4 offers little guidance in
distinguishing the performance of one index from
another. The equations display roughly similar ex
planatory power (based on R2and standard error) and
all exhibit positive first-order autocorrelation.14 The
estimated income and price (exchange rate) elastici
ties are statistically significant, and their signs meet e?c
ante expectations. In general, the estimated coef
ficients of the supply-side variables (relative export
prices and the rate of capacity utilization) are not
statistically significant.
There are some marked differences, however, in the
magnitude and timing of the response of real U.S.
exports to changes in the real trade-weighted value of
the dollar. Depending upon the exchange rate index
14Correcting for first-order autocorrelation had virtually no effect on
the parameter estimates. Also, including a lagged dependent vari
able on the right-hand side of the equation appeared to “correct” the
autocorrelation without affecting the estimated parameters. Further
more, all statistically significant coefficients of the lagged dependent
variable were significantly less than one.
chosen, this response takes place over a range of five to
eight quarters. Moreover, export demand can be said
to be inelastic (FRB and SDR), unit-elastic (MG-15, X101 and 7-Gr) or elastic (MG-40).15 Because policy
makers are chiefly interested in how much and how
quickly U.S. exports respond to a change in the dollar’s
value, the wide qualitative and quantitative diversity
among the estimated coefficients in table 4 is
troublesome.
The Import Model
A similar generic model was constructed for U.S.
real non-petroleum imports. U.S. demand for foreignproduced goods was assumed to be a function of U.S.
real income and the relative price of U.S. goods to
foreign-produced goods. The foreign supply of im
ports was assumed to be a function of the price of
,sThis, of course, is based on testing the null hypothesis that
r
2
8k= 1 .
k=1
11
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Table 5
Results for U.S. Non-Petroleum Imports Equations
Exchange Rate
SlnGNP
2ln(U.S.MP/FCPI)
SlnRER
InCAP
R2/SE
DW
P
SDR
2.551*
(44.98)
0-4
-1.126*
(6.97)
1-3
1.700*
(11.46)
1-6
0.368
(0.88)
0
0.996
0.019
2.26
___
FRB
2.248*
(29.11)
0-5
-1.198*
(7.10)
1-3
1.209*
(11.04)
1-6
0.666
(1.49)
0
0.996
0.018
2.35
—
MG-15
2.428*
(20.51)
0-4
0.034
(0.15)
1-6
0.804*
(4.48)
1-2
0.011
(0.02)
0
0.992
0.027
1.75
—
7-Gr
2.129*
(21.74)
0-6
-1.134*
(5.80)
1-3
1.854*
(9.71)
1-6
-0.545
(0.97)
0
0.995
0.020
2.01
—
MG-40
2.267*
(21.55)
0-8
-0.256
(1.57)
1
1.132*
(8.50)
1-4
0.644
(0.76)
0
0.993
0.025
1.73
—
X-101
2.204*
(13.62)
0-6
-0.257
(1.35)
1
0.925*
(5.46)
1-8
0.514
(0.61)
0
0.993
0.024
1.84
0.440
(3.35)
NOTE: The items listed under coefficient column headings are, in order: coefficient estimate, absolute value of t-statistic (in parentheses),
and lags estimated.
‘ Statistically significant at the 5 percent level.
imports relative to the foreign general price level and
the utilization of productive capacity abroad. The real
exchange rate again was used as the measure of U.S.
prices relative to those abroad. In the import model,
however, changes in the real exchange rate should
have a positive impact. That is, a rise in the real
exchange rate indicates that U.S. prices are rising
relative to those abroad; hence, U.S. consumers should
substitute relatively more foreign-produced for U.S.produced goods.
Generating a reduced-form estimating equation in
the same manner as before yields:
P
12) In IM, = a +
r
+
q
2 Piln GNP,_, + 2 -y, In (USMP/FCPI),_(
i= 0
j= l
2
s
8k In RER,_k +
k= 1
2
0,,, In FCAP,_m + e,,
The results from estimating this equation for each
exchange rate index, with appropriate lag length se
lections, are reported in table 5. Once again, the equa
tions differ little on the basis of the summary statistics
and estimated coefficients. Also once again, the esti
mated exchange rate effects on U.S. imports vary
widely: the adjustment lag varies from two to eight
quarters and import demand is either unit-elastic
(FRB, MG-15, X-101 and MG-40) or elastic (SDR and 7Gr) depending on the specific index. The results in
tables 4 and 5 indicate that changes in the dollar’s real
value affect the U.S. merchandise trade deficit; the
estimated magnitude and timing of the effects, how
ever, differ substantially across the exchange rate in
dexes examined."1
m=0
where:
IM
= U.S. real non-petroleum imports,
GNP
= U.S. real GNP,
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12
Federal Reserve Bank of St. Louis
USMP = U.S. non-petroleum im port unit value index,
FCP1 = index o f foreign CPI, and
FCAP = rate o f foreign capacity utilization.
16An investigation of the last eight in-sample errors for each equation,
however, reveals that most lie within one standard error of zero.
Hence, the in-sample results do not indicate that any exchange rate
index outperforms any other one.
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
had been known in advance, how well could changes
in export and import flows have been predicted? To
examine this issue, equations 1 and 2 were reestimated for the 1/1975-111/1984 period, and out-ofsample errors were calculated for exports and imports
for the eight quarters between IV/1984 and III/1986.
Summary statistics for these out-of-sample predictive
errors are reported in table 6; the errors are plotted in
charts 3 and 4.
Table 6
Out-of-Sample Forecast Summary
Statistics (estimation interval ;
1/1975-111/1984; forecast interval:
IV/1984-111/1986)
EXPORT EQUATIONS
Exchange Rate Index
Mean Error
SDR
FRB
MG-15
7-Gr
MG-40
X-101
0.006
-0.009
-0.052
0.007
-0.039
0.048
MAE
RMSE
0.026
0.030
0.058
0.015
0.051
0.048
0.028
0.035
0.069
0.018
0.061
0.053
0.034
0.038
0.081
0.056
0.067
0.081
0.042
0.046
0.090
0.064
0.074
0.103
The table reports the mean error, the mean absolute
error (MAE) and the root-mean-squared error (RMSE).
For the U.S. export equations in the table's upper half,
the 7-Gr index had the lowest MAE and RMSE values
and the second-smallest mean error. Performing
nearly as well were the FRB and SDR indexes. In
contrast, out-of-sample predictions using the X-101
and MG-40 indexes, which were designed to give
broader coverage to trade flows, show larger errors.
IMPORT EQUATIONS
SDR
FRB
MG-15
7-Gr
MG-40
X-101
-0.015
-0.024
-0.019
-0.027
-0.005
0.036
Because we do not know the actual exchange rate
elasticities for exports and imports or the correct
adjustment lag, e* ante, our only guide in choosing an
exchange rate index is its empirical performance. The
results, however, suggest that there was no notably
superior index. Thus, the new indexes do not appear
to add much, if anything, to our knowledge about the
response of trade flows to changes in the exchange
rate.17
OUT-OF-SAMPLE FORECAST ERRORS
An alternative criterion for choosing among alterna
tive exchange rate indexes is their relative perfor
mance in predicting trade flows beyond the range of
data used to estimate the coefficients for equations 1
and 2. This out-of-sample predictive criterion empha
sizes another practical application of an exchange rate
index: if the actual path followed by the dollar’s value
’'Testing for the temporal stability of the estimated exchange rate
elasticity for the various indexes during the floating exchange rate
period may indicate the superiority of one or more indexes over the
others. Given the lack of parsimony in the parameterization of the
estimated equations and the relatively short sample period, how
ever, this investigation could not be performed here.
A look at the individual export forecast errors in
chart 3 allows several interesting comparisons. First,
the performances of the FRB, SDR and 7-Gr indexes are
noticeably and consistently better than those of the
other three indexes. Second, the relatively poor perfor
mance of the X-101 index stands out clearly: it consis
tently underpredicts exports.
The two Morgan Guaranty indexes also perform
relatively poorly, generally overpredicting exports.
Surprisingly, however, the broader Morgan index (MG40) performs just about as badly as the narrow Morgan
index (MG-15). If broader indexes genuinely represent
more accurate measures of the foreign exchange value
of the dollar, the MG-40 should have outperformed the
MG-15. Moreover, the FRB index, whose coverage is
similar to the MG-15, outperformed both Morgan
indexes.'"
The out-of-sample error statistics for the U.S. non
petroleum import equations tell a similar story. The
narrow SDR and FRB indexes have the smallest MAE
and RMSE values, while error statistics for the broader
X-101 and MG-40 indexes are several times larger. In
fact, as table 6 indicates, the X-101 index, which has
the broadest coverage of trade flows, generally has the
worst forecasting performance for the indexes exam
ined. Conversely, the narrowest index, the SDR, has
the best error statistics for imports and second-best
'“Since the FRB and MG-15 indexes differ primarily in the use of
multilateral (FRB) vs. bilateral (MG-15) weights, it may be that the
weighting scheme used is more important than the countries in
cluded in the index. The use of different price indexes to deflate the
FRB and MG-15, however, may also affect the results.
13
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
C h a rt 3
O ut-of-S am p le Errors for Export Equations
1984
1985
for exports. Error statistics for the 7-Gr and FRB in
dexes are only slightly worse than those for the SDR.
The individual import forecast errors in chart 4,
while less disparate than those of the export equa
tions, offer similar comparisons. Although all ex
change rate indexes underpredict imports by the end
of the forecast period, the FRB and SDR indexes gener
ally exhibit the best performances; the performance of
the X-101 index is generally the worst, with the two
Morgan indexes and the 7-Gr somewhere in between.
1986
THE RESULTS FROM NONNESTED
TESTS
The fundamental question is whether the new in
dexes contain more (or better) information about the
impact of changes in the dollar's value on trade flows.
If the trade equations specified for the old and new
indexes were nested, testing whether the new indexes
add significantly to the information of the old indexes
would be a straightforward operation.20The specified
relationships between exports and imports and vari
ous measures of the exchange rate, however, are not
nested and require an alternative approach to hypoth
esis testing.
