The risk-free rate of return is defined by three characteristics of the investment it describes. Which set of three does the definition require?

Zero default risk, zero liquidity risk, and a return that holds its purchasing power across the holding period.

Zero default risk, zero liquidity risk, and no uncertainty about the amount of the return to be received.

Zero default risk, zero liquidity risk, and a return no lower than the rate of economic growth over the period.

Zero default risk, zero liquidity risk, and a yield fixed by the government rather than set in a competitive auction.

A client asks why the rate a valuation model labels risk-free is quoted as the yield on three-month United States Treasury bills, given that Treasury bills are not free of every kind of risk. Which answer describes what the quoted yield is doing?

The theoretical rate is observable in the market for private payment guarantees, and the bill yield stands in for it only because it is published daily at no cost to the analyst.

The bill yield is the theoretical rate itself, because the full faith and credit of the United States government makes a Treasury bill free of risk in every dimension an investor faces.

The theoretical rate cannot be observed, and the bill yield is the closest observable approximation because the government guarantee and the depth of the market remove default and liquidity risk.

The bill yield is known to fall short of the theoretical rate, so a model adds a small premium to it before using it as the baseline for a risky asset's required return.

An analyst estimates a company's cost of equity for a discounted cash flow model that projects ten years of cash flows, and separately computes a fund's Sharpe ratio for the past twelve months. Which risk-free rate belongs in each calculation?

The ten-year Treasury note yield in the cost of equity estimate and the three-month Treasury bill yield in the Sharpe ratio, each matched to the horizon the figure covers.

The three-month Treasury bill yield in both, because only a maturity of a few weeks carries so little interest rate risk that its yield approximates a riskless return.

The ten-year Treasury note yield in both, because the risk-free anchor should reflect the whole term structure of Treasury yields whatever period the figure covers.

The three-month Treasury bill yield in the cost of equity estimate and the ten-year Treasury note yield in the Sharpe ratio, because a valuation needs the current rate and a performance measure a settled one.

A fund holds a government-guaranteed obligation with no secondary market, and its manager says the holding is liquid enough to serve as the fund's risk-free asset because a buyer could be found within a few days at a negotiated discount. Measured against what a Treasury bill provides, what does that arrangement fall short of?

A buyer standing ready at any price at all, the price obtained being immaterial where the promise behind the obligation is unconditional and the amount repayable is fixed.

Conversion into cash at or near face value at virtually any moment the market is open, which a negotiated sale at a discount some days later does not provide.

A dealer quotation published every day, which establishes the holding's liquidity whether or not a sale at the quoted price can actually be completed on demand.

A settlement period on a completed sale no longer than the one a Treasury bill trade follows, the days taken to settle rather than the price realised being what falls short.

In the Capital Asset Pricing Model's expected return equation, the risk-free rate performs two functions at the same time. What are they?

It is the rate at which the expected market return is discounted to the present, and it is also the floor below which an individual asset's beta is not permitted to fall.

It is the base return available without taking risk, and it is also the rate at which an asset's systematic risk is scaled before the market risk premium is applied to it.

It is the base return available without taking risk, and it is also the figure the expected market return is measured in excess of to give the market risk premium.

It is the base return available without taking risk, and it is also the long-run average of the expected market return measured across a full market cycle.

The nominal risk-free rate rises by one percentage point a year while the equity risk premium investors demand is unchanged. Under the Capital Asset Pricing Model, how does the required return change for a defensive stock with a beta of one half and for a cyclical stock with a beta of two?

The defensive stock rises by two percentage points a year and the cyclical stock by half a point, because a low beta leaves a stock more exposed to the base return.

The defensive stock rises by half a percentage point a year and the cyclical stock by two points, because each asset's beta scales the increase in the base return.

Neither changes, because the premium demanded for bearing market risk absorbs any movement in the base return before beta is applied to it.

Both rise by one percentage point a year, because the increase passes into the base return while the premium that beta multiplies is unchanged.

A manager proposes a one-year position in a corporate bond whose expected return over the year is slightly below the yield available on three-month Treasury bills rolled across the same year. Reading the expected return equation, why is the position hard to defend?

The equation starts from the return obtainable without bearing any risk, so a position expected to return less than that leaves the investor uncompensated for the risk it adds.

The equation values corporate bonds from the market risk premium alone, and that premium is unavailable to any position whose expected return sits below a Treasury yield.

