You hold a diversifield $ 100,000 portfolio consisting of 20 stocks with 5000 invested in each . The portfolio's beta is 1.12. You plan to sell a stock with b=0.90 and use the proceeds to buy a new stock with b=1.75. what will the portfolio new beta be ?

PLEASE Help me so stuck on this problem

To find the new beta of the portfolio, we can use the formula:

New Beta = (Total Value of Old Stocks * Old Beta + Value of New Stock * New Beta) / Total Value of Portfolio

Let's calculate the values and find the new beta:

1. Calculate the total value of the old stocks:
Total Value of Old Stocks = Number of Old Stocks * Value of Each Old Stock = 20 * $5,000 = $100,000

2. Calculate the value of the new stock:
Value of New Stock = $5,000

3. Calculate the value of the new portfolio:
Total Value of Portfolio = Total Value of Old Stocks - Value of the Stock to Sell + Value of the New Stock
Total Value of Portfolio = $100,000 - $5,000 + $5,000 = $100,000

4. Calculate the new beta using the formula:
New Beta = (Total Value of Old Stocks * Old Beta + Value of New Stock * New Beta) / Total Value of Portfolio
New Beta = ($100,000 * 1.12 + $5,000 * 1.75) / $100,000

Calculating the expression:
New Beta = ($112,000 + $8,750) / $100,000
New Beta = $120,750 / $100,000
New Beta ≈ 1.2075

Therefore, the new beta of the portfolio will be approximately 1.2075.

To calculate the new portfolio beta, we need to consider the weights of the stocks in the portfolio, and how the beta of the new stock will impact the overall beta.

First, let's calculate the total investment in the portfolio:
Total Investment = Number of Stocks * Investment per Stock
Total Investment = 20 * $5000
Total Investment = $100,000

Next, let's calculate the current portfolio beta:
Portfolio Beta = Weighted Average of individual stock betas
Portfolio Beta = (Beta1 * Weight1) + (Beta2 * Weight2) + ... + (Beta20 * Weight20)

Since the investment in each stock is equal ($5000), the weight of each stock is 0.05 (5000/100000).

Portfolio Beta = (Beta1 * 0.05) + (Beta2 * 0.05) + ... + (Beta20 * 0.05)
Portfolio Beta = (1.12 * 0.05) + (1.12 * 0.05) + ... + (1.12 * 0.05)
Portfolio Beta = 1.12

Now, let's calculate the new portfolio beta after selling a stock with a beta of 0.90 and buying a new stock with a beta of 1.75.

Since the investment in each stock remains equal, the weight of each stock (except the one being sold) will still be 0.05. The weight of the new stock will also be 0.05.

Portfolio Beta (new) = (Beta1 * Weight1) + (Beta2 * Weight2) + ... + (BetaN-1 * WeightN-1) + (BetaN * WeightN)

where N is the total number of stocks (20) and N-1 is the total number of stocks after the sale.

Portfolio Beta (new) = (Beta1 * 0.05) + (Beta2 * 0.05) + ... + (BetaN-1 * 0.05) + (Beta_N * 0.05)
Portfolio Beta (new) = (1.12 * 0.05) + (1.12 * 0.05) + ... + (1.12 * 0.05) + (1.75 * 0.05)

Finally, calculate the new portfolio beta by substituting the values:
Portfolio Beta (new) = (1.12 * 0.05) + (1.12 * 0.05) + ... + (1.12 * 0.05) + (1.75 * 0.05)

Portfolio Beta (new) = (20 * 1.12 * 0.05) + (1.75 * 0.05)
Portfolio Beta (new) = 1.12 + 0.0875
Portfolio Beta (new) = 1.2075

Therefore, the new portfolio beta will be approximately 1.2075.