Risk premium

Risk premium is the additional return that investors require or expect for holding an investment that carries risk compared with a relatively risk-free investment. It is a fundamental concept in financial economics, asset pricing, portfolio management, and corporate finance.

The risk premium compensates investors for bearing different types of investment risk, depending on the context.

Calculation

A simplified risk-premium calculation is:

$Risk Premium = Expected Return - Risk-Free Rate$

For an asset $i$ :

${Risk Premium}_{i} = E (R_{i}) - R_{f}$

where:

$E (R_{i})$ = expected return of asset $i$ ;
$R_{f}$ = risk-free rate.

Market risk premium

The market risk premium is the additional expected return from investing in the market portfolio rather than a risk-free asset.

It is calculated as:

$Market Risk Premium = E (R_{m}) - R_{f}$

where:

$E (R_{m})$ = expected return of the market portfolio;
$R_{f}$ = risk-free rate.

The market risk premium is a key component of the Capital Asset Pricing Model (CAPM).

CAPM

Under the CAPM, an asset's expected return is determined by the risk-free rate plus a risk premium related to its systematic risk:

$E (R_{i}) = R_{f} + β_{i} [E (R_{m}) - R_{f}]$

where:

$E (R_{i})$ = expected return of asset $i$ ;
$R_{f}$ = risk-free rate;
$β_{i}$ = beta of asset $i$ ;
$E (R_{m}) - R_{f}$ = expected market risk premium.

The asset-specific systematic risk premium is therefore:

${Systematic Risk Premium}_{i} = β_{i} [E (R_{m}) - R_{f}]$

Example

Suppose the expected market return is 10% and the risk-free rate is 4%.

The expected market risk premium is:

$Market Risk Premium = 10 % - 4 % = 6 %$

If an asset has a beta of 1.2, its CAPM risk premium is:

${Risk Premium}_{i} = 1.2 \times 6 % = 7.2 %$

The CAPM-implied expected return is therefore:

$E (R_{i}) = 4 % + 7.2 % = 11.2 %$

Types of risk premium

Different financial contexts use different types of risk premiums.

Examples include:

Equity risk premium — additional expected return for investing in equities rather than a risk-free asset;
credit risk premium — compensation for bearing credit or default risk;
Liquidity risk premium — compensation for holding less-liquid assets;
Maturity risk premium — compensation associated with interest-rate risk over longer maturities;
Country risk premium — additional return associated with investing in a particular country or jurisdiction.

The appropriate risk premium depends on the type of risk being evaluated.

Equity risk premium

The equity risk premium represents the additional expected return from equities relative to a risk-free investment.

A simplified expression is:

$Equity Risk Premium = E (R_{m}) - R_{f}$

In many financial models, the expected market return is used as a proxy for the expected return on a broad equity market portfolio.

Risk premium and beta

Beta measures an asset's sensitivity to systematic market movements.

Under CAPM, the risk premium associated with an asset is proportional to its beta:

${Risk Premium}_{i} = β_{i} \times Market Risk Premium$

Therefore:

${Risk Premium}_{i} = β_{i} [E (R_{m}) - R_{f}]$

An asset with a higher beta has a larger CAPM-implied systematic risk premium, assuming the market risk premium is positive.

Risk premium and risk-adjusted return

Risk premiums are used in several risk-adjusted return measures.

For example, the Sharpe ratio uses excess return over the risk-free rate:

$Sharpe Ratio = \frac{R_{p} - R_{f}}{σ (R_{p})}$

The numerator:

$R_{p} - R_{f}$

represents the portfolio's realized excess return over the risk-free rate.

Risk premium and Treynor ratio

The Treynor ratio measures excess return relative to systematic risk:

$Treynor Ratio = \frac{R_{p} - R_{f}}{β_{p}}$

The measure therefore relates the realized risk premium of a portfolio to its beta.

Risk premium and Jensen's alpha

Jensen's alpha compares an investment's actual return with its CAPM-implied return.

It can be expressed as:

$α_{p} = R_{p} - [R_{f} + β_{p} (R_{m} - R_{f})]$

The term:

$β_{p} (R_{m} - R_{f})$

represents the portfolio's systematic risk premium under CAPM.

Risk premium and interest rates

Risk premiums can affect the yields required by investors on risky securities.

A simplified relationship is:

$Required Return = Risk-Free Rate + Risk Premium$

For example, if the risk-free rate is 4% and an investor requires a 3% risk premium:

$Required Return = 4 % + 3 % = 7 %$

The actual required-return calculation may include several separate risk premiums.

Importance

Risk premium is a fundamental concept in finance because it provides a framework for understanding why investors may require higher expected returns from riskier investments. It is used in asset pricing, portfolio construction, valuation, capital budgeting, cost-of-capital calculations, and risk-adjusted performance analysis.

Limitations

Risk premiums are generally estimates rather than directly observable quantities.

Their estimation can be affected by:

expectations about future returns;
the selected risk-free rate;
the measurement period;
the chosen market benchmark;
economic conditions;
investor risk preferences;
model assumptions.

Consequently, different analysts may estimate different risk premiums for the same investment or market.

Risk premium

Contents

Calculation

Market risk premium

CAPM

Example

Types of risk premium

Equity risk premium

Risk premium and beta

Risk premium and risk-adjusted return

Risk premium and Treynor ratio

Risk premium and Jensen's alpha

Risk premium and interest rates

Importance

Limitations

See also