# Risk Free Rate Calculator

Risk-free rate of return refers to the funds to invest in a no-risk of investments that can get yields. Generally, this rate of return will be regarded as the basic return, and then various risks that may arise are considered.

The risk-free rate represents the interest an investor would expect from an absolutely risk-free investment over a specified period of time. In practice, the risk-free rate of return does not truly exist, as every investment carries at least a small amount of risk, i.e. risk-free bond issues by a government or agency whose risks of default are so low as to be negligible.

## Why Calculate Risk-Free Interest Rate?

In theory, the expected rate of return of any investment cannot be lower than the risk-free rate of return, otherwise, no one will be willing to invest. For investors to take risks, the expected rate of return must be higher than the risk-free rate of return. In reality, there is no pure risk-free rate of return, because even the safest investment can’t be 100% risk-free. The risk-free rate of return is often represented by the interest rate of a three -month US Treasury bill.

## Method I – Government Bond

The risk-free rate is generally defined as the (more or less guaranteed) rate of return on short-term U.S. Treasury bills because the value of this type of security is extremely stable and the return is backed by the U.S. government. So, the risk of losing invested capital is virtually zero, and a certain amount of profit is guaranteed.

## Method II – Real Interest vs Nominal Interest Rates

A nominal interest rate refers to the interest rate before taking inflation into account.

Nominal Risk Free Rate = (1 + Real Risk Free Rate) × (1 + Inflation Rate) − 1

A real interest rate is the interest rate that takes inflation into account. This means it adjusts for inflation and gives the real rate of a bond or loan.

To calculate the real interest rate, you first need the nominal interest rate. The calculation used to find the real interest rate is the nominal interest rate minus the actual or expected inflation rate.

• `Real Risk Free Rate = (1 + Normal risk free rate) / (1 + inflation rate)`

## Method III – The Cost of Equity

The cost of equity can be calculated by using the CAPM (Capital Asset Pricing Model) formula that shows the return of a security is equal to the risk-free return plus a risk premium, based on the beta of that security. Below is an illustration of the CAPM concept.

Cost of Equity = Risk-Free Rate of Return + Beta * (Market Rate of Return – Risk-Free Rate of Return)

Where:

• Ra=Cost of Equity
• Rrf=Risk-Free Rate
• Ba=Beta
• Rm=Market Rate of Return

### Beta Coefficient

In finance, the beta (β or beta coefficient) of an investment is a measure of the risk arising from exposure to general market movements. The S&P 500 Index, has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the market.

A stock that swings more than the market over time has a beta above 1.0. If a stock moves less than the market, the stock’s beta is less than 1.0.

• High-beta stocks are supposed to be riskier but provide higher return potential.
• Low-beta stocks pose less risk but also lower returns.

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