Chapter 5
Yields, Risk Premium, and Terms of Trade
Abstract
The theoretical framework, Purchasing Power Parity (PPP), and Interest Rate Parity (IRP) have very clear implications. Under such idealized conditions, we expect that in an unfettered free market, real rates of returns will be equalized. Add tax rates, regulations, and/or transportation costs, and we can easily explain how economic disturbances give rise to deviation from PPP and IRP, which are correlated to the stock market’s relative performance. More importantly, some of the arguments presented here suggest that fiscal policy differences and other economic shocks will give rise to the changes in terms of trade, as well as impacting the risk premium as we have defined it. To the extent that we can establish the connection between the shocks/policy changes and the terms of trade and risk premium, one can easily develop a country-based portfolio strategy. For large enough economic shocks, the disturbance could last several months or years, creating a long wave that an astute portfolio manager with the appropriate framework may ride to the top of the charts.
Keywords
environments
Fisher equation
Interest Rate Parity
Law of One Price
Purchasing Power Parity
risk premium
In a frictionless world where factors and products are free to move, we would expect to find that the price of each commodity will be arbitraged across localities. That is, the Law of One Price or Purchasing Power Parity (PPP) will hold at the individual level. Under these conditions, if the tastes are the same across the different localities, one can then show that the consumer basket will be the same across the world. In such a case, the consumer price index (CPI) in local currency converted into a common currency will also be the same across the world. The Law of One Price or PPP can be extended to the broad consumer basket.
Profit maximization, and an absence of transaction costs are the starting point of our economic analysis. With these two assumptions, the arbitrage process applied to commodities leads to the PPP conditions outlined earlier [1]. And when the arbitrage is applied to securities, such as bonds, the arbitrage process leads to the Interest Rate Parity (IRP) [2]. The concept is the same, except that a time span is now involved. The arbitrage comparison is as follows: to compare the yields on, say one year bond/deposit in local currency or euros to those of a foreign security, investors first have to convert the euros into foreign currency; hence the spot exchange rate is needed. Then one has to invest in the foreign deposits and, at the end of the time period, repatriate the investment; thus a future exchange rate is needed to convert the foreign deposit back into local currency. The IRP requires that the euro yield matches the foreign yield plus any exchange rate change fluctuations. Again, if the yield comparisons occur between two countries within the Eurozone, there is no exchange rate fluctuation. Then IRP and arbitrage suggest that, absent transaction and/or transportation costs, the yields of countries in the Eurozone have to converge.
Next we introduce a modified version of the Fisher equation:
At this point, we can show that when both the PPP and IRP conditions hold, the real rates of return plus the risk premium are also equalized across these economies. Therefore the deviations from PPP and IRP may be interpreted as differences in either real rates of return or risk premium across the economies. We have already discussed and established the impacts of the terms of trade changes in the economy and financial markets. Up to this point we have ignored the effect of a changing risk premium, a deficiency that we intend to remedy next.
In addition to impacting the interest rate differential across national economies, the risk premium will also have an impact on valuation. The impact is easily established: the higher premium effectively increases the discount rate, and thus reduces the value of an income stream. If the two assets across national borders now have different risks, then it is safe to assume that the IRP condition will be “violated,” reflecting the gross of risk premium. If we are willing to assume that, in the long run, these violations of IRP will be corrected, then we have a mean-reverting process. During the risk increasing part, valuation will rise slower than expected and may even decline. In turn, during the period of declining risk premiums, then valuation will improve and may even appreciate.
The Different States of the World
The impact from risk premium increases on an asset valuation is analogous to a decline in the real rates of returns. In some cases the changing risk premium (i.e., the violations from IRP) will reinforce the effects of the real return and/or inflation differentials (i.e., the violations from PPP). However, in other cases these two effects will work to cancel each other out. Under some circumstances investors could face a signal extraction problem. For example, is a rising interest rate differential the result of an increase in risk premium (bearish scenario) or is it the result of an increase in the economy’s relative rate of return (bullish scenario)?
We contend that there is a way to deal with the signal extraction problem. A top-down approach helps a great deal. The nature of the different economic disturbances may help identify the source of the deviation from PPP and/or IRP and armed with that, one may be able to ascertain the net effect of the violations of PPP and IRP on the markets.
To simplify any possible signal extraction problems and to disentangle the impact of the different shocks, we begin by identifying the different states of the world that the IRP and PPP violations may generate.
The IRP condition holds while the PPP does not: This means that the interest rate differential across countries will be zero, while the inflation rate differential will not be so. In the special case, where there is no risk premium, the idealized situation of no transaction costs and perfect foresight, the equation shows that the real rate of return has to equalize across countries. This is a very important insight that allows us to simplify the framework. Under these circumstances, the real return differential across countries is the mirror image of the inflation differential across countries. This will give rise to two different states of the world:
- 1. Countries that have a below average and/or falling inflation will tend to have an above-average and rising rate of returns and thus should have an appreciating bourse relative to the EU index.
- 2. Countries that have an above average and or rising inflation will tend to have a below average and falling rate of returns and thus should have a depreciating bourse relative to the EU index.
- The PPP condition holds while the IRP does not. If PPP holds then it follows that the differences in yields between a country and the EU yield reflects that country’s risk premium relative to the EU.
- 3. Given most valuation models, positive risk premiums will, all else the same, result in a lower valuation. A rising risk premium results in a declining valuation in absolute terms and relative to the EU.