Overall, the out-of-sample results in table 6 and
charts 3 and 4 provide no support for the notion that
increasing the number of currencies in an exchange
rate index improves its out-of-sample forecasts of
trade flows. If anything, the results here suggest that
the narrow indexes perform marginally better.19
The test employed to investigate whether the new
indexes add significantly to the information in the old
19lt is possible that including more currencies in an index adds noise to
the measure from superfluous currency movements largely unre
lated to trade.
“ A nested test is one in which all of the information contained in the
null hypothesis is also contained in the alternative. For example, the
standard t-test that an estimated coefficient is statistically different
from zero is a nested test.
http://fraser.stlouisfed.org/
14
Federal Reserve Bank of St. Louis
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
C h a rt 4
O u t-o f-S a m p le Errors for Import Equations
1984
1985
indexes is the J-test.21 One specification of the trade
equation is hypothesized to be true and a second
specification, using a different exchange rate measure,
is hypothesized as the alternative specification. The Jtest requires estimating the alternative specification
and generating a vector of fitted values for the depen
dent variable (exports or imports). The specification
proposed under the null hypothesis is then estimated
with this vector of fitted values from the alternative
!,See Davidson and MacKinnon (1981). The J-test establishes one
specification as the null hypothesis, then tests whether an alterna
tive specification adds to the explanatory power of the specification
under the null hypothesis. For example, assume that we want to test
the specification,
H0: y = f(x, z) + e„
against the alternative,
1986
specification as an additional explanatory variable. If
the alternative measure of the exchange rate adds
explanatory power to the specification containing the
hypothesized “true” measure, the estimated coef
ficient of the vector of predicted values will be signifi
cantly different from zero. The conclusion drawn from
this result is that the specification with the alternative
exchange rate index is preferred to that with the
hypothesized true index. To complete the test, the
hypothesized true (null) and alternative indexes are
reversed and the same procedure is repeated. The
initially specified alternative can be preferred to the
null only if the null specification does not add explan
atory power to the alternative in the second stage of
the test. If the null does add explanatory power in the
second stage, then the test does not allow the choice
of one specification over the other.
H,:y = g(w, z) + e2.
The J-test is conducted simply by estimating
y = (1 — <f>)f(x, z) + <t>g +
e
,
where g is the vector of predicted y under the alternative hypothesis,
and testing whether ct> is significantly different from zero using a
conventional t-test. If the data are better fit to f(x, z), then 4> should
not be different from zero. Alternatively, if <(> is different from zero,
then g(w, z) adds to the explanatory power of f(x, z). To complete the
test, the process is repeated by reversing the null and alternative
hypotheses and repeating the same testing procedure.
15
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Table 7
J-Test Results for Export Equations
Exchange Rate Index
Under Null Hypothesis
Exchange Rate Index Under Alternative Hypothesis
SDR
SDR
FRB
MG-15
7-Gr
1.51
2.14*
MG-40
X-101
1.75
4.35*
—
2.14*
FRB
MG-15
7-Gr
MG-40
X-101
3.63*
—
4.46*
3.09*
—
3.76*
1.37
1.99*
—
4.29*
3.00*
1.77
2.15*
1.20
2.49*
3.09*
—
0.97
2.61*
5.56*
—
1.72
1.27
1.91
3.19*
1.75
5.85*
4.20*
2.10*
4.04*
"Statistically significant at the 5 percent level.
Table 8
J-Test Results for Import Equations
Exchange Rate Index Under Alternative Hypothesis
Exchange Rate Index
Under Null Hypothesis
SDR
SDR
FRB
0.42
—
MG-40
1.23
2.12*
1.87
X-101
2.80*
MG-15
7-Gr
FRB
MG-15
7-Gr
MG-40
X-101
7.18*
—
3.01*
-0.32
—
1.57
2.40*
6.98*
0.95
5.66*
—
3.93*
0.27
3.11*
1.16
—
2.44*
5.95*
1.11
6.23*
2.70*
5.78*
5.81*
2.61*
4.83’
4.39*
4.66*
0.71
3.85*
—
"Statistically significant at the 5 percent level.
Tables 7 and 8 present t-statistics for the J-tests
conducted. The left-hand columns of the tables list
the exchange rate indexes hypothesized as "true”
under the null hypothesis. The other columns show tstatistics, which indicate whether the specification
with an alternative exchange rate index adds signifi
cant information to the specification employing the
index in the left-hand column.
The results in table 7 for the export equations are
ambiguous in the sense that no index or set of indexes
clearly dominates the others. Of the 30 t-statistics
reported, 20 are significant and four more are nearly
significant at the 5 percent level. Moreover, there are
no consistent patterns in the t-statistics. For example,
each alternative index adds significantly to the infor
mation in the SDR index but the SDR index adds only
http://fraser.stlouisfed.org/
16
Federal Reserve Bank of St. Louis
to three of the five alternatives. Each alternative index
similarly adds to the X-101 index and the X-101 adds
only to three of the remaining five. In contrast to the
SDR results, however, the three indexes to which the
X-101 adds information are not the same three to
which the SDR index adds information. The remaining
results in table 7 also lack the transitivity that would
permit drawing any conclusions about a dominant
index or set of indexes with greater information
content.
The results for the import equations in table 8,
however, yield clearer conclusions. The FRB index
adds to the information of all other indexes in the
import equation, while none of the other indexes adds
to the information in the FRB measure. On this J-test
criterion, the 7-Gr index has the second-best perfor
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
mance, with only two indexes (FRB and SDR) adding to
its information and the 7-Gr adding to the information
of all measures but the FRB index. Consistent with
earlier results, the two indexes with the broadest cov
erage of currencies, the X-101 and MG-40, are domi
nated by the other indexes: all five indexes add to the
information of the X-101 and four of five contribute to
the MG-40. Consequently, the answer to the simple
question, “Does greater coverage of currencies, per se,
add to the information content of an exchange rate
index?” is clearly no.
CONCLUSIONS
Several new indexes of the dollar exchange rate have
been developed in the past year. The justification for
their construction was that the distribution of U.S.
trade flows had changed dramatically since the 1970s
and, for that reason, existing exchange rate indexes,
based on trade with industrialized countries, did not
reflect the recent increased importance of trade with
LDCs and Pacific-rim countries.
The key test of an exchange rate index, however, is
not its intuitive justification but its practical utility. A
consistent set of tests applied to the major existing
indexes indicated that the new broader measures
performed no better than the old measures. In fact, on
the basis of forecasting performance, they performed
worse than the existing, more narrowly based ex
change rate indexes. Additional tests, which exam
ined the marginal information content of the new
indexes, also found a traditional, narrow measure of
the dollar's value to dominate the newer indexes.
Hence, the new exchange rate indexes do not appear
to provide better answers to old questions about trade
flows.
REFERENCES
Bank of Japan, Research and Statistics Department. "On Effec
tive U.S. Dollar Exchange Rate Indices,” Special Paper No. 147
(December 1986).
Batten, Dallas S., and Michael T. Belongia. “The Recent Decline
in Agricultural Exports: Is the Exchange Rate the Culprit?” this
Review (October 1984), pp. 5-14.
Batten, Dallas S., and Daniel L. Thornton. “ How Robust Are the
Policy Conclusions of the St. Louis Equation?: Some Further
Evidence,” this Review (June/July 1984), pp. 26-32.
Belongia, Michael T. “ Estimating Exchange Rate Effects on Ex
ports: A Cautionary Note,” this Review (January 1986), pp. 5-16.
Clark, Peter B. “The Effects of Recent Exchange Rate Changes
on the U.S. Trade Balances,” in Peter B. Clark, Dennis E. Logue
and Richard J. Sweeney, eds., The Effects of Exchange Rate
Adjustments, the proceedings of a conference sponsored by
OASIA Research (Department of the Treasury, 1974), pp. 20136.
Cox, W. Michael. “A New Alternative Trade-Weighted Dollar Ex
change Rate Index,” Federal Reserve Bank of Dallas Economic
Review (September 1986), pp. 20-28.
Davidson, R., and J. G. MacKinnon. “ Several Tests for Model
Specification in The Presence of Alternative Hypotheses,"
Econometrica (May 1981), pp. 781-93.
Dutton, John, and Thomas Grennes. "The Measurement of Effec
tive Exchange Rates Appropriate for Agricultural Trade,” Depart
ment of Economics and Business, North Carolina State Univer
sity (November 1985).
Goldstein, Morris, and Mohsin S. Khan. "The Supply and Demand
for Exports: A Simultaneous Approach,” Review of Economics
and Statistics (May 1978), pp. 275-86.
Hervey, Jack L., and William A. Strauss. “The International Value
of the Dollar: An Inflation-Adjusted Index,” Federal Reserve Bank
of Chicago Economic Perspectives (January/February 1987), pp.
17-28.
Morgan Guaranty Trust Company. “ Dollar Index Confusion,”
World Financial Markets (October/November 1986), pp. 14-19.
Rosensweig, Jeffrey A. “A New Dollar Index: Capturing a More
Global Perspective,” Federal Reserve Bank of Atlanta Economic
Review (June/July 1986), pp. 12-22.
Spitaller, Erich. “Short-Run Effects of Exchange Rate Changes on
Terms of Trade and Trade Balance,” IMF Staff Papers (June
1980), pp. 320-48.
17
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Has Programmed Trading Made
Stock Prices More Volatile?
G. J. Santoni
I f there must be madness, something may be said fo r having it on a heroic scale.
— John Kenneth Galbraith, The Great Crash, p. 69.
Y people believe that stock prices have
become considerably more volatile in recent years,
■typical descriptions have characterized stock market
behavior as “careening through” trading ranges, sub
ject to “wild gyrations,” and the product of “unex
pected insanity.”1
The presumed source of the volatility is a trading
strategy called “programmed trading.”2This strategy,
which essentially involves trading on small and short
lived price differences for the same group of stocks in
the spot, futures and options markets, is not new. The
introduction of stock index futures around 1982 and
the application of computer techniques to monitor
price differences and trigger trades between markets,
however, are novel. These two innovations have re
duced the cost of transacting among the markets,
which has resulted in increased trading activity. The
increased activity, the size of the trades made by
individual players and the behavior of stock prices on
days when stock index futures and options contracts
G. J. Santoni is a senior economist at the Federal Reserve Bank of St.
Louis. Thomas A. Polimann provided research assistance.
’See “Abreast of the Market” (1987) and Clark (1987). Other exam
ples can be found in the Wall Street Journal on the following dates:
January 16; January 20; January 23.
