Global Fixed Income Research. 3-Month Forwards vs. Consensus Forecasts. 28 July 1999

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1 Global Fixed Income Research July Month Forwards vs. Consensus Forecasts 3M forwards on the USD, JPY, DEM, and GBP money markets have a systematic forecasting error that varies considerably from market to market and from phases of falling interest rates to those of rising. On average, forwards overestimate spots when interest rates are falling and underestimate when rates are rising. The biases indicate profit opportunities on the money markets. The USD and JPY forwards and Consensus forecasts are the most biased. Consensus is a poor predictor of subsequent actual spots especially for the JPY and the USD. The Consensus data can hardly be viewed as a proxy for market expectations. The USD forwards have the largest systematic error in their predictions of spots and generally overestimate spots or sometimes even predict a wrong direction of changes. The JPY forwards have a significant upward bias when interest rates are falling and a significant downward bias when rates are rising. Buy 3M forwards in booms and sell in recessions. Peter Fertig +9 (0) Peter.Fertig@dresdner-bank.com Artem Prokhorov The DEM forwards have a significant downward bias in the phases of falling interest rates. Sell 3M forwards during recessions. The GBP forwards have an equally significant upward bias in the phases of rising interest rates. Buy 3M forwards during booms. Forwards are generally far from market expectations. The relationship between forward bias and overall economic performance is weak, unless it is due to changes in risk or liquidity preferences. Online Research:

2 What forwards actually show market expectations of spots, expected near-term bond returns, or both has been a subject of heated debate. On one side of the controversy there is the Pure Expectation Hypothesis (PEH) saying that forwards are representative of market s expectations of spots. Therefore, if the world is rational, there should be no significant systematic error in their predicting the spot changes. In other words, forwards may well be quite inaccurate predictors but the entire forecast error should disappear in the course of time. It is assumed that traders are risk-neutral. All government bonds have therefore the same near-term expected return and any yield differentials among bonds imply expectations of future rate changes. No arbitrage is possible. On the other side there are proponents of the idea that market prices are set by traders and investors of different risk or liquidity preferences. Forwards differ from expected spots by a risk or a liquidity premium and show expected near-term returns rather than market s expectations of future spot rates (Liquidity or Risk Premium Hypothesis (RPH)). This debate has in turn raised the question as to whether an active yield-seeking investment strategy is altogether justifiable, if in the world of pure rational expectations, no room is left for adding value by trading in money markets. If yield seeking is justified, what investment strategies should be chosen. The paper presents results of a study that, firstly, evaluates forecasting ability of forward rates and of Consensus data, secondly, determines the systematic error (bias) in the forecasts, and thirdly, offers possible explanations of this bias as well as some investment recommendations. The analysis covers money markets for the world s major currencies, the USD, the JPY, the DEM, and the GBP, and helps construct value-adding investment strategies in these money markets. Bias in forwards: March 9 March 99 Forwards are biased in predicting consequent spots. In the time frame between March 199 and March 1999 all forwards were on average underestimating changes in spots except for the USD. Since for the JPY and the DEM there was one dominant phase of falling interest rates 1 starting from early 90s, the underestimation of negative changes in spots is consistent with permanent overestimation of spot rates themselves. This upward bias is very different in the two markets. The average bias in the JPY forward forecasts of spot changes was.1% of the corresponding spot rate average, whereas the DEM forward bias was as low as the more or less negligible 0.9%. Systematic error in forward forecasts of spot changes March 9 March 99 JPY USD DEM GBP Average difference between forward and spot (3M later) Average spot change (3M) Forward bias Forward bias (% of actual spot average) -.1% -7.90% -0.9% -1.3% 1 A term in a monthly time series of interest rates is defined as belonging to a phase of falling (rising) interest rates if the th preceding term is greater (less) than the th succeeding term.

3 3M JPY forward forecast, subsequent spot, and their differential Mar-9 Jul-9 Nov-9 Jul-90 Nov-90 Jul-91 Nov-91 Jul-9 Nov-9 Jul-93 Nov-93 Jul-9 Nov-9 Jul-95 Nov-95 Mar-9 3M JPY forward 3M JPY LIBOR Diff forward minus spot (rhs) Jul-9 Nov-9 Jul-97 Nov-97 Jul-9 Nov The significant upward bias in JPY forwards in the phase of falling rates implies profit opportunities for selling JPY forwards in recessions. Adding value on recessions in Germany should be more difficult. 3M DEM forward forecast, subsequent spot, and their differential Mar-9 Jul-9 Nov-9 Jul-90 Nov-90 Jul-91 Nov-91 3M DEM forward 3M DEM LIBOR Diff forward minus spot (rhs) Jul-9 Nov-9 Jul-93 Nov-93 Jul-9 Nov-9 Jul-95 Nov-95 Mar-9 Jul-9 Nov-9 Jul-97 Nov-97 Jul-9 Nov In the more complex US and UK interest rate trends in the period it is hard to say whether forwards generally underestimate or overestimate the future spot changes. GBP forwards were on average underestimating spot changes in this period, while USD forwards not only were greatly overestimating them, but were doing so with a wrong sign. Even though the trend in interest rates in USA and UK was very similar, forwards biases varied considerably with the USD leading at 7.90% and with the GBP at the second lowest level after DEM (1.3%). USD forwards display the largest bias in the opposite direction to the actual average spot change of this period. They were widely 3

