The formula for risk premium, also known as default risk premium, calculates the difference between the expected rate of return on investment and the risk-free rate. It is additional compensation that investors expect from an investment based on its level of risk.

Risk premium is a measure that reflects our perception of risks and how the risk and price of financial instruments are related.  It is also a key element used in estimating the cost of capital and share valuation. Only risky investments could potentially provide above-average returns, but there’s a risk of not receiving any returns at all.

The risk premium is based on historical returns, required returns and expected returns. Historical returns on financial instruments can’t be changed and information about historical returns can be easily found and is available for every investor. However, required and excepted rates of return differ from investor to investor, depending on their investing style and whether they are risk averse or risk seeking.

### How to calculate risk premium?

The risk premium is calculated by subtracting the risk-free rate from the expected rate of return.

$Risk\; Premium = r_{a} - r_{f}$

Where ra = expected asset or investment return, and rf = the risk free return.

### Example of risk premium calculation

Let’s assume the risk-free rate is 3%. This means a riskless government treasury bond offers an annual return of 3%. An investor invests in the stocks of a company and these stocks have an annual return of 5%.

$Risk\; Premium = 5\% - 3\% = 2\%$

### Factors that affect the risk premium

The starting point for risk assessment is primarily the state of the economy (including expectations of its further development), usually described by the dynamics of real GDP, CPI inflation and the level of interest rates. It reflects investors’ perception of investment risk in a given country or within a given market.

The market risk premium is an element of the CAPM model, defined as the difference between the rate of return on the market portfolio and the rate of return on risk-free values.

In practice, equity risk premium (ERP) is determined as the excess part of the total expected rate of return over the return on risk-free assets (usually long-term treasury bond yields). The return from equity is the sum of the dividend yield and capital gains. Stocks should provide a higher rate of return than an investment, for example in treasury bonds, which guarantee constant cash flows until the maturity date.

### Investment styles

Investment styles are determined by the following factors:

• The amount of capital,
• Volatility of share prices.
• Duration of the investment period,
• Level of risk aversion,
• Investor’s experience on the market (often measured in years),
• Investment strategies,
• Number of transactions a month,
• Individual investor’s goals,
• Macroeconomic market information tracked by the investor,
• Information from selected companies tracked by the investor,
• The degree of knowledge of market analysis techniques.

There are some examples of investment styles:

• Risk-seeking. Risk-seeking investors rather invest in shares with a higher risk level, but also with a higher premium.
• Risk-averse. Risk-averse investors would rather receive smaller cash flows, rather than risking and potentially receiving nothing.
• Active. Active investors are more risk loving. They believe they can outperform the overall market by picking stocks they expect to perform well.
• Passive. Passive investors are more risk averse. They tend to invest in a market index fund or less risky financial instruments which potentially may produce higher long-term results.
• Small cap. Investors tend to invest in small companies, which usually have the lowest capitalization. Small companies’ stocks prices are more volatile, which results a higher risk. Return on investment and risk premium is the highest in case of small companies.
• Large cap. Large cap investors usually invest in bigger companies and are less risk loving.