2See, for example, Stoll and Whaley (1987), Laderman and Frank
(September 29, 1986); Laderman, et. al (April 7, 1986); Stoller
(February 9,1987) and McMurray (February 12, 1987).
18
mature (triple witching days) have led many observers
to conclude that this trading strategy has increased
stock price volatility.3
The alleged increase in volatility has led both to
closer scrutiny by the Securities and Exchange Com
mission and to calls for legislative action.4In response
to these concerns, the Chicago Mercantile Exchange
voted recently to impose a 12-point daily price change
limit on its Standard and Poor's 500 stock index fu
tures contract and to move the expiration of the con
tract from the close to the opening of trading on
quarterly expiration days. The latter was also adopted
by the Chicago Board of Options Exchange for its
Standard and Poor’s 500 stock index option.
This paper examines the principles of trading be
tween the spot and futures markets for stocks and the
3See, for example, Laderman, et. al. (April 7,1986) who assert that
"Program trading, by its very nature, causes wild swings in the
markets.. . ’’ p. 32; and “ Program trading is a mixture of irony and
mystery. It breeds volatility.” p. 33. “Triple witching” is a reference to
the third Fridays of March, June, September and December. Stock
index futures contracts and options on the futures expire on these
days.
"See Laderman and Frank (September 29, 1986), p. 102. Stoller
(February 9, 1987) not only attacks programmed trading but all
speculative activity. Borrowing from John Kenneth Galbraith (1955),
he notes that “Wall Street, in these matters, is like a lovely and
accomplished woman who must wear black cotton stockings, heavy
woolen underwear, and parade her knowledge as a cook because,
unhappily, her supreme accomplishment is as a harlot.” p. 24.
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Glossary of Terms
“Arb”: Arbitrageur. A person who simultaneously
buys and sells the same good in two different
markets.
Basis: The difference between the price of a futures
contract and the price of an equal quantity of the
cash instrument.
Basis Point: 1/100 of one percent.
Bear Straddle: A spread in which the instrument
with the nearby maturity is sold and a similar
instrument with a more distant maturity is
purchased.
Bull Straddle: A spread in which the instrument
with the nearby maturity is purchased and a
similar instrument with a more distant maturity
is sold.
CBT: Chicago Board of Trade. This exchange trades
the Major Market Index Futures (MMI).
Hot Money: The money (wealth) tied up in pro
gram trading accounts.
IMM: International Monetary Market. This Chicago
exchange trades the Standard and Poor’s 500
Index futures.
Interest Elasticity: A ratio of the percentage
change in the price of a financial instrument to
claim that stock prices have become more volatile
since stock index futures were first introduced. In
addition, the paper examines whether programmed
trading has contributed to increased stock price vola
tility.
The paper focuses on stock index futures rather
than options because the market for options has been
less active than the market for futures so the concerns
noted above have focused on the more active futures
market.5
5See Belongia (1983) for a general discussion of options markets.
Kawaller (1986), p. 1 and 3, gives a general description of options on
financial futures. Black and Scholes (1973) present a formal analy
sis of option trading. Cinar (1987) discusses the effect of options on
stock prices.
the percentage change in the interest (discount)
rate.
Unwind: To reverse an earlier transaction.
KCBT: Kansas City Board of Trade. The exchange
trades the Value Line Index Futures.
NYFE: New York Futures Exchange. This exchange
trades the New York Stock Exchange Index
Futures.
Programmed trading: The use of computer pro
grams to analyze and trigger trading between
stock index futures contracts, options on the
index and the basket of stocks contained in the
index.
Spreading: The simultaneous purchase and sale of
two similar financial instruments of different
maturity.
The .01 Effect: Measures the change in the dollar
value of an instrument that results from a change
of one basis point in its yield. This depends on
the interest elasticity of the instruments.
Triple Witching Hour:The time when options and
futures on stock indexes expire. This happens on
the third Fridays of March, June, September and
December.
STOCK INDEX FUTURES CONTRACTS
Trading in stock index futures contracts was first
introduced by the Kansas City Board of Trade on
February 24, 1982. In April of the same year, the Chi
cago Mercantile Exchange, began trading a futures
contract based on the Standard and Poor’s Index of
500 common stocks. The introduction of both con
tracts was successful. By the end of 1982, daily trading
volume in the Standard and Poor’s futures contract,
the most successful of the two, was running at about
20,000 contracts.6
The success of the first two contracts induced other
major exchanges to introduce similar instruments.
6See Schwarz, Hill and Schneeweis (1986), pp. 87-88.
19
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Table 1
Stock Index Futures Contracts
Underlying
Instrument
Major Market
Index
Value Line
Index
S and P
500 Index
New York
Composite Index
Underlying
Instrument
Exchange
Trading
Hours
Contract
Size
Months
Traded
Price
Quoted In
Minimum
Fluctuation
Value of
Minimum Fluctuation
CBT
8:15-3:15
Index
times $250
monthly
Index
points
.05
$12.50
KCBT
9:00-3:15
Index
times $500
3,6,9,12
Index
points
.05
$25.00
IMM
9:00-3:15
Index
times $500
3,6.9,12
Index
points
.05
$25.00
NYFE
10:00-4:15
Index
times $500
3,6,9,12
Index
points
.05
$25.00
Last Trading
Day
Margins
Initial'
Average Daily
Volume'
Major Market
Index
3rd Friday of
contract month
$4,500
18,000
Value Line
Index
Last business day
of contract month
$6,500
4,000
S and P
500 Index
3rd Friday of
contract month
$6,000
60,000
New York
Composite Index
3rd Friday of
contract month
$3,500
15,000
'As of 1985.
The New York Futures Exchange, a unit of the New
York Stock Exchange, began trading a futures contract
based on the New York Stock Exchange Composite
Index in September 1983. Most recently, in July 1984,
the Chicago Board of Trade began trading a futures
contract based on the Major Market Index.
The Standard and Poor’s 500 futures contract,
which has been adopted by institutional investors, has
experienced the most success. For example, the esti
mated volume of trades in this contract was about
115,000 on April 14 of this year. The average daily
trading volume of the S&P 500 contract has been
running at about 4 to 5 times the daily trading volume
in the contracts based on both the New York Stock
Exchange and Major Market indexes and about 15
times the contract based on the Value Line Index.7
7ln addition, the Chicago Mercantile Exchange is currently trading a
futures contract based on 100 stocks in the Standard and Poor’s 500
Index (the “ Mini” S&P). Trading volume in this contract is very thin
compared with those mentioned in the text.
20
Characteristics o f the Contracts
A futures contract on a stock index is an agreement
between a seller (short position) and buyer (long posi
tion) to a cash settlement based on the change in the
stock index’s value between the date the futures con
tract is entered by the two parties and some future
date.8Table 1 summarizes some of the details regard
ing each of the stock index futures contracts men
tioned above (see the shaded insert on page 22 for a
general discussion of futures).
Table 2 presents the trading ranges for futures con
tracts on the Standard and Poor’s 500 Index (S&P
Futures) on February 6,1987. The delivery dates of the
contracts traded were the third Fridays of March, June
and September of 1987. Notice that open interest is
8See Schwarz, Hill and Schneeweis (1986), p. 9. Stock index futures
differ from commodity futures in that settlement of the former is
always by cash. Stock index futures contracts make no provision for
physical delivery of the stocks that are included in the index.
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Table 2
Trading Ranges for the Standard and Poor’s 500 Futures
Contract, February 6 , 19871__________________________
S&P 500 Index (CME) $500 times index
Month
Open
High
Low
Settle
Change
Open
interest
March
282.50
283.20
280.35
281.20
-1 .1 5
104,412
June
284.10
284.80
281.90
282.80
-1 .1 5
7,131
September
284.90
285.90
283.40
284.10
-1 .1 0
226
Estimated volume 85,705
S&P 500 index for stocks traded in the spot market closed at 280.04
'Wall Street Journal, February 9,1987.
greatest in the March (nearby) contract. The market is
relatively thin for the more distant contracts. The
March contract opened at 282.50 and traded in the
range of 283.20 —280.35 during the day. It closed at
281.20. Since the value of the futures contract is $500
times the index, the value of the March contract fluc
tuated between a high of $141,600 and a low of
$140,175.
The value of the contract at the close was $140,600
( = $500 X 281.20) which represented a decline in its
value of $575 from its close at $141,175 (= $500 x
282.35) on the previous day. Traders who maintained
long positions in this contract from the close on Feb
ruary 5 through the close on Februaiy 6 lost $575 (=
$500 X 1.15) per contract and this amount was de
ducted from their margin accounts at the close of
business on the 6th. The reverse was true for traders
who maintained short positions over the time interval.
The Basis
In addition to the information about the futures
contracts, table 2 also indicates that the Standard and
Poor’s 500 Index for stocks traded on the spot market
(S&P Index) closed at 280.04 on February 6, 1987.
Notice that this amount is different than the amounts
recorded at the close for all three of the S&P Futures
contracts. The difference between the values of the
S&P Futures contracts and the S&P Index is called the
basis; it can be measured in dollars or index points.
For example, at the February 6 close, the basis for the
March contract was about $580 (= $500 [281.20 —
280.04]) or 1.16 index points ( = 281.20 - 280.04).9The
basis differs systematically across the three futures
contracts; it is larger for more distant delivery months.
The qualitative relationship between the prices of the
S&P Index and the three S&P Futures contracts shown
in table 2 is generally the one that is observed; that is,
the value of the S&P Futures is larger than the S&P
Index, and the difference increases for more distant
contracts. A similar qualitative relationship exists be
tween the other stock index futures contracts dis
cussed above and their respective indexes.10
WHAT DETERMINES THE BASIS?
Whenever the basis deviates substantially from its
equilibrium (or theoretical) value, profitable trading
opportunities exist and arbitrageurs will attempt to
capture them. Program trading is a method of discov
ering and exploiting these profit opportunities. Since
the opportunities can arise when the equilibrium ba
sis changes, it is important to understand how the
equilibrium basis is determined and what things
cause it to change.
9The basis is “about” $580 because the New York Stock Exchange
closes at 4:00 p.m. Eastern Standard Time while the International
Monetary Market closes 15 minutes later at 3:15 p.m. Central
Standard Time.
