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October 1, 1 982
Volatility and Unpredictability
In the seven weeks from June 28 to August 18,
the new issue rate on large 90-day Certificates of Deposit (CDs) fell over 600 basis
points to 9.5 percent. All interest rates fell
in late August. For Treasury bills, the rates
reached a two-year low. Was the recent
decline in interest rates anticipated by the
market, and what caused the rapid drop? The
answer is that the decline was not anticipated, and it is hard to explain the magnitude
of the drop even with the benefit of hindsight.
Large, unanticipated changes in interest rates
make even short-term financial transactions
risky. That is why market participants closely
monitor interest rates. They hope that a careful reading of past movements will divulge
the current objectives of Fed policy, help
them to predict future interest rates, and
allow them to divine the true state of the
economy. However, extracting informa·tion
about changes in the real economy or monetary policy from observed movements in interest rates is almost as tricky as predicting
future changes in interest rates.
This Letter briefly analyzes the recent decline
in interest rates. It examines and contrasts
three factors: volatility-the absolute size of
movements in rates, predictability-anticipated changes in interest, and ex postexplanations -whether past movements can be
attributed to specific "causal" factors.
Volatility: a historical perspective
When analyzing the recent decline in interest
rates it is important to keep in mind the past
pattern of interest rates. Since late 1979, the
volatility of interest rates has increased dramatically. From 1 977 through 1979, the average (absolute) monthly change in gO-day CD
rates was 33 basis points. From January 1 980
through JuIy 1982, the average (absolute)
monthly change was 150 basis points. Volatility increased approximately fourfold.
In July, the monthly average 90-day CD rate
fell by 1 20 basis points. In August, it fell by
290 basis points. Viewed as isolated changes,
these substantial drops appear to indicate
something significant; however, viewed relative to previous monthly changes since 1979,
the decline is not unusual. Monthly changes
over 100 basis points occurred in almost twothirds of the months since 1979. Changes
greater than 300 basis points occurred 10
percent of the time. Cumulative two-month
average changes exceeded 400 basis points
20 percent of the time.
Volatility and unpredictability
Volatility does not necessarily measure the
unpredictability of a series. Some series have
large seasonal or trend components that are
easily predicted. For.example, strawberries
are a seasonal product with a sharply variable
price. But it is easy to pred ict that the average
price of strawberries in January will exceed
the average price of strawberries in July.
Predictable price changes, such as those due
to seasonal movements, do not increase risk.
If the changes were expected in advance,
long-term plans or contracts could incorporate them.
Financial analysts and the financial press
gamely publish predictions of future interest
rates, leading one to presume that interest
rates, like the price of strawberries, may
be volatile but predictable. The frequent
reversals in opinion suggest, however, that
accurate interest rate predictions are difficult
to make. Participants in financial markets,
nevertheless, must predict future interest rates
every day; they put their money on their
predictions.
Any multiperiod financial instrument is a
contract that contains an implicit bet about
future short-term rates. The market's current
prediction of future short-term rates is incorporated in the longer term rate. Any fore-
()pinions (:,xpl"p')sed in tl""lis nevvslettef" do not
necessari Iv reflect the views of thE' managernent
of the Federal Reserve Bank of San Frc.1nc:isco,
or of the Board elf Covernors of tlw Federal
Res(' rv c.' Sy:;; tern"
To assess the accuracy of the predictions
implicit in forward rates, I subtracted the
one-month forward rate for 90-day CDs from
the actual CD rate that occurred one month
later. I have used this difference to represent
forecasting error and to measure the unpredictability in interest (CD) rates. From 1977
through 1 979, the average (absolute) error
was 36 basis points. From 1 980 through July
1 982, the average (absol ute) error was 150
basis points. By this measure, unpredictability increased fourfold. The volatility measure
discussed earlier and the unpredictability
measure are virtually the same. One might
say that random walks would have predicted
as wellas the forward rate.
caster who disagrees with the market's
prediction implicit in longer term rates
can make or lose a great deal of money by
betting against the market. This is done either
by selling or buying financial instruments
or financial futures contracts. Moreover, if
investors bet heavily against the market, current rates will change.
A two-period example illustrates the basic
point. Consider a hypothetical case in which
an investor can buy a 60-day CD that yields
1 0 percent or two 30-day CDs in successive
periods. The 30-day CD pays a rate of 10
percent in the first month and 20 percent in
the second month, giving an average yield of
15 percent over two months. Investors will
attempt to purchase the two 30-day CDs
because the total yield exceeds the 60-day
CD rate. Banks will wish to sell the 60-day
CD. When the market clears, buyers and sellers must agree on the same price. The yield
on 60-day CDs wi II rise and the total yield on
30-day CDs will fall until the total yields for
sixty days will beequal for both types of CDs.
The rate on the 60-day instrument is, therefore, the geometric average of the two shorter
term CD's.
Interest rates are volatile and unpredictable.
The market did not expect rates to decline in
July or August. In fact, forward rates for July
and August show that the market actually
expected an increase in rates.
The chart shows what I call the market forecast error for 1982. It is the difference between the monthly average 90-day CD rate
and the forward rate predicted one month
earlier. The July error of -1 61 basis points,
while large, is only slightly above the average
error for the two and one half year period
since the change in Fed operating procedures. The August error of - 336 basis points
is a whopper. Nevertheless, the market made
errors this large in about 15 percent of the
months since 1979.
