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(21.2)
E0 1 rf (UK)
interest rate
This relationship is called the interest rate parity relationship or covered interest arbitrage parity
relationship. relationship,
Consider the intuition behind this result. If rf(US) is greater than rf(UK), money invested in or covered
the United States will grow at a faster rate than money invested in the United Kingdom. If this interest arbitrage
is so, why wouldn™t all investors decide to invest their money in the United States? One im- relationship
portant reason is that the dollar may be depreciating relative to the pound. Although dollar in-
The spot-futures
vestments in the United States grow faster than pound investments in the United Kingdom,
exchange rate
each dollar is worth progressively fewer pounds as time passes. Such an effect will exactly relationship that
offset the advantage of the higher U.S. interest rate. precludes arbitrage
opportunities.
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
Essentials of Investments, Management Companies, 2003
Fifth Edition




730 Part SIX Active Investment Management


To complete the argument, we need only determine how a depreciating dollar will affect
Equation 21.2. If the dollar is depreciating, meaning that progressively more dollars are re-
quired to purchase each pound, then the forward exchange rate, F0 (which equals the dollars
required to purchase one pound for delivery in the future), must exceed E0, the current ex-
change rate.
That is exactly what Equation 21.2 tells us: When rf (US) exceeds rf(UK), F0 must exceed
E 0. The depreciation of the dollar embodied in the ratio of F0 to E 0 exactly compensates for
the difference in interest rates available in the two countries. Of course, the argument also
works in reverse: If rf (US) is less than rf (UK), then F0 will be less than E0.


What if the interest rate parity relationship were violated? Suppose rf(US) is 6.15%, but the
futures price is $1.90/£ instead of $1.93/£. You could adopt a strategy to reap arbitrage prof-
21.3 EXAMPLE its. In this example, let E1 denote the exchange rate that will prevail in one year. E1 is, of
course, a random variable from the perspective of today™s investors.
Covered Interest
Arbitrage
Initial Cash Flow Cash Flow in One Year
Action (in $) (in $)

1. Borrow 1 UK pound in
E1(1.10)
London. Repay in one year. $ 2.00
2. Convert the pound to $2 and
lend in the United States. $ 2.00 2.00(1.0615)
3. Enter a contract to purchase
1.10 pounds at a (futures) price
of F0 $1.90/£ 0 1.10(E1 1.90)

Total $ 0 $0.033


In step 1, you borrow one pound in the United Kingdom (worth $2 at the current ex-
change rate) and, after one year, repay the pound borrowed with interest. Because the loan
is made in the United Kingdom at the U.K. interest rate, you would repay 1.10 pounds,
which would be worth E1(1.10) dollars. The U.S. loan in step 2 is made at the U.S. interest
rate of 6.15%. The futures position in step 3 results in receipt of 1.10 pounds, for which you
would first pay F0 (i.e., 1.90) dollars each and then convert into dollars at exchange rate E1.
The exchange rate risk here is exactly offset between the pound obligation in step 1 and
the futures position in step 3. The profit from the strategy is, therefore, riskless and requires
no net investment. This is an arbitrage opportunity.




>
2. What are the arbitrage strategy and associated profits if the initial future price is
Concept
F0 $1.95/pound?
CHECK
Ample empirical evidence bears out this theoretical relationship. For example, on January
25, 2000, the interest rate on U.S. Treasury securities with maturity of one-half year was
5.84%, while the comparable rate in the United Kingdom was 5.88%. The spot exchange rate
was $1.6450/£. Substituting these values into Equation 21.2, we find that interest rate parity
implies that the forward exchange rate for delivery in one-half year should have been 1.6450
(1.0584/1.0588)1/2 $1.6447/£. The actual forward rate was $1.644/£, which was so close
to the parity value that transaction costs would have prevented arbitrageurs from profiting
from the discrepancy.
Unfortunately, such perfect exchange rate hedging usually is not so easy. In our example,
we knew exactly how many pounds to sell in the forward or futures market because the
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
Essentials of Investments, Management Companies, 2003
Fifth Edition




