## What Is A Risk-Free Rate?

A risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the hypothetical rate of return; in practice, it does not exist because every investment has a certain amount of risk.

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For eg:

Source: Risk-Free Rate (wallstreetmojo.com)

These returns may be true for the government bonds of well-developed countries, like US treasury bonds or German government bonds. A risk-free rate is an important input in the Capital Asset Pricing Model (CAPM), which is the model used to determine the rate of return on investment with respect to the systematic risk associated with it.

**Risk-Free Rate Explained**

A risk-free rate is a return an investor can expect from an investment, given the risk associated is zero. Though it seems to be an effective concept, there is no investment that has no risk involved. Every investment option has a certain level of risk associated that may be minor or major.

A risk-free rate is used to calculate the expected rate of return on investment. US treasury bills, for example, are considered risk-free assets or investments as the US government fully backs them. There are three elements that can easily be studied depending on the risk-free rate. These include:

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For eg:

Source: Risk-Free Rate (wallstreetmojo.com)

**Inflation:-**The expected rate of inflation over the term of the risk-free investment;**Rental Rate:-**It is the real return over the investment period for lending the funds.**Maturity risk or Investment risk:Investment Risk:Investment risk is the probability or uncertainty of losses rather than expected profit from investment due to a fall in the fair price of securities such as bonds, stocks, real estate. In addition, each type of investment is prone to some degree of investment or default risk.read more**It is the risk related to the investment’s principal market value, i.e., it can be a rise or fall during the period to maturity as a function of changes in the general level of interest rates.

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For eg:

Source: Risk-Free Rate (wallstreetmojo.com)

While calculating the cost of equity using CAPMCost Of Equity Using CAPMCost of equity is the percentage of returns payable by the company to its equity shareholders on their holdings. It is a parameter for the investors to decide whether an investment is rewarding or not; else, they may shift to other opportunities with higher returns.read more, a Risk-free rate is used, influencing a business weighted average price of capital. Calculation of the capital cost takes place using the Capital Asset Pricing ModelUsing The Capital Asset Pricing ModelThe Capital Asset Pricing Model (CAPM) defines the expected return from a portfolio of various securities with varying degrees of risk. It also considers the volatility of a particular security in relation to the market.read more (CAPM).

CAPM describes the relationship between systematic riskSystematic RiskSystematic Risk is defined as the risk that is inherent to the entire market or the whole market segment as it affects the economy as a whole and cannot be diversified away and thus is also known as an “undiversifiable risk” or “market risk” or even “volatility risk”.read more and expected return. It determines the fairest price for the investment based on risk, potential returns & other factors.

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**Formula**

The formula that uses a risk-free rate to calculate the expected return has been mentioned below:

r_{a} = r_{rf }+ B_{a} (r_{m}-r_{rf})

Where,

- r
_{rf }= the rate of return for a risk-free security - r
_{m}= the broad market’s expected rate of return - r
_{e = }the expected return to be calculated for an investment - B
_{a}= Beta

### Examples

Let us consider the following examples to understand the risk-free rate meaning better:

#### Example 1 – US Treasury Bills

T bills are the short term obligation issued by the US Government. These are issued for one year or less than a year. These are the safest investment as they are backed by the US government. T bills carry a zero default riskDefault RiskDefault risk is a form of risk that measures the likelihood of not fulfilling obligations, such as principal or interest repayment, and is determined mathematically based on prior commitments, financial conditions, market conditions, liquidity position, and current obligations, among other factors.read more as they are fully guaranteed and credit by the US government and the Treasury Department.

Funds generated from selling Treasury bills, the government uses those funds for various public projects such as highways & schools. There are so many factors that influence treasury bills prices like monetary policyMonetary PolicyMonetary policy refers to the steps taken by a country’s central bank to control the money supply for economic stability. For example, policymakers manipulate money circulation for increasing employment, GDP, price stability by using tools such as interest rates, reserves, bonds, etc.read more, macroeconomic conditions, and supply& demand for the treasury. Longer treasury bills tend to have higher returns, but normally T bill’sT Bill'sTreasury Bills (T-Bills) are investment vehicles that allow investors to lend money to the government.read more maturity normally lies between few days to 12 months.

#### Example 2 – Calculation

Most of the time, the calculation of the risk-free rateCalculation Of The Risk-free RateA risk-free rate of return formula calculates the interest rate that investors expect to earn on investment with zero risks, especially default and reinvestment risks. It is usually closer to the base rate of a central bank and may differ for different investors.read more of return depends on the period under evaluation. Suppose the period is for one year or less than one year, then one should go for the most comparable government security, i.e., **Treasury Bills**. For example, if the treasury bill quote is .389, the risk-free rate is .39%.

If the time duration is in between one year to 10 years, then one should look for **Treasury Note. **For Example: If the Treasury noteThe Treasury NoteTreasury Notes are government-issued instruments with a fixed rate of interest and maturity date. As a result, it is the most preferred option because it is issued by the government (therefore, there is no risk of default) and also gives a guaranteed amount as a return, allowing the investor to plan accordingly.read more quote is .704, then the calculation of the risk-free rate will be 0.7%

Suppose the period is more than one year than one should go for **Treasury BondTreasury BondA Treasury Bond (or T-bond) is a government debt security with a fixed rate of return and relatively low risk, as issued by the US government. You can buy treasury bonds directly from the US Treasury or through a bank, broker, or mutual fund company.read more.** For example, if the current quote is 7.09, then the risk-free rate of return calculation would be 7.09%.

#### Example 3 – CAPM

If the risk-free rate is 7%, the market return is 12%, and the stock’s beta is 2, then the expected return on the stock would be:

Re = 7% + 2 (12% – 7%) = 17%

In the above CAPM example, the risk-free rate is 7%, and the market return is 12%, so the risk premium is 5% (12%-7%), and the expected return is 17%. The capital asset pricing model helps calculate the required rate of returnCalculate The Required Rate Of ReturnRequired Rate of Return (RRR), also known as Hurdle Rate, is the minimum capital amount or return that an investor expects to receive from an investment. It is determined by, Required Rate of Return = (Expected Dividend Payment/Existing Stock Price) + Dividend Growth Rateread more on equity based on how risky that investment is compared to risk-free.

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