Practice Problem – Portfolio Beta

Practice Question

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

Assume that you have a portfolio with $372 in stock X with a beta of 0.89, $743 in stock Y with a beta of 1.24, and $385 in RF. What would be the beta of your new investment, if you had another $244 to invest and you wanted to achieve a portfolio beta equal to the market beta?

Answer +
2.010
Explanation +
Step 1: Calculate Current Portfolio Value and Beta

Investments:

  • Stock X: $372 with β = 0.89
  • Stock Y: $743 with β = 1.24
  • Risk-Free: $385 with β = 0
Total = 372 + 743 + 385 = 1,500
Portfolio β = (372×0.89 + 743×1.24 + 385×0) / 1,500
            = (330.48 + 920.32) / 1,500
            = 1,250.80 / 1,500 ≈ 0.8339
Step 2: Solve for the Required Beta

You want the new portfolio beta to be 1 after investing $244 more.

New Total = 1,500 + 244 = 1,744
Let βₓ = beta of new security

1 = (1,250.80 + 244 × βₓ) / 1,744
=> 1,744 = 1,250.80 + 244 × βₓ
=> 244 × βₓ = 493.20
=> βₓ ≈ 493.20 / 244 ≈ 2.02
Final Answer

The beta of the new investment should be approximately 2.01 to achieve a portfolio beta of 1.