You have a $2 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio’s new beta be after these transactions?
To calculate the portfolio's new beta, we need to understand how beta works and how it is calculated.
Beta measures the sensitivity of a stock's returns to the market's returns. A beta of 1 implies that the stock's price has a tendency to move in line with the market, while a beta greater than 1 indicates the stock is more volatile than the market, and a beta less than 1 indicates the stock is less volatile.
Now, let's calculate the portfolio's new beta:
1. Calculate the existing portfolio's beta weighted by the amount invested in each stock:
The existing portfolio has a beta of 1.1, which means it is already 10% more volatile than the market.
2. Determine the proportion of the portfolio represented by the stock being sold:
Since the portfolio has $2 million invested across 20 stocks, each stock represents 5% of the total portfolio ($100,000 / $2,000,000).
3. Subtract the proportionate beta of the stock being sold from the existing portfolio's beta:
The beta of the stock being sold is 0.9, which is 0.2 less than the portfolio's current beta of 1.1. Since this stock represents 5% of the portfolio, we subtract 0.2 * 5% = 1% from the portfolio's beta.
4. Add the proportionate beta of the stock being purchased to the existing portfolio's beta:
The beta of the stock being purchased is 1.4, which is 0.3 higher than the portfolio's current beta of 1.1. Since this stock also represents 5% of the portfolio, we add 0.3 * 5% = 1.5% to the portfolio's beta.
5. Calculate the new beta of the portfolio:
The new beta of the portfolio is the summation of the adjusted beta of the stock being sold and the adjusted beta of the stock being purchased.
1.1% - 1% + 1.5% = 1.6%
Therefore, the portfolio's new beta will be 1.6.