You hold a diversified portfolio consisting of a $5 000 investment in each of 20 different common stocks. The portfolio beta is equal to 1.12. You have decided to sell a lead mining stock (b=1.0) at $5 000 net and use the proceeds to buy a like amount of a s steel company stock(b=2.0). what is the new beta of the portfolio?
To calculate the new beta of the portfolio after selling the lead mining stock and buying the steel company stock, you can use the formula:
New Beta = [(Original Portfolio Value * Original Portfolio Beta) - (Amount Sold * Beta of Stock Sold) + (Amount Bought * Beta of Stock Bought)] / (Original Portfolio Value)
Given the information provided, let's break down the calculation:
Original Portfolio Value = $5,000 * 20 = $100,000
Amount Sold = $5,000
Beta of Stock Sold = 1.0
Amount Bought = $5,000
Beta of Stock Bought = 2.0
Now, plug these values into the formula:
New Beta = [($100,000 * 1.12) - ($5,000 * 1.0) + ($5,000 * 2.0)] / $100,000
Simplifying the expression:
New Beta = [($112,000 - $5,000) + $10,000] / $100,000
New Beta = $117,000 / $100,000
New Beta = 1.17
Therefore, the new beta of the portfolio after the transaction is 1.17.