By how much is the US dollar overpriced?

This Economic Digest is prepared by Dr Samih Azar (Professor of Economics and Finance at Haigazian University):

 The US dollar keeps on climbing. The daily change tops one thousand pounds, or some 2.5% a day, which is equivalent to an astounding 625% a year. This abrupt and never-ending monetary deterioration no longer surprises anybody. The Lebanese have become insensitive and adamant and have learned to expect continually the worse. Nonetheless, there is a widespread feeling that something unfair and inequitable is unfolding. The intuition of the ordinary people is that the dollar has gone too far and is ashamedly breaking all previous and imaginable records. One needs not be a sophisticated investor to recognize that there is something wrong and obscure underneath. Although there is evidence that the foreign exchange market reacts naturally to fundamental news and events, like for example the current and evolving political temper, the issue is not whether the dollar reacts but whether it overreacts. In this vein, a naïve question can be asked: why did not the dollar react favorably to the oil and gas potential riches and why were not these factored in a lower price of the dollar? This remains a puzzle. The purpose of the present digest is not to provide a theoretical explanation on whether the dollar is correctly priced, which is obviously untrue, but to document the amount of mispricing. The sample studied consists of monthly data from December 2007 till June 2022.

This can be modelled as follows: the first question is whether the foreign exchange market too risky? There are two ways to answer this question. First, a crude measure of risk is the standard deviation of returns. Assuming that monthly returns are independent of each other, then the annualized standard deviation becomes equal to the monthly standard deviation multiplied by the square root of 12. This indicator is around an annual 28.6% for the dollar rate. As a comparison, the same indicator is around 5.05% for the Canadian dollar, 7.46% for the sterling pound, 20% for the US S&P 500 stock market index return (which is a well-diversified portfolio), and around 27% for the average stock in the US Dow Jones Industrial Average (DJIA) that is made up of thirty blue-chip stocks. Based on this yardstick the Lebanese rate per US dollar has a risk commensurate with the 30 US Dow stocks, i.e., is commensurate with the speculative US stock market and is out of reach relative to the major international currencies, and, therefore, fares badly, and thus one can say that the market is indeed too risky especially to risk averse amateurs.

A second method to assess riskiness is to find the degree of risk that investors accept to hold by purchasing the dollar. This is measured by what professionals in the field call the Coefficient of Relative Risk Aversion (CRRA). An estimate of it is obtained by searching for the CRRA that equates exactly the expected utility of the risky asset, which is the rate of return on the dollar, to the expected utility of the risk-free return, which is the rate of interest on dollar deposits. This coefficient is found to be 3.0391. A high CRRA is indicative of an asset that is perceived by investors as having high riskiness. Acceptable and normal CRRAs are positive and either below 10 or more strictly below 5. Based on this method investors seem to consider the dollar as having high riskiness, close to that of the US Nike stock! In other terms the foreign exchange market in Lebanon has indeed high risk. But is this risk compensated for?

Let us turn now to the main question. Is the dollar fairly priced? Or better still is it over compensated? If yes, by how much? To answer to this question, one needs to compare actual return outcomes with theoretical, expected, or fundamental outcomes. One usual and common outcome indicator is the average risk premium of each asset. The average risk premium is calculated as the difference between the asset’s average return and the average return of the risk-free asset. The dollar average return is the sum of the interest yield and the capital gains yield from the appreciating currency. The actual realized premium is calculated as 19.19% for the sample period. The expected premium is (based on the Arrow-Pratt coefficient of risk aversion, which is proportional to the CRRA and to the variance of returns) around 12.43% for the dollar. This translates to the fact that while investors were expecting an annual positive and relative return of 12.43%, they got a much higher actual annual return of 19.19%. They were overcompensated by 6.76% yearly. As a conclusion the dollar is definitely not fairly priced as actual yields outstrip expected yields.

Is the dollar market in equilibrium? The answer to this question depends on the answer to the previous one. If actual and theoretical premiums are equal, then this denotes equilibrium in the financial market. If they are not, then there is disequilibrium, and markets are expected to adjust ultimately. Obviously the two are not equal for the dollar market, which needs to be reappraised, and is assuredly out of equilibrium.

By how much is the dollar overpriced? What is the recommendation to the investor? Is there any announced reward to the Lebanese people? The foregoing reveals that the dollar is severely overvalued, and hence there are probably significant and profitable opportunities from trading the dollar. In the future the dollar is expected to fall dramatically and drive the actual premium close to the theoretical one. Thus, other things being equal, today’s recommendation is to sell the dollar, and hope and count for a reversal of events and trend. One can estimate the extent of overpricing. The difference in yields between actual and predicted is 6.76% per annum. Therefore, the dollar is overpriced by 6.76% per year. For the sample period studied, this represents an overpricing of around 98%. Based on this, the correct price of the US dollar is presently around 25,000, lower than even the Sayrafa rate price. That is the good holiday news to the Lebanese! Seasons greetings.

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