731
21 International Investing


pound-denominated proceeds in the United Kingdom were riskless. If the U.K. investment
had not been in bills, but instead had been in risky U.K. equity, we would know neither the ul-
timate value in pounds of our U.K. investment nor how many pounds to sell forward. That is,
the hedging opportunity offered by foreign exchange forward contracts would be imperfect.
To summarize, the generalization of Equation 21.1 is that
1 r(US) [1 r(foreign)]E1/E 0 (21.3)

where r(foreign) is the possibly risky return earned in the currency of the foreign investment.
You can set up a perfect hedge only in the special case that r(foreign) is itself a known number.
In that case, you know you must sell in the forward or futures market an amount of foreign cur-
rency equal to [1 r(foreign)] for each unit of that currency you purchase today.


<
3. How many pounds would the investor in Example 21.2 need to sell forward to Concept
hedge exchange rate risk if: (a) r(UK) 20%; and (b) r(UK) 30%?
CHECK

Country-Specific Risk
In principle, security analysis at the macroeconomic, industry, and firm-specific level is simi-
lar in all countries. Such analysis aims to provide estimates of expected returns and risk of
individual assets and portfolios. To achieve the same quality of information about assets in a
foreign country is by nature more difficult and hence more expensive. Moreover, the risk of
coming by false or misleading information is greater.
Consider two investors: an American wishing to invest in Indonesian stocks and an In-
donesian wishing to invest in U.S. stocks. While each would have to consider macroeconomic
analysis of the foreign country, the task would be much more difficult for the American in-
vestor. The reason is not that investment in Indonesia is necessarily riskier than investment in
the U.S. You can easily find many U.S. stocks that are, in the final analysis, riskier than a num-
ber of Indonesian stocks. The difference lies in the fact that the U.S. investment environment
is more predictable than that of Indonesia.
In the past, when international investing was novel, the added risk was referred to as political political risk
risk and its assessment was an art. As cross-border investment has increased and more resources Possibility of
have been utilized, the quality of related analysis has improved. A leading organization in the expropriation of
field (which is quite competitive) is the PRS Group (Political Risk Services) and the presenta- assets, changes in tax
tion here follows the PRS methodology.1 policy, restrictions on
the exchange of
PRS™s country risk analysis results in a country composite risk rating on a scale of 0 (most
foreign currency for
risky) to 100 (least risky). Countries are then ranked by composite risk measure and divided domestic currency, or
into five categories: very low risk (100“80), low risk (79.9“70), moderate risk (69.9“60), high other changes in the
risk (59.9“50), and very high risk (less than 50). To illustrate, Table 21.4 shows the placement business climate of a
country.
of five countries in the September 2001 issue of the PRS International Country Risk Guide.
The countries shown are the two largest capitalization countries (U.S. and Japan) and the three
most populous emerging markets (China, India, and Indonesia). Surprisingly, Table 21.4
shows that the U.S. ranked only 20th in September of 2001, having deteriorated from the 11th
rank in the previous year. Japan actually ranked higher at 13. Both these developed countries
placed in the “very low risk” category. Of the three emerging markets, it is not surprising to
see Indonesia ranked 115th of 140 countries, placing it in the “high risk” category, while
China ranked 60th, in the “low risk” category, and India ranked 92nd, in the “moderate risk”
category.
The composite risk rating is an average of three measures: political risk, financial risk,
and economic risk. Political risk is measured on a scale of 100“0, while financial and eco-
nomic risk are measured on a scale of 50“0. The three measures are added and divided by
1
You can find more information on the website: http://www.prsgroup.com.
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
Essentials of Investments, Management Companies, 2003
Fifth Edition




732 Part SIX Active Investment Management



TA B L E 21.4
Composite risk ratings for October 2000 and September 2001

Rank, Composite Risk Composite Risk Sept. 2001 Rating Minus Rank,
Sept. 2001 Country Rating, Sept. 2001 Rating, Oct. 2000 Oct. 2000 Rating Oct. 2000

Very low risk
13 Japan 86.5 83.5 3 12
20 United States 83.3 83.8 0.5 11
Low risk
60 China 72.5 73.5 1 47
Moderate risk
92 India 64.8 63.3 1.5 89
High risk
115 Indonesia 59.8 56.5 3.3 118

Source: International Country Risk Guide, September 2001, Table 1.


