## What Is the Risk-Free Rate of Return?

The risk-free rate of return is the theoretical rate of return of an investment with zero risk. The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time.

The so-called “real” risk-free rate can be calculated by subtracting the current inflation rate from the yield of the Treasury bond matching your investment duration.

### Key Takeaways

- The risk-free rate of return refers to the theoretical rate of return of an investment with zero risk.
- Investors won’t accept risk greater than zero unless the potential rate of return is higher than the risk-free rate.
- In practice, the risk-free rate of return does not truly exist, as every investment carries at least a small amount of risk.
- To calculate the real risk-free rate, subtract the inflation rate from the yield of the Treasury bond matching your investment duration.

## Understanding the Risk-Free Rate of Return

In theory, the risk-free rate is the minimum return an investor expects for any investment. Investors will not accept additional risk unless the potential rate of return is greater than the risk-free rate. If you are finding a proxy for the risk-free rate of return, you must consider the investor’s home market. Negative interest rates can complicate the issue.

### Important

In practice, a truly risk-free rate does not exist because even the safest investments carry some small amount of risk.

Different countries and economic zones use different benchmarks as their risk-free rate. The interest rate on a three-month U.S. Treasury bill (T-bill) is often used as the risk-free rate for U.S.-based investors.

The three-month U.S. Treasury bill is a useful proxy because the market considers there to be virtually no chance of the U.S. government defaulting on its obligations. The large size and deep liquidity of the market contribute to the perception of safety.

A foreign investor whose assets are not denominated in dollars incurs currency risk when investing in U.S. Treasury bills. The risk can be hedged via currency forwards and options but affects the rate of return.

The short-term government bills of other highly rated countries, such as Germany and Switzerland, offer a risk-free rate proxy for investors with assets in euros (EUR) or Swiss francs (CHF). Investors based in less highly rated countries that are within the eurozone, such as Portugal and Greece, are able to invest in German bonds without incurring currency risk. By contrast, an investor with assets in Russian rubles cannot invest in a highly-rated government bond without incurring currency risk.

## Importance of Risk-Free Rate

The risk-free rate serves as a fundamental building block in finance as it has a role in financial modeling, investing, and valuations. As a baseline rate, it provides a benchmark against which the return on all other investments is measured. In valuation models such as discounted cash flow analysis, this is used as the discount rate to determine the present value of future cash flows

The risk-free rate also helps price financial instruments and determine appropriate rates of return for investment strategies. For instance, it influences the pricing of bonds, options, and derivatives as it’s a key input in pricing models. The risk-free rate also plays a part in cost-of-capital calculations. It helps companies assess the required return on investment projects and determine their optimal capital structure based on what that company could earn should it choose to not take on any risk.

Last, the risk-free rate is important to investors. By comparing the expected return of an investment to the risk-free rate, investors can assess whether the potential return justifies the level of risk taken. For example, if you knew you could earn 5% risk-free, what amount of risk would you be willing to take on to earn a 7% return? Would that amount of risk change if you knew you could only earn a risk-free rate of 2%?

## Risk-Free Rate and Financial Asset Pricing

In valuation models such as the capital asset pricing model (CAPM), the risk-free rate is used as the baseline rate of return against which the expected returns of risky assets are compared. According to CAPM, the expected return of an asset is determined by adding a risk premium, which compensates investors for bearing additional risk, to the risk-free rate. As a result, changes in the risk-free rate directly influence the required rate of return for risky assets.

In bond pricing, the risk-free rate determines bond yields. Bonds are priced based on their present value, which is calculated by discounting future coupon payments and principal repayment using the prevailing risk-free rate. When the risk-free rate increases, the present value of future cash flows decreases, leading to a decline in bond prices and an increase in bond yields. The opposite is true when the risk-free rate decreases (the PV of cash flow goes up and so does the bond’s price).

As touched on earlier, the risk-free rate also influences the pricing of options and other derivatives through models such as the Black-Scholes model. The risk-free rate is an input in these types of option pricing models, and the risk-free rate (just like with other models) affects the value of options by influencing the cost of carrying the underlying asset.

## Factors That Influence the Risk-Free Rate

The risk-free rate is complex. There are a lot of variables that contribute to what that rate is, and the risk-free rate is subject to fluctuations. Very broadly speaking, some of the high-level factors that influence the risk-free rate include:

**Monetary Policy:**Central banks influence the risk-free rate through their monetary policy decisions, particularly changes in the target interest rates. For example, when a central bank raises interest rates to combat inflation or cool down an overheating economy, it tends to increase the risk-free rate. Conversely, lowering interest rates can lower the risk-free rate to stimulate borrowing and economic activity.**Economic Conditions:**Macroeconomic factors such as economic growth, inflation, employment levels, and consumer sentiment can impact the risk-free rate. Strong economic growth and low unemployment may lead to higher risk-free rates, reflecting higher opportunity costs of holding risk-free assets. On the other hand, economic downturns or recessions may prompt central banks to lower interest rates, reducing the risk-free rate.**Inflation Expectations:**Inflation expectations can also influence the real return of risk-free assets. Investors demand compensation for expected inflation to preserve their purchasing power. Therefore, changes in inflation expectations can influence the risk-free rate because higher inflation expectations typically lead to higher risk-free rates.**Supply and Demand for Government Securities:**The risk-free rate is often closely tied to the yields on government securities. Investments like treasury bonds are generally considered low-risk investments. Changes in the supply and demand dynamics for these securities can influence their yields and, consequently, the risk-free rate. Increased demand for government bonds can drive their prices up and yields down, leading to lower risk-free rates.**Market Sentiment and Risk Appetite:**Last, investor sentiment and risk appetite play a role in setting the risk-free rate. During times of uncertainty or market volatility, investors may seek the safety of risk-free assets. This increases the demand for risk-free assets, therefore potentially lowering the risk-free rate. Meanwhile, when investors are optimistic about markets, they may be more willing to take risks (meaning there’s less appetite for risk-free assets so the rate will increase).

