Question

Suppose you hold a diversified portfolio consisting of a $10,000 invested equally in each of 10 different common stocks. The portfolio’s beta is 1.120. Now suppose you decided to sell two stocks with betas of 0.950 and 1.100, respectively and buy one stock with a beta of 1.750. What would the portfolio’s new beta be?

Answer 1

$10,000 is equally invested in 10 different stocks. So, each investment

= Total Investment / Number of stocks

= $10,000 / 10

= $1,000

Portfolio Beta

= Weighted average of beta of the stocks of the portfolio

Weight of each stock at present

= Value of investment / Total value of the portfolio

= $1,000 / $10,000

= 0.10 or 10%

Now, two stocks are sold and one stock is bought

So, weight of one stock bought in place of two stocks

= 0.10 + 0.10

= 0.20

Now, Value of ( Investment x Beta of portfolio ) before sale of two stocks

= $10,000 x 1.120

= 11,200

Now, value of (Investment x Beta of portfolio) after selloff

= Value before sale – Investment 1 x Beta 1 – Investment 2 x Beta 2 + Investment 3 x Beta 3

Where,

Investment 1 x Beta 1 = $1,000 x 0.950 =

Investment 2 x Beta 2 = $1,000 x 1.100

Investment 3 x Beta 3 = $2,000 x 1.750

= 11,200 – 950 – 1,100 + 3,500

= 12650

So, Portfolio Beta

=Value of( Investment x Beta of portfolio) after selloff / Total Investment

= 12650 / 10000

= 1.265