Question

ou have a $4 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio’s new beta be after these transactions? Show your work

Answer 1

Answer: 1.108

Explanation:

You have $4 million invested.

You would like to divest $100,000 from a stock with beta 0.9 to the tune of $100,000.

The entire portfolio has a beta of 1.1.

This beta is an average of all the betas in the portfolio.

Proportion of Portfolio to be divested = $\frac{100,000}{4,000,000}$

= 0.025

Beta of stock to be divested expressed as;

= 0.025 * 1.1

= 0.0275

This will be reinvested in a stock with beta 1.4

Beta of stock to be bought expressed as;

= 0.025 * 1.4

= 0.035

New beta

= 1.1 - 0.0275 + 0.035

= 1.108