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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) "-- cIi..'\r:'.. "-< ""'\ \,)j (\3) iT ,-A ro, "'S\ .u )''1-::,1 '1("L\ _(tl-\' h ( I (('v 0 11 "-' (7"V ((\\ ,,\JJ in this do nol reflect the' vievvs of tlH' nlanagernellt R(:'serve [sank of San Franci-ico, or of thp BCiard 01 Coven)()(s of the Federai Reserve Svstem. 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 3 yl?ln G l?pl?/\aN oYl?PI 0 l?!UJOJ!Jl?:) euozpv • l?>JSl?IV • G !!l?Ml?H • f) \QI"@J(d[ \ill,,@CS (G) TI"@J(@[P)@d[ :n 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.... 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