Finance

The Capital Asset Pricing Model

The Capital Asset Pricing Model

The Capital Asset Pricing Model was proposed in the mid-1960s by William Sharpe, John Lintner, and Jack Treynor. The Capital Asset Pricing Model allows investors to calculate the trade-off between risk and return for their individual securities and diversified portfolios.

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The Capital Asset Pricing Model states that the expected return on investment is proportional to its β i.e.

Terminologies:

  • Systematic Risk:

The risk involved here is the systematic risk i.e. the risk due to fluctuation in the markets. Recession, wars are some examples of systematic risks.

  • Expected Return of Investment:

This is an estimate of how much an investment will return throughout its life.

  • Risk-Free Rate:

This is a parameter which is different for every country and is equal to the rate of return of its government bonds. The risk of getting this amount of return is typically zero.

  • BETA of the investment:

β is the sensitivity of the stock towards fluctuation in the market. For example, if the stock price rises by 20% when the market rises by 10%, its β would be 2.

  • Market Risk Premium:

This is the additional return that an investor incurs above the risk-free return. This return can be thought of as compensation for investing in a riskier stock. The greater the risk of investment, the higher is the expected return.

The CAPM models infer that all the investments should lie on the line joining the risk-free government bonds (β =0) and the normal market portfolio (β = 1). This line is known as the Security Market Line.

 

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Assumptions of the CAPM:

  • The prime focus of the investors is to maximize return and the expected utility of their terminal wealth. They do so by choosing amongst different portfolios based on each portfolio’s expected return and standard deviation.
  • All investors can borrow or lend an unlimited amount at a given risk-free rate of interest.
  • All investors have proper estimations of the expected returns, variances, and covariances among assets.
  • Perfect Liquidity of assets.
  • Zero transaction costs.
  • There are no taxes.
  • All investors are price takers (that is, all investors assume that their own buying and selling activity will not affect stock prices).
  • The return on assets follows a Normal probability distribution.
  • The government/treasury bills are completely devoid of risk.
  • Investors borrow and lend money at the same interest rate.

These assumptions do not hold true in the real-world scenario and so some modifications are applied to the CAPM model.

CAPM: Example

This example calculates the expected return on a stock, using the Capital Asset Pricing Model (CAPM) formula.

Given that:

  • The stock trades on the BSE.
  • The risk-free rate of return on government bonds is 4.5%.
  • The average excess historical annual return for stocks is 7.5%.
  • The beta of the stock is 1.5.

To calculate: the expected return of the security using the CAPM formula.

Solution:

Expected return on investment = Risk Free Rate + [Beta x Market Return Premium]

Expected ROI = 4.5% + [1.5 x 7.5%]

Answer: Expected ROI = 15.75%

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Author: Abhay Kanodia

About the author: An undergraduate student from the Birla Institute of Technology and Sciences, Pilani(BITS Pilani). Exploring the fields of finance and data analytics and its applications in other different domains.

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