The US 10-Yr Treasury Rate is 4.2%, inflation in Peru is 9% and the inflation rate in the US is 3%. Using the interest rate arbitrage approach, what is the risk-free rate in Peru.[Fill in the blank]单项选择题
A
a. 10.3%
B
b. 9.2%
C
c. 7.4%
D
d. 11.4%
E
e. 10.6%

Question

The US 10-Yr Treasury Rate is 4.2%, inflation in Peru is 9% and the inflation rate in the US is 3%. Using the interest rate arbitrage approach, what is the risk-free rate in Peru.[Fill in the blank]

BlackTom AI · Accepted Answer

Real (inflation‑adjusted) interest rates should be equal across countries under the interest‑rate arbitrage approach, so use the Fisher relation: (1 + nominal) = (1 + real) × (1 + inflation). Solve for the common real rate in the US, then apply it to Peru.

1) Knowledge points and formulas
- Fisher equation: 1 + nominal = (1 + real) × (1 + inflation).
- Interest‑rate arbitrage implies identical real (risk‑free) rates across countries absent capital controls or risk premia.
- Steps: compute US real rate from US nominal and US inflation; then compute Peru nominal rate from that real rate and Peru inflation.

2) Step‑by‑step reasoning and calculations
- US nominal rate = 4.2% → 1 + nominal_US = 1.042
- US inflation = 3% → 1 + inflation_US = 1.03
- Solve for real rate: 1 + real = (1 + nominal_US) / (1 + inflation_US)
  = 1.042 / 1.03 = 1.011650485...
  → real ≈ 0.011650485 = 1.1650485% ≈ 1.165%

- Now compute Peru nominal using Peru inflation = 9% (1 + inflation_PE = 1.09):
  1 + nominal_PE = (1 + real) × (1 + inflation_PE)
  = 1.011650485 × 1.09 = 1.103
  → nominal_PE = 1.103 − 1 = 0.103 = 10.3%

3) Intermediate steps shown above (division then multiplication) lead to 10.3%.

4) Why this is correct
- The calculation enforces equality of real rates via Fisher’s multiplicative formula, not by simply adding inflation differentials. That multiplicative adjustment yields exactly 10.3% for Peru’s nominal risk‑free rate.

5) Why other options are incorrect
- b (9.2%), c (7.4%), d (11.4%), e (10.6%): none follow the Fisher equality. A common mistaken shortcut is to add the inflation differential to the US nominal (4.2% + (9% − 3%) = 10.2%), which still is not an offered option and is less accurate than the correct multiplicative Fisher method. The listed wrong answers result from incorrect arithmetic or using additive rather than multiplicative (Fisher) relationships.

Conclusion: Using interest‑rate arbitrage and the Fisher relation gives a Peru risk‑free (nominal) rate of 10.3%, which matches answer (a).

The US 10-Yr Treasury Rate is 4.2%, inflation in Peru is 9% and the inflation rate in the US is 3%. Using the interest rate arbitrage approach, what is the risk-free rate in Peru.[Fill in the blank]单项选择题

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