10The Value Line Index may represent an exception to this general
statement because of the averaging method used to calculate it.
See Modest and Sundaresan (1983), pp. 19-20.
21
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Futures: A General Discussion
What is a Futures Contract?
A futures contract is an agreement between a
seller and a buyer to trade some well-defined item
(wheat, corn, Treasury bills) at some specified fu
ture date at a price agreed to now, but paid in the
future at the time of deliveiy.
There are three prices that must be kept straight
when discussing these contracts: the spot price, the
forward price and the futures price. The spot price
is the price of the item today for delivery today. The
price of the item in the future for deliveiy then is
called the forward price. The price of the item today
for delivery in the future is called the futures price.
The futures price is specified in the futures con
tract. Essentially, it is a prediction of the forward
price at maturity of the contract.1
The Relationship Between Spot and
Futures Prices
The futures price of a commodity is equal to the
spot price plus the cost of storage, insurance and
foregone interest earnings associated with holding
the good over the interval of the contract. A similar
relationship exists between the spot and futures
prices of financial instruments (like stock index
futures). Since the storage and insurance costs of
holding these financial instruments is veiy low,
however, the spread between spot and futures
prices is largely determined by the interest cost.2
ward price of the item. Of course, because it is a
guess, it typically will be wrong.3When the forward
price that is realized is higher than the futures price
that was agreed on, the buyer o f the futures con
tract gains because he can purchase the item at the
previously agreed upon futures price and immedi
ately sell it at the higher current spot price. The
seller of the futures contract loses because he must
sell the item whose current spot price is higher
than the price he previously agreed to sell at when
he entered the futures contract. The reverse occurs
when the forward price that is realized is less than
the futures price that was agreed upon.
Some Common Criticisms o f
Futures Markets
It may appear that futures markets are simply a
convenient form of gambling on forward prices.
This has been a common criticism of futures mar
kets along with the allegation that trading in futures
increases price variation in the spot market.4Specu
lative bets about price changes, however, are not
unique to futures market trading. Economic deci
sions to buy or sell any storable good, by their
nature, are speculative bets about the future course
of the price. Furthermore, futures markets serve
some valuable social functions such as allocating
the consumption of storable goods over time as
well as providing a means, through hedging, to
reduce the risk of unexpected price changes.5
It Pays To Be Right
Because futures markets typically are very active
and are open to virtually anyone who can meet
fairly modest capital requirement rules, futures
prices represent an aggregate guess about the for-
3While typically wrong, the futures price will not consistently
under- or over-predict the forward price. That is, the futures price
is an unbiased predictor. If this were not true, it would be possible
for traders to profit by exploiting the bias which would quickly
eliminate it. See Fama (1970).
'See, for example, Working (1977), pp. 25-31.
“See Working (1977), p. 293; Cagan (1981), p. 178; and Green
(1986), p. 80, for a discussion of these common criticisms of
futures markets. This paper examines the second allegation for
the case of stock index futures.
2See, for example, Schwarz, Hill and Schneeweis (1986), pp.
326-46; Figlewski (1984), pp. 658-60; Cornell and French
(1983), pp. 2-4; and Modest and Sundaresan (1983), pp. 22-23.
5For discussion of the social functions fulfilled by futures markets
see Working (1977), pp. 25-31 and pp. 267-97; Alchian and
Allen (1977), pp. 132-39; and Cagan (1981).
22
FEDERAL RESERVE BANK OF ST. LOUIS
The equilibrium difference between the S&P Index
and S&P Futures (the equilibrium basis) is related to
the equilibrium differences between the spot and fu
tures prices of each of the stocks in the Standard and
Poor’s Composite Index." Consequently, understand
ing the basis for individual stocks is helpful in analyz
ing the basis for S&P Futures contracts.
The Cost o f Carry
In equilibrium, the difference between the spot
price of a stock and its expected price at some future
date is determined by the cost of holding the stock
(termed "carrying the stock forward” ) from the
present to the future date. This is called "the cost of
carry."
As mentioned above, the storage and insurance
costs of carrying stock is very low. However, a person
who purchases stock gives up the rate of return he
would have received if he invested in the next best
available alternative. Economists call this foregone
rate of return the opportunity cost of the investment;
finance analysts call it the cost of capital. Both agree
that it is equal to the market rate of interest (return)
adjusted for the systematic risk associated with hold
ing the particular stock.12
In order to focus on one thing at a time, suppose the
stock that is being carried forward pays no dividends
and that the cost of capital is 12.5 percent per year.13
Assume that it is now March 20, 1987 and the trader
wants a forecast of the stock’s forward price on June
19 — 91 days from now. If the spot price of the stock on
March 20th is $50, the foregone income that could be
earned by investing the $50 at 12.5 percent for three
months is $50 (1.125)23 — $50 = $1.49; this is the cost of
carry. The March 20th spot price plus the cost of carry
is a forecast of the stock's forward price on June 19 (91
days from now). In this example, the forecast of the
stock’s price on June 19th is $51.49 ( = $50.00 + $1.49).
"The discussion focuses on the Standard and Poor’s index not only
for convenience but also because the Standard and Poor’s futures
contract is the most widely traded; it accounts for about 75 percent
of all trading in stock index futures. See, Wall Street Journal (March
2,1987).
12See Brealey and Meyers (1984), p. 133. Systematic risk is given by
fj, which is a measurement of the sensitivity of the investment's
return with respect to the market return. Roughly, (5 is the percent
age change in the present value of the investment project divided by
the percentage change in some market index of capital values such
as the Standard and Poor’s composite index ibid., pp. 166-67. The
cost of capital, i, is calculated as i = fi(im- i() + i(, where imand i, are
the market and risk free rates of return.
13See Cornell and French (1983), Modest and Sundaresan (1983)
and Figlewski (1984) for a formal analysis of the cost of carry.
MAY 1987
The Cost o f Carry with Dividends
Computing the cost of carry is only slightly more
complicated if the stock pays dividends. Suppose that
the stock in the previous example is scheduled to pay
a dividend of $.50 on April 21, 1987. The dividend
reduces the cost of carry by slightly more than $.50
because the dividend paid on April 21 can be invested
between April 21 and June 19. Consequently, the value
of the dividend as of June 19 is slightly higher than
$.50.14For the example considered, the cost of carry is
$50 (1.125)-25 - $.50 (1.125)167 - $50 = $.98. Notice that
the dividend payment reduces both the cost of carry
(from $1.49 to $.98) and the March 20th forecast of the
stock’s price on June 19th (from $51.49 to $50.98).
The Cost o f Carry Is Lower fo r Nearby
Delivery Dates
This discussion helps explain why the basis ob
served in table 2 is lower for futures contracts with
nearby delivery dates. Because the holding period is
shorter, the interest earnings foregone are less for
nearby delivery dates. Similarly, as each contract ap
proaches its delivery date, the cost of carrying the
stock shrinks for the period remaining until delivery,
other things the same; the cost of carry is zero on the
delivery date. This is shown in figure 1. Figure 1 as-
Figure 1
The C ost o f C arry
Ct = Pt( 1 + i)(T- ,! - D t + „ ( 1 + i) lT - ' — >_P,
Where: C,
T
i
Pt
Dt + a
=
=
=
=
=
the
the
the
the
the
cost of carry at t
delivery date
cost of capital
stock’s spot price at t
expected dividend receipt o days from t
14This adjustment may seem trivial. When one is computing the basis
for a stock portfolio that runs into the millions of dollars, as is the
case for programmed trading, however, this adjustment can be very
important. Notice that .167 = 60/360 where 60 is the number of
days between the dividend receipt on April 21 and June 19.
23
FEDERAL RESERVE BANK OF ST. LOUIS
sumes that the cost of capital (i) and the dividends (D)
the stock is expected to pay are unchanged during the
holding period.
The Cost o f Carry Is Uncertain
Since expected dividends can change during the
holding period, the cost of cany is not known with
certainty. The only thing known with certainty is that
the cost of carry will be zero on the day the futures
contract is scheduled for delivery.
A change in the expected dividend will cause the
line showing the cost of cany in figure 1 to rotate
through the point labeled T. An increase in D causes
the cost of cany to rotate downward, while a decrease
in D causes the cost of cany to rotate upward.15
The Cost o f Carry and the Basis
The expected cost of carry and the basis are closely
related.16To illustrate this for a simple case, suppose
for a moment that the S&P Index contains only one
share of stock. Suppose that the March 20th spot price
of the share is $50 (the level of the index is 50) and that
,5The cost of carry generally will vary with changes in the cost of
capital, i. Whether a direct or indirect relationship exists, however, is
problematic. To see this, let
(1) E(t)P(T) = F(t) = PfDe'1- 8"1-"
(2) P(t) = - ^ L
(3) B(t) = F(t) - P(t).
where
E(t)P(T) = The period t expectation of the forward price
atT.
F(t) = The futures price in period t of a contract dated
for delivery at T.
P(t) = The spot price in period t.
i = The cost of capital.
8 = The expected dividend rate.
E(t)-ir = The period t expectation Of the perpetual stream
of profits (i t ) assumed to be of constant amount
in each period.
B(t) = The basis in period t.
Substitution gives
B(t)
dl
the expected cost of carry is $1.50 per share for the
next three months (from March 20th to June 19th). If
the current price of the S&P Futures contract dated for
June delivery is $52.00, the $2.00 basis (= $52.00 —
$50.00) exceeds the $1.50 expected cost of carry. The
arbitrageur will sell (go short in) June futures at a price
of $52.00 per contract and buy (go long in) spot shares
of the stock at $50.00. He does this because he expects
the price of the June futures to fall to $51.50 (the spot
price plus the expected cost of carry). At that price, he
can cover his futures position (by purchasing a June
futures) at a cost of $51.50 per contract. His gain is $.50
per contract — the difference between the sale price of
the futures contract ($52.00) and the cost of covering
the contract ($51.50).17
The arbitrageur’s long, spot position serves to hedge
his short, futures position against unexpected
changes in the price of the stock. For example, sup
pose both the June futures price and the spot price
rise by $3.00 immediately after the arbitrageur sells the
futures and buys the stock spot. The June futures
price rises to $55.00 per contract and the spot price
increases to $53.00 per share. After the price change,
the basis ($2.00 = $55.00 — $53.00) still exceeds the
expected cost of carry ($1.50) by $.50 so the arbitrageur
expects the price of the June futures to fall to $54.50
per contract.18 At that price he will cover his short
position at a loss o f $2.50 per contract (= $52.00 —
$54.50). This loss, however, is more than offset by his
$3.00 per share gain ( = $53.00 — $50.00) on his spot
position. His net gain is $.50 (= $3.00 — $2.50) — the
same as in the previous case. By hedging in the spot
market, the arbitrageur protects the expected gain
from unexpected changes in the price of the stock.
