Risk-Free Rate
The risk-free rate is the theoretical return on an investment that carries zero default risk and zero reinvestment risk, serving as the baseline compensation for the time value of money against which all risky asset returns are measured. In practice, short-term government Treasury yields—particularly U.S. Treasury bills—are used as proxies for the risk-free rate in developed markets.
Key takeaways
- The risk-free rate equals the pure time preference for money (real risk-free rate) plus expected inflation—the Fisher equation decomposition.
- U.S. 3-month Treasury bill yields are the most common proxy for the short-term risk-free rate; 10-year Treasury yields are used for long-horizon valuations.
- Every asset pricing model (CAPM, APT, DCF) uses the risk-free rate as the floor return: all risky assets must offer a premium above it.
- Rising risk-free rates directly compress equity valuations by increasing discount rates, making future cash flows worth less in present value terms.
- The SOFR (Secured Overnight Financing Rate) has replaced LIBOR as the benchmark risk-free rate for derivatives contracts in the U.S. following the LIBOR transition.
Explanation
The risk-free rate represents the purest form of the time value of money—the compensation investors require simply for deferring consumption, absent any credit, liquidity, or volatility risk. In theory, a truly risk-free rate requires an instrument with guaranteed nominal repayment (no default), perfect liquidity, and no reinvestment uncertainty. In practice, no instrument perfectly satisfies all three conditions, but short-term sovereign debt of major developed-market governments with independent central banks and their own currency comes closest—particularly U.S. Treasury bills, German Bunds, and UK Gilts.
The Fisher equation decomposes the nominal risk-free rate into its economic components: R_nominal = R_real + π_expected, where R_real is the real risk-free rate (compensation for time preference and productive investment opportunities) and π_expected is expected inflation. The real risk-free rate is relatively stable over long periods, fluctuating around 0–2% in developed economies; most of the variation in nominal risk-free rates over time reflects changes in inflation expectations. The dramatic rise in nominal risk-free rates in 2022–2023 (from near zero to above 5% for U.S. T-bills) reflected the Federal Reserve's response to the highest inflation since the early 1980s.
The risk-free rate performs a critical anchoring function in asset valuation. In DCF models, it is the baseline discount rate to which risk premiums are added to arrive at the required return for each asset. When risk-free rates rise, the present value of all future cash flows declines, compressing equity valuations particularly sharply for long-duration growth stocks whose cash flows are expected further in the future. The 2022 rate shock—during which the 10-year Treasury yield rose from 1.5% to 4.3%—produced the worst year for both stocks and bonds simultaneously since the 1970s, driven primarily by this rate-induced present-value contraction.
The transition away from LIBOR as a benchmark rate—completed in June 2023—reshaped the practical definition of risk-free rates in derivatives markets. LIBOR (London Interbank Offered Rate) was the benchmark for trillions in interest rate swaps, floating-rate bonds, and loans, but its unsecured interbank credit component meant it was never truly risk-free. SOFR (Secured Overnight Financing Rate) in the U.S., SONIA (Sterling Overnight Index Average) in the UK, and €STR in the Eurozone are now the dominant risk-free rate benchmarks, calculated from actual overnight repo transactions in the deepest, most liquid short-term government funding markets.
Cross-country differences in risk-free rates are a fundamental driver of currency markets. In uncovered interest parity theory, a country with a higher risk-free rate should experience currency depreciation over time proportional to the rate differential, as capital flows in to capture the yield advantage until the expected exchange rate adjustment equalizes returns. In practice, the 'carry trade' exploits persistent deviations from interest parity by borrowing in low-rate currencies (JPY, CHF) and investing in high-rate currencies (AUD, NZD, emerging markets), generating carry returns that can persist for years before unwinding sharply during risk-off events.
Formula
Nominal Risk-Free Rate = Real Risk-Free Rate + Expected Inflation (Fisher Equation); CAPM: E(R) = R_f + β × ERP
Example
A discounted cash flow (DCF) valuation of a technology company projects free cash flows of $1 billion annually for five years, growing at 3% into perpetuity. With a 10-year Treasury yield (risk-free rate) of 4.5%, an equity risk premium of 5.5%, and a company beta of 1.2, the CAPM-implied discount rate is 4.5% + 1.2 × 5.5% = 11.1%. The terminal value (end of Year 5) = $1.03B × 1.03 / (0.111 - 0.03) = $13.1 billion. The present value of the terminal value discounted at 11.1% over 5 years = $13.1B / (1.111)^5 = $7.74B. If the risk-free rate rises to 5.5% (from 4.5%), the new discount rate is 12.1%, and the terminal value PV falls to $13.5B / (1.121)^5 = $7.60B—a decline that, combined with lower PVs of near-term cash flows, would reduce the total equity value by approximately 8–10%, illustrating how sensitive equity valuations are to risk-free rate movements.
Related terms
Beta Business Cycle Carry Trade Central Bank Default Deleveraging Developed Markets Discount Rate Discounted Cash Flow Duration Emerging Markets Equity