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August 28, 1981
Canthe ProsBeatthe Market?
Increasingly volatile financial markets put a
prem i u m on accu rate forecasts of interest
rates. However, those forecasts might have
little value for individual investors if security
prices already reflect such forecast information. In the extreme case, if the market efficiently utilizes all available information, an
investor could not profit from more accurate
forecasts than those already incorporated in
security prices. On the other hand, if particular interest-rate forecasts are in fact superior,
but are neither generally available nor believed by the market, an investor could increase the return on his portfolio by trading
on such information.
This Weekly Letter examines whether an individual investor can profit from trading on
the information contained in the interest-rate
forecasts of market professionals. It does this
by comparing the accuracy of their forecasts
with the accuracy of the market's own forecasts, as implied by the term structure of
yields. We utilize the data compiled by The
Goldsmith-Nagan Bond and Money Market
Letter, which has surveyed professional analysts' forecasts at quarterly intervals since
September 1969. In our comparison, we focus on the forecasts of the 3-month Treasurybill rate for 6 months in the future.
Measuring the market's forecast
Our measure of the market's forecast is derived from the term structure of Treasury-bill
yields-specifically
from the 6-month-ahead
"forward rate." This is the interest rate on a
3-month Treasury bill 6 months ahead that
would be required to equalize expected retu rns on 6- and 9-month bi lis over a 9-month
holding period. The forward rate provides the
appropriate measure, because investors can
either buy a 6-month bill and reinvest the
proceeds in a 3-month bill or hold a 9-month
bill until maturity. Prices on 6- and 9-month
bills thus should be bid up or down until
the expected yields become equal over a
9-month holding period. Therefore, the for-
ward rate can be seen as measuring market
participants' average forecast of the 3-month
bi II rate 6 months hence.
This forward rate also contains a premium to
compensate investors in the 9-month bill for
their sacrifice of liquidity. So to arrive at a
measure of the market's expectation of the
3-month bi II rate 6 months hence, we must
subtract from the forward rate an estimate of
this liquidity premium, which averaged
about 50 basis points over 1970-79 but
varied somewhat with the risk of interest-rate
changes.
To maximize returns, investors should pursue
a more sophisticated strategy than simply
switching into long-term securities when they
expect interest rates to fall, so as to "lock in"
the yield, and doing the opposite when they
expect interest rates to rise. They should realize that profits actually depend on whether
interest rates change by more or less than the
amount already anticipated by the market.
Thus, investors trading on forecast information ought to lengthen the maturity of their
security holdings only if this forecast shows
interest rates below those forecasted by the
market, and shorten them only when the opposite is true.
For example, suppose that near a businesscycle peak a particular interest-rate forecast
indicates a larger decline in rates than what
the market anticipates. An investor trading on
that information thus should buy securities
maturities longer than his desired investment period. If this interest-rate forecast turns
out to be correct, he would obtain higher
yields than if he had chosen shorter maturities, because of the greater capital gains created by the unanticipated decline in interest
rates. But in contrast, if the market's forecast
turns out to be correct, the return from a
longer maturity would be no higher than that
on a security maturing over the investment
period (except for a liquidity premium); and if
ill)
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casts that use all available information should
take into account any such systematic time
pattern, as well as other relevant factors, and
thus should be at least as accurate as a forecast of no change.
rates fall by lessthan either the market's or the
investor's forecast anticipates, the return
would be reduced by capital losses.
Alternatively, if the forecast utilized by the
investor predicts slower declines in interest
rates than the market's forecast, the investor
should purchase securities with maturities
shorterthan investment period. Then ifthe
his
forecast is correct, he would obtain a higher
return from "rolling over" a series of shortterm securities than from purchasing maturities equal to his planned investment period.
Once again, however, if the market's forecast
turns outto be the correct one, nothing would
be gained from this course of action; and if
rates fall by more than the forecast of either
the market or the investor, the return would
be lower.
In our comparison, the root-mean-squared
error (RMSE) of the market's forecast, at 1.24
percentage points, is slightly lower than that
of a forecast of no change; but the RMSEof
the analysts' forecast, at 1 .1 0 percentage
points, is.even lower. So both the market and
the analysts were able to improve upon the
accuracy of a forecast assuming no change.
Even more importantly, however, standard
statistical tests reveal that the greater accuracy of the analysts' forecast, compared to the
market's, cou Id not have occurred by chance
alone. (Also, the approach used to estimate
the liquidity premium more likely caused an
understatement, rather than an overstatement, of the true difference between the
market's and the analysts' forecasting errors.)
The 1 4-basis-point difference between the
RMSEs is relatively modest. Nevertheless, our
results indicate that investors could have
improved profits significantly by trading on
the information contained in the analysts'
forecast. A strategy of shorten i ng matu rities
when the analysts' forecast was above the
market's forecast-and lengthening them
when the opposite was true-would have
improved overall returns.
Professionals the market
vs.
