By

Konstantin Vasilev Member of the Board of Directors of Cbonds, Ph.D. in Economics

Updated September 11, 2023

**What Is the Risk-Free Rate?**

The risk-free rate of return pertains to the hypothetical rate of return achievable from an investment devoid of any risk. It characterizes the interest that an investor would anticipate from utterly zero-risk financial instruments within a designated timeframe.

The so-called "real" risk-free rate can be computed by deducting the prevailing inflation rate from the yield of the Treasury bond aligning with your investment’s duration.

**Risk-Free Rate of Return Explained**

In principle, the risk-free rate signifies the minimal return an investor anticipates from any investment. Investors are unwilling to embrace additional risk unless the potential return surpasses the risk-free rate. When seeking an approximation for the risk-free rate of return, one must take into account the investor’s domestic market, particularly considering the complexities that negative interest rates can introduce.

Distinct nations and economic regions adopt varying benchmarks as their benchmarks for the risk-free rate. Often, the interest rate associated with a three-month U.S. Treasury bill (T-bill) is employed as the risk-free rate for investors situated in the United States.

The utility of the three-month U.S. Treasury bill as a proxy stems from the market’s widespread belief that the likelihood of the U.S. government defaulting on its commitments is nearly nonexistent. The substantial scale and robust liquidity of the market contribute to this sense of security.

For a foreign investor whose holdings are not denominated in U.S. dollars, investing in U.S. Treasury bills introduces currency risk. This risk can be mitigated using currency forwards and options, but it does influence the overall rate of return.

In the case of investors with assets denominated in euros (EUR) or Swiss francs (CHF), the short-term government bills from other well-rated countries, like Germany and Switzerland, serve as suitable risk-free rate proxies. Investors hailing from eurozone countries with lower credit ratings, such as Portugal and Greece, can invest in German bonds without exposing themselves to currency risk. Conversely, an investor holding assets in Argentinian pesos cannot engage in investments involving highly-rated government bonds without taking on currency risk.

The significance of the risk-free rate extends to the computation of the Sharpe ratio. This analytical metric serves to assess the risk-adjusted returns of either an individual security or an entire investment portfolio.

**Negative Interest Rates**

Negative interest rates can arise in specific economic conditions, introducing complexity to the computation of the risk-free rate of return and its implications for investors. As of 2021, a flight to safety amid the prolonged European debt crisis led to negative interest rates in the most secure nations like Germany and Switzerland, as investors sought refuge from high-yield instruments. In the United States, political disagreements in Congress regarding the debt ceiling occasionally resulted in limited bill issuance, causing supply shortages that drove prices down. Although Treasury auctions enforce a zero lower limit on yields, secondary market trading sometimes witnesses bills trading with negative yields.

In Japan, persistent deflation prompted the Bank of Japan to adopt ultra-low and occasionally negative interest rates to stimulate economic activity. Negative interest rates push the concept of risk-free returns to an extreme, with investors being willing to pay for the privilege of placing their funds in assets they perceive as secure.

## Calculating the Risk-Free Rate

Determining the risk-free interest rate lacks a unanimous methodology, resulting in a diverse array of risk-free interest rate equations that purport to quantify this rate directly. Consequently, some analysts opt to examine what are referred to as "proxies" for the risk-free interest rate. Potential proxies include short-term government bonds, inter-bank lending rates, or AAA-rated corporate bonds issued by entities deemed "too big to fail."

Nevertheless, the proxy-based approach to risk-free interest rate calculation presents numerous challenges. For instance, government bonds can only be genuinely risk-free if the risk of default is entirely absent. While the likelihood of such bonds defaulting is exceedingly remote, occasional defaults do transpire, casting doubt on their suitability as proxies. Moreover, the potential for governments to resort to "printing more money" to fulfill obligations introduces a risk of devaluation.

Nonetheless, several risk-free interest rate formulas offer effective means of calculation. One such approach involves subtracting the prevailing inflation rate from the yield of Treasury bills over the investment’s duration. This computation can be articulated using the subsequent risk-free rate formula:

*Risk-Free Interest Rate = Real Risk-Free Interest Rate + Inflation Premium*

## Example

U.S. Treasuries serve as a prime illustration of risk-free assets, given the assurance that the government will not default on its debt obligations. Consequently, the interest rate paid on three-month U.S. Treasury bill is frequently adopted as a substitute for the short-term risk-free rate, owing to its virtual immunity from default risk. risk free security

Treasury bills (T-bills) are regarded as devoid of default risk due to their representation and backing by the unwavering commitment of the U.S. government. These bills are offered at a discount from their face value through a weekly auction characterized by competitive bidding. Unlike their counterparts, Treasury notes and Treasury bonds, T-bills do not provide conventional interest payments. Available in different maturities and denominations of $1,000, they are also accessible for direct purchase by individuals from the government.

In contrast, riskier assets encompass a spectrum of investments that carry higher levels of uncertainty and volatility. These assets, which may include stocks, corporate bonds, or real estate, offer the potential for greater returns but come with an increased likelihood of loss or price fluctuations. Unlike risk-free assets like T-bills, the value of riskier assets can be influenced by factors such as market sentiment, economic conditions, and company performance. Investors often demand a higher expected return, known as a risk premium, to compensate for the additional risk they take on when allocating their resources to these more volatile and unpredictable investment options.

## Difference between Nominal Risk-Free Rate and Real Risk-Free Rate

Two perspectives emerge when discussing risk-free rates: the nominal risk-free rate and the real risk-free rate. The disparity arises from the influence of inflation.

The nominal risk-free rate typically pertains to the current yield of the 3-month T-bill, neglecting the effect of inflation. On the other hand, the real risk-free rate encompasses the yield of the 3-month T-bill adjusted by factoring out the impact of inflation.

The real risk-free rate signifies the yield an investor would require for a potential investment to be shielded from inflationary risk, provided that inflation rates remain consistent or decrease.

## Common Sources of Risk

Risk can manifest in various forms, encompassing absolute risk, relative risk, and default risk. Absolute risk, characterized by volatility, can be readily quantified using common metrics such as standard deviation. Relative risk, when employed in the context of investments, is commonly depicted by comparing the price fluctuations of an asset to an index or a base. As the chosen risk-free asset is extremely short-term, it remains inapplicable to both absolute and relative risk assessments. Default risk, specifically regarding the potential for the U.S. government to default on its debt obligations, becomes pertinent when utilizing the 3-month T-bill as the reference for the risk-free rate.

## Capital Asset Pricing Model

The Capital Asset Pricing Model (CAPM) is a fundamental framework in finance that establishes a systematic approach for assessing the relationship between an asset’s expected return and its risk in the context of a diversified portfolio. Central to the CAPM is the concept of the risk-free rate, which serves as a benchmark representing the minimum return an investor can expect from an investment devoid of risk. This rate is often tied to the yield of a risk-free asset, such as a short-term government bond, and serves as the foundation for assessing the risk and potential return of other assets. The CAPM utilizes the risk-free rate as a key component in calculating the expected return of an asset, factoring in the risk it carries in relation to the overall market. This model aids investors in making informed decisions by enabling them to evaluate whether an asset’s anticipated return justifies the risk it poses in comparison to the risk-free rate.