4 predicting higher spots even when the spots were falling. An idea that, perhaps, could explain this clash between the USD and the GBP is that GBP market expectations (that are probably much closer to forwards than those of the USD, as shown in the following) reflect the economic situation and monetary policy characteristics in both recessions and booms equally well. The USD forwards are probably the worst reproducers of expectations. 3M USD forward forecast, subsequent spot, and their differential Mar-9 Jul-9 Nov-9 Jul-90 Nov-90 Jul-91 Nov-91 Jul-9 Nov-9 Jul-93 Nov-93 Jul-9 Nov-9 Jul-95 Nov-95 Mar-9 Jul-9 Nov-9 3M USD forward 3M US TREASURY BILL Diff forward minus spot (rhs) Jul-97 Nov-97 Jul-9 Nov Interestingly enough, the two overseas currencies show the largest systematic errors in their forwards, which are way ahead of those of the other two European currencies. The 7.9% bias of the USD forwards is at the same time almost twice as large as the.1% JPY forward bias. On average, the USD forwards were even predicting the wrong direction of the spot change. This supports the argument that the RPH has been a more appropriate stance for explaining the behavior of JPY forwards in the phase of predominantly falling interest rates, and that of USD forwards in the period of mixed phases. In other words, traders in these markets were relatively more risk-sensitive over the period reviewed, and forward rates were implying expected near-term returns rather than market s expectations of future spot changes. The DEM and GBP forward biases in this time frame were around 1% of the spot average. This makes them practically negligible and contributes to the viewpoint that treats DEM and GBP forwards as pure spot expectations of rational markets. These markets traders are probably on average more risk-neutral than USD & JPY traders. The only way to prove this, however, is by considering a wider time span with a balanced number of falling and rising rate phases for both currencies. This is done in the further course of this paper.

5 Bias in Consensus forecasts: March 9 March 99 The bias in Consensus spot forecasts for Japan in the last 10 years has been the worst among the four money markets (3.9%). This can probably be attributed to the high level of price rigidity of the economy and to the consequently questionable validity of the rational expectation assumption in recessions. The difference between this period s forwards average and Consensus average shows that the risk premium has not been very high in this market. Forwards are relatively close to the market s expectations of future spots, but the market s expectations are not arrived at rationally. Thus, neither forwards nor Consensus forecasts are good enough for the JPY. It can also be the Consensus poor ability to reflect market expectations that causes the discrepancy. Risk premium and Consensus bias March 9 March 99 JPY USD DEM GBP Difference between average forward and average Consensus forecast 0.% 5.5% 1.1% -0.1% Consensus bias Consensus bias (% of actual spot av.) -3.9% -.35% 0.0% -1.39% USD forwards illustrate the best example of RPH. There has been a huge discrepancy between the forward and Consensus averages in the period. The Consensus bias is quite large and the forward bias is the biggest among the currencies. If Consensus can be a fair reproducer of US money market expectations, the USD forwards depict the expectations extremely poorly, and the Consensus forecast is very far from where it should be. This can be probably explained by possible differences between expectations formation schemes for US Treasury Bills and for JPY, DEM, GBP Interbank Rate shown in the Consensus, or by Euro-centrism of the Consensus forecasts. Average size of absolute forecast error March 9 March 99 JPY USD DEM GBP Av. error size of forward forecast Av. error size of consensus forecast Av. error size of no-change forecast Consensus is the most accurate predictor of spots everywhere except GBP. Average absolute errors of Consensus forecasts have been on average less than those of forward rates and of the no-change assumption during the 10-year time span. In general, however, the magnitude of errors made by all predictors is significant. The GBP forwards do a slightly better job in predicting spots than Consensus. The UK is also the only money market where Consensus forecast error has a larger bias than forwards do. Although the figures are relatively small as compared with the other markets, this can be viewed as a reason why GBP forwards are more accurate predictors of spots. In the total error size of forwards there is a somewhat smaller systematic bias than in Consensus. It is important however to remember that those considerations might no longer hold if an adequate phase of a rising interest rate for DEM and JPY was available in the analysis of the Consensus forecasting ability. 5

