CAPM – Portfolio Beta

Practice Question

Intro to Finance
Capital Asset Pricing Model (CAPM)
Portfolio Beta
Short Answer

What is the beta of a portfolio consisting of $2,000 cash, $5,000 invested in a stock with a beta of 1.6, and $3,000 invested in a well-diversified portfolio?

Answer +
Final Answer: 1.100
Explanation +

Step 1: Identify the Portfolio Components

  • Cash: $2,000 (Beta = 0)
  • Stock: $5,000 (Beta = 1.6)
  • Well-diversified portfolio: $3,000 (Beta = 1.0)

Step 2: Calculate Portfolio Weights

  • Total portfolio = $10,000
  • Weight of cash = \( \frac{2,000}{10,000} = 0.2 \)
  • Weight of stock = \( \frac{5,000}{10,000} = 0.5 \)
  • Weight of diversified portfolio = \( \frac{3,000}{10,000} = 0.3 \)

Step 3: Compute Portfolio Beta

\[ \beta_p = (0.2 \times 0) + (0.5 \times 1.6) + (0.3 \times 1.0) \] \[ \beta_p = 0 + 0.8 + 0.3 = 1.1 \]

Conclusion: The portfolio beta is 1.1, meaning the portfolio is slightly more volatile than the market.