#
Risk-Free Rate

The interest rate that a risk-free investment would yield for the investor.

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

The first thing that should be known when discussing the risk-free rate is the fact that this rate doesn’t exactly exist. It doesn’t truly exist because no such investment has absolutely no risk.

As you will learn, all investments have some sort of risk. The risk-free rate exists as a term in finance because certain investments have almost no risk.

The rate is used as a baseline metric for investment returns in a given market, so refer to this rate as a theoretical rate of estimated return. Hence, this rate is also called the risk-free rate of return.

The yield of the Treasury bond that corresponds to the tenure of your investment can be subtracted from the current inflation rate to determine the so-called "real" risk-free rate.

The risk-free rate is a key concept when valuing potential investments and balancing portfolios. It is simply the current interest rate paid on any investment deemed to be ‘risk-free’ (i.e., US/UK/German government bonds, savings accounts, etc.).

This theoretical rate is a rate of return that an investor would receive through interest payments with almost no risk involved.

This type of investment would compensate investors for the time that the investor holds the investment, in a type of investment called treasury bills. In practice, there are things that we can use to represent the risk-free rate, although these investments would still carry some risk.

The risk-free rate is used in the Capital Asset Pricing Model (CAPM) to value assets, and all portfolios should contain a certain percentage of money in risk-free assets as a means of diversification. Another way of thinking about the risk-free rate is that it is the absolute minimum return an investment should offer.

## Key Takeaways

- The risk-free rate is a theoretical rate of return representing an investor's return with no risk involved.
- The risk-free rate can be used as a baseline metric for investment returns and economic climate.
- There is no such investment that carries absolutely zero risk.
- Due to their minimal default risk, government bonds such as the 3-month United States Treasury bill and the 10-year United States Treasury bonds represent the risk-free rate.
- To find the real risk-free rate, subtract the current inflation rate from the nominal risk-free rate from the bond of your choice.

## Finding the Risk-Free Rate

You may be wondering, how is it possible to represent such a rate?

Although estimating a true risk-free rate is difficult, some investments come close enough.

Investors often use government bonds' yields as a benchmark since they represent minimal risks. Government bonds are securities that are backed by the United States government.

These bonds are reliable benchmarks for the risk free rate because the investment’s risk is the U.S. defaulting on its bond obligations.

This event has such a low probability because the government could hypothetically print money to pay off its debts, unlike other financial institutions that could potentially fail to fulfill debt obligations.

As this kind of investment can be called the risk free rate, selecting a relevant government bond that best suits your investment horizon is important.

Although all government bonds are generally less risky than other investments, bonds vary in terms of the coupon rate (interest rate) and maturity. Typically, the three-month United States Treasury bill represents the risk free rate.

Accessing up-to-date information regarding these government bonds, such as their yields, could come from many reliable sources such as financial news websites and central bank websites, amongst other options providing such information readily accessible on online platforms.

## Note

Obtaining an accurate estimation of the risk-free rate of return is crucial when determining potential earnings without risking a loss on any investments.

Because investing in bonds involves a transaction in the financial markets, the bond will change with the current economic environment.

## Risk-Free Rate Calculation

When dealing with variables in economics and finance, we often have real and nominal versions of different variables or metrics.

Real variables are known as variables that are adjusted for inflation. On the other hand, nominal variables are raw monetary values that are not adjusted for other factors, such as inflation.

When dealing with this rate, it can be represented in two ways:

- Real
- Nominal

## Note

Nominal variables are more likely to be misleading because they do not capture the effects of inflation.

The nominal risk free rate is simply the given rate of the investment you decide to choose as your risk free rate. It represents the nominal return an investor would earn on their investment if there were no inflation.

To find the real risk free rate, you need the nominal risk free rate from a treasury bond of your choice with almost no risk. Then, you can find the inflation rate from various public economics sources reporting inflation rates.

Take the selected nominal rate and subtract the inflation rate to calculate the real rate,

Here is a representation of that calculation in a simple formula:

*(Real Risk Free Rate) = (Nominal Risk-Free Rate) - (Inflation Rate)*

## Note

It is important to remember that the nominal risk-free rate estimate may not be accurate given the constantly changing market conditions. Therefore, the risk-free rate should be both selected and evaluated carefully due to the ever-changing economic environment.

