FOREIGN EXCHANGE RISK PREMIUM Let us now consider the effects of foreign exchange risk on the determi-

nation of forward exchange rates. As mentioned previously, the forward exchange rate may serve as a predictor of future spot exchange rates. We may question whether the forward rate should be equal to the expected future spot rate, or whether there is a risk premium incorporated in the forward rate that serves as an insurance premium inducing others to take the risk, in which case the forward rate would differ from the expected future spot rate by this premium. The empirical work in this area has

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young man I lost many cases that I should have won; when I was older I won many that I should have lost. Therefore, on average, justice was done.” Is it comforting to know that on average the correct verdict is reached when we are concerned with the verdict in a particular case? Likewise, the forward rate could be unbiased and “on average” correctly predict the spot rate without ever actually predicting the future realized spot rate. All we need for unbiasedness is that the forward rate is just as likely to guess too high as it is to guess too low.

The effective return differential between two countries’ assets should

be dependent on the perceived risk of each asset and the risk aversion of the investors. Now let us clarify what we mean by risk and risk aversion. The risk associated with an asset is the contribution of that particular asset to the overall portfolio. Modern financial theory has commonly associated the riskiness of a portfolio with the variability of the returns from that portfolio. This is reasonable in that investors are concerned with the future value of any investment, and the more variable the return from an investment is, the less certain we can be about its value at any particular future date. Thus, we are concerned with the variability of any individual asset insofar as it contributes to the variability of our portfolio return (our portfolio return is simply the total return from all our investments).

Risk aversion implies that an investor who is faced with two assets with equal return will prefer the asset with the lowest risk. In terms of investments, two individuals may agree on the degree of risk associated with two assets, but the more risk-averse individual would require a higher interest rate on the riskier asset to induce him or her to hold it than would the less risk-averse individual. Risk aversion implies that people must be paid to take risk. Individuals with bad credit must pay a higher interest rate than those with good credit, otherwise lenders would only lend to the good credit individuals.

FAQ: Are Entrepreneurs Risk Lovers? It is a common perception that entrepreneurs love to take risks, and are a “special breed” of business people. That seems to contradict the idea in eco-

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risk averse. They spend a lot of time to make sure that their risk is minimal in their investments, or spend large amounts on research to make sure that the expected return is sufficient. John Paulson, for example, did a lot of research on the housing market in the U.S. in the mid-2000s, deciding that the housing bubble must burst. By buying Credit Default Swaps that gave him a short position, he benefited a great deal from the downturn. In fact, in 2007 alone

he had profits of $15 billion. So entrepreneurs are just like other people, try- ing to minimize their risk exposure and only investing where the expected payoff is large enough to cover the risk of the investment.

It was already stated that the effective return differential between assets of two countries is a function of risk and risk aversion. The effective return differential between a U.S. security and a security in the United Kingdom is

i US 2 ðE t11 2E t Þ =E t 2i UK 5 f ðrisk aversion; riskÞ ð8 :1Þ The left-hand side of the equation is the effective return differential

measured as the difference between the domestic U.S. return, iUS, and the foreign asset return, (E t11 2E t )/E t 2i UK . We must remember that the effective return on the foreign asset is equal to the interest rate in terms of foreign currency plus the expected change in the exchange rate, where E t11 is the expected dollar price of pounds next period. The right-hand side of Equation (8.1) indicates that changes in risk and risk aversion will cause changes in the return differential.

We can view the effective return differential shown in Equation (8.1) as a risk premium. Let us begin with the approximate interest parity relation:

ð8 :2Þ To convert the left-hand side to an effective return differential, we

i US 2i UK 5 ðF 2 E t Þ =E t

must subtract the expected change in the exchange rate (but since this is an equation, whatever is done to the left-hand side must also be done to

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Thus, we find that the effective return differential is equal to the percentage difference between the forward and expected future spot exchange rate. The right-hand side of Equation (8.3) may be considered

a measure of the risk premium in the forward exchange market. Therefore if the effective return differential is zero, then there would appear to be no risk premium. If the effective return differential is positive, then there is a positive risk premium on the domestic currency (the currency in the numerator of E t , in this case the dollar) since the expected future spot price of dollars is higher than the prevailing forward rate. In other words, traders offering to buy dollars for pounds in the future will receive a premium using the forward market, in that dollars are expected to appreciate (relative to pounds) by an amount greater than the current forward rate. Thus the trader can buy cheaper dollars using the forward market. Conversely, traders wishing to sell dollars for delivery next period will pay a premium to be able to use the forward market to ensure a set future price.

For example, suppose E t 5$2.10, E t11 5$2.00, and F5$2.05. The foreign exchange risk premium is

ðF 2 E t11 Þ =E t 5 ð$2:05 2 $2:00Þ=$2:10 5 0:024

and the expected change in the exchange rate is equal to ðE t11 2E t Þ =E t 5 ð$2:00 2 $2:10Þ=$2:10 5 20:048 The forward discount on the pound is

ðF 2 E t Þ =E t 5 ð$2:05 2 $2:10Þ=$2:10 5 20:024 Thus, the dollar is expected to appreciate against the pound by

approximately 4.8 percent, but the forward premium indicates an appreciation of only 2.4 percent if we use the forward rate as a predictor of the future spot rate. The discrepancy results from the presence of a risk premium that makes the forward rate a biased predictor of the future spot rate. Specifically, the forward rate overpredicts the future dollar price of pounds in order to allow the risk premium.

Given the positive risk premium on the dollar, the expected effective

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The expected return from holding a U.K. bond is

i UK 1ðE t11 2E t Þ =E t 5 0:124 2 0:048 5 0:076 The return from the U.S. bond is 0.10, which exceeds the expected

effective return on the foreign bond; yet this can be an equilibrium solution given the risk premium. Investors are willing to hold U.K. investments yielding a lower expected return than comparable U.S. investments because there is a positive risk premium on the dollar. Thus, the higher dollar return is necessary to induce investors to hold the riskier dollar-denominated investments.

FOREIGN EXCHANGE RISK PREMIUM Let us now consider the effects of foreign exchange risk on the determi-