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# Reading 19: Foreign Exchange Parity Relations-LOS j 习题精选

Session 4: Economics for Valuation
Reading 19: Foreign Exchange Parity Relations

LOS j: Calculate the real interest rate, given nominal interest rates and expected inflation rates, using the international Fisher relation and its linear approximation.

George Canyon, CFA, an international trader and analyst with Canyon Trading, wants to use the international Fisher relation to determine his trading strategies for the Chinese yuan. Based on his analysis, the expected inflation rate is 7% and the real interest rate is 3%. In order to determine a price for certain corporate debt Canyon is interested in buying, he will use the exact method of the international Fisher relation. Therefore, the nominal interest rate that he should use is:

 A) 10.2%.
 B) 4.0%.
 C) 10.0%.

Using the international Fisher relation: (1 + r) = (1 + real r) × (1 + E (i))

Where:
r = nominal interest rate
real r = real interest rate
E (i) = expected inflation

The nominal interest rate is:
(1 + r) = (1 + 0.03) × (1 + 0.07)
(1 + r) = (1.102)
r = 0.102 or 10.2%

George Canyon, CFA, an international trader and analyst with Canyon Trading, wants to use the international Fisher relation to determine his trading strategies for the Chinese yuan. First, he needs to confirm that the interest and inflation rate relationships are consistent with those of the United States. In his analysis, he determines that the Chinese nominal interest rate is 10.2%, while the U.S. inflation rate is 3% and the nominal interest rate is 6.1%. According to the international Fisher relation, the Chinese inflation rate should be:

 A) 3.00%.
 B) 6.10%.
 C) 6.98%.

Using the international Fisher relation:

Exact methodology: (1 + rFC) / (1 + rDC) = (1 + E (iFC)) / (1 + E (iDC))

Linear approximation: rFC – rDC = E (iFC) – E (iDC)

By substituting:
(1 + 0.102) / (1 + 0.061) = (1 + iFC) / (1 + 0.03)
(1 + iFC) = 1.0698
iC = 6.98%

If the expected inflation is 100% and the real required rate of return is 6%, the nominal interest rate according to the exact form of the Fisher effect is closest to:

 A) 12.0%.
 B) 112.0%.
 C) 6.0%.

According to the Fisher effect, the relationship between the nominal interest rate and the real interest rate and the expected inflation rate is (1 + r) = (1 + real r)[1 + E(i)]; therefore, the problem yields 1 + r = (1.06)(2) = 2.12, or r = 112%.

The Asian Spec Fund, managed by Jonathan Khamal, CFA, engages in currency speculation for its clients. Khamal believes that there is an opportunity to speculate on the Malaysian Ringgit. He believes that the international Fisher relation holds for most currencies on the assumption that real interest rates are constant among developed and emerging countries, but may not hold for Malaysia. The Malaysian nominal interest rate is 7.6% and the annual inflation rate is 4.5%. According to his calculations, the Malaysian real interest rate is:

 A) 2.97%.
 B) 3.50%.
 C) 3.97%.

According to the international Fisher relation:

(1 + Nominal interest rate) = (1 + real interest rate) × (1 + inflation rate)

By substituting, solve for the real interest rate:

(1 + 0.076) = (1 + r) × (1 + 0.045)
(1 + r) = 1.076/1.045
(1 + r) = 1.0297
r = 2.97%

Michael Zotov, CFA, is the economist and portfolio manager of the Zotov Investment Fund. Zotov believes that the Polish economy is due for a significant recovery as a result of governmental austerity programs enacted this year. Nominal interest rates and inflation have begun to trend lower. He wants to be sure that the real interest rate, the real cost of money in Poland, has also declined. The Polish nominal interest rate is 12.3%, while inflation holds at 9%. Assuming the international Fisher relation holds, the Polish real interest rate is:

 A) 3.03%.
 B) 1.03%.
 C) 2.93%.

