BID-ASK SPREAD

Definition

A risk premium is the extra return an investor requires to hold a risky asset instead of a risk-free asset. It compensates investors for taking on additional uncertainty in exchange for the potential of higher returns.

In formula terms:

$$\text{Risk Premium} = \text{Expected Return} - \text{Risk-Free Rate}$$

Origins

• "Risk" comes from the early Italian risco meaning "danger or peril."

• "Premium" comes from the Latin praemium, meaning "reward" or "prize."
  The concept was formalized in modern portfolio theory by economists like Harry Markowitz and William Sharpe, with the Capital Asset Pricing Model (CAPM) introducing a systematic way to quantify it.

Usage

• Equities – Equity risk premium: extra return over Treasury bills.

• Bonds – Credit risk premium for corporate vs. government bonds.

• FX markets – Currency risk premium for emerging market currencies.

• Real estate – Compensation for illiquidity and market risk.

• Private equity – Premium for lack of transparency and exit uncertainty.

How Risk Premium Works

1. Identify the risk-free rate – Typically from government securities like U.S. Treasuries.

2. Estimate expected return – Based on historical data, market outlook, or asset pricing models.

3. Subtract the risk-free rate – The remainder is the risk premium.

4. Interpret the result – Higher premiums indicate higher compensation for risk.
   
   

Types of Risk Premium

• Equity Risk Premium – Excess return over the risk-free rate for stocks.

• Credit Risk Premium – Extra yield for lending to riskier borrowers.

• Liquidity Premium – Extra return for holding less liquid assets.

• Inflation Risk Premium – Compensation for uncertainty in purchasing power.

• Sovereign Risk Premium – Higher yield for lending to riskier countries.

   

Key Takeaway

• Compensates investors for bearing additional risk.

• Varies across asset classes, markets, and economic conditions.

• Central to asset pricing, portfolio construction, and capital budgeting.

• Higher volatility usually means a higher required premium.

Context in Financial Modeling

Risk premiums are key inputs for:

• Discount rates in DCF valuations.

• Cost of equity estimation via CAPM.

• WACC (Weighted Average Cost of Capital) calculations.

• Scenario analysis for different market risk levels.
  
  

Nuances & Complexities

• Time-varying – Risk premiums change with economic cycles.

• Forward-looking vs. historical estimates – Forward-looking methods rely on market expectations, while historical methods use past returns.

• Behavioral biases – Risk perception can deviate from actual risk.

• Country-specific factors – Political instability, currency volatility, and governance risk can widen premiums.

   

Mathematical Formulas

1. General Formula

$$\text{Risk Premium} = E(R) - R_f$$

Where:

• $E(R)$ = Expected return of the risky asset

• $R_f$ = Risk-free rate
  
  

2. CAPM Formula

$$E(R_i) = R_f + \beta_i (E(R_m) - R_f)$$

Here:

• $\beta_i$ = Asset’s sensitivity to market returns

• $E(R_m) - R_f$ = Market Risk Premium

Related Terms

• Cost of Capital
  
  

• Beta
  
  

• Capital Asset Pricing Model (CAPM)
  
  

• Yield Spread
  
  

• Sharpe Ratio
  
  

• Systematic Risk

Real-World Applications

Example 1: Equity Market

• Risk-free rate = 3%

• Expected market return = 9%

• Market risk premium = 6%

Example 2: Corporate Bond

• 10-year U.S. Treasury yield = 4%

• BBB corporate bond yield = 6.5%

• Credit risk premium = 2.5%

Example 3: Emerging Market Debt

• U.S. Treasury yield = 3%

• Brazilian government bond yield = 9%

• Sovereign risk premium = 6%

References & Sources

• Investopedia: Risk Premium Definition