1 What should be the Beta of a replacement stock if an inves

1. What should be the Beta of a replacement stock if an investor wishes to achieve a portfolio Beta of 1.0 by replacing Stock C in the following equally weighted portfolio: Stock A= .9 Beta; Stock B= 1.1 Beta; Stock C= 1.35 Beta?

A. 0.93 Beta

B. 1.00 Beta

C. 1.08 Beta

D. 1.15 Beta

Please show calculation

Solution

Answer is (b) beta of replacement stock is 1

0.9*1/3 + 1.1*1/3 + x*1/3 = 1

As we need the new portfolio beta 1

0.3 + 0.367 + ×/3 = 1

×/3 = 0.33

Therefore x = 1

Means beta of replacement stock is 1.00