In our analysis, we compared the accuracy
of the Goldsmith-Nagan panel's 6-monthahead forecasts of the 3-month Treasury-bill
rate with the market's forecast, as measured
by the root-mean-squared error. (The sample
period covered 1970-1 through 1979-11.)We
also considered the accuracy of a simple forecast of no change, where the interest rate is
assumed to follow a "random walk." Such a
forecast may be regarded as a minimum
standard of accuracy for forecasting the
3-month bill rate. This contrasts with results
from markets for longer-term securities,
where a fore<;:ast no change may actually
of
be more accurate than any other forecast.
Sourcesof information
Both forecasts contain two parts-an autoregressive component that extrapolates from
past changes in the bill rate, and a remaining
component based on other information. The
analysts'
forecast superior themarket's
was
to
forecast both respects. autoregressive
in
The
component of the market's forecast was not
significantly different from a prediction of no
change, or a random walk. Indeed, the market's forecast failed to incorporate an upward
drift in the bill rate attributable to rising inflation in the forecast period, even though this
drift could have been extrapolated from past
data. In contrast, the autoregressive component of the ana Iysts' forecast conta ined a pos-
Short-period returns on longer-term securities
are dominated by capital gains or losses resulting from changes in market prices. Any
systematic pattern in such returns would be
quickly eliminated as investors bid prices up
or down in attempts to profit from them. In
contrast, returns on 3-month Treasury bills
held to maturity cannot be affected by such
speculation, because the price at the end of
three months is fixed contractually. Therefore, even a fully anticipated time pattern in
3-month Treasury bill yields is not likely to be
arbitraged away. Moreover, interest-rate fore2
itive time trend of 54 basis points per year, as
well as significant correlations with past fluctuations in the bill rate. In addition, the remaining component of the analysts' forecast
contributed significantly to forecasting accuracy, while the corresponding component of
the market's forecast did not.
thus should be able to improve the accuracy
of their forecasts by taking into account any
such existing time patterns. The GoldsmithNagan panel of forecasters in fact did so, and
also used additional information unrelated to
the bill rate's past history to improve the
accuracy of their forecasts. Moreover, the
information contained in this panel's forecasts was not fully reflected in the prices of
Treasury bills, so that individual investors
could have increased their profits by utilizing
these or similar forecasts.
In summary, our evidence indicates that the
market's forecast of the 3-month Treasury bill
rate, as implied by a term structure of yields,
was not significantly different from a prediction of no change-or a random walk.
While we may expect a random walk in
short-period yields of stocks or bonds, even a
fully anticipated time pattern in the return on
bills held to maturity is not likel V to be arbitraged away. Forecasters of Treasury-bill rates
Adrian W. Throop
(The author wishes to thank Mr. Peter Nagan
for permitting use of his survey data on
professionals' forecasts.)
Accu racy of Forecasts
Root Mean Squared Error (RMSE)
1970-1through 1979-111
(percentage points)
Forecast of No Change
1 .25
Market's Forecast
1 .24
Analysts' Forecast
1.10
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B AN KI N G D ATA-TWE L F TH FEDERAL RESERVE STRla
DI
(Dollar amounts in millions)
Selected
Assets ndliabilities
a
Large
Commercial
Banks
Loans (gross,adjusted)and investments*
Loans (gross,adjusted)- total#
Commercial and industrial
Realestate
Loansto individuals
Securitiesloans
U.s. Treasurysecurities*
Other securities*
Demand deposits - total#
Demand deposits- adjusted
Savingsdeposits - total
Time deposits - total#
Individuals, part. & corp.
(LargenegotiableCD's)
WeeklyAverages
of Daily Figures
MemberBankReserve
Position
ExcessReserves + )/Deficiency (- )
(
Borrowings
Net free reserves(+ )/Net borrowed(- )
Amount
Outstanding
8/12/81
151,192
130,150
39,577
53,609
23,081
1,334
6,136
14,906
40,249
28,780
29,939
85,166
77,235
35,006
Weekended
8/12/81
60
60
0
Change
from
8/5/81
-
160
127
96
136
67
12
22
11
-1 ,794
64
-
348
1,328
1,303
889
Changefrom
year ago
Dollar
Percent
12,380
13,037
5,917
6,247
754
333
131
522
- 3,881
- 3,309
491
22,585
22,868
12,066
8.9
11.1
17.6
13.2
- 3.2
33.3
- 2.1
3.4
- 8.8
-10.3
1.7
36.1
42.1
52.6
Weekended
8/5/81
Comparable
year-agoperiod
33
44
- 11
- 61
31
- 92
* Excludestrading account securities.
# Includes items not shown separately.
Editorial
comments beaddressed theeditor(WilliamBurke) to theauthor.... Free
may
to
or
copies this
of
andotherFederal
Reserve
publications beobtained calling writingthePublic
can
by
or
Information
Section,
Federal
Reserve
Bank San Francisco, Box7702,SanFrancisco
of
P.O.
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Phone
(415)544-2184.
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