Calculate Portfolio Beta
What is the concept of portfolio beta?
Explain how the portfolio beta is calculated.
Concept of Portfolio Beta
A portfolio refers to a collection of investments, such as stocks, bonds, mutual funds, real estate, or other types of assets, held by an individual or an entity. A portfolio is typically constructed with the goal of achieving specific investment objectives, such as capital appreciation, income generation, or risk diversification.
Calculation of Portfolio Beta
The portfolio Beta can be calculated as the weighted average of the Beta of each stock, where the weights are based on the respective investments in each stock.
Given:
- Investment in stock X = $200
- Investment in stock Y = $300
- Investment in stock Z = $500
- Beta of stock X = -0.6
- Beta of stock Y = -1.9
- Beta of stock Z = -1.1
Let's calculate the portfolio Beta:
Portfolio Beta = (Weight of stock X * Beta of stock X) + (Weight of stock Y * Beta of stock Y) + (Weight of stock Z * Beta of stock Z)
Weight of stock X = Investment in stock X / Total investment
Weight of stock Y = Investment in stock Y / Total investment
Weight of stock Z = Investment in stock Z / Total investment
Total investment = Investment in stock X + Investment in stock Y + Investment in stock Z
Plugging in the values and calculating:
Total investment = $200 + $300 + $500 = $1000
Weight of stock X = $200 / $1000 = 0.2
Weight of stock Y = $300 / $1000 = 0.3
Weight of stock Z = $500 / $1000 = 0.5
Portfolio Beta = (0.2 * -0.6) + (0.3 * -1.9) + (0.5 * -1.1) = -0.12 - 0.57 - 0.55 = -1.24
Therefore, the portfolio Beta is -1.24.