The equation treats the Treasury bill yield as the highest expected return any asset may carry, so an expected return below that yield is the only result the model permits.

The equation requires a negative beta for such a position, and a holding whose beta is negative cannot be combined with holdings whose betas are positive.

Expected inflation over the coming year rises by two percentage points, the nominal three-month Treasury bill yield rises by about the same amount, and the real return investors require for deferring consumption is unchanged. What has happened to the compensation the bill provides in purchasing-power terms?

It has risen by about two percentage points a year, since the yield on the security from which the rate is read has risen by that amount.

It is unchanged, the additional nominal yield doing no more than replacing the purchasing power the investor expects to lose over the year.

It has risen by about four percentage points a year, the higher nominal yield being added to the expected inflation that the yield compensates for.

It has fallen by about two percentage points a year, since expected inflation is deducted from a nominal yield that the market has not yet repriced.

In a period when the nominal Treasury bill yield sits below the rate of inflation, an investor continues to hold bills rather than any risky asset. What is that investor obtaining, and at what cost?

A higher expected return later in exchange for a negative real return now, since a bill yield lying below inflation must rise by the date the holding matures.

Protection of purchasing power, obtained at the cost of a nominal return below what risky assets are expected to deliver over the same holding period.

Certainty of the nominal amount and immediate liquidity, obtained at the cost of a loss of purchasing power that is guaranteed rather than merely possible.

Nothing that amounts to a cost, since the loss of purchasing power is caused by inflation rather than chosen, and the stated yield is still received in full.

A foundation's mandate is to preserve and grow the purchasing power of its endowment, and it wants an observable risk-free baseline against which to judge any risky allocation. Which quoted yield gives it that baseline, and what does that yield promise?

The yield on the longest Treasury bond on offer, the only maturity whose quoted yield is fixed in purchasing-power rather than in nominal terms.

The quoted yield on Treasury bills of matching maturity, which already reflects the inflation occurring over the holding period and so needs no adjustment.

The gap between the nominal Treasury yield and the inflation-protected yield of one maturity, which states the real return obtainable over the holding period.

The stated yield on Treasury Inflation-Protected Securities, which is earned over and above whatever inflation turns out to be across the holding period.

One manager returned eight percent over a calendar year in which three-month Treasury bills yielded six percent. Another manager returned eight percent over a different calendar year in which bills yielded nothing. How does the risk premium each manager earned compare?

The absolute returns match, but the manager in the year of zero bill yields earned an eight point premium over the riskless alternative against two points for the other.

The two records are equivalent, because each client received eight percent and the Treasury bill yield was available to neither of the portfolios.

The manager in the year of six percent bill yields did better, because producing eight percent then meant overcoming a higher cost of capital inside the portfolio.

The manager in the year of zero bill yields did better by six points of return, because the gap between the two years' bill yields is added to the return produced.

The Sharpe ratio, the Treynor ratio and Jensen's alpha are computed for the same portfolio over the same year. What do the three measures share, and where do they differ?

All three apply the same risk adjustment to the excess return, and they differ in the baseline that each measures performance above.

All three measure performance above a baseline set by the risk-free rate, and they differ in the risk adjustment applied to that excess.

All three measure performance above the return on the broad equity market, and they differ in whether the risk-free rate enters the calculation at all.

All three measure performance above a baseline set by the risk-free rate, and they differ in the period over which that baseline rate is averaged.

Over a year a bond portfolio returned three percent while three-month Treasury bills yielded four and a half percent, and the portfolio's volatility was well below that of the equity market. What does comparison with the risk-free rate establish about the portfolio's performance?

The portfolio performed as intended, because a holding of low volatility is properly judged against a benchmark set beneath the prevailing Treasury bill yield.

The portfolio outperformed once risk is accounted for, because its return per unit of volatility exceeds what a riskless holding delivers at no volatility at all.

The portfolio underperformed in absolute terms, because a certain alternative paid more and modest volatility does not redeem a return beneath that floor.

Comparison with the risk-free rate establishes nothing about a realised return, because the rate is a baseline for returns expected before the fact alone.

An analyst discounts a private company's projected cash flows at the current ten-year Treasury yield and at nothing more. What does the resulting present value do, and why?

It overstates the value, because a projected cash flow stream has to be discounted at the rate the company earns on its invested capital rather than at a market yield.

