Question

An investor earned a 5 percent nominal risk-free rate over the year. However, over the year, prices increased by 2 percent. Was the investor's real risk-free rate less than his nominal rate of return?

Answer 1

The investor's real risk-free rate of return of 3% is less than the nominal rate of 5%, because inflation, which was 2%, must be subtracted from the nominal rate to get the real rate. The real return reflects the actual gain in buying power, in contrast with the nominal return which does not account for inflation.

Step-by-step explanation:

The real risk-free rate of return is the nominal risk-free rate adjusted for inflation. When an investor earns a 5 percent nominal risk-free rate and experiences a 2 percent increase in prices due to inflation, the real gain is less than the nominal rate. To calculate the real rate of return, we subtract the inflation rate from the nominal interest rate. Using the formula:

Real Risk-Free Rate = Nominal Risk-Free Rate - Inflation Rate

For this example:

Real Risk-Free Rate = 5% - 2% = 3%

Therefore, the investor's real risk-free rate of return is indeed less than the nominal rate of return when adjusted for inflation. This difference is crucial because nominal gains can be misleading, especially when they are subject to income tax without considering inflation.