Harvey detected some variation in risk across different contexts and times. Financial literature clearly shows that not only the risk premium associated with currency determines the variation in risk over time, but systematic market risks must also be taken into account. Drawing on the status of the topic, we committed to the task of deriving the classical equation 4 in our own model. In the original version, as seen in equation 5 , the spread on interest rates P fw added to the current exchange rate is determined by the difference between exchange rates subject to exchange rate term fw, i.
However, when doing a simple inspection of the relationship given in equation 12 it follows a likely problem of non-normality assumption of the original data extracted from the money market. In a preliminary trial, as expected, the addition of the logarithmic function to equation 13 allows the data grouped a behavior close to normal see table 4. Normality tests were done on the Fw exchange rate to a one-month period and for a 3 month Fw.
The analysis of panel A in table 4 , on the exchange rate at one month, shows that both curves are asymmetrically positive. Also, equation 13 generates a kurtosis closer to 0 in comparison to the equation 12 which means a more symmetrical distribution. This is ratified by the normal distribution index that shows greater symmetry 2. These results suggest the use of equation 13 can be more efficient and capture the differential in interest rate between countries.
In what follows we will identify, precisely, the change in the behavior of unadjusted spreads, consequence of a steady behavior. A kurtosis 0. Taking a look at the traditional equation 4 , we understand that it is subject to the spot rate but also to the behavior of interest rates in an open economy adjusted statistically by a logarithmic function; however, we note the absence of a permanent measure and unexpected volatility of exchange rates.
There have been several attempts to correctly estimate the level of risk without a strong advance in the field. For example, Brealey et al. Inclusion of the risk premium under the CAPM approach. As long as we focus cornerstone in the development of our predictive equation seems no more than a chimera, then, our company is impossible.
However, we must accept that there are also important and significant advances in the design of the risk premium. If the risk premium of a country decreases, we would expect a drop in interest rates as a significant increase in growth. Then, this risk premium would affect the relationship in the adjusted interest rate and the spot rate as follows:.
The reduced form of the forward exchange rate would be expressed as:. To shape our risk premium proxy , a CAPM approach methodology has been used. Thus, equation 15 under the proposed Damodaran is extended to incorporate an underlying risk that is calculated from a spread between sovereign bonds and the relative standard deviation, RP.
By adding this underlying risk we would be solving the problem caused by the methods of risk measurement which only added risk to the country risk discount rate bond spread. The assumption made by Damodaran is fundamental because it is, correctly, assumed that the whole country risk is not "non-diversifiable". Damodaran's proposal to measure the country risk RP i incorporates the relative standard deviation as follows:.
As proposed by Damodaran, the spread of sovereign bonds would be a useful indicator to approximate quantification of country risk, but, not enough. The spread between interest rates on sovereign bonds is a biased indicator due to investment policies and it is not adjusted for investment decisions of participants. We, therefore, propose a more specific proxy that will redefine the spread according to the proposal made in equation 13 since they correspond directly to the expectations set by investors, but in this case:.
With respect to the adjustments that are made to other variables in the CAPM, we propose the following:. R f : Given that this is the risk free rate, it adapts to the risk-free rate of the base currency, A rate. This is consistent because it assumes that investors prefer to shape their minimum performance expectations from historical behavior of the local risk-free rate country A. However, in our attempt to refine the risk variable, we should observe the following restrictions:.
The elements of the risk premium are divided by to give them a marginal approach,. The risk premium is calculated additive but not a residual, so that market variables join the unit. This approach provides a factor which is interpreted directly as the percentage that the investor in country "A" would have in terms of the situation in the United States. Then, is composed as follows:. We will prove whether or not the model proposed here can predict prices of financial assets.
Our data includes mexican peso MXP against the U. The data spans from January to May , which is collected from Bloomberg. The interest rates comes from the central banks of the involved countries. A test is necessary to measure the degree of success of the function 14 through a practical assessment test which measures the accuracy of forward simulation calculated against the exchange rate at maturity, i.
Figure B gives the behavior of the estimation errors found for forward exchange rates to a month. Moreover, as long as time goes further the error hits Although significant levels warn volatility in the exchange rate behavior, note that the predictive model 14 succeeds, much higher than other models based only on interest rates. The tests were made on random errors and they show a predictive ability to forecast Contrary to the findings of Bekaert and Hodrick in the sense that, for them, the premium does not depend on the conditional variance of forecast error, this is included, successfully, in equation Table 6 shows the accuracy of the classic formulas studied in this paper to forecast the forward exchange rate of the peso against the dollar.
The results suggest, again, to be less predictive in classical models compared to equation Much of this predictive failure can be explained by the lack of a risk premium which equation 18 does contain. How reliable are these results? To this purpose, we apply a validation model that allows us to obtain objective results. Such is the case of U-Thiel index whose results are displayed in table 6 and show that in all the predictions of equation 14 it produces consistent results and investors make rational decisions as our predictors have a better predictive performance than random walk since the index is less than 1.
