Risk Free Rate Formula How To Calculate Rf In Capm

What is the Risk-Free Rate Formula?

A risk-free rate of return formula calculates the interest rate that investors expect to earn on an investment that carries zero risks, especially default risk and reinvestment risk, over some time. It is usually closer to the base rate of a Central Bank and may differ for the different investors. It is the rate of interest offered on sovereign or government bonds or the bank rate set by the country’s Central Bank. These rates are the function of many factors like – Rate of Inflation formulaRate Of Inflation FormulaThe rate of inflation formula helps understand how much the price of goods and services in an economy has increased in a year. It is calculated by dividing the difference between two Consumer Price Indexes(CPI) by previous CPI and multiplying it by 100.read more, GDP Growth rate, foreign exchange rate, economy, etc.

The risk-free rate of returnRisk-free Rate Of ReturnA risk-free rate is the minimum rate of return expected on investment with zero risks by the investor. It is the government bonds of well-developed countries, either US treasury bonds or German government bonds. Although, it does not exist because every investment has a certain amount of risk.read more is a key input in arriving at the cost of capitalCost Of CapitalThe cost of capital formula calculates the weighted average costs of raising funds from the debt and equity holders and is the total of three separate calculations – weightage of debt multiplied by the cost of debt, weightage of preference shares multiplied by the cost of preference shares, and weightage of equity multiplied by the cost of equity.read more and hence is used in the capital asset pricing modelCapital 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. This model estimates the required rate of return on investment and how risky the investment is compared to the total risk-free asset. It is used in the calculation of the cost of equityCalculation Of The Cost Of EquityCost of Equity (Ke) is what shareholders expect for investing their equity into the firm. Cost of equity = Risk free rate of return + Beta * (market rate of return - risk free rate of return). read more, which influences the company’s WACC.

Below is the formula to derive the Cost of Equity using the risk-free rate of return using the model :

CAPM Model

where,

Re: Cost of Equity
Rf: Risk-free rate
Rm: Market Risk PremiumMarket Risk PremiumThe market risk premium is the supplementary return on the portfolio because of the additional risk involved in the portfolio; essentially, the market risk premium is the premium return investors should have to make sure to invest in stock instead of risk-free securities.read more
Rm-Rf: Expected ReturnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability.
read more

However, It is usually the rate at which the government bonds and securities are available and inflation-adjusted. The following formula shows how to arrive at the risk-free rate of return:

This risk-free rate should be inflation-adjusted.

Explanation of the Formula

The various applications of the risk-free rate use the cash flows in real terms. Hence, the risk-free rate must also be brought to the same real terms, which is inflation-adjusted for the economy. Since the rate is mostly the long-term government bonds – they are adjusted to the rate of inflation factor and provided for further use.

The calculation depends upon the time period in evaluation.

If the period is up to 1 year, one should use the most comparable government security, which is the Treasury BillsTreasury BillsTreasury Bills (T-Bills) are investment vehicles that allow investors to lend money to the government.read more, or simply the T-Bills
If the period is between 1 year to 10 years, one should use a Treasure Note.
If the period is more than ten years, one can consider selecting Treasure Bond.

Examples of instruments with Risk-Free Rates

The government of any country is assumed to have 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 can print money to pay back their debt obligation as required. Therefore, the interest rate on zero-coupon government securities like Treasury BondsTreasury BondsA 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, Bills, and Notes, are generally treated as proxies for the risk-free rate of return.

If the period is between 1 year to 10 years, one should use a Treasure Note.

Examples of Risk-Free Rate of Return Formula (with Excel Template)

Let’s see some simple to advanced examples to understand it better.

Example #1

Use the following data for the calculation of the risk-free rate of return.

10 Year Government Bond Rate: 3.25%
Inflation Rate: 0.90%
Market Return: 6%
Beta: 1.5

The risk-free rate of return can be calculated using the above formula as,

=(1+3.25%)/(1+0.90%)-1

The answer will be –

Risk-free Rate of Return = 2.33%

The cost of equity can be calculated using the above formula as,

=2.33%+1.5*(6%-2.33%)

Cost of Equity will be –

Cost of Equity = 7.84%

Example #2

Below is the information for India, for the year 2018

Rate of Inflation: 4.74%
10 Year Government Bond: 7.61%

=(1+7.61%)/(1+4.74%)-1

Risk-free Rate of Return = 2.74%

Applications

The rate of return in India for the government securities is much higher than the U.S. rates for the U.S. Treasury. It is factored by the growth rate of each economy and the stage of development at which each stands. Therefore, the investors are shifting and considering investing in Indian government securities and bonds. The availability of such securities is easily accessible as well.

The largely used models involving the risk-free rate are:

Modern Portfolio Theory – Capital Asset Pricing Model
Black Scholes Theory – Used for Stock Options and Sharpe RatioSharpe RatioSharpe Ratio, also known as Sharpe Measure, is a financial metric used to describe the investors’ excess return for the additional volatility experienced to hold a risky asset. You can calculate it by,
Sharpe Ratio = {(Average Investment Rate of Return – Risk-Free Rate)/Standard Deviation of Investment Return}
read more – is a model used for the financial market dynamics containing derivative investment instruments.

The relevance of Risk-Free Rate of Return Formula

It can be seen from the two perspectives: the business and the investors’ perspective. From an investor’s point of view, a rising risk-free rate of return signifies a stable government, a confident treasury, and, ultimately, the ability to expect high returns on one’s investment. On the other hand, a rising risk-free rate scenario can be problematic for businesses. The companies would have to now meet the investors’ expectations of higher returns by improving stock prices. It might turn stressful as the business would now have to show good projections and have to thrive on meeting these profitabilityProfitabilityProfitability refers to a company’s ability to generate revenue and maximize profit above its expenditure and operational costs. It is measured using specific ratios such as gross profit margin, EBITDA, and net profit margin. It aids investors in analyzing the company’s performance.read more projections.

What is the Risk-Free Rate Formula?#

Explanation of the Formula#

Examples of instruments with Risk-Free Rates#

Examples of Risk-Free Rate of Return Formula (with Excel Template)#

Example #1#

Example #2#

Applications#

The relevance of Risk-Free Rate of Return Formula#

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