Interest rates ; Forecasting ; Speculation

Adrian W. Throop

English

Research Papers in Economics

August 28, 1981 
Can the Pros Beat the 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 informa-
tion. In the extreme case, if the market effi-
ciently 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 partic-
ular interest-rate forecasts are in fact superior, 
but are neither generally available nor be-
lieved by the market, an investor could in-
crease the return on his portfolio by trading 
on such information. 
This Weekly Letter examines whether an in-
dividual 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 fore-
casts, 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 ana-
lysts' forecasts at quarterly intervals since 
September 1969. In our comparison, we fo-
cus on the forecasts of  the 3-month Treasury-
bill rate for 6 months in the future. 
Measuring the market's forecast 
Our measure of the market's forecast is de-
rived 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 re-
tu 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 real-
ize 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 informa-
tion 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 op-
posite is true. 
For example, suppose that near a business-
cycle 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 
wi~h maturities longer than his desired invest-
ment period. If this interest-rate forecast turns 
out to be correct, he would obtain higher 
yields than if he had chosen shorter maturi-
ties, because of the greater capital gains cre-
ated 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 IF~~(dl~ff'©\l1  l~~~cerrw~ 
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rates fall by less than 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 his investment period. Then ifthe 
forecast is correct, he would obtain a higher 
return from "rolling over" a series of short-
term securities than from purchasing maturi-
ties 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. 
Professionals vs. the market 
In our analysis, we compared the accuracy 
of the Goldsmith-Nagan panel's 6-month-
ahead 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 fore-
cast 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 of no change may actually 
be more accurate than any other forecast. 
Short-period returns on longer-term securities 
are dominated by capital gains or losses re-
sulting 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. There-
fore, even a fully anticipated time pattern in 
3-month Treasury bill yields is not likely to be 
arbitraged away. Moreover, interest-rate fore-
2 
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 fore-
cast of no change. 
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 RMSE of 
the analysts' forecast, at 1.10 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 accu-
racy 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 overstate-
ment, of the true difference between the 
market's and the analysts' forecasting errors.) 
The 14-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. 
Sources of information 
Both forecasts contain two parts-an auto-
regressive component that extrapolates from 
past changes in the bill rate, and a remaining 
component based on other information. The 
analysts' forecast was superior to the market's 
forecast in both respects. The autoregressive 
component of  the market's forecast was not 
significantly different from a prediction of no 
change, or a random walk. Indeed, the mar-
ket's forecast failed to incorporate an upward 
drift in the bill rate attributable to rising infla-
tion in the forecast period, even though this 
drift could have been extrapolated from past 
data. In contrast, the autoregressive compo-
nent of  the ana Iysts' forecast conta  i  ned a pos-itive time trend of 54 basis points per year, as 
well as significant correlations with past fluc-
tuations in the bill rate. In addition, the re-
maining component of the analysts' forecast 
contributed significantly to forecasting accu-
racy, while the corresponding component of 
the market's forecast did not. 
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 pre-
diction 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 likelV to be arbi-
traged away. Forecasters of Treasury-bill rates 
thus should be able to improve the accuracy 
of their forecasts by taking into account any 
such existing time patterns. The Goldsmith-
Nagan 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 fore-
casts 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. 
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) 
1970-1 through 1979-111 
(percentage points) 
Forecast of No Change  1  .25 
Market's Forecast  1.24 
Analysts' Forecast  1.10 
3 BANKING DATA-TWELFTH FEDERAL RESERVE DISTRla 
(Dollar amounts in millions) 
Selected Assets and 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) 
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 
Change 
from 
8/5/81 
- 160 
- 127 
- 96 
136 
- 67 
- 12 
- 22 
- 11 
-1,794 
64 
- 348 
1,328 
1,303 
889 
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Change from 
year ago 
Dollar  Percent 
12,380  8.9 
13,037  11.1 
5,917  17.6 
6,247  13.2 
- 754  - 3.2 
333  33.3 
- 131  - 2.1 
522  3.4 
- 3,881  - 8.8 
- 3,309  -10.3 
491  1.7 
22,585  36.1 
22,868  42.1 
12,066  52.6 
Weekly Averages  Weekended  Weekended  Comparable 
of Daily Figures  8/12/81  8/5/81  year-ago period 
Member Bank Reserve Position 
Excess Reserves (  + )/Deficiency (  - )  60  33  - 61 
Borrowings  60  44  31 
Net free reserves (+ )/Net borrowed( - )  0  - 11  - 92 
* Excludes trading account securities. 
#  Includes items not shown separately. 
Editorial comments may be addressed to the editor (William Burke) or to the author ....  Free copies of this 
and other Federal Reserve publications can be obtained by calling or writing the Public Information Section, 
Federal Reserve Bank of  San Francisco, P.O. Box 7702, San Francisco 94120. Phone (415) 544-2184. 

Can the pros beat the market?

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Can the pros beat the market?

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Research Papers in Economics