It understates the value, because the Treasury yield sits above the rate a private company can borrow at once its collateral and its covenants are taken into account.

It states the value correctly, because the Treasury yield alone already embeds the market's compensation for the risks that a private company's cash flows carry.

It overstates the value, because the Treasury yield covers only the time value of money and carries no premium for the business, financial or liquidity risk of the cash flows.

Why does a single change in the Federal Reserve's policy rate move the valuations of corporate bonds, equities and other assets at the same time?

The policy rate moves the risk-free rate, and the discount rate used to value any asset's future cash flows is anchored to that same rate.

The same leveraged investors hold every asset class, and their funding costs track the policy rate, forcing them to sell across their holdings at once.

Every asset class is priced by dealers quoting directly from the policy rate, so a change in the target passes into quoted prices before cash flows are reconsidered.

Expected cash flows on every asset are forecast from the policy rate, so a change in the target revises the numerator of each valuation rather than its discount rate.

A client with a two-year horizon plans to hold thirteen-week Treasury bills and roll each maturing bill into a new one. She says the plan locks in today's bill yield for the full two years. Why is she wrong?

Each new bill is bought at a yield set administratively rather than by the market, so the two-year return is only ever the rate set on each rollover date.

Each maturing bill's proceeds must be reinvested at whatever yield prevails on that date, so only the first thirteen weeks are fixed at today's rate.

Each maturing bill is repaid at a price that depends on where yields stand on that date, so the amount available to reinvest is not known in advance.

Each rollover carries a transaction charge deducted from the proceeds, so the realised two-year return falls below the quoted yield by the sum of those charges.

A ten-year Treasury note is bought at issue and sold during its third year, by which time yields on comparable Treasury securities have risen substantially. What does the seller realise on that sale?

More than the amount paid for the note, because three years of the term have run and the shorter remaining life makes the note worth more to a buyer than it was at issue.

The full face amount plus the interest accrued to the sale date, because the government's unconditional promise to repay attaches to whoever holds the note on the date the position is closed.

The amount paid for the note, because a rise in yields changes what newly issued Treasury securities pay without altering the market price of securities already outstanding.

An analyst values a company in a country whose government has defaulted before and whose currency has been unstable. What does that do to the risk-free rate in the valuation, and what is the remedy?

The valuation drops the risk-free rate entirely, because the equity risk premium on its own can carry the required return where no riskless benchmark is observable.

The domestic government yield remains the risk-free benchmark, because the risk-free rate is defined by a government's legal power to tax rather than by its record of repayment.

The company's own cost of borrowing replaces the risk-free rate, because no government yield plays any part in valuing a private issuer where the sovereign's repayment record is poor.

The domestic government yield is not a credible risk-free benchmark, so the analyst adjusts it for sovereign credit risk or works instead from a dollar-denominated instrument.

How are Treasury bills sold to investors when they are first issued?

At auctions held every week, which accept both competitive and non-competitive bids from investors.

Through a fixed-price subscription each quarter, at which the Treasury sets the yield and allots bills to applicants in turn.

Through a negotiated sale to a single lead dealer each month, which then resells the bills to investors at a markup.

Through continuous sales at a rate the Federal Reserve posts each day, at which any investor may buy bills in any amount.

Which pair of features makes the probability that a Treasury bill pays less than it promised effectively zero for practical purposes?

Its listing on a national securities exchange, combined with the deposit insurance that covers every Treasury holding.

Its short time to maturity, measured in weeks, combined with the government's unconditional obligation to repay it.

Its pledge of specific federal property as collateral, combined with a sinking fund that retires bills before they mature.

Its short time to maturity, measured in weeks, combined with a coupon that is reset to the market rate every month.

The risk-free rate rises by one percentage point while the return investors expect on the broad market stays the same. Under the Capital Asset Pricing Model, what happens to the equity risk premium?

It widens by one percentage point, because a higher risk-free rate raises the compensation investors demand for bearing market risk.

It is unchanged, because the premium depends only on the volatility of the market and not on the level of the risk-free rate.

It narrows by beta times one percentage point, because beta scales every change made to any of the inputs of the equation.

It narrows by one percentage point, because the premium is the expected market return measured in excess of the risk-free rate.

What adjustment does a Treasury Inflation-Protected Security make for changes in consumer prices?

Its principal is adjusted each month for changes in the Consumer Price Index for All Urban Consumers.

