Table of Contents
SERIES 65 | FINANCIAL REGULATION COURSES
The risk-free rate of return is the theoretical rate of return available on an investment that carries zero default risk, zero liquidity risk, and zero uncertainty about the return to be received — the minimum compensation an investor requires simply for deferring consumption over time, before any premium is added for bearing investment risk. In practice, because no investment is entirely without risk in every dimension, the risk-free rate is approximated using the yield on short-term United States Treasury securities — primarily Treasury bills — on the grounds that the full faith and credit guarantee of the United States government effectively eliminates default risk, and that the extreme liquidity of the Treasury market eliminates meaningful liquidity risk. The risk-free rate is the foundational building block of the Capital Asset Pricing Model, the anchor of the Sharpe ratio and other risk-adjusted performance measures, the starting point for the equity risk premium calculation, and the baseline against which all investment returns must be measured to assess whether adequate compensation is being received for risk assumed.
The yield on three-month United States Treasury bills is the most widely used practical approximation of the short-term risk-free rate in the United States financial system. Treasury bills are direct obligations of the United States government backed by its full faith and credit under 31 U.S.C. 3101, auctioned weekly through the competitive and non-competitive bidding process governed by 31 CFR Part 356 — the Uniform Offering Circular for Treasury marketable securities. They are the most liquid short-term fixed income instruments in the world — a twenty-seven-trillion-dollar market traded through twenty-three primary dealers in continuous two-sided markets — meaning they can be converted to cash immediately at or near face value at virtually any moment during market hours.
Because Treasury bills mature in four, thirteen, or twenty-six weeks and carry the government's unconditional repayment obligation, the probability of receiving less than the promised return is — for all practical investment purposes — zero. This combination of zero default risk and near-perfect liquidity is what makes the Treasury bill yield the closest observable approximation to the theoretical risk-free rate.
The ten-year Treasury note yield serves as the risk-free rate proxy in applications where the investment horizon being modelled is long-term rather than short-term — particularly in the Capital Asset Pricing Model when used to estimate the cost of equity capital for corporate valuations, discounted cash flow models, and long-horizon investment decisions. The rationale for using the ten-year yield in long-term applications is maturity matching — if the investment decision being evaluated will generate cash flows over ten or more years, the risk-free rate used as the discount anchor should reflect the term structure of risk-free rates over a comparable horizon rather than the overnight or three-month rate.
The choice between the three-month T-bill yield and the ten-year Treasury yield as the risk-free rate depends on the specific application. For the Sharpe ratio and other performance measures evaluated over monthly or annual periods, the three-month bill yield is standard. For CAPM-based cost of equity estimates used in multi-year corporate finance models, the ten-year yield is standard.
The Capital Asset Pricing Model — developed by William Sharpe, John Lintner, and Jan Mossin in the 1960s building on Harry Markowitz's mean-variance portfolio framework — places the risk-free rate at the centre of the expected return equation for any risky asset.
The CAPM equation states that the expected return on any risky asset equals the risk-free rate plus the asset's beta multiplied by the equity risk premium — the expected market return minus the risk-free rate.
Expected return equals the risk-free rate plus beta multiplied by the quantity expected market return minus the risk-free rate.
The risk-free rate in this equation performs two functions simultaneously. First, it is the intercept — the return available to any investor regardless of risk, the baseline below which no investment should rationally price on an expected basis. Second, it is the anchor for the equity risk premium — the market risk premium is the expected excess return of the broad equity market above the risk-free rate, and beta translates that market-level premium into the appropriate asset-level expected return based on the asset's systematic risk.
Changes in the risk-free rate therefore propagate through the CAPM to affect the required return on every risky asset. When the Federal Reserve raises the federal funds rate — which influences Treasury yields across the curve — the risk-free rate rises, the required return on all equity increases by the same amount assuming unchanged equity risk premium, and the discount rate applied to future corporate earnings rises. Higher discount rates reduce the present value of future cash flows, producing lower equity valuations for any given earnings stream — the mechanism through which Federal Reserve tightening reduces equity prices that has been empirically observed across multiple tightening cycles.
The observable Treasury bill and note yields are nominal risk-free rates — they promise a fixed dollar return without adjustment for inflation. The real risk-free rate — the return in purchasing power terms after adjusting for inflation — is the economically more fundamental concept, reflecting the true compensation for deferring consumption rather than merely the nominal dollar return.
The relationship between the real and nominal risk-free rates is expressed through the Fisher equation covered in the Real Interest Rate entry of this dictionary. The nominal risk-free rate approximately equals the real risk-free rate plus expected inflation. When inflation expectations rise, the nominal risk-free rate rises even if the real required return for deferring consumption is unchanged — the additional nominal return merely compensates investors for expected purchasing power erosion rather than providing genuine additional real returns.
The real risk-free rate is directly observable through the yield on Treasury Inflation-Protected Securities — TIPS — whose real yield is stated explicitly on the security and whose principal is adjusted monthly for changes in the Consumer Price Index for All Urban Consumers under 31 CFR Part 356. A five-year TIPS yielding one and a half percent provides a guaranteed one and a half percent real return above inflation regardless of what actual inflation proves to be. The spread between the nominal Treasury yield and the TIPS yield of the same maturity is the breakeven inflation rate — the market's implied forecast of average inflation over the holding period.