- 4. In contrast, negative risk premiums will, all else the same, result in a higher valuation in both absolute terms and relative to the EU. In addition, a decline in the risk premium results in a valuation over and above that implied by either the PPP or a rising relative rate of return in the economy in question.
- The previous paragraphs suggest that it is extremely important to identify the nature of the disturbances to determine whether the bourses’ relative performance will be below or above the relationship suggested by the PPP or IRP relationships. The discussion also suggests that it is extremely important to identify the beginning, peak, and end of the risk premium and/or inflation/real rate of return cycles, since they allow us to anticipate markets’ accelerations or decelerations, a key ingredient to a successful international investment strategy.
- The IRP and PPP violations reinforce each other: That gives rise to two different scenarios.
- 5. A rising risk premium and deteriorating terms of trade will reinforce each other to reduce a country’s competitiveness. The rising risk premium will reduce the discount rate, while the declining terms of trade reduces the real rates of return. Either of these two variables is sufficient to reduce asset valuations. The two combined will reinforce each other and produce what would appear to be turbocharged valuation results, both in absolute terms and relative to the EU. The asset decline will be larger than what would normally by implied by the PPP and/or real rate of return relationships.
- 6. A falling risk premium and improving terms of trade will each have a positive impact on valuation, both in absolute terms and relative to the EU. Hence the combined effect will reinforce each other, turbocharge the valuation, and create the impression of overshooting when compared to the historical relationships when the two effects are not jointly present.
- The IRP and PPP violations work to cancel each other out. These are the most difficult situations for investors. They will have to make a determination as to which of the two opposing forces will dominate, and then invest accordingly. Depending on the situation, we could get one of these different outcomes.
- 7. If the bullish factor dominates, that is improving terms of trade or a declining risk premium, then we expect valuations to rise in both absolute and relative terms, and thus an increased exposure to that economy may be warranted.
- 8. If the bearish factor dominates, that is a deteriorating terms of trade or a rising risk premium, then we expect valuations to decline, both in absolute and relative terms. Thus, a reduced exposure to that economy may be warranted.
Identifying the Different Environments
The creation of the euro is a good example to attempt to identify some of the environments outlined in the previous paragraphs. Since we argue that Germany is the anchor country, it follows that the other countries converged to Germany’s inflation rate during the transition to the euro. Again, if Germany is the anchor country, then it is the benchmark against whom the risk premium is measured.
The first part of the information presented in Fig. 5.1A shows the convergence effect. Fig. 5.1B denotes the PPP or IRP world. Fig. 5.1C illustrates the divergence of bond yield caused by the financial crisis.
Figure 5.1 Eurozone bond yields.
The three episodes/sections in the graphs can be used to illustrate the usefulness of the PPP and IRP approach. One aspect that we have already discussed is the investment implication of the convergence effect. We anticipated it then, and looking back we can explain the context of the risk premium. The adoption of the The Euro resulted in a convergence that eliminated the relative risk premium of the member countries. Since the country with the best inflation track record became the anchor of the monetary union, the inflation rate of the whole region converged to that of the country with the superior monetary policy. Viewed this way, Germany’s inflation did not deteriorate, that is Germany did not lose, while the inflation outlook improved for the rest of the Eurozone. The risk premium of the Eurozone members fell and, as a result, valuation rose. The gains were the largest for those countries, which experienced the largest decline in risk premium.
However, the financial crisis reversed many of the gains or reduction in risk premium experienced by the EU countries with the weaker financial conditions. While we could enumerate the differences in fiscal policies across the countries in the Eurozone, ex-post there is a very simple way to identify the different groups: separate them by changes in the risk premium in the aftermath of the financial crisis.
Fig. 5.2A and B separate the countries into those who experienced the largest increase in the risk premium and the rest of the Euro countries. Upon inspection of the figures, it is visually apparent that the countries with the largest increase in risk premium are none other than the Portugal, Ireland, Italy, Greece, and Spain (PIIGS). Within the second group, it is apparent that Belgium is the country with the largest risk premium increase. However, the increase is smaller than any of the PIIGS. The disparity in risk premium increases could be easily explained in terms of the fiscal policies adopted by these countries, that is the tax and spending rates, as well as their debt levels.
Figure 5.2 Selected Eurozone countries risk premium.
Summary
The theoretical framework, PPP, and IRP have very clear implications. Under such idealized conditions, we expect that in an unfettered free market, real rates of returns will be equalized. Add tax rates, regulations, and/or transportation costs, and we can easily explain how economic disturbances give rise to deviation from PPP and IRP, which are correlated to the stock market relative performance. The framework also shows that increases in risk premiums may sometimes reinforce or offset the terms of trade deviations. When the risk premium reinforces the terms of trade effect, the former will add an additional impetus to the market and the relative performance could very well be interpreted as an overshooting. However, as we have argued, the relationship is completely justified and explained by the two explanatory variables. More importantly, some of the arguments presented here suggest that fiscal policy differences and other economic shocks will give rise to the changes in terms of trade, as well as impacting the risk premium as we have defined here. To the extent that we can establish the connection between the shocks/policy changes and the terms of trade and risk premium, one can easily develop a country-based portfolio strategy. For large enough economic shocks, the disturbance could last several months or years, creating a long wave that an astute portfolio manager with the appropriate framework may ride to the top of the charts.
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