What Is the Risk-Free Rate of Return?

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The risk-free rate of return is the theoretical return on an investment that carries no risk of financial loss: the investor receives exactly the promised payment, on time, with certainty. No real asset meets that standard perfectly. In practice, analysts use the yield on short-term debt issued by a highly rated government in the investor’s own currency as a stand-in. For U.S. dollar investors, the usual proxy is the three-month U.S. Treasury bill. The risk-free rate is the baseline against which every riskier investment is judged: if an asset cannot be expected to beat it, there is no reason to take on that asset’s risk.

How the Risk-Free Rate Works

The minimum required return

In finance theory, the risk-free rate is the floor for any investment decision. An investor who can earn a certain return with no risk will accept extra uncertainty only if the expected return is higher. That extra expected return is the risk premium, and the gap between an asset’s return and the risk-free rate is called its excess return.

The level of the floor changes the trade-off. Suppose a hypothetical investor can earn 5% risk-free and is offered a risky investment expected to return 7%. The risk is compensated by only 2 percentage points. If the risk-free rate were 2%, the same 7% investment would offer a 5-point cushion.

Why the three-month Treasury bill is the standard proxy

The three-month T-bill comes closest to the textbook ideal for U.S. investors for three reasons:

1. Default risk is considered negligible. The bill is a direct obligation of the U.S. government, which borrows in its own currency, and markets treat the chance of non-payment as very small.
2. The maturity is short. With only about 13 weeks to run, the bill’s price barely moves when interest rates change, and inflation has little time to erode its value.
3. The market is large and liquid. T-bills trade in very high volume, so an investor can buy or sell without materially moving the price.

Of the three common kinds of risk, absolute risk (volatility, usually measured by standard deviation), relative risk (movement against a benchmark) and default risk, only the last matters much for a three-month bill, because it is held briefly and pays a fixed amount at maturity. That remaining default risk is judged minimal.

The investor’s home currency matters

A security is only “risk-free” relative to the currency the investor measures wealth in. A euro-based investor who buys U.S. T-bills takes on exchange rate risk: if the dollar weakens against the euro, the return measured in euros can be negative even though the Treasury pays in full. That risk can be hedged with currency forwards, but hedging has a cost that changes the effective return.

For this reason, each currency area uses its own proxy: short-term German government debt for euros and Swiss government bills for Swiss francs. Investors in lower-rated eurozone countries such as Portugal or Greece can still buy German debt without currency risk, because both are denominated in euros. An investor whose assets are in a currency without a highly rated government issuer, such as the Russian ruble, cannot reach a top-rated government bond without taking on currency risk. In India, analysts commonly use domestic government securities (G-secs), such as 91-day Treasury bills for short horizons or the 10-year government bond for long-horizon valuation. Whatever proxy you use, take its current market yield on the date of the analysis, not a remembered rule of thumb.

Nominal vs. Real Risk-Free Rate

The yield quoted on a T-bill is a nominal rate: it says how many dollars you get back, not what those dollars will buy. The real risk-free rate strips out inflation and measures the gain in purchasing power. It is often described as the pure time value of money, the reward for postponing consumption with no default risk involved.

The relationship is given by the Fisher equation:

Exact: (1 + nominal rate) = (1 + real rate) × (1 + expected inflation)

Approximation: real rate ≈ nominal rate − expected inflation

Hypothetical example: a one-year government bill yields 4.5% and expected inflation over the year is 3.0%.

• Approximation: 4.5% − 3.0% = 1.5% real
• Exact: (1.045 ÷ 1.030) − 1 = 1.456% real

The approximation works well when rates are low and becomes less accurate as nominal rates and inflation rise.

The nominal risk-free rate therefore compensates you for time (the real rate) and for expected inflation. It includes no meaningful credit premium, because default risk is assumed away, and little or no liquidity premium, because the proxy is chosen for its liquidity. Corporate bonds, by contrast, add premiums for both credit and liquidity on top of the risk-free rate.

In the U.S., Treasury Inflation-Protected Securities (TIPS) offer a market-based view of the real rate, because their principal adjusts with the Consumer Price Index and their yield is quoted in real terms. Comparing a TIPS yield with a nominal Treasury yield of the same maturity gives the “breakeven” inflation rate the market is pricing. Realized inflation, shown in U.S. inflation by year, may differ from what investors expected.

The real risk-free rate is not quite the same as “the real rate of interest” in general. A real rate can be computed for any security by subtracting inflation from its yield; the real risk-free rate is the real rate on a default-free security specifically.

