Risk-Free RateDefined along with Formula & How to Calculate

Written By:
Lisa Borga

Reviewed By:
FundsNet Staff

The risk-free rate of return is a crucial theoretical concept for investment which refers to the guaranteed return that could be earned from an investment with no risk.

For individual investors and companies, this rate of return helps to determine what investments or capital projects are worth investing in by serving as a minimum rate of return.

Anything below this rate of return is not worth investing capital in.

In actual practice, every investment carries some level of risk, no matter how small, so the closest substitute to a guaranteed investment must be used instead.

This is generally regarded to be the interest paid by the U.S. government’s 3-month Treasury Bill (T-bill).

These are guaranteed by the U.S. government, and though it is possible that the government will default on its securities, the chances of this happening are extremely low.

This more practical risk-free rate is calculated by subtracting the current rate of inflation from the yield offered by the T-bill for the investment period.

This will offer the current risk-free rate for a given period of time.

Essential Points

• The risk-free rate of return refers to a hypothetical rate of return offered by an investment that carries no risk.
• Because there is no truly risk-free investment, the closest practical substitute is used instead, which is generally considered to be short-term government debt.
• In order to calculate a risk-free rate, the rate of inflation is subtracted from the T-bill yield for the particular investment period.

The Risk-Free Rate Explained

Investment is always a practice of balancing the risk of loss against expected returns.

Generally, with all other factors being equal, greater risk equates to greater returns.

Before accepting the risk of any given investment, an investor will want to know that the rate of return is greater than what they could earn from a risk-free investment.

The most common proxy for a risk-free rate of return is the yields offered by short-term U.S. government debt, most notably the 3-month T-bill.

There are two reasons for this. The first is that they are fully backed by the U.S. government.

The U.S. government has never defaulted on its debt, and the probability of this happening is assumed to be virtually nonexistent.

As a result, these are the safest asset that an investor could own.

The second reason is that the market for U.S. government debt is extremely large and liquid without any close competition.

In April 2022, the Securities Industry and Financial Markets Association estimated that the Market Cap for securities issued by the U.S. Treasury was $23.3 trillion, with active trading of $679 billion.

As a result, those trading in T-bills can be near certain that there will be willing buyers for these securities should they need to convert them into cash, and in general, U.S. investors will often see the current risk-free rate marked as the current yield offered by 3-month T-bills.

However, though foreign investment in U.S. government debt is common, with the Board of Governors for the Federal Reserve System estimating in January 2022 that foreign investors hold approximately 35% percent of outstanding Treasury securities, this can, in some cases, increase an investor’s risk.

For non-U.S. investors with assets not denominated in dollars may face the prospect of currency risk.

As a result, the short-term debt of other countries offering a low risk of default can be used to offer a similarly low-risk investment.

However, for some investors, it may not be possible to invest in highly rated countries’ bonds without facing currency risk.

Nominal Risk-Free Rate Versus Real Risk-Free Rate

There are two common ways to consider risk-free, and this includes the nominal risk-free rate and the real risk-free rate.

The way these two rates differ is in how they account for inflation.

The nominal risk-free rate inflation rate is simply the observed return from a risk-free asset, generally 3-month T-bills.

This does not account for the effect of inflation in determining the actual returns necessary for an investment not to experience inflation risk.

In contrast, the real risk-free rate represents the yield that an investor would need in order to negate inflation risk if inflation rates were to remain at the same or a lower level.

This is generally determined by subtracting the inflation rate from the nominal value.

How Is the Risk-Free Rate Used?

The risk-free rate is a crucial tool for building different models for many financial calculations, particularly valuation models.

These models can help investors to gain an understanding of how risk can impact investment returns.

Using these models, the potential return from a risk-free asset becomes a baseline for calculating risk premiums.

A risk premium is an additional return that investors expect in return for taking on the additional risk of losing their investment.

For example, if an investor purchases shares of stock instead of a relatively safe investment such as government bonds, they have accepted a high risk of losing the money they have invested.

However, in exchange, they expect to earn a higher rate of return.

In addition to calculating risk premiums, the risk-free rate is an essential part of calculating the cost of equity through the capital asset pricing model (CAPM), which describes the relationship between systemic risk and expected return.

This formula can help investors to find the fair value of an asset based on its potential return and the risk of loss.

