Question

You own a portfolio that has four stocks: A, B, C, and D. The portfolio has 50% of your money in stock A, 10% in B, 15% in C, and 25% in D. The betas of stocks A to C are 0.83, 1.50, and 1.42, respectively. If the portfolio beta is 1.6, what is the beta of stock D?

Answer 1

WB = BA(WA) + BB(WB) + BC (WC) + BD(WD)

1.6 = 0.83(0.5) + 1.50(0.1) + 1.42(0.15) + BD(0.25)

1.6 = 0.415 + 0.15 + 0.213 + 0.25BD

1.6 = 0.778 + 0.25BD

1.6-0.778 = 0.25BD

0.822 = 0.25BD

BD = 0.822/0.25

BD = 3.288

Explanation: The question relates to Beta of a portfolio. The Beta of a portfolio is the aggregate of Beta of each stock multiplied by the weight of each stock. The Beta of stock D was not given, thus, it becomes the subject of the formula.