Portfolio beta given weights 0.6 and 0.4 and betas 1.3 and 0.5 equals what?

Portfolio beta given weights 0.6 and 0.4 and betas 1.3 and 0.5 equals what?

• A. 0.50
• B. 0.84
• C. 0.98
• D. 1.20

Answer: (C)

The main idea here is that a portfolio’s beta is the weighted average of the betas of its components. Each asset’s beta is scaled by how much of the portfolio it represents, and then those contributions are summed. Compute the contributions: 0.6 × 1.3 = 0.78 and 0.4 × 0.5 = 0.20. Add them together: 0.78 + 0.20 = 0.98. So the portfolio beta is 0.98. This means the portfolio’s value is expected to move about 0.98% for every 1% move in the market, slightly less than the market because part of the portfolio is held in the lower-beta asset.

The main idea here is that a portfolio’s beta is the weighted average of the betas of its components. Each asset’s beta is scaled by how much of the portfolio it represents, and then those contributions are summed.

Compute the contributions: 0.6 × 1.3 = 0.78 and 0.4 × 0.5 = 0.20. Add them together: 0.78 + 0.20 = 0.98. So the portfolio beta is 0.98.

This means the portfolio’s value is expected to move about 0.98% for every 1% move in the market, slightly less than the market because part of the portfolio is held in the lower-beta asset.