Its coupon rate is reset each year to the latest inflation reading, while the principal stays at its face amount.

None after issue, the security being sold at a discount sized to cover the inflation the Treasury forecasts for its life.

Its principal is adjusted each month for changes in the personal consumption expenditures price index.

Expected inflation over the coming year falls by one and a half percentage points, and the real return investors require for deferring consumption does not change. What happens to the nominal yield on three-month Treasury bills, and to the compensation they provide in purchasing-power terms?

The nominal yield falls by about one and a half points, and the compensation in purchasing-power terms falls by the same amount.

The nominal yield falls by about one and a half points, while the compensation in purchasing-power terms is unchanged.

The nominal yield is unchanged, while the compensation in purchasing-power terms rises by about one and a half points.

The nominal yield rises by about one and a half points, and the compensation in purchasing-power terms rises with it.

A conservative bond fund returned 5 percent in a year when three-month Treasury bills also yielded 5 percent, and its volatility was a fraction of the equity market's. The client is pleased with a steady positive return. What risk premium did the fund earn?

Five percentage points, because a positive return achieved with low volatility is itself the premium earned for the risk taken.

A premium in proportion to its low volatility, because a fund's premium is its return divided by the standard deviation of returns.

Two and a half percentage points, half of the fund's return, because the other half compensates for the time value of money.

None, because its return matched what the riskless alternative paid, leaving the risk it carried with no compensation at all.

Besides bonds priced off the Treasury yield curve and equities valued by discounting free cash flow, which other valuation does the risk-free rate enter directly?

The fair value of options, which the pricing models estimate using the risk-free rate as one of their inputs.

The book value of a company's equity, which accountants restate each year using the current risk-free rate.

The spot exchange rate between two currencies, which is fixed by the gap between their governments' risk-free rates.

The spot price of physical commodities, which dealers set by applying the risk-free rate to the previous day's price.

An analyst first values a private company's projected cash flows at the ten-year Treasury yield alone, then adds premiums for the company's business, financial and liquidity risk to that rate. What does the second step do to the valuation, and why?

It raises the present value, because a discount rate built up from several separate premiums reflects the cash flows more completely than a single rate does.

It lowers the present value, because the premiums raise the discount rate above the risk-free minimum the cash flows were first discounted at.

It leaves the present value unchanged, because those same premiums are already embedded in the Treasury yield the analyst used in the first step.

It lowers the present value, because adding premiums shortens the period over which the projected cash flows are discounted back to today.

A ten-year Treasury note is bought at issue. Yields on comparable Treasuries then rise substantially, and the holder keeps the note until it matures. What does the rise in yields do to the payments the holder receives?

It reduces the face amount repaid at maturity in line with the fall in the note's market price over the years during which it was held.

It raises the coupons paid over the remaining years, since a note's coupon rate is reset to the prevailing market yield after any rise.

It leaves the promised coupons and face amount intact, the fall in price reaching a holder who sells before maturity rather than one who holds.

It reduces the coupons paid over the remaining years, since the Treasury lowers the coupon rate on notes whose market price has fallen.

A retiree lives on the interest from a portfolio of thirteen-week Treasury bills, rolling each bill into a new one as it matures. Short-term rates then fall steeply over the following year. What happens to her income?

It stays at the original level until the portfolio is sold, since each bill's yield is fixed for as long as she keeps rolling it.

It rises, since the price of each bill she holds increases as rates fall and that gain is paid out together with the interest.

It falls only if a bill defaults, since the government's repayment obligation fixes the income from every future bill as well.

It falls as each maturing bill is reinvested at the lower prevailing yield, even though every bill she holds pays in full.

Risk-Free Rate of Return: T-Bills, CAPM and Real Rates

What Is the Risk-Free Rate of Return?

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 Treasury Bill as the Risk-Free Proxy

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 to fifty-two 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 Risk-Free Rate in the CAPM Framework

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.

Nominal Versus Real Risk-Free Rate

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 — a market-implied measure commonly read as the expected average inflation over the holding period, though not a pure forecast, because it also carries an inflation risk premium and a liquidity premium on TIPS.

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.

The Risk-Free Rate as the Numerator Foundation in Risk-Adjusted Measures

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 and the Time Value of Money

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.

The Limitations of the Risk-Free Rate Concept

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.

Examination Relevance and Key Takeaways

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.