Lineamientos para el fortalecimiento de capacidades

In this section, we discuss an indirect approach to modelling fair value, which is fre- quently used in financial markets. Relatively few macroeconomic assumptions are being made with regard to the drivers of the fair value. Instead, the approach depends on the assumption that speculative activity is the principal cause for misaligned exchange rates. To our knowledge, this Indirect Fair Value (IFV) approach has not been pre- viously formalised in the academic literature.

Market participants use this kind of model as a way to assess where the exchange rate would be had speculative activity not pushed it away from a loosely defined fair value concept. The idea that speculative activity can create these deviations is based on two assumptions. First, speculative order flow has an impact on exchange rates (Lyons, 2001). Second, one has to assume that speculative order flow is mean reverting over the medium term. The latter is a corollary of the definition of speculative activity, which is based on the assumption that speculators will at some stage reverse their position and realize either a profit or a loss.

Two measures of speculative positioning often employed in this approach are risk reversals or International Money Market (IMM) positioning (Mogford and Pain,2006). The former is defined as the difference between the implied volatility between compa- rable out-of-the-money call and put options. When the majority of speculative investors expect appreciation, demand for call options will likely rise relative to the demand for puts. As a result the relative price, and implied volatility, will increase for the call options relative to the put options. The second measure is based on the weekly Com-

3.4. Models/Taxonomy

mitments of Traders (COT) Report, which contains information about the positioning size of so-called non-commercial traders on the IMM futures exchange, part of the Chi- cago Mercantile Exchange (CME).6 _{The report is restricted to data for the most liquid} exchange rates against the US dollar.

These measures of speculative positioning tend to be stationary and highly correlated with spot exchange rates (Campa et al., 1998; Mogford and Pain, 2006). Moreover, indicators of speculative positioning also tend to be strongly autocorrelated (Dunis and Lequeux, 2001), which implies that periods of speculatively driven misalignments tend to persist for a certain time, but typically not more than a few months.

Most measures of speculative positioning have a clearly defined neutral point. For example risk reversals are equal to zero when the implied volatilities of equivalent out- of-the-money call and put options are identical. A similar argument applies to the net positions of non-commercial traders on the IMM. In practice, however, indicators of speculative positioning tend to oscillate around a non-zero mean. Speculative investors may on average perceive that the appreciation of a currency is more likely than the depreciation, or vice versa. Moreover, these indicators can display structural breaks, or trend stationarity.

In practice, these factors tend to affect the choice of sample size. On one hand the sample has to be large enough to guarantee stationarity and the mean reverting properties of the indicators of speculative positioning. On the other hand, longer samples create the risk of having to deal with trends or structural breaks in the positioning variable. Practitioners tend to look at daily or weekly data with sample sizes between 6 months and 3 years, which emphasizes the more trading-oriented concept of fair value underlying this approach. This approach also highlights that the statistical properties of the input variables play a far bigger role than in most other concepts of fair value.

More formally, we can express the relation between the level of the exchange rate

6_{See www.cftc.gov/marketreports/commitmentsoftraders/index.htm for details on the COT}

3.4. Models/Taxonomy

and the variables of speculative positioning in an equation similar to (3.1):

et=β′Zt+θ′St+ǫt, (3.10)

where et is the spot exchange rate observed in the market, Zt is a vector of broadly

defined fundamentals,Stcontains variables reflecting speculative activity,ǫtis a residual

term, andβ andθare coefficient vectors. Given that the focus is on relatively short-term deviations from fair value, and daily or weekly data, some of the fundamental variables inZt can potentially be approximated by linear and higher-order time trends.

The exchange rate etis typically expressed in nominal terms and expected to display

some form of long-run relationship with Zt. Equation (3.10) is estimated using coin-

tegration techniques, hence et and Zt are expected to display unit roots, whereas St is

expected to be stationary around a constant mean, as mentioned above. When these criteria are not satisfied, the model fails to produce a fair value estimate.

Having estimated Equation (3.10) it is possible to use the parameter estimates to calculate fair value in the following way:

¯

et = ˆβ′Zt+ ˆθ′S,¯ (3.11)

with the overbar denoting the value of S that is consistent with neutral speculative positioning. As we discussed above, neutral speculative positioning is not well defined in the presence of a non-zero mean in the S, though in most cases the natural choice would be to simply use the sample mean.

With most of the focus on modeling the transitory forces, users of these fair value models are typically agnostic with regards to the choice of fundamental variables in Zt.

Moreover, as practitioners tend to focus on very short-term deviations from fair value, there is a strong preference for financial and macro data available at daily or weekly frequency.

We illustrate the concept using the exchange rate of the Canadian dollar against the US dollar from January 2004 to January 2007. The daily spot exchange rate is