The risk premium of an asset is the excess return it generates which can be seen as compensation for taking on extra risk. In other words, investors demand higher returns if they are to be persuaded to invest in an asset which could incur losses, rather than investing their capital in assets where returns are guaranteed and consistent.

Strategies such as risk premia and hedge funds often aim to multiply the potential gains from an asset’s risk premium by applying tools such as short selling, leverage and derivatives.

An investment’s risk premium is the return above what a risk-free alternative would yield. The risk-free rate of return is usually represented by government bonds, usually in the form of US treasury bills – which can sometimes also act as a proxy for the risk-free rate in other developed economies.

The risk-free rate is frequently based on government bond yields since state-backed bonds are considered a proxy for risk-free investing, as defaults are unlikely in most cases. Interestingly, many developed economies, particularly in Europe, have over the past decade had negative risk-free rates when stripping out inflation. This is because of large-scale quantitative-easing programmes administered by central banks.

While individual assets and portfolios carry risk premiums, so do broad financial markets. The market risk premium, or equity risk premium, is often represented by major benchmark indices such as the S&P 500 Index, and measures the extra return of equity markets over risk-free alternatives.

Traditional size-based indices like the S&P 500 allow investors to capture the market risk premium, while newer, alternative indices target specific underlying risk premiums in order to deliver better returns or control risk.

Long-only smart beta indices aim to deliver better risk-adjusted returns relative to the benchmark, while risk premia strategies use short selling, leverage, and derivatives to generate and amplify absolute returns.

Momentum and value strategies, for example, aim for superior returns by targeting underlying stock characteristics, or risk premiums. These are alpha strategies since they target benchmark-beating returns in a long-only portfolio. Equal risk contribution indices, meanwhile, strive to control volatility risk. In doing so, they tend to offer more stable returns but usually with lower risk premiums than momentum and value strategies.

The risk premium forms a core part of the capital asset pricing model (CAPM), which is widely used to determine the price of risky assets. The CAPM model shows the relationship between risk and expected returns, allowing investors to allocate capital efficiently.

To calculate the risk premium of an equity or other asset, the investment’s beta is multiplied by the difference between broad market returns and the returns from risk-free alternatives. Adding the risk-free rate of return to this gives the expected return of an asset:

Expected return = RF + β(MR – RF)

Where:

RF = risk-free rate of return

β = the asset’s beta value

MR = Expected return from the market

In this model, β(MR – RF) is the asset’s risk premium.

The difference between the expected return from the market and the risk-free rate expresses the market’s excess return. To calculate an asset’s risk premium, the market’s excess return is multiplied by beta since beta indicates how an investment reacts to moves in the market.

A beta of 1, for example, means the asset moves exactly in line with the market and so expected return is the same as the expected return from the market. A beta of more than 1 means the asset carries a higher risk premium while a beta of less than 1 implies a lower premium.

As an example, consider investing in the shares of a US-listed mining business. If the stock has a beta of 1.2 (implying that its rises and falls are more exaggerated than the market’s), while the market is expected to deliver returns of 5% over a period and the risk-free rate of return is 0.5%, then the stock’s risk premium is 5.4% (using the above pricing model).

The risk premium model, which is central to CAPM, is one of many financial tools which help investors allocate their capital in the most efficient way.

One limitation to calculating the expected risk premium and forecasting expected returns from an asset is the difficulty of accurately forecasting future market returns (or the market risk premium).