Expected Inflation and Nominal Risk-Free Rate Calculation - CFA Level 1 Exam Preparation

Calculating the Nominal Risk-Free Rate - CFA Level 1 Exam Preparation

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Question

Due to an overheated economy and dramatic monetary stimulus, the U.S. inflation rate is anticipated to increase significantly from its current level. Specifically, the inflation rate is expected to increase from 3.5% to 8% per year, and this increase should be considered significantly large by historical standards. The current nominal interest rate in the U.S., as measured by the quoted rate on U.S. 10-year notes, is 6.75%. Further, the real inflation-free rate of interest is currently at

3.25% per year, and this rate is not anticipated to change. Assuming this increase in inflation has not been factored in, what is the appropriate value for the nominal risk-free rate?

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Explanations

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A. B. C. D. E. F.

C

When either the real "inflation-free" interest rate or the expected inflation rate are significantly large, the nominal risk free rate is calculated using a different equation than that which is used for lower expected inflation rates. Specifically, the calculation of the nominal risk-free rate of interest when the inflation-free rate of interest and/or the inflation premium are significantly high, the calculation of the nominal risk-free rate is as follows:

Nominal RFR = (1 + Real RFR)(1 + E(I)) - 1

Where: Real RFR = the real inflation-free rate of interest and E(I) = the anticipated inflation rate,

In this example, all of the necessary inputs have been provided. Imputing these values into the equation above will yield the following:

Nominal risk-free interest rate = {[(1 + 0.0325)(1 + 0.08) - 1] * 100} = 11.51%

When the inflation-free rate of interest and/or the inflation premium are low, then the equation above can be simplified to the following:

Nominal RFR = Real RFR + Inflation premium.

If you chose 11.25%, remember that when the real inflation-free rate of interest and/or the inflation premium are significantly large, the calculation of the nominal risk-free rate must involve a different equation than when these rates are small.

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