## Risk-Free Rate Representation

There are two common ways to represent the risk-free rate:

**1. 3-Month United States Treasury Bill**

The three-month treasury bill is a short-term financial investment that the United States government issues.

This T-bill is considered safe because the U.S. government backs this T-bill. The United States is unlikely to default on its obligations, so this 3-month investment is considered a risk-free investment in the United States.

## Note

The 3-month United States treasury bill is also known as the U.S. 3-month T-bill.

The risk-free rate is a 3-month investment in this case because a three-month investment has a lower chance of drastic fluctuation compared to a year-long investment.

The bill also poses a low risk because of its flexibility and liquidity in the market. It is flexible because it allows investors to re-invest or adjust their investment strategies after the 3 months.

The 3-month T-bill can be considered liquid compared to other bills because of higher trading volume and demand for short-term investments. This means that investors can sell these financial instruments more easily without worrying about a lack of buying volume.

Due to these factors, many label this 3-month bill as an investment with zero risk.

## Note

It is important to remember that there is no true risk-free rate and that even safe investments, such as the 3-month T-bill, involve some risk.

**2. 10-Year United States Treasury Bond**

The 10-Year United States Treasury Bond is similar to the 3-month risk-free rate but has an investment time length of 10 years.

The 10-year U.S. treasury bond is sometimes used as a benchmark for the risk-free rate of return because it also has a low default risk, a predictable market forecast time, and a plethora of historical market data.

Although different from the 3-month T-bill, the 10-year treasury bond is considered to be a risk-free rate in many cases. Even if it is considered the safest bond representing the risk-free rate, it still carries some risk.

### Risk-Free Rate Examples

Let’s say the current 10-year treasury bill rate is 4.09%. This means that we can call the interest rate benchmark and the risk-free rate of return 4.09%.

This 10-year T-bill is typically interpreted as a benchmark rate for other government and corporate bond yields, as well as things like mortgage rates, CD rates, and many other bank loans.

However, we can also break down what would happen if we actually invested in this treasury bill. Let’s say you want to invest $1000 at a 4.09% rate.

To calculate the investment amount on a Treasury bill with a face value of $1,000 and a yield or rate of 4.09%, you need to determine the purchase price of the T-bill.

Treasury bills are typically sold at a discount to their face value, and the difference between the purchase price and the face value represents the investor's return on investment.

The discount rate is the same thing as the risk-free rate of return attached to the T-bill, so we can easily calculate the initial investment amount by setting up this formula:

*P = F/(1+r)^t*

Where:

**P =**Present Value (What you’d need to invest)**F =**Face Value (1000)**R =**Interest Rate (.0409)**T =**Time (10 Years)

If you plug in these values in the appropriate variables, you should come out with P= $671.88.

So, if you invest $671.88 of capital for this T-bill, you could redeem up to $1000 in interest payments by its maturity date 10 years down the line. This utilizes the least risky form of investment since it relies on the U.S. government to pay back the interest, and it can be sold very easily.

## Note

For these types of investments, you don’t have to wait until the maturity date, and you could sell the bill early, collecting a lower total amount of interest.

As said earlier, these treasury bills are typically used for benchmarks since the returns aren’t very significant over a 10-year period. Many index funds can generate an 8-12% return annually, which would make significantly more than a treasury bill could.

Regardless, it is a better investment than holding cash in an inflationary environment, and it serves as a necessary example for the risk-free rate as well as other important types of interest rates.

## Conclusion

The risk-free rate is an interesting concept that can be used in economic and financial analysis. In reality, it's difficult to pinpoint a true risk-free rate because all investments must carry some sort of hypothetical risk.

However, we do have investments that come close, such as certain government bonds. These bonds are reliable benchmarks for the risk-free rate because they're backed by the government and have minimal default risk.

The most common examples are the 3-Month United States Treasury Bill and the 10-Year United States Treasury Bond. They represent the risk-free rate because the U.S. government is unlikely to default on its obligations, especially in these two-time frames.

To calculate the real risk-free rate (adjusted for inflation), you subtract the current inflation rate from the nominal risk-free rate of your chosen bond.

To find the initial investment amount on a 10-year treasury bill, you can use the discount rate, the time of the investment, and the face value in this simple formula: P= F/(1+r)^t.

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