The formula for CAPM is:

CAPM (Re) = Rf + β(Mr – Rf)

Where:

CAPM (Re): Cost of Equity

Rf: Risk-Free Rate

β: Beta

Mr: Market Risk Premium

In addition to calculating CAPM, the risk-free rate is a critical factor in calculating the Sharpe ratio, which is a widely used analytical tool for evaluating the excess return on an investment or portfolio for a period in comparison with a benchmark which most commonly is the risk-free rate of return.

Sharpe Ratio = (Rx – Rf) / SRTN

Where:

Rx: Expected Return on Investment

Rf: The Risk-Free Rate of Return

SRTN: Standard deviation of Excess Return

For both of these tools, a higher ratio is desirable and indicates a better investment.

Also, in calculating either of these valuation models, U.S. T-bills with different maturation periods are typically used for the risk-free rate.

In general, the maturity period should be chosen to best match the duration of projected cash flows for the investment under consideration.

Risk-free Rate Formula

In most cases, calculating the nominal risk-free rate is extremely simple and just requires finding the yield for a 3-month T-bill.

This does not require any additional calculations and does not account for the impact of inflation.

However, in some cases, it is more appropriate or desirable to use the real risk-free rate, and this is a little more complex.

In order to calculate the real risk-free rate, inflation must be taken into account.

Thus, the real risk-free rate formula is:

Real Risk-Free Rate = Risk-Free Rate – Inflation Rate

For example, consider an investor that is trying to decide whether or not to invest in a savings account that will yield a 3.00% growth over the following year.

The current nominal risk-free rate is 2.00%, which is the yield for a 1-year T-bill.

Simply using the nominal risk-free rate, the investor would be making a surplus of 1.00% over the risk-free rate, which would seem to indicate that the investment would be a good choice.

However, taking the real risk-free rate into account may tell a very different story.

Assuming an inflation rate of 8.2%, which is what it was in September of 2022, the investor can calculate the real risk-free rate by subtracting the current inflation rate.

This is 2.00 – 8.20%, which results in a real risk-free rate of -6.20%.

Comparing this rate with the expected yield for the savings account shows that the investor will be falling 3.20% short of keeping up with the current rate of inflation.

As a result, if the investor is looking to grow their money or keep pace with inflation, they should likely reconsider their investment.

In an economy dealing with high inflation, it is often necessary to accept higher-risk investments in order to earn yields capable of growing or retaining purchasing power.

How Zero or Negative Interest Rates Affect the Risk-free Rate

In an economy that is slowing or in the midst of a recession, central banks may take action with monetary policies, including reducing interest rates.

In some extreme cases, this may result in zero or even negative interest rates in order to encourage consumers and financial institutions to spend, invest, or lend money, boosting the amount flowing through the economy.

This has occurred in numerous instances throughout the European debt crisis as well as in Japan in response to long-running struggles with deflation.

In recent years, the U.S. Federal Reserve has responded to the economic difficulties brought on by the COVID-19 pandemic by reducing the federal funds target rate to zero.

This, in turn, caused yields for T-bills to drop to extraordinarily low levels.

The United States Treasury is prohibited from selling T-bills with a negative yield at auction, and the lowest level that these yields can drop to is zero.

However, in the secondary market, sellers often place these bills for sale at a premium, and in the right circumstances, this may result in a negative real yield.

Despite this, investors may still purchase these T-bills due to the high degree of security they offer.

Though investors may even lose purchasing power off of these investments when inflation is considered, they may still purchase these T-bills under the assumption that they may lose more off of higher-risk investments.

During periods with low inflation, zero or even negative interest rates, risk-free rates of return are taken to extreme lows.

During these periods, investors are often more likely to look for safe investments.

In Summary

The risk-free rate of return is only a theoretical concept describing an investment with zero risk.

However, it has extremely valuable real-world applications.

By using a proxy value such as the yields on T-bills and other high-quality government bonds, it is possible to use this concept in a number of useful ways.

The risk-free rate of return is used in many financial calculations, which can help investors to measure the potential value of an investment opportunity as well as whether its projected returns would outpace inflation for the investment period.

When it comes to investment, it is crucial to balance the risks and returns carefully, and this is just what the risk-free rate of return helps investors to do.