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I would like to thank Thomas Reichmann for encouraging me to undertake this study and for his insightful comments at various stages of development. Discussions with Thierry Pujol and Carlos Vegh, who read the first draft, provided precious suggestions to improve both the exposition and the content. I am also grateful to Laura Papi for her comments and to Valerie Ball for her assistance. The views expressed are the author’s alone and do not necessarily, reflect the view of the International Monetary Fund. For any shortcomings the usual disclaimer applies.
This rational expectation parallel can be explained through an analogy with consumption theory: Engle (1974) points out that Friedman’s permanent income has a natural interpretation in the frequency domain. Rational individuals modify their consumption behavior in response to long swings in their income. Here the hypothesis is that likewise individuals make portfolio choices based on long swings in the value of their domestic currency.
Note that E(π-π*) is a short notation for the conditional expectation E(πt+l=π* t+1|It) where the subscripts refer to discrete time intervals and It is the information set at time t.
Consider the following example: an investor purchases an asset for TL 100 paying 10 percent in transaction fees. Assume the asset yields zero real return. When inflation is 100 percent at the end of the holding period the asset is sold at TL 200 plus another 10 percent transaction fee. So the investor obtains TL 180 net of transaction costs out of an initial outlay of TL 110. The nominal return is therefore about 64 percent and the real loss roughly 22 percent. When inflation is zero the initial outlay is TL 110 and the asset is sold at TL 100 less the 10 percent transaction cost. So, out of a TL 110 initial investment the investor gets TL 90, with an 18 percent loss.
As an aside, the Engle method is entirely based on the periodogram and therefore does not involve the choice of a window that introduces an element of arbitrariness in the spectral estimate (on this topic see, for example, Priestley (1981)).
A second sequence of matrices could in principle be used where the elements aii are set to zero proceeding from the bottom, i.e., aii = 0 for i = T to 1. In other words, the frequencies could be removed starting from the highest. But in this case the estimates of the coefficients would be complex numbers.
The regressions were performed using a MATLAB code written by the author which is available on request.
One must also notice that in empirical finance risk is calculated from past price volatility, but an analogous measure for currency is not equally meaningful.