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

Risk-free rateis the minimum rate of return that is expected on investment with zero risks by the investor, which, in general, is the government bonds of well-developed countries; which are either US treasury bonds or German government bonds. It is the hypothetical rate of return, in practice, it does not exist because every investment has a certain amount of risk.

### Risk-Free Rate of Return Reflects 3 Components

**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:**It is the risk which is related to the investment’s principal market value i.e., it can be rise or fall during the period to maturity as a function of changes in the general level of interest rates.

### 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 risk as they are fully guaranteed and credit by the US government and the Department of the treasury.

Funds generated from selling Treasury bills, the government uses those funds for various public projects such as highway & schools. There are so many factors that influence treasury bills prices like monetary policy, macroeconomic conditions, and supply& demand for the treasury. Longer treasury bills tend to have higher returns but normally T bill’s maturity lies between few days to 12 months.

### Calculation of Risk-Free Rate

- Most of the time the calculation of the risk-free rate of return depends on the time period that is under evaluation. If the time period is for one year or less than one year than one should go for the most comparable government security i.e.,
**Treasury Bills**. For example, if the treasury bill quote is .389 then the risk-free rate is .39%. - If the time duration is in between one year to 10 years than one should look for
**Treasury Note.**For Example: If the Treasury note quote is .704 than the calculation of risk-free rate will be 0.7% - If the time period is more than one year than one should go for
**Treasury Bond**For example if the current quote is 7.09 than the calculation of the risk-free rate of return would be 7.09%.

### Risk-Free Rate in CAPM

While calculating the cost of equity using CAPM, a Risk-free rate is used, which influences a business weighted average cost of capital. Calculation of cost of capital takes place by using the Capital Asset Pricing Model (CAPM).

CAPM describes the relationship between systematic risk and expected return. It determines the fairest price for the investment, based on risk, potential returns & other factors.

#### CAPM Formula & Risk-Free Return

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

- r
_{rf }= the rate of return for a risk-free security - r
_{m}= the broad market’s expected rate of return

#### CAPM Formula Example

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 to calculate the required rate of return on equity based on how risky that investment is when compared to a totally risk-free.

### Summary

- Risk-free rate is a rate of return of an investment with zero risks.
- It is the hypothetical rate of return, in practice, it does not exist because every investment having a certain amount of risk.
- US treasury bills consider as risk-free assets or investment as they are fully backed by the US government.
- In the cost of Equity, a Risk-free rate is used for CAPM calculation.
- Calculation of cost of capital takes place by using the Capital Asset Pricing Model (CAPM).
- CAPM describes the relationship between systematic risk and expected return

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