7500$ investment in each of 20 stocks ( beta of portfolio=1.12). suppose you decide to sell one stock that have beta 1 for 7500$, and use them to buy another one of beta=1.75 calculate the beta of new portfolio ?
Easy.
total sum beta now is
(1.12*20-1.12+1.75)=23.03
portfolio beta now=23.03/20=1.15
Caution, if you had not vested equal amounts in each stock, the computation would have to weighed each beta to the value of the stocks, and it would be a little more complicated, but easy for a spreadsheet calc to keep up with.
To calculate the new beta of the portfolio after selling one stock with a beta of 1 and buying another stock with a beta of 1.75, you will need to follow these steps:
Step 1: Find the beta-weighted value for the sold stock:
- Since you had $7,500 invested in each of the 20 stocks, the total value of the portfolio before selling the stock is 20 * $7,500 = $150,000.
- Calculate the weight of the sold stock in the portfolio by dividing the value of that stock by the total portfolio value: $7,500 / $150,000 = 0.05.
- Multiply the weight of the sold stock by its beta: 0.05 * 1 = 0.05.
Step 2: Find the beta-weighted value for the bought stock:
- Calculate the weight of the bought stock by subtracting the weight of the sold stock from 1: 1 - 0.05 = 0.95.
- Multiply the weight of the bought stock by its beta: 0.95 * 1.75 = 1.6625.
Step 3: Calculate the new beta of the portfolio:
- Add up the beta-weighted values of the sold and bought stocks: 0.05 + 1.6625 = 1.7125.
- This new value will represent the beta of the portfolio after making the change.
Therefore, the beta of the new portfolio is approximately 1.7125.