According to the international Fisher relation:

(1 + Nominal interest rate) = (1 + real interest rate) × (1 + inflation rate)

By substituting, solve for the real interest rate:

(1 + 0.123) = (1 + r) × (1 + 0.09)
(1 + r) = 1.123/1.09
(1 + r) = 1.0303
r = 3.03%

The Asian Spec Fund, managed by Jonathan Khamal, CFA, engages in currency speculation for its clients. Based in Paris, Khamal believes that there is an opportunity to speculate on the Malaysian Ringgit. The current spot exchange rate is 4.417 Malaysian Ringgit per euro. He believes that the international Fisher relation holds on the assumption that the ratios of interest and inflation rates are equal among developed and emerging countries. For comparative purposes, one of Malaysia’s main financial trading partners is Europe. The current nominal interest rate for the European Economic Community is 11.76% and the annual inflation rate is 8.50%. The Malaysian nominal interest rate is 7.60% and the annual inflation rate is 4.50%. According to his calculations, the result of the international Fisher relation and its linear approximation are:

 A) 0.96 and (-0.04).
 B) 1.04 and 0.04.
 C) 0.96 and 0.04.

Using the international Fisher relation:

Exact methodology: (1 + rFC) / (1 + rDC) = (1 + E (iFC)) / (1 + E (iDC))

Linear approximation: rFC – rDC = E (iFC) – E (iDC)

By substituting for the international Fisher relation:

(1 + 0.076) / (1 + 0.1176) = (1 + 0.045) / (1 + 0.085)
1.076 / 1.1176 ≈ 1.045 / 1.085
0.9628 ≈ 0.9631

By substituting for the linear approximation of the international Fisher relation:

0.076 – 0.1176 ≈ 0.045 – 0.085
- 0.0416 ≈ -0.0400

Michael Zotov, CFA, is the economist and portfolio manager of the Zotov Investment Fund based in Germany. Zotov believes that the Polish economy is due for a significant recovery as a result of governmental austerity programs enacted this year. Nominal interest rates and inflation have begun to trend lower. For comparative purposes, he wanted to use Europe as a benchmark since most of his investor base is in Germany. The current spot exchange rate is 4.6404 Polish Zioty per euro. He wants to see if the ratio of interest rates between Poland and the European Economic Community (EEC) are the same as the ratio of inflation rates according to the international Fisher relation. The current nominal interest rate for the EEC is 11.76% and the annual inflation rate is 8.50%. The Polish nominal interest rate is 12.30% and the annual inflation rate is 9.00%. According to his calculations, the result of the international Fisher relation and its linear approximation are:

 A) 1.005 and ?0.005.
 B) 0.995 and ?0.005.
 C) 1.005 and 0.005.

Using the international Fisher relation:

Exact methodology: (1 + rFC) / (1 + rDC) = (1 + E(iFC)) / (1 + E (iDC))

Linear approximation: rFC – rDC = E(iFC) – E(iDC)

By substituting for the international Fisher relation:

(1 + 0.123) / (1 + 0.1176) = (1 + 0.09) / (1 + 0.085)
1.123 / 1.1176 ≈ 1.09 / 1.085
1.0048 ≈ 1.0046
1.005 ≈ 1.005

By substituting for the linear approximation of the international Fisher relation:

0.123 – 0.1176 ≈ 0.09 – 0.085
0.0054 ≈ 0.0050
0.005 ≈ 0.005

Simon Peak, CFA, an international trader and economist for Canyon Peak Trading, feels that the interest and inflation rate differentials should be similar for both China and the United States. The inflation rates for China and the U.S. were 7% and 3%, respectively. Using the linear approximation of the international Fisher relation to calculate the inflation differential, his result is:

 A) 3.2%.
 B) 3.0%.
 C) 4.0%.

Using the linear approximation for the international Fisher relation:
rC – rUS = E (iC) – E (iUS) = 0.07 – 0.03 = 0.04 or 4.0%

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