On the other hand, suppose the price of the June
futures is $51.00. In this case, the $1.00 basis ( = $51.00
— $50.00) is less than the $1.50 expected cost of carry.
The arbitrageur will short the stock and go long in the
June futures. The arbitrageur expects the price of the
June futures to rise to $51.50 per share. At that price,
he will sell his June futures contract at a gain o f $.50
per contract (= $51.50 - $51.00). Again, his short spot
position hedges his expected gain against unexpected
changes in the price of the stock. Since virtually any-
E(t)u [ec-sirr-o- 1]
aB(t) _
di
MAY 1987
E(t)ir (T-Qe"-*^-"
E(t)Tr
i2
1
J
i
= P(t) {e fl-^ -'iK T -t) - 1/i] + 1/i}^0.
■>
16See, for example, Cornell and French (1983), pp. 2-3. The example
assumes that the equilibrium spot price is given so that the futures
price adjusts to the cost of carry. In fact, spot and futures prices are
determined simultaneously.
http://fraser.stlouisfed.org/
24
Federal Reserve Bank of St. Louis
’7The arbitrageur always has the alternative of holding the stock until
(the June delivery date of the futures contract at which time the stock
is sold and the proceeds are used to settle the futures contract.
Since the arbitrageurs’ investment in the stock is expected to be
$51.50 per share as of the settlement date (= $50.00 + $1.50),
expected profits are $.50 per share.
18ln fact, if the interest rate does not change, the expected cost of
carry will rise slightly because of the higher spot price.
FEDERAL RESERVE BANK OF ST. LOUIS
Figure 2
The Cost o f Carry and Transaction Costs
MAY 1987
gous to the spot price of the stock in the previous
discussion and the S&P Futures multiplied by $500
minus the S&P Index multiplied by $500 is the basis.19
In principle, the cost of carry is calculated the same
way as for an individual stock. There are two impor
tant practical differences, however.
First, because the S&P Index represents a welldiversified basket of stocks, it typically is assumed that
the risk of unanticipated changes in the value o f this
basket is roughly equal to the market’s risk. Conse
quently, the cost of capital for the S&P Index is the
market rate o f return.20
A profitable trading opportunity exists when:
1 ) The basis is greater than the cost of carry plus transaction cost
(C + K)
2) The basis is less than the cost of carry minus transaction cost
(C -K )
Where:
C = the cost of carry
K = transaction cost
one can take advantage of these trading opportunities,
large deviations of the basis from the cost of cany do
not persist.
A second important practical difference is that the
trader must track the dividend policies of 500 com
panies and the dates on which the shares trade exdividend in order to compute the cost of carry. These
calculations must be made quickly and accurately
because profitable trading opportunities that result
from differences between the basis and cost o f carry
persist only for a short time.
Because both the monitoring and transaction costs
increase with the number of companies included in
the arbitrage portfolio, traders do not track all 500
stocks in the S&P Index. Instead, they identify a subset
of the 500 stocks whose combined value has closely
followed the value of the index in the past.21 Thus
traders accept some additional risk because the values
of their narrower portfolios are unlikely to move pre
cisely with the S&P Index. The added risk is accepted
to reduce the expense of tracking the cost of carry for
the broader portfolio.
Small differences between the basis and cost of
carry may persist, however, if the transactions cost of
making the appropriate trades is greater than the
expected gain. In terms of figure 1, transaction costs
can be represented by bands around the line repre
senting the cost of carry. This is shown in figure 2. The
vertical distance between the solid line and the
dashed lines represent the transaction cost. If the
basis deviates from the cost of carry but remains
within the bands (as represented by point A, for exam
ple), no profitable arbitrage trading is possible. If the
basis moves outside the bands (to point B, for exam
ple), arbitrageurs will exploit the profitable trading
opportunities caused by this large discrepancy. The
trading will continue until the basis has been driven
back within the bands.
INDEX FUTURES AND THE
VOLATILITY OF STOCK PRICES
TRADING STOCK INDEX FUTURES
Various commentators have alleged that trading be
tween the stock index futures market and the spot
The analysis discussed above is directly applicable
to trading among the stocks that make up the S&.P
Index and the S&P Futures contract. Rather than one
stock, however, the S&P Index represents a basket of
500 stocks. The S&P Index multiplied bv $500 is analo
Of course, computer programs are another way to
reduce the expense of calculating and continuously
updating the cost of carry as new information be
comes available. “Program trading” refers to computer
programs that compute the cost of carry and signal
profitable trading opportunities. Programmed trading
is a less costly (more efficient) method of exploiting
profitable trading opportunities between the spot and
futures markets.
’“Recall that the value of an S&P Futures contract is $500 times the
index. See table 1.
20That is, p is assumed to equal 1 so that i = p(im- i,) + i, = im.
21See Schwarz, Hill and Schneeweis (1986), p. 91.
25
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Table 3
A Comparison of Percentage Changes in the Standard and Poor’s 500 Index
Pre- and Post-April 1982
Panel A: Means and Standard Deviations of %AS&P 500 Index
Pre-April 1982
Post-April 1982
Mean
Standard
Deviation
Differences
in Means
1.68
.306
1.74
.176
1.07
.95
.069
.88
.065
1.17
Period
Mean
Standard
Deviation
Weekly’
.130
Daily2
.004
Ratio of
Variances
Panel B: Means and Standard Deviations of %AS&P 500 Index: Settlement vs. Nonsettlement Days
Settlement Days
Nonsettlement Days
Period
Mean
Standard
Deviation
Mean
Standard
Deviation
Differences
in Means
Ratio of
Variances
Daily3
.150
.97
.069
.88
.081
1.21
where: %AS&P 500 Index = Ain (S&P 500 Index) 100
'The data begins on the first week of January 1975 and ends on the last week of December 1986; it excludes data from April 1982.
?The data begins on 1/2/80 and ends on 12/31/86; it excludes data from April 1982.
3The data begins on 5/1/82 and ends on 12/31/86.
"Statistically significant at the 5 percent level.
market for stocks has increased the volatility of stock
prices. This criticism has a long history.22Our analysis,
however, does not imply that stock prices will exhibit
greater volatility as a result of this trading. Rather, it
suggests that such trading results in a closer corre
spondence between prices in the spot and futures
markets. Since there is no reason to suspect, a priori,
that this trading increases the volatility of prices in the
spot market, we must rely on the data to help answer
this question.23
The following analysis addresses three key ques
tions: 1) Has stock price variability increased since
stock index futures began trading early in 1982? 2) Are
stock prices more variable on days when futures con
tracts are scheduled for delivery (triple witching
days)? 3) Is stock price variability related to trading
activity in stock index futures?
^See Working (1977), pp. 267-97.
231bid., p. 295.
http://fraser.stlouisfed.org/
26
Federal Reserve Bank of St. Louis
Percentage Changes In the S&P 500:
Pre- and Post-April 1982
The Standard and Poor’s futures contract began
trading on April 21, 1982. This is the most active
contract and accounts for about 75 percent of all
trading in stock index futures.24
Table 3 compares the period before and after April
1982 using weekly and daily percentage changes in the
Standard and Poor’s 500 Index. Percentage differences
are employed to control for the general increase in the
level of the index from 1975 through 1986.25
Panel A of table 3 examines the mean and standard
deviation of weekly and daily percentage changes in
24See, Wall Street Journal (March 2, 1987).
25The index rose from an average level of 86.18 in 1975 to an average
level of 236.34 in 1986. A one-point change in the index represented
a much larger percentage change in 1975 (about 1.2 percent) than a
one-point change in 1986 (about .4 percent).
FEDERAL RESERVE BANK OF ST. LOUIS
the index. As indicated, the mean of the weekly per
centage change in the index prior to April 1982 was
.130 percent. After April 1982, the mean rose to .306
percent, an increase of .176 percentage points in the
later period. In the case of the daily data, the mean of
the daily percentage change increased by .065 per
centage points in the later period. Neither increase is
statistically significant at conventional confidence lev
els (t-scores are 1.30 and 1.39, respectively). The differ
ences in the means before and after April 1982 could
easily have been produced by chance variation in the
data.
Comparing the means, however, masks much of the
variation in the data, because increases in the index
are offset by decreases when the mean is computed.
The standard deviation is a better indicator of varia
tion because it measures the spread in the data
around the mean.26 For example, the standard devia
tion of the weekly data before April 1982 is 1.68. If these
percentage changes in the index are normally distrib
uted, about 67 percent of the weekly observations fall
within the range of .13 ± 1.68 (or —1.56 percent to 1.80
percent). The standard deviation of the weekly data
after April 1982 is 1.74 which is about the same as for
the earlier period. In fact, the two are not significantly
different in a statistical sense (the ratio of the variances
= 1.07). A similar conclusion holds for the daily data.
In this case, the standard deviation is somewhat
smaller in the more recent period, but is not signifi
cantly smaller in a statistical sense 27
Panel B of table 3 compares variation in the index on
days when S&P 500 Futures contracts mature (settle
ment days) to variation on all other days (nonsettle
ment days) for the post-April-1982 period. In the case
of settlement days, the data are percentage changes in
the S&P 500 Index from the close on the day before a
settlement day to the close on the settlement day. For
nonsettlement days, the data are percentage changes
in the daily closing value of the index excluding the
changes on settlements days. As indicated in panel B,
the mean percentage change is larger on settlement
than on nonsettlement days; but the difference be
tween the two is not statistically significant at conven
tional confidence levels (t-score = .36). Similarly, the
“ See Wonnacott and Wonnacott (1977), pp. 24-25.
27ln addition, both the mean absolute deviation (MAD) and mean
absolute value (MAV) of the weekly and daily percentage changes
in the index were examined for the two periods. Like the standard
deviation, these measure variation and, for this data, each measure
tells a similar story. As in the case of the standard deviation, both the
MAD and MAV are slightly higher for the weekly data (about 2
percent higher) and slightly lower for daily data (about 11 percent
lower) in the post-April 1982 period.
