ریسک ارز خارجی و مداخله بانک مرکزی متغیر با زمان : برآورد سود از مداخله و حدس و گمان

Failure to risk-adjust estimates of profits, from central-bank foreign exchange intervention or from private speculation, can have large effects on the estimated profits, including changing signs. Many choices arise in deciding how to adjust profits for risk. The time period over which a market model is fit has mixed effects on calendar-year profits; variations in profits across calendar years is much more important than the period over which the market model is fit. In some cases, but not in all, results are sensitive to whether a US stock market index is used or a world market index. For non-US central banks or private speculators, the relevant market index might be denominated in USD, but alternatively might be denominated in a foreign currency. For the Swedish central bank, estimated profits decline importantly if an index measured in USD is used instead of an index measured in SEK. In estimating market models where beta is conditioned on some measure of intervention, likely candidates are intervention or cumulative intervention; the first has an effect for one or a few days, the second has long-term effects. Estimates show that the choice can make an important difference, though the effects are not all one way.

Central banks are often accused of making large losses on their foreign-exchange market intervention, even in periods without acute balance of payment crises. The literature contains many estimates of central bank profits and losses from foreign-exchange intervention (Sweeney, 1997 gives a review). Recent work suggests that most estimates are unreliable for a number of reasons (Sweeney, 1997, Sweeney, 1999a, Sweeney, 1999b and Sjöö and Sweeney, 2001). Past work fails to adjust estimated profits for the foreign-exchange risk premium that exposed positions are expected to earn part of the estimated profits is payment for risk. These reported profits, therefore, are flawed estimates of economic profits, sometimes seriously flawed. Further, much work fails to take account of the fact that the exposed position on which the central bank earns intervention profits is an integrated variable, or at the least a near integrated variable, so that usual statistical inference can be badly misleading. This paper explores risk-adjustment of estimated profits; Sjöö and Sweeney (1999) discuss the integrated variable issue. Most previous work on central-bank intervention profits uses simple rates of return rather than abnormal rates of return, i.e., rates of return adjusted for risk. Even with risk adjustment, work in other asset markets shows that inferences can depend strongly on how returns are adjusted for risk, a major issue in event studies. Frequently, abnormal returns are found from market models, the simplest of operational asset pricing models. For analyzing global investments, the market proxy used is critical for results (Reilly and Akhtar, 1995), and may well be critical for judging intervention profitability. The same risk-adjustment issues apply to estimated profits earned by foreign-exchange speculators, for example, from following mechanical trading rules. Early work on trading rules does not risk-adjust profits, for example, Fama and Blume (1966) on the US stock market. Sweeney (1988) discusses shortcomings in their work and proposes profit measures that use mean-adjustment for risk. Early work on speculative profits in foreign-exchange markets does not adjust for risk (Dooley and Shafer, 1976 and Logue et al., 1978). Later work uses mean-adjustment for risk (Sweeney, 1986, Surajaras and Sweeney, 1992 and Levich and Thomas, 1993, for example), and in a few cases uses market-model adjustment (for example, Sweeney, 1990 and Sweeney and Lee, 1990). Several issues arise in using market models to find abnormal rates of return on foreign-currency positions. First, market-model parameter estimates often vary over time. Experiments below show no clear pattern in estimated calendar-year profits from using shorter or longer estimation periods. The profit variations across calendar years are much more important than the period over which the market model is fit. Second, beginning in the 1980s event-study researchers often take care to allow for the possibility that changes in betas are associated with the events studied (Brown et al., 1988 and Chan, 1988, for example). A central bank may take a long position when risk is high, earn a risk premium as a result, and appear to make profits. In estimating profits, variations in beta that are associated with intervention must be accounted for in estimating market models to calculate abnormal returns. In experiments below, taking account of such associations often affects estimated intervention profits, importantly reducing Fed profits, less clearly affecting profits for the Swedish central bank, the Riksbank. Time-varying beta risk can also be of great importance for estimating private speculators’ foreign-exchange profits. As reported below, foreign-exchange market betas, conditioned on central-bank intervention, can and often do show substantial and significant time variation. Conditioning betas on intervention can importantly affect estimated profits both for central banks and for private speculators (Sweeney, 1996). Third, choice of market index can be critical for any asset pricing model with a market factor. Some asset pricing models suggest a value-weighted world market index that includes all assets; such an index is not and may never be available (Roll, 1977). Further, in practice portfolios have large home country bias; for example, US pension funds allocate only 10% of their portfolios to foreign assets even though foreign assets make up 70% of the world market portfolio (Solnik, 1997). Thus, using a world market index may not be reasonable. A common approach in testing asset pricing is to use a range of indices to investigate sensitivity (Stambaugh, 1982), the tack taken here. Fed intervention profits are relatively insensitive to the index used, but Swedish central bank profits can be importantly affected. Fourth, for a small open economy like Sweden, the currency in which the world market index is measured may be important. Dollars are not an obvious choice for a Swedish speculator or the Swedish Riksbank. Currency denomination for the index reflects whether the central bank or speculator considers exchange-rate risk as idiosyncratic or systematic. In experiments below, Riksbank profits are sensitive to measuring the market index in Swedish crowns or dollars. Fifth, the literature uses several measures of intervention, including intervention and cumulative intervention (Dominguez and Frankel, 1993a and Dominguez and Frankel, 1993b). A central bank's intervention profits in each period are the product of its cumulative intervention to the start of the period times the abnormal rate of return during the period. In any association between beta and intervention, the intervention variable need not be cumulative intervention. Experiments below compare results for conditioning the exchange rate's market beta on intervention cumulative intervention. An important issue, not addressed here, is the role of predetermined variables in the market model estimated for risk adjustment. In asset pricing models estimated on monthly data, a wide variety of predetermined variables are significant in predicting coming rates of return. This paper's models are estimated with daily data for use with daily intervention; because relatively few series are available on a daily basis, investigating the role of predetermined variables is left for later work. Section 2 discusses briefly the measurement of intervention profits. Section 3 reports empirical results that shed light on how the market-model estimation period affects estimated profits from Fed intervention. Section 4 discusses the effects of alternative market indices on intervention profits for the US. Section 5 extends this discussion by considering the effects on the Swedish Riksbank's intervention profits from denominating ‘the’ market in USD or alternatively in SEK. This section also considers the effects of conditioning the market beta on alternative measures of central bank intervention. Section 6 offers a summary and some conclusions.

