Question

Your retirement fund consists of a $5,000 investment in each of 15 different common stocks. The portfolio's beta is 1.20. Suppose you sell one of the stocks with a beta of 0.8 for $5,000 and use the proceeds to buy another stock whose beta is 1.6. Calculate your portfolio's new beta.

Answer 1

Answer:

portfolio's new beta is 1.25

Explanation:

Total number of stocks available in the portfolio = 15

Total portfolio = 1.20

Beta of stock to be sold = 0.8

Beta of stock to be purchased = 1.6

Weight of one stock (replacing stock) = 1/15

New portfolio beta = Total portfolio - (Weight * Beta of selling stock) + (Weight * Beta of purchasing stock)

New portfolio beta = 1.20 - [(1/15) * 0.8] + [(1/15) * 1.6]

                               = 1.20 - 0.05333 + 0.10667

                               = 1.25334

                               ≈ 1.25

Answer 2

The new beta of the portfolio is 1.25.

The beta of the portfolio is the weightage of each financial asset held in the portfolio. It shows the capacity of each asset to grow with the change in the price fluctuations of assets.

Computation:

Given,

Old portfolio beta =1.20

Beta of stock to be sold =0.8

beta of stock purchased =1.6

Total stocks available =15

The formula used to compute the new portfolio beta is:

$\text{Beta}=\text{Total Portfolio}-[(\text{Weightage}\times\text{Beta of Selling Stock})+(\text{Weightage}\times\text{Beta of Purchased Stock})]$

The values will be substituted in the formula:

$\begin{aligned}\text{New Portfolio Beta}&=1.20-[(\frac{1}{15}\times0.8)+(\frac{1}{15}\times1.6)]\\&=1.25\end{aligned}$

Thus, the beta of new portfolio is 1.25.

To know more about portfolio beta, refer to the link:

https://brainly.com/question/10678271