6 With the DEM forwards and Consensus forecast biases making up less than 1% of spots, and with the gap between average forwards and average Consensus forecasts negligibly small, the German money market shows the closest relationship between Consensus and forwards forecasts of spots and actual subsequent spot rates. The Consensus panelists have obviously had a much better flair for German money market sentiment than for that of any other country in study. The forwards and Consensus forecasts have been reliable indicators of future spot developments in the 10-year frame of mostly falling rates. A vigorous yield-seeking strategy in the German money market has been relatively harder to implement. Bias in forwards: March March 99 A wider time period of 17 years between March 19 and March 1999 conveys distinct phases of falling and rising interest rates in the four money markets and offers an opportunity to study the behavior of forwards in different phases of the economic cycle separately. Unfortunately, the Consensus data are not fully available for the wider time frame. However, the major considerations concerning the forwards bias remain valid. Systematic error in forward forecasts of spot changes JPY USD DEM GBP Phases Down Up Down Up Down Up Down Up Average difference between forward and spot (3M later) Average spot change (3M) Forward bias Forward bias (% of actual spot average) M USD forward forecast, subsequent spot, and their differential Mar- Sep- Mar-3 Sep-3 Mar- Sep- Mar-5 Sep-5 Mar- Sep- Mar-7 Sep-7 Mar- Sep- Mar-9 Sep-9 Sep-90 Sep-91 Sep-9 Sep-93 Sep-9 Sep-95 Mar-9 Sep-9 Sep-97 3M USD forward 3M US TREASURY CONSTANT MATURITIES Diff forward minus spot (rhs) Sep

7 The finding of the 10-year analysis that forwards underestimate spot changes in recessions generally holds for the longer period with distinct phases of falling and rising rates in all the money markets. It can be seen that in phases of rising rates, forwards also underestimate spot changes on average. USD forwards form a special case. They also underestimate spot changes when rates are falling but, again, in a wrong direction. When rates are rising, forwards overestimate spot changes. Thus, US spot rates are permanently overestimated. 3M JPY forward forecast, subsequent spot, and their differential Mar- Sep- Mar-3 Sep-3 Mar- Sep- Mar-5 Sep-5 Mar- Sep- Mar-7 Sep-7 Mar- Sep- Mar-9 Sep-9 Sep-90 Sep-91 Sep-9 Sep-93 Sep-9 Sep-95 3M JPY forward 3M JPY LIBOR Diff forward minus spot (rhs) Mar-9 Sep-9 Sep-97 Sep Japanese forwards considered in the phases of both falling and rising interest rates (although not over the entire 17-year span) show a peculiarity. They have relatively large biases in both kinds of interest rate behavior that cancel each other out over time. There is no reason to believe that the longer-run forward trends do not mirror the market expectations of the future JPY spots. In the separate falling (rising) rate phases there is nevertheless a significant bias, which can be used in investment strategies. Systematic error in forward forecasts of spot changes JPY USD DEM GBP Phases Both Both Both Both Average difference between forward and spot (3M later) Average spot change (3M) Forward bias Forward bias (% of actual spot average) 0.1% -7.5% -1.% 1.% The 17-year consideration does not change much in the USD forward bias, which continues to be the largest among the money markets (7.5%). This confirms the viability of active yield-seeking strategies in this money market. 7

8 3M DEM forward forecast, subsequent spot, and their differential Mar- Sep- Mar-3 Sep-3 Mar- Sep- Mar-5 Sep-5 Mar- Sep- Mar-7 Sep-7 Mar- Sep- Mar-9 Sep-9 Sep-90 Sep-91 Sep-9 Sep-93 Sep-9 Sep-95 Mar-9 Sep-9 Sep-97 3M DEM forward 3M DEM LIBOR Diff forward minus spot (rhs) Sep The 17-year results make corrections to the 10-year DEM and GBP results. The DEM and the GBP show a total bias that is higher than that of the JPY, but still lower than the US one. At the same time the two European forwards have almost opposite biases. The DEM has a significant downward bias in the falling rate phases (.0%), whereas the GBP has an equally significant upward bias in the rising rate phases (.1%). 3M GBP forward, subsequent spot, and their differential Mar- Sep- Mar-3 Sep-3 Mar- Sep- Mar-5 Sep-5 Mar- Sep- Mar-7 Sep-7 Mar- Sep- Mar-9 Sep-9 Sep-90 Sep-91 Sep-9 Sep-93 Sep-9 Sep-95 Mar-9 Sep-9 Sep-97 3M GBP forwards 3M GBP LIBOR Diff forward minus spot (rhs) Sep This gives yield-seeking strategies a raison d être in the DEM market during recessions and in the GBP market during booms. Market expectations cannot be taken at face value, however. Market expectations of spot changes are directly related to the market s view on the economic conditions and the direction of monetary policy. If the market expects an increase in the economic

9 growth rate and in credit demand, it expects rates to rise. Moreover, central banks often influence inflation and growth rates by raising interest rates when the economy is overheated and lowering rates when there is a risk of deflation. Thus, the major mechanism through which a relationship between state interference in the economy (or the overall economic situation) and forwards bias is the way in which market expectations are formed. This paper shows that forwards are generally far from market expectations. To this extent, there probably exists a weak relationship between overall economic development (or state policy) and the forwards bias, unless it is due to risk or liquidity preferences. 9

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