Calculating the Risk-Free Rate From a T-Bill

T-bills pay no coupon. They are sold below face value at weekly auctions, and at maturity the holder receives the full face value; the discount is the investor’s return. Bills are issued in maturities ranging from a few weeks to one year.

Hypothetical example: a 13-week (91-day) bill with $10,000 face value is bought for $9,875.

• Dollar return: $10,000 − $9,875 = $125
• Holding-period return: $125 ÷ $9,875 = 1.266%
• Annualized investment yield (365-day basis): 1.266% × 365 ÷ 91 ≈ 5.08%

Treasury bills are also quoted on a bank discount yield basis, which divides the discount by face value (not price) and uses a 360-day year:

• $125 ÷ $10,000 × 360 ÷ 91 ≈ 4.95%

The two numbers describe the same bill, but the discount yield understates the return the investor actually earns on money invested. When plugging a risk-free rate into a model, use the investment yield (also called the bond-equivalent or coupon-equivalent yield), or an annualized yield on a consistent basis, rather than the discount quote.

The same logic applies to longer government bonds: use the yield to maturity, not the coupon rate. A coupon is fixed when the bond is issued; the yield reflects what a buyer earns at today’s price, which is what a risk-free benchmark is supposed to represent.

How the Risk-Free Rate Is Used

The capital asset pricing model

CAPM builds the expected return on a risky asset from the risk-free rate upward:

Expected return = Rf + β × (Rm − Rf)

where Rf is the risk-free rate, β (beta) measures the asset’s sensitivity to market movements, and Rm − Rf is the market risk premium.

Hypothetical example: Rf = 4%, β = 1.2, expected market return = 9%.

• Market risk premium: 9% − 4% = 5%
• Expected return: 4% + 1.2 × 5% = 10%

If the risk-free rate fell to 2% and the market risk premium stayed at 5%, the required return would drop to 2% + 6% = 8%. A change in the risk-free rate moves the required return on every asset priced this way.

Discount rates, cost of capital and valuation

The risk-free rate is the base layer of most discount rates. In a discounted cash flow (DCF) analysis, future cash flows are discounted at a rate that starts with the risk-free rate and adds premiums for the risk of those cash flows. The cost of equity from CAPM then feeds into the weighted average cost of capital (WACC), which companies use as the hurdle rate for projects. A project’s net present value or internal rate of return is judged against that hurdle, so a higher risk-free rate raises the bar that new investments must clear.

The risk-free yield sets the starting point of a discount rate, not the whole rate. Only a cash flow that is itself risk-free should be discounted at the risk-free rate alone; anything riskier gets a premium on top.

The rate also frames a company’s own choices. It represents what the business could earn on its cash with no risk, which is the opportunity cost of committing capital to a project or of choosing one capital structure over another.

Excess return and the Sharpe ratio

Performance measures compare returns with the risk-free rate rather than with zero. The Sharpe ratio divides excess return by volatility:

Sharpe ratio = (Portfolio return − Rf) ÷ standard deviation of portfolio returns

Hypothetical example: a portfolio returns 8% with a 10% standard deviation and the risk-free rate is 3%. Sharpe ratio = (8% − 3%) ÷ 10% = 0.5. A portfolio that merely matches the risk-free rate has a Sharpe ratio of zero, no matter how it got there.

Some textbook exercises set Rf = 0% for simplicity. That assumption means excess return equals total return; it is a modeling shortcut, not a statement about actual market rates.

Bond pricing

A bond’s price is the present value of its future payments. When the risk-free rate rises, those payments are discounted more heavily and prices fall, so yields rise; when the rate falls, prices rise.

Hypothetical example: $1,000 due in one year is worth $1,000 ÷ 1.04 = $961.54 at a 4% discount rate and $1,000 ÷ 1.05 = $952.38 at 5%. Riskier bonds are priced off the same base plus a credit spread, so a move in the risk-free rate shifts yields across the bond market.

Option and derivative pricing

The Black-Scholes model and related option pricing models include the risk-free rate as an input. It enters through the cost of carrying the underlying asset and the present value of the strike price. All else equal, a higher risk-free rate raises the value of a call option and lowers the value of a put. Forward and futures prices also embed the risk-free rate through cost-of-carry relationships.

Matching Maturity to the Purpose

“The risk-free rate” is not a single number even within one currency, because government yields differ by maturity. The three-month bill is the standard proxy for short horizons and for performance measures like the Sharpe ratio, which are computed over short periods.

