Question

Suppose you held a diversified portfolio consisting of a $1,000 investment in each of 10 different common stocks. The portfolio's beta is 1.60. Now suppose you decided to sell one of the stocks in your portfolio with a beta of 4.90 for $1,000 and use the proceeds to buy another stock with a beta of 1.00. What would your portfolio's new beta be? 1.2100 1.0000 -2.3000 1.9900

Answer 1

Answer: your portfolio's new beta be 1.265

Step-by-step explanation:

$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