MAY 1987
standard deviation is larger on settlement days (.97 vs.
.88), but is not significantly larger in a statistical sense
(the ratio of the variances = 1.21). Thus, the data in
table 3 suggest that the share prices of companies
included in the S&P Index did not become statistically
more variable on average after the S&P Futures con
tract began trading nor were they more variable on
settlement (triple witching) days.
Intra-Day Variation: Pre- and
Post-April 1982
The above data measures price variation from dayto-day. Some commentators have expressed concern
about intra-day movements in stock prices. The data
in panel A of table 4 examine one measure o f the intra
day price spread in the S&P Index for pre- and postApril 1982 data: the difference between the daily high
and low of the index divided by the close and multi
plied by 100.28
Panel A indicates that the mean intra-day spread
was 2.03 percent before April 1982 and 1.38 percent
after. The difference, —.65 percent, is statistically sig
nificant (t-score = 17.29) and indicates that the intra
day percentage spread declined after April 1982.
Panel B examines whether the post-April 1982 intra
day price spreads have been unusually large on triple
witching days.29 The data indicates that the mean
intra-day percentage spread is slightly larger on triple
witching days than on nonsettlement days (1.56 vs.
1.38); the difference, however, is not statistically sig
nificant at conventional confidence levels (using the
pooled variances, the t-score = 1.48).
To summarize, the data in table 4 indicate that there
was a statistically significant decline in the intra-day
percentage price spread in the post-April 1982 period.
There was no statistically discernible difference, how
ever, between the spreads on triple witching days vs.
other post-April-1982 trading days.
Price Variation and Trading Activity in
S&P Futures
The data in table 5 help assess whether stock price
variability is related to trading activity in S&P Futures
contracts. The data are correlation coefficients for
daily trading volume in S&P Futures contracts (V) and
“ Scaling the difference between the high and low by the daily low
rather than the close produces virtually identical results.
^See, for example, Stoller, and Laderman and Frank (September 29,
1986), pp. 96-97.
27
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Table 4
A Comparison of Intra-Day Price Spreads
Panel A: Means Pre- and Post-April 1982
Pre-April 1982
Post-April 1982
Mean
Mean
Differences
in Means
2.03
1.38
-.6 5 *
Intra-Day Price Spread1
Panel B: Means on Settlement and Nonsettlement Days: Post-April 1982
Settlement Days
Nonsettlement Days
Mean
Mean
1.56
1.38
Intra-Day Price Spread2
Differences
in Means
.18
Intra-Day Price Spread = [(H-L)/C]100
where: H = the daily high of the S&P Index
L = the daily low of the S&P Index
C = the daily close of the S&P Index
'The data begins on 1/2/80 and ends on 12/31/86; it excludes data from April 1982.
2The data begins on 5/1/82 and ends on 12/31/86.
'Statistically significant at the 5 percent level.
several measures of price variation in the S&P Index:
the daily percentage change in the S&P Index (P), the
absolute value of the daily percentage change in the
S&P Index (AP) and the intra-day percentage price
spread (S). Respectively, these correlations indicate
whether the volume of trades in S&P Futures generally
is associated with an increase or decrease in the S&P
Index, larger or smaller changes (either up or down) in
the S&P Index, and larger or smaller intra-day price
spreads.
An examination of table 5 indicates that the coef
ficient of correlation for V and P is not significantly
different from zero in a statistical sense. The same
holds in the case of V and AP. This data suggests that
neither the direction nor the magnitude of changes in
the S&P Index are associated with trading volume in
the S&P Futures market. The coefficient of correlation
for V and S, however, is negative and significantly
different from zero in a statistical sense; larger trading
volume in S&P Futures contracts generally was associ
ated with smaller intra-day price spreads. The table 5
data are not consistent with the claim that trading
activity in S&P Futures was associated with increased
variation in the S&P Index.
http://fraser.stlouisfed.org/
28
Federal Reserve
Bank of St. Louis
CONCLUSION
Numerous commentators have claimed that stock
prices have been more variable since stock index fu
tures contracts began trading. The alleged increase in
volatility led to both closer scrutiny of the market by
the Securities and Exchange Commission and calls for
legislative action. The presumed increase in stock
price volatility has been attributed to programmed
trading — the practice of trading between the spot
and futures markets for stocks. While this trading
strategy is not new, the introduction of stock index
futures contracts around 1982 and the application of
computer programming techniques to trigger trades
between the markets are novel.
This paper discusses the theory that underlies pro
grammed trading and examines various measures of
stock price variation. The results of the analysis are not
consistent with the claim that trading activity in the
S&P Futures contract is associated with increased
price variation in the spot market for stocks.
While closer scrutiny and regulation of trading in
stock index futures markets may be justified on other
grounds, the evidence presented here suggests that
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Cinar, E. Mine. “ Evidence on the Effect of Option Expirations on
Stock Prices,” Financial Analysts Journal (January/February
1987), pp. 55-57.
Table 5
Clark, Lindley H. Jr. “Where Is the Soaring Stock Market Leading
Us?” Wall Street Journal (January 27, 1987).
Correlations Between Volume and
Measures of Variation in the S&P Index
(Daily data: May 1982-December 1986)
Cornell, Bradford, and Kenneth R. French. “The Pricing of Stock
Index Futures,” Journal of Futures Markets (Spring 1983), pp. 114.
Daily Volume1
Percentage Change in the
S&P Index
-.0 0 6
Absolute Value of the Percentage
Change in the S&P Index
.049
- .286*
The Intra-Day Price Spread
'Total daily volume for all delivery months.
'Statistically significant at the 5 percent level.
Fama, Eugene F. “ Efficient Capital Markets: A Review of Theory
and Empirical Work,” Journal of Finance, Papers and Proceedings
(May 1970), pp. 383-^17.
Figlewski, Stephen. “ Hedging Performance and Basis Risk in Stock
Index Futures,” Journal of Finance (July 1984), pp. 657-69.
Galbraith, John Kenneth.
The Great Crash (Houghton Mifflin, 1955).
Green, Edward J. “ Financial Futures and Price-Level Variability,”
Financial Futures and Options in the U.S. Economy (Board of
Governors of the Federal Reserve System, 1986), pp. 79-89.
Kawaller, Ira G. "The Rudiments of Options on Futures: A Primer for
the Uninitiated,” Market Perspectives (Chicago Mercantile Ex
change, 1986).
Laderman, Jeffrey M., and John N. Frank. “ How Chicago Zaps Wall
Street,” Business Week (September 29, 1986), pp. 92-102.
regulation based on the proposition that it has in
creased price volatility in the spot market would be
misdirected.
Laderman, Jeffrey M., et. al. “Those Big Swings on Wall Street,”
Business Week (April 7,1986), pp. 32-36.
REFERENCES
Modest, David M., and Mahadevan Sundaresan. “The Relationship
Between Spot and Futures Prices in Stock Index Futures Markets:
Some Preliminary Evidence," Journal of Futures Markets (Spring
1983), pp. 15-41.
“Abreast of the Market.”
Wall Street Journal (January 26, 1987).
Alchian, Armen, and William R. Allen. Exchange and Production:
Competition, Coordination and Control, 2nd. ed. (Wadsworth,
1977), pp. 131-39.
Belongia, Michael T. “Commodity Options: A New Risk Manage
ment Tool for Agricultural Markets,” this Review (June/July, 1983),
pp. 5-15.
McMurray, Scott. “Chicago Merc Seeks to Curb Market Swings,”
Wall Street Journal (February 12,1987).
Schwarz, Edward W., Joanne M. Hill, and Thomas Schneeweis.
Financial Futures (Dow Jones-lrwin, 1986).
“Stocks End Day Mixed as Market Recovers From the Roller
Coaster,” Wall Street Journal (January 27,1987).
Stoll, Hans R., and Robert E. Whaley. “ Program Trading and Expiration-Day Effects,” Financial Analysts Journal (March/April
1987), pp. 16-28.
Black, Fischer, and Myron Scholes. “The Pricing of Options and
Corporate Liabilities,” Journal of Political Economy (May/June
1973), pp. 637-54.
Stoller, Stephen D.
1987), p. 24.
Brealey, Richard, and Stewart Meyers.
nance (McGraw-Hill, 1984).
Principles of Corporate Fi
Working, Holbrook. Selected Writings of Holbrook Working (Chicago
Board of Trade, 1977).
Cagan, Phillip. “ Financial Futures Markets: Is More Regulation
Needed?" Journal of Futures Markets (Vol. 1, no. 2, 1981), pp.
169-92.
Wonnacott, Thomas H., and Ronald J. Wonnacott. Introductory
Statistics for Business and Economics (John Wiley and Sons,
1977), pp. 22-25.
“The $18 Billion Bet,” Barron's (February 9,
29
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Agricultural Banks: Causes of
Failures and the Condition of
Survivors
Michael T. Belongia and R. Alton Gilbert
T
■M. HE number of bank failures has risen sharply in
recent years. From 1943 to 1981, no more than 17
commercial banks ever failed in a single year. Since
1982, when 34 banks failed, the number of failures has
risen each year, reaching 144 in 1986. The failed banks
have been concentrated increasingly among small,
rural banks in general and agricultural banks in partic
ular. In the years 1984 through 1986, about half of the
340 failed banks were agricultural banks, those with
ratios of agricultural loans to total loans above the
unweighted national average. Agricultural banks make
up about one-third of all banks.'
Although the current downturn in the farm econ
omy has been both extensive and protracted, the
number of agricultural bank failures in recent years
represents only a small percentage of all agricultural
banks. This article examines the financial condition of
both the surviving and failed agricultural banks to
determine why some banks have failed while most
have survived. The results have important implica
tions for the ability of banks in rural areas to continue
to finance local farm business.
REASONS FOR AGRICULTURAL BANK
FAILURES
The rise in failures among agricultural banks
reflects the continuing financial distress of farmers in
the 1980s. Although agriculture has been a declining
industry for some time, its downturn since 1981 has
been unusually abrupt and severe.2The financial dis
tress in the agricultural sector has its roots in the
accumulation of farm debt in the 1970s. As chart 1
shows, the price of farmland and the value of farm
debt rose sharply and persistently throughout the
1970s.