For long-horizon work, such as valuing a company whose cash flows stretch decades ahead, analysts commonly use a long-term government bond yield instead, often the 10-year Treasury in the U.S. The reasoning is that the benchmark should cover roughly the same period as the cash flows being valued. The trade-off is that a long bond is default-free but not price-risk-free: its market value can swing considerably before maturity as rates change. Whichever maturity you choose, use it consistently across the inputs of the same model.

What Moves the Risk-Free Rate

Several forces push risk-free yields up or down:

• Monetary policy. Central banks set short-term policy rates, such as the Federal Reserve’s federal funds target. Short-term government yields track policy rates closely, so a rate hike to fight inflation tends to lift the T-bill yield, and a cut tends to lower it.
• Economic conditions. Strong growth and low unemployment raise the opportunity cost of holding safe assets and tend to coincide with higher rates. Recessions tend to bring rate cuts and lower yields.
• Inflation expectations. Investors demand compensation for expected inflation, so higher expected inflation generally lifts nominal risk-free yields.
• Supply and demand for government debt. Heavy issuance can push yields up; strong demand bids prices up and yields down.
• Risk appetite. In periods of market stress, investors move into safe assets, raising their prices and lowering their yields. When investors are optimistic and willing to take risk, demand for safe assets softens.

Common Proxies for the Risk-Free Rate

• Government bills and bonds: short-term bills such as U.S. T-bills for short horizons, longer-term bonds for valuations that span many years, and inflation-indexed bonds such as TIPS for the real risk-free rate.
• Overnight reference rates. In the U.S., the Secured Overnight Financing Rate (SOFR) replaced LIBOR, which was phased out. SOFR is based on overnight loans backed by Treasury securities and serves as a near-risk-free reference rate for loans and derivatives.
• Central bank policy rates, such as the federal funds rate or the European Central Bank’s main refinancing rate, which anchor the short end of the yield curve.
• Cash equivalents, such as money market funds or insured deposits, for very short horizons, though they are not the benchmark used in formal models.

Limitations of the Risk-Free Rate

Nothing is truly risk-free. Even large governments carry some default risk, however small. The assumption that a government bond cannot default is reasonable for some issuers and plainly wrong for others.

The rate is not stable. Because it responds to policy, inflation and sentiment, the risk-free rate can change substantially over a few years. A valuation built on today’s rate may look very different after a policy cycle, which makes the rate an imperfect anchor for long-term analysis.

It differs by country. Economic conditions, monetary policy and geopolitical risk vary, so one country’s risk-free rate cannot be applied to another market. Using a U.S. rate to value a business in a riskier economy understates that economy’s risk.

Liquidity can dry up. Government debt markets are normally deep, but during severe financial stress, trading conditions can deteriorate and safe-asset yields can jump around. The proxy itself can become volatile when it is needed most.

Rates can be negative. Short-term German and Swiss government yields were below zero for extended periods in the 2010s. A negative risk-free rate breaks the intuition of a “minimum return” and makes CAPM and discounting inputs harder to interpret.

Distinctions Readers Often Confuse

Default-free vs. risk-free. “Default-free” means the issuer will pay as promised. A 30-year Treasury is treated as default-free, but its price can fall sharply when rates rise, and inflation can eat into its real value. Only a short-term, default-free, home-currency bill comes close to being risk-free in the full sense.

Risk-free rate vs. borrowing rate. Theory often assumes investors can borrow and lend at the same risk-free rate. In reality, individuals and companies borrow at higher rates that include a credit spread for their own default risk. A company’s cost of debt is the risk-free rate plus its spread, not the risk-free rate itself.

Risk-free rate vs. deposit rate. A bank deposit carries the bank’s credit risk, which deposit insurance offsets up to a limit. Deposit rates are also set by the bank and can lag market yields. For a saver, an insured deposit may be effectively risk-free up to the limit, but it is not the market benchmark used in pricing models.

Risk-free rate vs. policy rate. A central bank’s policy rate is an administered target for overnight lending between banks. T-bill yields are market prices that reflect expectations of where policy rates will be over the bill’s life, so the two move together but are not identical.

FAQs

The Bottom Line

Investors, analysts and companies use the risk-free rate as the base layer of discount rates, CAPM returns, Sharpe ratios and bond and option prices. Pick a proxy in your home currency, match its maturity to the horizon of the cash flows, and use its current market yield on the analysis date. Treat it as a starting point that changes over time, and add premiums for any cash flow that carries risk.