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Heterogeneous Beliefs in a Sticky-Price Foreign Exchange Model

Expectations formations

According to questionnaire surveys (see cited references in Section 1), the relative importance of technical versus fundamental analysis in the foreign exchange market depends on the planning horizon in currency trade. For shorter planning horizons, more weight is placed on technical analysis, while more weight is placed on fundamental analysis for longer planning horizons. In the present paper, we formulate this observation as

(4)

where denote market expectations and expectations formed by fundamental analysis and chartism, respectively. Moreover, ω (τ) is a weight function that depends on the planning horizon, τ :

ω (τ) = 1-exp (- τ) (5)

Technical analysis, or chartism, utilizes past exchange rates in order to detect patterns that are extrapolated into the future. Focusing on past exchange rates is not considered as a shortcoming for currency traders using this technique since a primary assumption behind chartism is that all relevant information about future exchange rate movements is contained in past movements.

Further, fundamental analysis is based on a model that consists of macroeconomic fundamentals only, which in the present paper is a stickyprice monetary foreign exchange model due originally to Dornbusch (1976) (see the benchmark model in Section 2.1). The most commonly used technique among currency traders using chartism is the moving average model (e.g., Taylor and Allen, 1992, and Lui and Mole, 1998).

According to this model, buying and selling signals are generated by two moving averages; a shortperiod moving average and a longperiod moving average, where a buy (sell) signal is generated when the shortperiod moving average rises above (falls below) the longperiod moving average. In its simplest form, the shortperiod moving average is the current exchange rate and the longperiod moving average is an exponential moving average of past exchange rates.

Thus, when chartism is used, it is expected that the exchange rate will increase (decrease) when the current exchange rate is above (below) an exponential moving average of past exchange rates:

(6)

where MA is an exponential moving average of past exchange rates, i.e., the longperiod moving average. Moreover, the longperiod moving average can be written as

(7)

where the weights given to current and past exchange rates sum up to 1:

(8)

Finally, when fundamental analysis is used, it is expected that the exchange rate will adjust to its fundamental value according to a regressive adjustment scheme:

(9)

where 0 ≤ δ ≤ 1 and s is (the logarithm of) the spot exchange rate in longrun equilibrium, i.e., the exchange rate’s fundamental value. Note that when δ = 1, it is expected that the exchange rate will be in longrun equilibrium the next time period.

By Mikael Bask and Carina Selander

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