Question

An individual has $50,000 invested in a stock with a beta of 0.4 and another $60,000 invested in a stock with a beta of 1.1. If these are the only two investments in her portfolio, what is her portfolio's beta? Round your answer to two decimal places.

Answer 1

Given : Investment in stock A = $50,000

Beta of stock A = 0.4

Investment in stock B = $60,000

Beta of stock B = 1.1

To Find: Portfolio Beta

Solution: Beta of a security may be defined as degree of responsiveness of security return with respect to the market return. Beta of a portfolio is the weighted average beta of the securities comprising such a portfolio.

Total investment in portfolio = $50,000 + $60,000 = $110,000

Weightage of security A in portfolio, i.e
`W_(1)` =
`(50,000)/(110,000)` = 0.4545

Weightage of security B in the portfolio, i.e
`W_(2)` =
`(60,000)/(110,000)` = 0.5455

Beta of porfolio = Beta of A ×
`W_(1)` + Beta of B ×
`W_(2)`

= 0.4 × 0.4545 + 1.1 × 0.5455

= 0.7818

Hence, the portfolio beta is 0.78 approx.