# Equity Risk Premium

Equity risk premium is the return in excess of the risk free rate which must be earned by equities to convince investors to take on the risk inherent in them.

Equity risk premium on the market is an input in the capital asset pricing model. According to the capital asset pricing model, required rate return on a stock equals risk free rate plus the product of beta coefficient and equity risk premium on the market.

## Formula

Equity Risk Premium (on the market)

= Rate of Return on the Stock Market − Risk Free Rate

Rate of return on the stock market is the return on the relevant stock exchange. Stock indices such as S&P 500, approximates the market return.

Risk free rate is the rate of return on securities that are assumed to be risk free. Return on long-term government securities is normally considered risk free.

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

Equity Risk Premium (on an individual stock)

= Beta Coefficient × (Return on the Stock Market − Risk Free Rate)

## 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].

Equity risk premium (on market) = 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 so as to stop investors from divesting from equities and investing in the risk free rate.

Equity risk premium on MSFT stock = MSFT beta coefficient × equity risk premium on market = 1.1 − (13.4% 7minus; 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.

Written by Obaidullah Jan