## Proxies for the Risk-Free Rate

Several alternatives are commonly used to represent the risk-free rate in financial analysis and valuation. If you can’t seem to get ahold of the risk-free rate or need a close alternative, some of those proxies include:

**Government Treasury Securities:**Short-term government treasury securities such as Treasury bills (T-bills) or longer-term treasury bonds are often considered the closest approximation to risk-free assets in many countries. The yields on these securities are typically used as proxies for the risk-free rate, particularly for short to medium-term investment horizons. This is because it’s largely assumed (at least in specific countries) that the government will not go bankrupt and default on its debt.**SOFR:**Although LIBOR has been phased out, SOFR has taken its place. These types of reference rates have historically been used as a proxy for the risk-free rate, particularly for international transactions and contracts denominated in currencies other than the domestic currency.**Central Bank Policy Rates:**Central banks may set other target rates, such as the Federal Reserve’s Federal Funds Rate in the U.S. There are also similar-type rates around the world such as the European Central Bank’s main refinancing rate in the Eurozone.**Inflation-Indexed Bonds:**Inflation-indexed bonds, such as Treasury inflation-protected securities (TIPS) in the U.S., offer yields adjusted for inflation and are sometimes used as proxies for the real risk-free rate. By subtracting the expected inflation rate from the nominal yield on these bonds, you can get a rough estimate of the real risk-free rate.**Cash or Cash Equivalents:**For very short-term investment horizons, cash or cash equivalents, such as money market funds or bank savings accounts, may be considered proxies for the risk-free rate.

## Limitations of Risk-Free Rate

While the risk-free rate is a real and important concept in financial analysis, it has several limitations that investors and analysts should consider:

The risk-free rate assumes risk neutrality, meaning it represents the return an investor can earn without taking on any risk. However, in reality, all investments involve some degree of risk, even if it’s a really, really small amount of risk. Think about how even the largest governments in the world could fail due to uncertain situations.

The risk-free rate is also influenced by various market factors including monetary policy decisions, economic conditions, and investor sentiment. Changes in these factors can lead to fluctuations in the risk-free rate over time, meaning it can be hard to use it as a stable benchmark for long-term financial analysis. In addition, inflation erodes the purchasing power of money over time, meaning that the real (inflation-adjusted) risk-free rate may be lower than the nominal rate.

The risk-free rate varies across countries and currencies. What could be the risk-free rate in the United States may be different than the risk-free rate in Russia. This reflects differences in economic conditions, monetary policies, and geopolitical risk. Using a single risk-free rate for all countries may not properly reflect the riskiness of certain markets or geographical regions.

Last, certain proxies for the risk-free rate like the ones above may not fully reflect liquidity risk. In times of market stress or financial crises, liquidity in these markets may dry up. This means the price of these goods may dramatically increase and cause the rate of return to substantially decrease, meaning there could be some volatility in the risk-free rate as well.

## Why Is the U.S. 3-Month T-Bill Used As the Risk-Free Rate?

There can never be a truly risk-free rate because even the safest investments carry a very small amount of risk. However, the interest rate on a three-month U.S. Treasury bill is often used as the risk-free rate for U.S.-based investors. This is a useful proxy because the market considers there to be virtually no chance of the U.S. government defaulting on its obligations. The large size and deep liquidity of the market contribute to the perception of safety.

## What Are the Common Sources of Risk?

Risk can manifest itself as absolute risk, relative risk, and/or default risk. Absolute risk as defined by volatility can be easily quantified by common measures like standard deviation. Relative risk, when applied to investments, is usually represented by the relation of price fluctuation of an asset to an index or base. Since the risk-free asset used is so short-term, it is not applicable to either absolute or relative risk. Default risk, which, in this case, is the risk that the U.S. government would default on its debt obligations, is the risk that applies when using the 3-month T-bill as the risk-free rate.

## What Are the Characteristics of the U.S. Treasury Bills (T-Bills)?

Treasury bills (T-bills) are assumed to have zero default risk because they represent and are backed by the good faith of the U.S. government. They are sold at a discount from par at a weekly auction in a competitive bidding process. They don’t pay traditional interest payments like their cousins, the Treasury notes and Treasury bonds, and are sold in various maturities in denominations of $1,000. Finally, they can be purchased by individuals directly from the government.

## The Bottom Line

The risk-free rate of return is the theoretical rate of return that an investor would expect on an investment with zero risk. Any investment with a risk level greater than zero must offer a higher rate of return. In practice, this rate of return doesn’t truly exist: every investment carries some amount of risk, even if that risk is small.

The three-month U.S. Treasury bill is often used as a proxy for a risk-free rate of return in U.S. markets because the risk of default by the government is low. Other countries and economic zones may use different proxies, such as euros or Swiss francs.