Correctly predict the prognosis of adjusting the risk premium. Despite the progress shown on the robustness of equation 14 the presence of a marginal risk is still possible. Note the high "peaks" that estimation errors reach: from These findings, however, give us the opportunity to continue refining our proposal, which basically seeks to have a greater degree of modeling and control of random errors.
In this sense, Mosqueda finds that the earning power theory is an approach that would help to explain the random behavior of the variables that make up the prospective model. Indeed, this theory establishes the relationship between profit and capital resources to generate and promote profits.
Here, the formation of expectations rests on historical data which is estimated from past information enough to predict future events. In this sense, equation 14 would follow from the modeling of a risk premium set given its historical performance:. We show the results on the forward exchange rate calculated by the adjusted risk premium see table 7. In all cases risk premium was overstated. In this case the forecast of the peso against the euro demanded a greater degree of adjustment. Also, the regression on the adjusted premium is observed in a multiple correlation coefficient that is very high: a R 2 of 0.
With respect to three-month forward, it also recognizes the need for a greater degree of adjustment on the risk premium because the behavior of the estimation errors may become, mostly, a volatile and erratic behavior over time.
The increase in the coefficient of determination R 2 and R 2 Adj. In previous studies, Mark , for example, found multiple correlation coefficients with levels ranging from 0. On the other side, Neely and Sarno , incorporated the value at risk approach, replicating the study of Mark with coefficients of determination similar to Mark's: 0, for the Canadian dollar, 0.
Based on the above, we can infer that by the adjustment to the risk premium for the possibility of Premium and given a non-seasonal historical behavior, it is possible to achieve a higher degree of predictive ability. In this sense, it is clear the relevance of incorporating the adjusted risk premium, , because it captures, as suggested by Harvey , the performance variant of the premium demanded by investors across different contexts and times. In light of these findings we can conclude that the results are encouraging because they not only model the behavior of the risk premium but the function given in equation 14 has a dynamic characteristic that makes it more powerful.
Note, for example, that the high degree of accuracy and specification permits to reinforce the idea that interest rates can be an unbiased proxy for the exchange rate subject to adjustment under the CAPM approach. We noticed a close and strong correlation between changes in spot rates and forward estimates for equation 14 that allows us to infer that it is possible to keep accurate prices with consistent forecast regarding the terms.
The spot exchange rate itself is an unbiased proxy for forward exchange rates when it is adjusted to the expectations that are formed by investors. The latter goes along the line of Jensen who already establishes the need for a prime to offset risk. Despite the findings of other studies, we found no random relationship in the appropriate level of risk that investors expect, but on the contrary, we see some rationality in shaping expectations of risk that would occur from the different adjusted economic positions of countries.
The results provided by economic models, mainly those based on interest rates, are better specified than those obtained in a study of random walk. Agmon, T. Amihud The forward exchange rate and the prediction of the future spot rate. Journal of Banking and Finance 5: Aliber, R. El juego internacional del dinero. Buenos Aires: Ateneo. Andrada-Felix, J.
Sosvilla-Rivero y F. Marzo- abril. Baillie, R. Bollerslev Common stochastic trends in a system of exchange rates. Journal of Finance A multivariate generalized ARCH approach to modelling risk premia in forward foreign exchange markets. Journal of International Money and Finance 9: Barnhart, S. Szakmary Testing the unbiased forward rate hypothesis: evidence on unit roots, co-integration, and stochastic coefficients.
Journal of Financial and Quantitative Analysis Bekaert, G. Hodrick On biases in the measurement of foreign exchange risk premiums. Journal of International Money and Finance Brealey, R. Myers and F. Allen Principles of Corporate Finance. Caballer V. Working paper. Campbell, J. MacKinlay The econometrics of financial markets. Princeton University Press. Cornell, W. Dietrich The efficiency of the market for foreign exchange under floating exchange rates. Review of Economics and Statistics Cumby, R.
Is it Risk? Explaining deviations from uncovered interest parity. Journal of Monetary Economics Damodaran, A. Investment evaluation. Domowitz, I. Hakkio Monetary variance and the risk premium in the foreign exchange market. Journal of International Economics Elliott, J. Nelson y L. Tarpley Robin Where do companies attempt earnings management, and when do auditors prevent it?
Working paper Cornell University. Engel, C. Long run PPP may not hold after all. Eun, C. Resnick International Financial Management. Fama, E. Forward and Spot Exchange Rates. Efficient capital markets: a review of theory and empirical work.
Journal of Finance, American Finance Association 25 2. The equity premium in textbooks. The theory of interest: as determined by the impatience to spend income and opportunity to invest it. New York: The Macmillan Company. Harvey, C. The World Price of Covariance Risk. Some anomalous evidence regarding market efficiency. Journal of Financial Economics 6 2 : Kaminsky, G.
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