﻿ Capital Asset Pricing Model (CAPM) | Formula | Example

# Capital Asset Pricing Model

Capital asset pricing model (CAPM) is a model which establishes a relationship between the required return and the systematic risk of an investment. It estimates the required return as the sum of risk free rate and product of the security’s beta coefficient and equity risk premium.

Investors face two kinds of risks: systematic risk and unsystematic risk.

Systematic risk is the risk of the whole economy or financial system going down and causing low or negative returns. For example, the risk of recession, enactment of unfavorable regulation, etc. Systematic risk can’t be avoided by adding more investments to the portfolio (i.e. diversification) because a downturn in the whole economy affects all investments.

Unsystematic risk on the other hand is the risk specific to a particular investment. For example, unfavorable court ruling affecting the company, major disruption in the company’s supply chain, etc. Such risks can be mitigated by adding additional investments to a portfolio. For example, a portfolio of 100-stocks is less prone to a negative performance of one company due to any specific event affecting it.

Since unsystematic risk can be eliminated through diversification, the capital asset pricing model doesn’t provide any reward for taking such a risk. It measures the required return based on the level of systematic risk inherent in a particular investment.

## Formula

Required return = risk free rate + beta coefficient × equity risk premium

Risk free rate is the rate of return on an investment which has zero risk. It is normally estimated as equal to the yield on a 10-year government bond.

Beta coefficient is a statistic which measures the systematic risk of a particular investment relative to the broad market. A beta efficient of more than 1 means that the investment carries more systematic risk than the market and that of less than 1 means less systematic risk than the broad market.

Equity risk premium equals the rate of return on the broad market such as S&P 500 minus the risk free rate. It is an estimate of the reward the equity investors require to take the systematic risk inherent in a portfolio of securities representative of the equity market.

Capital asset pricing model effectively notches the equity risk premium up or down based on the beta coefficient of the relevant stock which is reflected in the higher or lower required return.

## Example

ExxonMobil Corporation (NYSE: XOM) has a beta coefficient of 0.88. Estimate its cost of equity if the risk free rate is 4% and return on the broad market index is 8%.

Solution

Under capital asset pricing model,

Cost of equity = risk free rate + beta coefficient × equity risk premium

Equity risk premium = broad market return – risk free rate

Cost of equity = risk free rate + beta coefficient × (broad market return – risk free rate)

Cost of equity (XOM) = 4% + 0.88 × (8% – 4%) = 4% + 0.88 × 4% = 7.52%

The required return (cost of equity) estimated based on CAPM should be compared with the investor expectation of return on the stock keeping in view the company’s operations and future growth potential. If the expected return is higher than the required return, the stock is a good investment (on standalone basis) and vice versa.

Written by Obaidullah Jan, ACA, CFAhire me at