Ra-formula

CAPM Formula (Table of Contents)

The linear relationship between the expected return on investment and its systematic risk is represented by the Capital Asset Pricing Model (CAPM) formula.

CAPM is calculated according to the below formula:-

CAPM

Where:

  • Ra = Expected return on an investment
  • Rrf = Risk-free rate
  • Ba = Beta of the investment
  • Rm = Expected return on the market

And Risk Premium is the difference between the expected return on market minus the risk free rate (Rm – Rrf).

Market Risk Premium

The market risk premium is the excess return i.e. the reward expected to compensate an investor for the taking up the risk which is inherent in the portfolio as investing in stock market is always higher than investing in government bonds. Therefore it is a difference between the expected return on market and the risk free rate. The market rate of return, Rm, can be estimated based on past returns or projected future returns. For example, the US treasury bills and bonds are used for the risk free rate.

Expected return

The “Ra” refers to the expected return of an investment over the period of time.

Risk-free rate

The “Rrf” denotes the risk-free rate, which is equal to the yield on a 10-year US Treasury bill or government bond. The risk-free rate is the return that an investment which earns no risk, but in the real world it includes the risk of inflation. The risk-free rate should also be of the country where the investment is made, and the maturity period of the bond should also match the time period of the investment. Normally the risk free rate of return which is used for estimating the risk premium is usually the average of historical risk-free rates of return and not generally the current risk free rate of return.

Beta

The beta which is represented as “Ba” in the formulae of CAPM is a measure of the volatility of a security or a portfolio and is calculated by measuring how much the stock price changes with the return of the overall market. Beta is a measure of systematic risk. For example, if a company’s beta is equal to 1.7 then it means it has 170% of the volatility of returns of the market average and the stock prices movements will be rather extremes. If the beta is equal to 1, then the expected return on investment is equal to the return of the market average. If the beta is -1 then it means the stock prices are less risky and volatile.

Application of CAPM model

We will see a few examples of CAPM which is most often used to determine what the fair price of an investment should be. When we calculate the risky asset’s rate of return using CAPM, then that rate can also be used to discount the investment’s future cash flows to their present value and finally arrive at the investment’s fair price.

Examples of CAPM Formula

Let’s take an example to find out the CAPM for a company: –

You can download this CAPM Formula Excel Template here – CAPM Formula Excel Template

Example 1

Say the Stock A is expected to bring in returns of 14% over the next year and that the current risk-free rate is 6%, and you want to calculate whether it is profitable to invest in this. You have calculated the stock’s beta value which is 1.7. The overall stock market has a beta of 1.0. This implies that the stock carries a higher level of risk than the overall risk. Therefore we expect a higher return than the market’s 14% anticipated return over the next year.

The Expected Return can be calculated as below:

  • Required Return (Ra) = Rrf + [Ba * (Rm – Rrf)]
  • Required Return (Ra) = 6% + 1.7 * (14% – 6%)
  • Required Return (Ra) = 6% + 13.6%
  • Required Return (Ra) = 19.6%

This calculation tells you that you will get 19.6 % on your investment.ca

Example 2

Let’s suppose an investor is thinking of investing in one of the three stocks available in the market. The below information is available to estimate the rate of return of the three stocks.

  • Stock A with a beta of 0.80
  • Stock B with a beta of 1.20
  • Stock C with a beta of 1.50

The risk-free rate is 5.00% and the expected market return is 12.00%.

We can calculate the Expected Return of each stock with CAPM formula.

  • Required Return (Ra) = Rrf + [Ba * (Rm – Rrf)]

Expected Return of Stock A

  • E(RA) = 5.0% + 0.80 * (12.00% – 5.0%)
  • E(RA) = 5.0% + 5.6%
  • E(RA) = 10.6 %

Expected Return of Stock B

  • E(RB) = 5.0% + 1.20 * (12.00% – 5.0%)
  • E(RB) = 5.0% + 8.4%
  • E(RB) = 13.4 %

Expected Return of Stock C

  • E(RC) = 5.0 %+ 1.50 * (12.00% – 5.0%)
  • E(RC) = 5.0 % + 10.5%
  • E(RC) = 15.5%

Therefore we see that it is best to invest in stock C. So, it is seen that higher the beta, the higher will be the expected return according to the CAPM formula.

Example 3

Now we will see an application problem of expected return. We can calculate Net Present Value using the expected return or the hurdle rate from the CAPM formula as a discounted rate to estimate the net present value of an investment

The following information is given:

  • β =1.3
  • Rrf = 6%
  • Rm =13%

So the hurdle rate or expected return from the project is calculated as below:

  • Required Return (Ra) = Rrf + [Ba * (Rm – Rrf)]
  • Ra = 6% + 1.3 * (13%- 6%)
  • Ra = 6% + 9.1%
  • Ra = 15.1%

Information specific to the project that you are planning to invest is as follows. The figures are in lakhs:

  • Initial Investment= ₹5,000
  • Expected payments done: ₹ 6,000 in 2nd year, ₹ 5,000 in 5th year

Net Present Value Calculation (NPV): Taking in the note the time value of money we calculate the NPV as below:

Npv = – initial investment +summation of ( value of investment/ (1+ rate)^ no.of years)

So initial investment is 5000, and then 6000 is invested in the second year and 5000 in the 5 th year. just put the values to get the results

  • NPV = -5,000 +( 6,000/1.151^2 )+ (5000/1.151^5 )
  • NPV = ₹ 2004.085713

Therefore the net value of investment done is ₹ 2004.085713.

Assumptions of CAPM Formula

  1. Investors hold diversification across a range of investments so they eliminate unsystematic risk.
  2. Investors can lend and borrow any amounts under the risk free rate.
  3. CAPM considers a market to be ideal and does not include taxation or any transaction cost in an account.
  4. Assume all information is available at the same time to all investors.
  5. Every investor is against to exposure to risk.

Limitations

The limitation of this CAPM formula is the higher the risk of the asset, the greater is the expected return which is always not true.

CAPM Formula Calculator

You can use the following CAPM Calculator


Ra = Rrf + [Ba X (Rm - Rrf)]
0 + [0 X (0 - 0)] = 0

CAPM Formula in Excel (With Excel Template)

Here we will do the same example of the CAPM formula in Excel. It is very easy and simple. You need to provide the three inputs i.e Risk-free rate, Beta of the investment and Expected return on the market

You can easily calculate the CAPM using Formula in the template provided.

The Expected Return can be calculated as below:

CAPM

We can calculate the Expected Return of each stock with CAPM formula.

Calculation

Expected Return from the project is calculated as below:

CAPM

The net value of the investment is Calculated as:

Calculation

Recommended Articles

This has been a guide to a CAPM formula. Here we discuss its uses along with practical examples. We also provide you with CAPM Calculator with downloadable excel template. You may also look at the following articles to learn more –

  1. Formula for Debt Ratio
  2. Guide to Tax Equivalent Yield Formula
  3. Examples of Price to Earnings Formula
  4. Return on Average Assets Formula
  5. Guide to Systematic Risk vs Unsystematic Risk

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