During periods of negative real interest rates — when the nominal risk-free rate falls below the inflation rate, as occurred extensively during 2021 and 2022 when CPI inflation rose well above the Federal Reserve's near-zero policy rate — the risk-free rate ceases to provide even inflation protection. Investors are effectively paying for the certainty and liquidity of Treasury holdings by accepting guaranteed purchasing power losses. This phenomenon — negative real risk-free rates — distorts the CAPM framework and produces asset valuations at elevated multiples that require higher-than-historical risk premiums to make sense, a dynamic extensively discussed in financial markets during the zero-interest-rate policy period of 2009 to 2022.
Every major risk-adjusted performance metric uses the risk-free rate as the baseline for computing excess return — the numerator that measures how much above the minimum acceptable return the investment delivered.
In the Sharpe ratio, excess return equals portfolio return minus the risk-free rate — the risk premium earned per unit of total risk. In the Treynor ratio, the same excess return is divided by beta rather than standard deviation. In Jensen's alpha, the CAPM expected return — which incorporates the risk-free rate — is the benchmark against which actual performance is measured. In each case the risk-free rate is the floor — returns below the risk-free rate represent underperformance in absolute terms regardless of the risk taken to achieve them.
This is why the risk-free rate is the most fundamental number in investment performance evaluation. A portfolio manager who earns eight percent in a year when three-month Treasury bills yield six percent has earned only a two percent risk premium above the riskless alternative — a potentially inadequate return for the equity or credit risk assumed. The same eight percent return when Treasury bills yield zero percent represents an eight percent risk premium — substantially more attractive compensation for risk assumed. The absolute return level is identical in both cases. The risk-adjusted comparison is completely different.
The risk-free rate is the empirical approximation of the rate at which money grows when it is invested with certainty — the rate that quantifies the time value of money in practice rather than in theory. In discounted cash flow analysis, the risk-free rate enters the discount rate as the minimum required return before any premium for business risk, financial risk, or illiquidity is added. This application connects the risk-free rate directly to the valuation of every financial asset — from corporate bonds priced off the Treasury yield curve to equity valuations computed through WACC-discounted free cash flow models to the fair value of options estimated through risk-free rate-dependent pricing models.
The Federal Reserve's influence over the risk-free rate through monetary policy — setting the federal funds rate target under the dual mandate of 12 U.S.C. 225a and implementing that target through open market operations and the interest on reserve balances rate — makes Federal Reserve policy decisions the single most important determinant of asset valuations across all asset classes simultaneously, because every asset's present value is computed by discounting future cash flows at a rate anchored to the risk-free rate.
Several limitations of the risk-free rate concept must be understood for rigorous application in investment analysis.
No investment is entirely risk-free. Even Treasury securities carry inflation risk — the nominal return is certain but the purchasing power of that return depends on future inflation that cannot be known with certainty at the time of investment. They carry reinvestment risk — the coupon and principal proceeds from a Treasury security must be reinvested at whatever rates prevail in the future. And they carry interest rate risk if sold before maturity — a Treasury note's market price falls when interest rates rise. The risk-free label is therefore accurate with respect to default risk and liquidity risk but not with respect to all dimensions of investment risk.
The appropriate maturity for the risk-free rate depends on the investment being evaluated — using the three-month T-bill rate as the risk-free rate when discounting a thirty-year cash flow stream introduces a maturity mismatch that understates the appropriate risk-free anchor. Treasury yields at different maturities differ as a consequence of the yield curve's shape — the term structure of interest rates — and matching the risk-free rate maturity to the investment horizon is a critical analytical discipline.
In markets outside the United States, there may be no truly default-free government security — sovereign governments with histories of default or currency instability may not provide a credible risk-free benchmark in their domestic currency, requiring adjustments for sovereign credit risk or the use of US dollar-denominated instruments as a global risk-free proxy.
The risk-free rate of return is tested on the Series 65 examination in the context of the CAPM, risk-adjusted performance measures, the equity risk premium, the time value of money, and the relationship between Federal Reserve policy and asset valuations.
The key points to retain are these.
The risk-free rate of return is the theoretical rate available on a zero-default-risk, fully liquid investment — approximated in practice by the yield on United States Treasury securities backed by the full faith and credit of the United States government under 31 U.S.C. 3101 and auctioned under 31 CFR Part 356. The three-month Treasury bill yield is the standard short-term risk-free rate proxy. The ten-year Treasury note yield is the standard long-term risk-free rate proxy used in CAPM-based corporate valuation models where the investment horizon spans multiple years.
In the CAPM, the expected return on any risky asset equals the risk-free rate plus beta multiplied by the equity risk premium — the expected market return minus the risk-free rate. Rising risk-free rates increase the required return on all risky assets, reducing the present value of future cash flows and producing lower asset valuations — the mechanism through which Federal Reserve tightening under the dual mandate of 12 U.S.C. 225a transmits into equity market valuations. The nominal risk-free rate approximately equals the real risk-free rate plus expected inflation per the Fisher equation. The real risk-free rate is directly observable through TIPS yields under 31 CFR Part 356 — the spread between nominal Treasury and TIPS yields of the same maturity is the breakeven inflation rate. Negative real risk-free rates — when the nominal rate falls below inflation — produce distorted CAPM valuations and elevated asset price multiples as investors accept guaranteed purchasing power losses in exchange for certainty and liquidity. The risk-free rate is the baseline for all risk-adjusted performance measures — the Sharpe ratio, Treynor ratio, and Jensen's alpha all compute excess return as the portfolio return minus the risk-free rate, making the risk-free rate the floor below which any return represents absolute underperformance regardless of risk assumed.