In evaluating central-bank intervention profits, or a private speculator's profits from foreign exchange positions, results can be quite sensitive to how the profits are adjusted for risk. This paper explores several issues in risk-adjustment, focusing in particular on how changes in systematic risk may be associated with central bank intervention. Since the 1980s, event-studies often allow for the possibility that changes in betas are associated with the events studied. Intervention can be thought of as the ‘event’ in studies of central-bank intervention profits. Hence, it is important to investigate association between intervention and the market beta of the return on a currency position. For example, a central bank might take a long position when risk is high, earn a risk premium as a result, and appear to make profits when it is only compensated for risk. In estimating profits, systematic associations of beta and intervention must be accounted for in estimating the market model used to calculate abnormal rates of return. Time-varying beta risk can also be of great importance for estimating private speculators' foreign-exchange profits. For example, Surajaras and Sweeney (1992) report results for profits mean-adjusted for risk, and state that the estimated profits are little changed if market-model adjustment is used. Their view is justified by the fact that market betas for foreign-exchange appreciation are typically close to zero, so market-model and mean-adjustment are very close in this case. But, as reported above, foreign-exchange market betas can and often do show substantial and significant variation over time when the betas are conditioned on central-bank intervention. In other words, using an unconditional market model to adjust foreign-exchange profits for risk can give very different results from using a model where the market beta is conditioned on intervention. Market-model parameter estimates often show variability over time. Experiments reported here show that estimated profits vary greatly across calendar years, but that choice of market model within a calendar year has relatively small effects on the estimated profits. One might estimate profits over a multiyear period by taking a whole-period estimate, or by estimating profits for each year and then summing them. For Fed intervention, the whole-period profits are substantially smaller than the profits across years for DEM intervention, but the reverse is true for JPY intervention. There is a good deal of dispute over which market index to use in an asset pricing model that includes a market factor. A common approach, reported on above, is to use a range of indices to investigate whether inferences are sensitive to the index chosen. In comparing three US stock market indices and one world market index, estimated profits for Fed intervention are relatively insensitive to which US index is used, but use of a world index has important positive effects on estimated profits from DEM intervention. Similar experiments are reported for the Swedish central bank, the Riksbank, for a world market index and the Stockholm Stock Exchange index. For a small open economy like Sweden, what currency should the world market index be measured in? For example, for the Swedish Riksbank, the market index might be measured in Swedish crowns (SEK) or in USD. Similarly, for an American speculator a world market index measured in dollars may appear natural, but not for a Swedish speculator. The choice of currency denomination for the index will reflect whether the central bank or speculator views exchange-rate risk as idiosyncratic or systematic. Experiments show that Riksbank intervention profits are sensitive to the market index used. With the market measured in SEK, profits tend to be positive and substantial, but profits tend to be smaller and even negative when the index is measured in USD. The literature uses several measures of intervention, including intervention itself, but also cumulative intervention. A central bank's intervention profits in each period are equal to the central bank's cumulative intervention to the start of the period times the abnormal return during the period. However, in any association between beta and intervention, the intervention variable need not be cumulative intervention. Experiments above show that for Riksbank profits, results are sensitive to whether beta is conditioned on intervention or cumulative intervention, but there is no clear pattern of one or the other intervention measure giving reliably higher intervention profits.