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The real risk-free rate is a foundational concept in finance. It represents the return on an investment with zero risk of financial loss and zero inflation impact. It is the baseline interest rate before considering inflation or other risk factors. For most government securities, this rate is often assumed to be derived from short-term securities, like Treasury bills, under conditions where no inflation or maturity risk premium exists.
The real risk-free rate is key to understanding how much return investors can expect to receive purely from the time value of money, i.e., the opportunity cost of not using the money until a future date. In our example, the real risk-free rate is given as 3%. This tells us that without considering expected inflation or any other premiums, an investor should earn 3% purely as compensation for deferring consumption.

Expected inflation involves predicting the future rise in general price levels of goods and services. This prediction affects the purchasing power of money, thus impacting the yield on long-term securities. Investors demand compensation for the anticipated erosion of purchasing power over time.
In the calculation of yield for Treasury securities, we factor in expected inflation over the term of the security. For 2-year Treasury securities, we calculate an average expected inflation of 3% based on anticipated inflation rates of 2% in the first year and 4% in the second. For a 3-year security, we average 2% for the first year and 4% for the subsequent two years, resulting in an expected inflation rate of approximately 3.33%.
This component is crucial as it directly influences the yield, ensuring that the investment retains its value against inflationary pressures.

The maturity risk premium compensates investors for the uncertainty associated with longer-term investments. As bonds or other securities mature over an extended period, changes in interest rates and economic conditions can affect the investment’s final value, introducing risk to the investor.
However, in our exercise, the maturity risk premium is explicitly stated to be zero. This simplification means we do not add any percentage to the yield beyond the real risk-free rate and expected inflation. When analyzing real-world scenarios, this might not always be the case. The exclusion here underlines the focus on understanding the fundamental yield components, allowing us to see how yields are structured when this variable is controlled or absent.