# Equity Risk Premium

Equity risk premium (also called equity premium) is the return on a stock in excess of the risk-free rate which must be earned by the stock to convince investors to take on the risk inherent in it.

Equity risk premium is an important input in determination of a company's cost of equity under the capital asset pricing model (CAPM) and its stock valuation. As per CAPM, required rate return on a stock equals risk-free interest rate plus the equity risk premium on the stock. Equity risk premium on an individual stock is the product of beta coefficient and market (equity) risk premium.

Market risk premium (MRP) equals the difference between average return on a broad market index, such as S&P 500, and the risk-free rate. Equity risk premium differs from the market risk premium in that it relates to a single stock while the MRP is the average equity risk premium of the broad market.

## Estimation Methods

There are primarily two ways in which we can calculate the equity risk premium approach:

- Comparing required return determined using the dividend discount model with the risk-free rate.
- Comparing historical market return with historical risk-free rate

### Dividend Discount Model Method

Under the dividend discount model method, we find the required return on equity (r_{e}) and then subtract the risk-free rate. This is shown in the formula given below:

Equity Risk Premium = | D_{1} | + g − r_{f} |

P_{0} |

Where *D _{1}* is the expected annual dividend next year,

*P*is the current stock price,

_{0}*g*is the growth rate and

*r*is the risk free rate.

_{f}### Historical Method

Under the historical method, market (equity) risk premium (MRP) is determined by comparing the average return on the broad market with the risk-free rate.

Market Equity Risk Premium (MRP) = r_{m} − r_{f}

Where *MRP* is the market (equity) risk premium, *r _{m}* is the rate of return on the broad stock market index, such as S&P 500 and

*r*is the risk-free interest rate.

_{f}Risk-free interest rate is the rate of return on securities that are assumed to be risk-free. Return on long-term government securities is considered risk-free.

Equity risk premium on an individual stock equals the product of market equity risk premium and the stock's beta coefficient.

Individual Stock Equity Risk Premium (ERP_{i})

= Beta Coefficient (β) × Market Risk Premium

= Beta Coefficient × (Market Return - Risk-Free Rate)

Beta coefficient is a measure of systematic risk of a stock, i.e. the risk which cannot be diversified away.

## Example

During 2012, S&P 500 increased from 1,257.60 to 1,426.19. The relevant risk-free rate is the rate of return on 10-year US bonds, and it equals 1.8%. Find the equity risk premium on the market. Assume beta coefficient of Microsoft (NYSE: MSFT) is 1.1, calculate the individual equity premium of its stock.

**Solution**

Rate of return on the stock market i.e. S&P 500 is 13.4% [=(1,426.19 − 1,257.6) ÷ 1,257.6].

Market (Equity) Risk Premium

= Rate of Return on Market − Risk-free Rate

= 13.4% − 1.8%

= 11.6%

11.6% represents the return which must be earned by S&P 500 or else the value of its constituent stocks will fall.

MSFT Equity Risk Premium

= β_{MSFT} × MRP

= 1.1 − (13.4% − 1.8%)

= 11.6%

It means that investors require Microsoft stock to earn 11.6% more than the return earned by risk-free investments; otherwise they will no longer invest in Microsoft.

by Obaidullah Jan, ACA, CFA and last modified on

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