In actual financial markets, the future ratethe rate for the second CD, is not known
today and must be predicted. The current
60-day rate and the current 30-day rate,
called spot rates, are known. Because the
market will equilibrate the yields on these
two investment plans, knowing that the
60-day rate is the geometric average of the
30-day rates allows us to work backwards to
calculate the future rate. For example, the
forward rate-the 30-day CD rate implied for
the next period -is about 14 percent when
the current 60-day rate is 12 percent and the
current 30-day rate is 10 percent.
Predictable vs. explainable
Although there is ample evidence that
changes in interest rates are extremely hard to
predict even one month ahead, this does not
mean that they cannot be explained. Expost
hindsight is usually keener than foresight. To
explain past movements in interest rates,
there must be a stable correlation between
the unanticipated change in interest rates and
the change in "causal" variables. If the causal
variables are unpredictable, they explain
why interest rates changed ex post,but they
provide no assistance in forecasting.
If interest rates form a volatile but predictable
series, forward rates will deviate from current
spot rates, but forward rates will be accurate
forecasts of future spot rates.
2
VOLATI LI TY AND UNPREDICTABILITY
OF I NTEREST RATES
Basis pOints
100
\
-100
-200
-300
F
M
A
M
A
1982
By working backwards, however, unanticipated changes in interest rates may provide
valuable information about changes in the
causal variables themselves. For example,
economic theory posits that the demand for
money depends on income (money for transactions balances) and interest rates (financial
assetsare substitutes) plus other less important influences. Therefore, changes in interest
rates, which can be observed daily, may provide information about current changes in the
real economy or in the Federal Reserve's
policy intentions. This information is valuable because money and income can only be
observed with a lag.
predictions for 90-day CD rates using the
forward rate as the market forecast. The average (absolute) forecast error over the past 32
months was 150 basis points-a large error
for a one-month ahead forecast. Forecasting
further in the future would be even more
treacherous.
The unpredictability of interest rates makes
financial transactions risky, their timing and
maturity critical. Purchasers of CDs in june,
for example, received a substantially higher
interest rate than those who purchased CDs
in August.
An investor who believes interest rates will
fall in the future would try to lock in the
current rate with a long maturity intrument,
while one who believes interest rates will rise
will go into short maturities until the rate rises.
The unpredictability in rates makes these
term structure gambles extremely risky.
As an example of an ex postrelationship, I
regressed the unanticipated change in CD
rates on the monthly growth of non-borrowed
reserves, an indicatorof monetary policy, and
the growth in industrial production, an indicator of real activity in the economy. The
results showed that roughly 80 percent of
the unanticipated change in CD rates, in the
sample history period from january 1 960
through August 1982, could be explained
by changes in non borrowed reserves and
industrial production.
The July and August rate decline was not
anticipated by the market. Furthermore, the
observed monetary stimulus does not seem
to have been large enough to explain the
decline in rates. The lack of a solid ex post
explanation of observed changes in interest
rates makes investors and policymakers
nervous. Does the decline signal a real economy that is weaker than preliminary data
indicates, or have investors' expectations
suddenly changed? In either case, what does
it mean for the future? If the real economy
were so weak, why is the stock market booming? And if investors' expectations changed
suddenly in the past, will they change again
in the future? At the moment, the market
seems to be hedging its bets-the August
forward rate for September is predicting
a 1 percent increase in CD rates.
In july and August, nonborrowed reserves
grew rapidly, putting downward pressure on
interest rates. However, using the historical
relationship, the growth in nonborrowed
reserves only explained about one-third of
the decrease in interest rates and industrial
production was virtually unchanged. In short,
most of the recent unanticipated drop in CD
rates cannot be explained ex postby the
simple historical relationship.
Summaryand conclusions
Interest rates are extremely volatile and unpredictable. I examined one-month ahead
RogerCraine
3
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BANKING DATA-TWELffH FEDERAL
RESERVE
DISTRICT
(Dollar amounts.in millions)
Selected Assetsand Liabilities
Large Commercial Banks
Loans (gross, adjusted) and investments*
Loans (gross, adjusted) - total#
Commercial and industrial
Real estate
Loans to individuals
Securities loans
U.s. Treasury securities*
Other securities*
Demand deposits - total #
Demand deposits - adjusted
Savings deposits - total
Time deposits - total #
Individuals, part. & corp.
(Large negotiable CD's)
Weekly Averages
of Daily Figures
Amount
Outstanding
Change
from
9/15/82
9/8/82
162,100
142,193
45,762
57,439
23,525
2,542
6,556
13,351
42,354
28,020
31,424
99,042
89,191
37,010
-
-
Change from
year ago
Dollar
Percent
738
731
638
15
16
163
90
83
564
38
224
134
188
89
-
Weekended
Weekended
9/15/82
9/8/82
9,852
10,907
6,538
3,036
499
1,006
841
1,896
329
114
1,573
13,790
12,080
3,025
6.5
8.3
16.7
5.6
2.2
65.5
14.7
- 12.4
0.8
0.4
5.3
16.2
15.7
8.9
Comparable
year-ago period
Member Bank ReservePosition
Excess Reserves ( + )/Deficiency ( - )
Borrowings
Net free reserves (+ )/Net borrowed (-)
100
142
42
140
14
126
62
20
42
* Excludes trading account securities.
# Includes items not shown separately.
Editorial comments may be addressedto the editor or to the author, , , . Freecopiesof this and other Federal
Reservepublications can be obtained bycalling or writing the Public Infonnation Section,FederalReserve
Bank of San Francisco,P.O. Box 7702, SanFrancisco94120. Phone(415) 544-2184.
@FedFRASER