Risk-Free Rate

The risk-free rate is the return an investor could earn with certainty over a given horizon, used in finance as the baseline from which every other expected return is measured. In practice the assumption is anchored to a U.S. Treasury security, on the reasoning that repayment by the federal government is treated as certain. Why a premium is paid over that baseline, and what its ingredients are, belongs to the page on the risk premium. This page is about the baseline itself: what "risk-free" does and does not mean, which security stands in for it, and how much the answer depends on that choice.

The name is the source of most of the confusion. It describes a convention rather than an observed price, and no government body publishes a series called the risk-free rate. What Treasury does publish is a daily yield curve. Its methodology page describes it: "The Treasury's official yield curve is a par yield curve derived using a monotone convex method," built from "indicative, bid-side market price quotations (not actual transactions) for the most recently auctioned securities obtained by the Federal Reserve Bank of New York at or near 3:30 PM each trading day." So the underlying inputs are quotations that move daily, across a range of maturities, and any single "risk-free rate" is a choice made from that curve.

Take "risk-free" literally and three risks remain, which is the practical heart of the term. The first is inflation risk. A nominal Treasury pays a fixed number of dollars, and if prices rise faster than that return the holder ends the period with fewer goods than they started with. Treasury's response to precisely this problem is a separate product: as TreasuryDirect puts it of Treasury Inflation-Protected Securities, "as the name implies, TIPS are set up to protect you against inflation," with a principal that "goes up with inflation and down with deflation." That a distinct security exists for the purpose is the clearest evidence that an ordinary Treasury does not carry the protection.

The second is reinvestment risk, and it lands hardest on the shortest and supposedly safest instrument. A 13-week Treasury bill pays a rate fixed at its auction, and the rate available at the next auction thirteen weeks later is unknown today. An investor holding a rolling series of bills has no certainty about anything beyond the current one, so the "certainty" of a short bill is certainty about a short period, not about a horizon.

The third is interim price risk, and here the Securities and Exchange Commission is unusually direct. Its investor bulletin on interest rate risk states as "a fundamental principle of bond investing" that "market interest rates and bond prices generally move in opposite directions. When market interest rates rise, prices of fixed-rate bonds fall. This phenomenon is known as interest rate risk," and then removes the obvious escape hatch: "Interest rate risk is common to all bonds, even U.S. Treasury bonds." It also notes that "the longer the bond's maturity, the greater the risk that the bond's value could be impacted by changing interest rates prior to maturity."

The same bulletin states the default-free-but-not-risk-free distinction outright, which is the whole of this page in two sentences of the SEC's own: "When the U.S. government guarantees a bond, it guarantees that it will make interest payments on the bond on time and that it will pay the principal in full when the bond matures," and, against the misconception that a government obligation cannot lose value, "the U.S. government does not guarantee the market price or value of the bond if you sell the bond before it matures." A 30-year Treasury held to maturity pays what it promised. Sold in year three, it pays whatever the market will give.

From those three risks follows the second half of the story, which is that there is no single risk-free rate. Treasury builds its curve from bills of 4, 6, 8, 13, 17, 26 and 52 weeks, notes of 2, 3, 5, 7 and 10 years, and bonds of 20 and 30 years, and those maturities carry different yields on the same afternoon. Which one is "the" risk-free rate depends on the horizon of the question. Comparing a one-year investment against a safe alternative calls for a short bill; discounting a cash flow thirty years out calls for something at the far end of the curve. A page on the equity risk premium already notes that published estimates vary partly by "which risk-free asset is used," and this is the dependency behind that observation.

The practical consequence is that the choice propagates. The risk-free rate is subtracted in the numerator of a Sharpe ratio, it is the baseline of every risk premium, and it is the discount rate at the bottom of a present-value calculation. Change the assumption and all three outputs change, without any new information about the investment itself. That is why two competent analysts can publish materially different figures for the same asset and both be doing the arithmetic correctly: the disagreement is upstream, in a parameter neither of them observed.

In use, the risk-free rate is an input someone selects. The analyst decides on the horizon of the decision, reads a yield of matching maturity off the Treasury curve, and uses it as the baseline. Everything downstream is a subtraction or a division involving that number.

A hypothetical shows the sensitivity. Suppose a fund returned 11 percent over a period with a standard deviation of 15 percent, and the analyst uses a risk-free rate of 4 percent, the same hypothetical baseline used in the worked examples on the risk premium and Sharpe ratio pages. The excess return is 11 percent − 4 percent = 7 percent, and the Sharpe ratio is 7 ÷ 15 = 0.47. Now suppose a second analyst, looking at the same fund over the same period, matches the horizon differently and uses 2 percent. The excess return is 9 percent and the Sharpe ratio is 9 ÷ 15 = 0.60. The fund's performance did not change. A reported measure of its risk-adjusted quality rose from 0.47 to 0.60, better than a quarter higher, on a parameter choice.

The same lever moves a present value, and there it moves further. A cash flow of $100,000 due in 30 years, discounted at 4 percent, is worth $100,000 ÷ (1.04 raised to the 30th power) = $30,832 today. Discounted at 2 percent it is $100,000 ÷ (1.02 raised to the 30th power) = $55,207. Two percentage points of assumption, applied over thirty years, changes the answer by $24,375, which is 79 percent of the smaller figure. Long-horizon numbers are the most sensitive to the choice and the least often published with the assumption stated.

Why the convention is useful

• It gives every risky return a common baseline, which is what makes returns on different assets comparable at all.
• The proxy is anchored to a real, liquid, daily-priced market with a published methodology, rather than to an estimate.
• Treasury publishes the whole curve, so an analyst can match the maturity to the horizon of the question instead of using one number for everything.

Where it misleads

• "Risk-free" names only the absence of default risk. Inflation risk, reinvestment risk and interim price risk all remain, and the SEC states that interest rate risk reaches Treasury bonds too.
• There is no single correct value, so any number described as "the" risk-free rate has had a maturity choice made for it, usually silently.
• It is not a promise of a real return. A default-free nominal return below the inflation rate is a loss of purchasing power.
• Every measure built on it inherits the choice, so a Sharpe ratio or an equity risk premium quoted without its assumed baseline cannot be compared with another one.
• The convention says nothing about liquidity or about the price at which a security can actually be sold on a bad day.