The growth of farm income, however, did not keep
pace with the rise in farm debt. Some farmers bor
rowed heavily to purchase higher priced land in antic
ipation of future appreciation; others borrowed to
offset their declining real returns to investments in
farming and to finance current consumption. These
trends left farmers with heavy debt burdens as they
entered the 1980s.
Michael T. Belongia is a senior economist and Ft. Alton Gilbert is an
assistant vice president at the Federal Reserve Bank of St. Louis. Paul
Crosby provided research assistance.
In 1981, these trends changed abruptly. A severe
and protracted worldwide recession, which lowered
foreign incomes sharply, reduced export sales of U.S.
farm products and real net farm income. At the same
time, the rate of inflation and expectations of future
'In recent years, the unweighted average ratio of agricultural loans to
total loans for all commercial banks has been around 17 percent.
This paper uses 17 percent throughout as the criterion for identifying
agricultural banks. Melichar (1987) reports that, on December 31,
1986, there were 4,700 banks that had ratios of agricultural loans to
total loans above the unweighted national average of 15.7 percent.
2See Belongia and Gilbert (1985) and Belongia (1986) for more detail
on changes in farm prices, income and asset values since 1981.
Belongia and Carraro (1985) discuss the deterioration in portfolio
quality for major farm lenders over the same period.
30
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
C h a rt 1
Farm Land Values and Farm Debt
1972
73
74
75
76
77
78
79
8C
81
82
83
84
85
1986
N O T E : The s u rv e y o f la n d p ric e s is c o n d u c te d e a r ly in e a c h c a le n d a r y e a r. The d e b t re fle c ts fa rm d e b t (e x c lu d in g CCC lo a n s ) a t the
e n d o f th e p r io r c a le n d a r y e a r to m a tc h th e tim in g o f d e b t a n d la n d v a lu e s a s c lo s e ly a s p o s s ib le .
inflation suddenly were reduced, lessening the de
mand for assets like farmland, which are viewed as
hedges against inflation. With declining returns to the
business of farming and diminished expectations of
appreciation in farmland prices, the demand for farm
land fell and prices declined. Finally, the 1981 tax bill
may have raised the real rate of interest which, in a
standard model of asset prices, also would tend to
reduce land prices.3
With lower export sales and lower income, many
farmers could not generate sufficient cash flow to
service their debts. Moreover, with land values declin
ing sharply, farmers could not pay off their debts by
selling their land. As a result, banks have recorded
losses on loans to such farmers.4 The banks with
relatively large losses have failed.
3See, for example, Holland (1984) for arguments and evidence on this
issue.
“Estimates of farm debt unlikely to be repaid and the consequences of
allowing different groups to bear the losses are found in Bullock
(1985).
THE SELECTION OF AGRICULTURAL
BANKING DATA
The analysis of banking data begins with the selec
tion of counties in which agricultural banks failed
between January 1, 1984, and December 9, 1986. From
the set of all farm bank failures, many banks were
deleted. For example, banks in states that permit bank
branching beyond the county of a bank’s headquar
ters were eliminated because income and balance
sheet data are not available on the individual
branches. Banks in other states were excluded be
cause there were no failures of agricultural banks. The
remaining sample includes counties in the 10 states
listed in table 1.
Table 1 indicates the number of farm bank failures
that occurred in the 10 states from 1984 through 1986.
To check for clustering of failures in particular regions
of a state, the table also lists the number of counties in
which farm bank failures occurred. As the table indi
cates, multiple failures within a county during the
31
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Table 1
Numbers of Farm Bank Failures and
Counties in which Failures Occurred:
1984-86
State
Failures
Counties
Alabama
Colorado
Illinois
Iowa
Kansas
Minnesota
Missouri
Texas
Wisconsin
Wyoming
1
5
4
23
29
12
17
12
1
1
1
5
4
20
25
12
15
12
1
1
TOTAL
105
96
three-year period were limited to Iowa, Kansas and
Missouri. Even in these states, such failures were
spread across nearly equal numbers of counties. Only
two counties (one in Iowa in 1985 and another in
Kansas in 1986) experienced more than one bank
failure in a single year.
BANK PERFORMANCE BEFORE THE
FARM SECTOR DECLINE
The next stage of the analysis compares the perfor
mance in 1981 of the agricultural banks that failed
between 1984 and 1986 with that of agricultural banks
in the same counties that had not failed as of June
1986. We then analyze the condition of the surviving
agricultural banks in 1986.
There were 519 agricultural banks in June 1981 in
the 96 counties identified in table 1; 105 failed between
1984 and 1986, and 414 still were in operation as of
June 1986. The first comparison assesses whether the
banks that ultimately failed were in relatively good
financial condition in 1981. If they were not, their
failure may have been largely unrelated to the farm
sector decline in recent years.
32
Table 2 presents several indicators of asset compo
sition and financial performance for the failed and
surviving banks. Loan and asset ratios are as of June
1981, whereas returns on equity (ROE) and total assets
(ROA) are based on averages for the year 1981.5In 1981,
the banks in these two groups appeared to be similarly
able to absorb loan losses: they had comparable pri
mary capital/assets ratios of 9.52 percent and 9.11
percent. Furthermore, returns on assets and equity
were not significantly different, at the 5 percent level,
for the two groups of banks. Thus, these banks gener
ated similar earnings and had a similar capacity to
absorb losses in the value of their assets.
Because discussions of the financial distress in the
agricultural sector generally emphasize the effects of
declining farmland prices, we might expect the agri
cultural banks that have failed to be among those with
relatively high percentages of their loans secured by
farm real estate. This, however, is not the case. Loans
secured by farm real estate accounted for only 5 per
cent of total loans at the surviving banks in 1981 and
only 4 percent of total loans at the banks that subse
quently failed. While table 2 shows that the surviving
banks invested smaller percentages of their loans in
farm production loans not secured by farm real estate,
the difference is statistically significant at only the 10
percent level.
As of June 1981, banks that failed had slightly higher
ratios of commercial and industrial loans to total
loans, but these ratios are not significantly different for
the failed and surviving banks. The surviving banks
had significantly higher ratios of nonfarm real estate
loans to total loans than the failed banks. Thus, the
reasons why some banks have failed while others have
survived cannot be tied directly to the declines in real
estate prices in rural areas.
Differences in the composition of investments indi
cate that, in June 1981, the banks that ultimately failed
chose securities with higher default risk than the
banks that have survived. The failed banks had higher
5Data for only 102 failed banks are presented because data for three
banks identified as failures could not be traced back to 1981. There
also was a problem with the data for one solvent bank; thus, only 413
observations could be used.
Report of Condition data for June 30 are used to calculate loan and
asset ratios because most farm loans are booked by this time of each
year but are paid off in the third and fourth quarters. June 30 data
thus avoid the problems of omitting some loans (as first-quarter data
would do), loan repayments and end-of-year “window-dressing.”
Annual averages are used for ROE and ROA data, however, to avoid
possible distortions from using what typically is a good quarter for
earnings to calculate annualized rates of return.
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Table 2
Descriptive Statistics for Agricultural Banks That Failed between 1984-86 and
Those That Survived___________________ ______________ ________ _____________
Solvent Banks
(n = 413)
Failed Banks
(n = 102)
Standard
deviation
Mean
50 %
(1.54)
18
53
5
(1.34)
4
4
5
Farm non-real-estate loans/total loans
45
(1.84)
18
49
20
Commercial and industrial loans/total loans
17
(1.22)
10
18
11
Nonfarm real estate loans/total loans
17
(3.82)
11
12
8
Total loans/total assets
53
(5.44)
12
60
12
Federal government securities/total investments'
60
(2.86)
21
53
24
State and local government securities/total investments'
26
(2.15)
18
30
22
Variable
Agricultural loans/total loans
Farm real estate loans/total loans
Mean
Standard
deviatio
%
19
Primary capital/assets
9.52
(1.08)
2.43
9.11
5.87
Return on equity (ROE)
14.64
(1.16)
6.30
15.48
7.59
Return on assets (ROA)
1.36
(0.41)
0.66
1.33
0.70
NOTE: All loan and asset ratios are June 1981 data. ROE and ROAare based on net income after taxes. Annual average values for assets
and equity capital are calculated by giving the December 1980 and December 1981 Report of Condition values weights of
one-eighth and the March, June and September values weights of one-fourth. The t-statistics in parentheses are for null
hypotheses that the mean values for solvent and failed banks are equal.
'For the purposes of this paper, investments are defined to include all securities plus federal funds sold.
ratios of state and local government securities to total
investments and lower ratios of federal government
securities to total investments.
CONTROLLING FOR DIFFERENCES IN
LOCAL ECONOMIC CONDITIONS
The difference between the ratios of total loans to
total assets at failed and surviving banks yields the
highest t-statistic. In June 1981, the ratio of loans to
assets was GO percent, on average, for the banks that
failed, but only 53 percent for the surviving banks.
Thus, the agricultural banks that have failed had rela
tively higher ratios of loans to assets in 1981.
Before attributing cause-and-effect to higher loan
ratios and bank failure, however, it should be noted
that this relationship might be spurious. For example,
most failed banks could have been located in areas
with stronger loan demand in 1981 and larger losses in
subsequent years. Conversely, most surviving banks
could be located in counties with lower loan demand
33
FEDERAL RESERVE BANK OF ST. LOUIS
MAY 1987
Table 3
Within-County Differences Between Agricultural Banks That Failed and
Those That Survived: June 1981__________________________________
Variable
Farm real estate loans/total loans
Farm non-real-estate loans/total loans
Total loans/assets
Standard
deviation
Minimum
Maximum
-0.4%
(1.31)
6.07
-2 1 %
37%
4.7
(4.41)
21.37
-5 9
67
8.7
(11.18)
15.51
-4 4
54
Mean
NOTE: t-statistics in parentheses for differences in means.
in 1981 and lower loss rates since then. A closer look at
the data, controlling for the potential effects of local
economic factors, is required to investigate this
possibility.
Local influences on bank performance can be held
constant in a variety of ways. One is to compare the
loan ratios for June 1981 of each bank that subse
quently failed with those of banks located in the same
counties that survived. If the lower loan ratios at the
surviving banks displayed in table 2 reflect differences
in loan demand, the spreads between loan ratios at
failed banks and surviving agricultural banks in the
same counties will tend to be small and not signifi
cantly different from zero.
