Risk Premium Formula

The risk premium for equity and debt investments

Investors have several options for investing their money to make a profit. They can choose between these options depending on the risk which they can afford to take and the returns which they are looking for. Usually, the United States government bonds called Treasury Bills (T-bills) are considered risk free since the possibility of default is very low. When the maturity period is more than ten years, the bonds are called Treasury bonds or T-bonds. Since this T- bills and T-bonds are risk-free, there are many investors, and the returns on this debt are fairly low. For getting better returns, investors should be willing to take risks.

Risk Premium

The Risk Premium is the additional return which the investor will get on his or her investment for taking the risk of investing. The investor can invest either in fixed insurance securities or bonds issued by companies, mutual funds, or stocks of companies, which all have some risk compared to treasury bills. There is a risk that the company will default and not pay back the principal and interest for company bonds. For equity investments, there is a possibility that the share prices will decrease, and no dividends will be paid to the investor.

Historically, investors’ returns in the stock market have been higher than the returns for debt or bond investors over the long term. Hence most investors who wish to get the best possible returns for their investment invest at least part of their money in the stock market. However, there is no guarantee that these investors will always profit in the short term since the stock market prices fluctuate rapidly due to several macroeconomic, political, and other factors. Hence the equity investor expects an equity risk premium to compensate him for taking the risk of investing in shares.

Risk Premium Formula

The risk premium formula shows that the return of a security is equal to the risk-free return plus a risk premium, based on the beta of that security that analysts and investors use.

There are several formulas for calculating the risk premium, depending on the kind of investment. For all kinds of investments, the risk premium is as follows

Risk premium = a – rf

where ra is the returns from the specific asset or investment, while rf is the return from the risk-free investment

Another parameter that is also calculated is the market risk or risk of investing in the stock market, which is calculated as follows :

Market risk premium = rm – rf

where rm is the average return for the stock market and rf returns on investments that are risk-free. The average stock market returns are usually based on the returns for many stocks, typically market indices like the Dow or S&P 500. The market risk is also called the systemic risk since all stocks are affected.

The risk premium for a specific stock

On the other hand, the unsystematic risk is the risk that is associated only with a specific stock that is chosen by the investor. If the investor diversifies his investment portfolio, his risk will become more similar to the market risk. Hence investors are often advised to diversify their investment. The returns for the stock include the increase in the share price and dividends.

For calculating the risk premium for a particular stock, the capital asset pricing model (CAPM) has been used as follows

Ra = rf + Ba( rm – rf )

where Ra is the expected returns for the stock and Ba or beta for the stock is an indicator of the volatility or risk involved. Conventionally the volatility of the market is set as 1, so if the stock is as volatile as the market, the risk of the stock is the same as the market.

This can be reworked to form the Risk premium for a specific stock = Ra – rf= Ba (rm-rf)

There are other models for calculating the risk premium like Gordon’s growth model where

k = (D/P) + g

where k is the expected returns in percentage, D = dividend per share, P = price of shares, g = annual growth in dividend

Another way to calculate the expected return uses the inverse of the P/E ratio

k= E/P

where k= expected return, E is the earnings per share for the previous twelve months, P = share prices. These methods do not consider the fluctuations in the share prices over a period of time. In reality, the stock market is cyclical, and prices may fluctuate rapidly.

The risk premium for equities

Though the stock prices will vary over the short term and may give negative returns, experts agree that the stock market will compensate the investor more for taking the risk of investing than debt. In the short term, the risk premium for stock investors is typically 3%, while in the long term of thirty years or more, the risk premium for those who invest in equities is 5.5%. Some CFOs estimate that when compared to the T-bills, the risk premium for shares is 5.6%, and if T-bonds are considered, the risk premium is estimated at 3.8%. Due to the tech and internet sector boom, the risk premium of the stock market increased. It is usually impossible to predict the risk premium on equity investments, though investors can use the historical information available to choose their investment.

Risk for Debt

Though the returns on bonds and debt are more predictable than equities, there is always some risk involved. For bonds, the interest rate and duration of the bond are defined. However, some companies may not repay the interest and the principal amount, resulting in default, loss of money for the investor. Hence, while investing in bonds offering a higher interest rate, the investor has to consider the risk premium and the chance of default by the bond issuer.

Other considerations

Though T-bonds and T-bills are used extensively for calculating the risk-free returns, they do not consider inflation. Hence it is advisable to use Treasury Inflation protected securities (also called TIPS) for the calculations. Additionally, the taxes on the various investments should be considered before choosing a particular option since these can adversely affect the investment’s overall returns.



Igor has been a trader since 2007. Currently, Igor works for several prop trading companies. He is an expert in financial niche, long-term trading, and weekly technical levels. The primary field of Igor's research is the application of machine learning in algorithmic trading. Education: Computer Engineering and Ph.D. in machine learning. Igor regularly publishes trading-related videos on the Fxigor Youtube channel. To contact Igor write on: igor@forex.in.rs

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