Political Risk Variables Financial Risk Variables Economic Risk Variables
TA B L E 21.5
Government stability Foreign debt (% of GDP) GDP per capita
Variables used in
Socioeconomic conditions Foreign debt service Real annual GDP growth
PRS™s political
risk score Investment profile (% of GDP) Annual inflation rate
Internal conflicts Current account Budget balance (% of GDP)
External conflicts (% of exports) Current account balance (% GDP)
Corruption Net liquidity in months
Military in politics of imports
Religious tensions Exchange rate stability
Law and order
Ethnic tensions
Democratic accountability
Bureaucracy quality


two to obtain the composite rating. This amounts to a weighted average of the three mea-
sures with a weight of .5 on political risk and .25 each on financial and economic risk. The
variables used by PRS to determine the composite risk rating of the three measured are
shown in Table 21.5.
Table 21.6 shows the three risk measures for the five countries in Table 21.4, in order of the
September 2001 ranking of the composite risk ratings. The table shows that by political risk,
the five countries ranked in the same order. But in the financial risk measure, the U.S. ranked
below China and India (!), and by the economic risk measure, the U.S. ranked above Japan, and
India ranked below Indonesia. More interesting are the ratings forecasts for one and five years.
These forecasts are quite pessimistic about the U.S., whose composite rating is expected to con-
tinue to deteriorate over the years 2002“2006. (This may have been prescient, since it appears
this report was prepared prior to the September 11, 2001, attacks.) At the same time, the ratings
of three of the other four countries were expected to improve over the next five years.
The country risk is captured in greater depth by scenario analysis for the composite mea-
sure and each of its components. Table 21.7 (A and B) shows one- and five-year worst case
and best case scenarios for the composite ratings and for the political risk measure. Risk sta-
bility is defined as the difference in the rating between the best and worst case scenarios and
is quite large in most cases. The worst case scenario is in some cases sufficient to move a
Bodie’Kane’Marcus: VI. Active Investment 21. International Investing © The McGraw’Hill
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21 International Investing



TA B L E 21.6
Current risk ratings and composite risk forecasts

Current Ratings Composite Ratings

Political Risk, Financial Risk, Economic Risk, Year Ago, Current, One-Year Five-Year
Country Sept. 2001 Sept. 2001 Sept. 2001 Oct. 2000 Sept. 2001 Forecast Forecast

Japan 90 45.5 37.5 83.5 86.5 84.5 85.5
United States 89.5 37.5 39.5 83.8 83.3 82.5 80.5
China 62 45 38 73.5 72.5 72.5 76.5
India 56 40.5 33 63.3 64.8 64 68
Indonesia 49.5 35 35 56.5 59.8 52.5 64.5

Source: International Country Risk Guide, September 2001, Table 2B.




TA B L E 21.7
Composite and political risk forecasts

A. Composite Risk Forecasts

One Year Ahead Five Years Ahead

Current Worst Most Best Risk Worst Most Best Risk
Rating Case Probable Case Stability Case Probable Case Stability

Japan 86.5 79.5 84.5 88 8.5 78.5 85.5 91 12.5
United States 83.3 75 82.5 85.5 10.5 73 80.5 84 11
China 72.5 68 72.5 74.5 6.5 67 76.5 81 14
India 64.8 58 64 66.5 8.5 60 68 70.5 10.5
Indonesia 59.8 45 52.5 55 10 46.5 64.5 68.5 22

B. Political Risk Forecasts

One Year Ahead Five Years Ahead

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