This, however, is not the case. The ratios of non-real
estate farm loans to total loans were about 5 percent
age points higher, on average, at the banks that subse
quently failed than at the surviving banks in the same
counties; this difference is statistically significant at
the 5 percent level (see table 3). The banks that subse
quently failed also had ratios of total loans to total
assets that were almost 9 percentage points higher, on
average, than the surviving banks located in the same
counties. In contrast, differences between ratios of
farm real estate loans to total loans were essentially
zero numerically and not significant statistically.
Comparisons of failed and surviving banks located
in the same counties sharpen rather than reduce the
distinctions between the failed and surviving banks.
The banks that failed had accepted greater risks than
other banks in the same counties by investing higher
percentages of their assets in loans generally and
more of their loans in farm loans.
http://fraser.stlouisfed.org/
34
Federal Reserve Bank of St. Louis
There also is evidence that the agricultural banks
which maintained relatively high ratios of loans to
assets tended to make poorer quality loans. Melichar
found that, as of December 31, 1985, the banks with
higher ratios of loans to deposits tended to have
higher ratios of nonperforming loans to total loans.6
Thus, the distinction between the failed and surviving
banks based on their ratios of loans to assets may
reflect differences in loan quality as well as the risk
inherent in operating banks with relatively high ratios
of loans to assets.
PERFORMANCE OF THE SURVIVING
BANKS
Table 4 presents data for banks that were still in
business as of year-end 1986; the smaller number of
observations, 400, reflects problems with the data for
some banks, which were deleted. Although still sol
vent, earnings at these surviving institutions declined
substantially over the five-year period, as comparisons
with the 1981 ROE and ROA figures indicate. Losses
also led to a numerically small but statistically signifi
cant reduction in the average capital ratios of these
institutions. The average capital/assets ratio of 8.94
percent in 1986, nonetheless, is substantially above
regulatory guidelines for a minimum ratio of primary
capital to total assets of 5.5 percent.7
Table 4 also indicates reductions in the ratios of
both agricultural loans to total loans and of total loans
6Melichar (1986), pp. 445-46.
7See Gilbert, Stone and Trebing (1985).
MAY 1987
FEDERAL RESERVE BANK OF ST. LOUIS
Table 4
Descriptive Statistics for Solvent Banks: June 1981 and June 1986 (n = 400)
Variable
June 1986 Mean
June 1981 Mean
Agricultural loans/total loans
49.89%
(2.00)
Total loans/assets
52.50
(9.06)
9.52
(3.19)
14.64
(14.24)
Primary capital/assets
Return on equity (ROE)'
Return on assets (ROA)'
June 1986 Minimum
1.96%
97.19%
44.77
9.66
82.26
8.94
2.96
23.41
0.006
-94.96
32.83
0.20
-6 .6 2
3.77
47.39%
1.36
(15.55)
June 1986 Maximum
NOTE: 1-statistics in parentheses for the difference between mean values in 1981 and 1986.
’ ROE and ROA are annual average rates of return.
Table 5
Surviving Banks: Measures of Performance in 1986 for Those
with Positive and Negative Earnings
Mean
Standard
deviation
Minimum
Maximum
9.76%
0.24
5.36
0
82.25%
32.83
23.41
74.67
9.66%
-94.96
2.76
0
81.35%
0
18.08
191.76
BANKS WITH POSITIVE EARNINGS (n = 285)
Total loans/assets
Return on equity
Primary capital/assets
Problem loans/capital'
42.66%
9.49
9.52
11.13
13.64
5.34
2.69
13.71
BANKS WITH ZERO OR NEGATIVE EARNINGS (n = 115)
Total loans/assets
Return on equity
Primary capital/assets
Problem loans/capital’
49.99%
- 23.49
7.50
43.23
11.47
23.01
2.48
37.61
NOTE: All ratios based on data for June 1986, except return on equity, which is for the year 1986.
’ Problem loans are defined as those more than 30 days past due or in nonaccrual status.
to assets that are statistically significant. Thus, the
surviving banks, which had assumed lower risk than
the failed banks in 1981 by investing smaller shares of
their assets in loans, reduced their exposure to losses
on loans even more during the following five years.
A Closer Look at the Condition o f
Survivors
The result in table 4 that surviving banks, on average,
had a zero return on equity in 1986 might imply that it
is only a matter of time before many of them join the
ranks of the 102 failures in the sample. Such a conclu
sion, however, would be hasty, as the data in table 5
indicate.
If the 400 surviving banks are divided into groups
with positive and negative ROE for 1986, we find that
the surviving banks fall into the disparate categories of
very healthy or very troubled. The 285 banks with
positive earnings in 1986 had significantly lower ratios
of loans to assets than the banks with negative eam35
FEDERAL RESERVE BANK OF ST. LOUIS
ings. The top portion of table 5 indicates that over 70
percent of the survivors had positive ROEs in 1986 and
an average ROE of 9.49 percent; while down from the
1981 ROE average, it nonetheless compares favorably
with the 1986 national averages for both agricultural
and nonagricultural banks. The banks with positive
earnings also have higher capital ratios. Moreover,
further significant reductions in earnings and capital
ratios appear unlikely, since the ratio of problem loans
to primary capital is 11 percent, on average, for this
group of banks. The remaining 115 banks, or 29 per
cent of the survivors, are in poor financial condition.
The bottom portion of table 5 shows ROE to be an
average o f —23 percent, and these banks are likely to
have additional losses; on average, their problem loans
exceed 40 percent of their capital.
As a further check on the financial health of the
surviving agricultural banks, the 400 solvent banks
were grouped on the basis of the ratio of problem
loans to capital for June 1986 data. The mean value for
this ratio was 20.36 percent. Table 6 indicates that 68
percent of. these banks have a problem loan/capital
ratio less than 20 percent; for about 12 percent of the
banks, problem loans are greater than 50 percent of
capital. These figures suggest that, while problem
loans are likely to have large, adverse effects on future
earnings for some institutions, they do not appear to
threaten the solvency of most of the surviving banks.
IMPLICATIONS OF BANK FAILURES
FOR FARMERS
Because farmers typically borrow from banks in
their own communities, a fincil question o f interest is
whether sound farm banks still remain in counties in
which agricultural banks have failed. As of the fourth
quarter of 1986, at least one agricultural bank showed
positive earnings in 87 of the 96 counties. Moreover,
the average ratio of primaiy capital to total assets was
9.06 percent for these banks. Thus, there remains at
least one agricultural bank in sound financial condi
tion in over 90 percent of the counties in which an
agricultural bank has failed.8
It is important to add, however, that the remaining
agricultural banks have relatively low ratios of total
8ln calculating the number of counties with agricultural banks in
December 1986, the investigation is not limited to the 400 surviving
banks that were agricultural banks in 1981. Some surviving banks
reduced the share of their loans to farmers below 17 percent by
1986, and others that were agricultural banks in 1986 either were not
in business in 1981 or were not classified as agricultural banks at that
time.
http://fraser.stlouisfed.org/
36
Federal Reserve Bank of St. Louis
MAY 1987
Table 6
Distribution of Surviving Banks by
the Ratio of Problem Loans to
Primary Capital
Problem loan/
capital ratio
0-10%
11-20
21-30
31-40
41-50
51-60
61-70
71-80
81-90
91-100
> 100
Number
of banks
202
71
43
22
16
14
9
6
3
3
11
Percent
of total1
Cumulative
percentage1
50.5%
17.8
10.8
5.5
4.0
3.5
2.3
1.5
0.8
0.8
2.8
50.5%
68.3
79.1
84.6
88.6
92.1
94.4
95.9
96.7
97.5
100.3
1Figures may not sum to 100 percent due to rounding.
loans to total assets. The healthy agricultural banks in
the 87 counties had average ratios of total loans to total
assets of 40 percent as of December 31, 1986. Con
versely, many banks that had higher ratios of loans to
assets have failed.
CONCLUSIONS
Agricultural banks that failed in recent years were
not in weaker condition before the recent years of
financial stress in the agricultural sector. In 1981, both
the banks that later failed and those that survived had
similar profit rates and capital ratios. The banks that
failed, however, had invested higher percentages of
their assets in loans, in particular agricultural produc
tion loans, and lower percentages of their investments
in federal government securities. Each difference ex
posed the banks to a relatively higher risk of losses.
About 70 percent of the surviving agricultural banks
remained in relatively strong financial condition in
1986. The other surviving banks reported large losses
and large amounts of troubled loans relative to their
capital. The banks in relatively strong condition in
1986 also had the lowest ratios of total loans to assets
among the surviving banks. Finally, while over 90 per
cent of the counties in which agricultural banks have
failed still are served by at least one agricultural bank
in sound financial condition, these remaining banks
have relatively low ratios of loans to assets.
FEDERAL RESERVE BANK OF ST. LOUIS
REFERENCES
MAY 1987
Institute (February 1985).
Belongia, Michael T. “The Farm Sector in the 1980s: Sudden Col
lapse or Steady Downturn?” this Review (November 1986), pp.
17-25.
Gilbert, R. Alton, Courtenay C. Stone and Michael E. Trebing. “The
New Bank Capital Adequacy Standards,” this Review (May 1985),
pp. 12-20.
Belongia, Michael T., and Kenneth C. Carraro. “The Status of Farm
Lenders: An Assessment of Eighth District and National Trends,”
this Review (October 1985), pp. 17-27.
Holland, A. Steven. “ Real Interest Rates: What Accounts for Their
Recent Rise?” this Review (December 1984), pp. 18-29.
Belongia, Michael T., and R. Alton Gilbert. “The Farm Credit Crisis:
Will It Hurt the Whole Economy?” this Review (December 1985),
pp. 5-15.
Bullock, J. Bruce. “ Farm Credit Situation: Implications for Agricul
tural Policy," FAPRI #4-85, Food and Agricultural Policy Research
Melichar, Emanuel. “Agricultural Banks under Stress,” Federal Re
serve Bulletin (July 1986), pp. 437-48.
---------------“ Farm Credit Developments and the Financial Condi
tion of Agricultural Banks,” a preliminary report for the National
Agricultural Credit Committee, Board of Governors of the Federal
Reserve System (March 16,1987).
37
@FedFRASER