Final answer:
To design a portfolio with a beta of zero, invest approximately $2,949.85 in Stock B.
Step-by-step explanation:
To design a portfolio with a beta of zero, you need to include a risk-free security along with the stocks. Beta measures the sensitivity of a stock's returns to the overall market returns. A beta of zero means that the stock's returns are not affected by market movements. Since Stock A has a beta of 1.69 and Stock B has a beta greater than 1, neither of these stocks alone will give you a portfolio with a beta of zero.
To calculate how much you should invest in Stock B, you need to use the formula:
Amount Invested in Stock B = Total Portfolio Value × Beta of Stock B / (Beta of Stock A + Beta of Stock B)
Given that the combined value of your portfolio is $5,000, we'll assume that the beta of Stock B is 2.
Amount Invested in Stock B = $5,000 × 2 / (1.69 + 2) = $2,949.85
Therefore, you should invest approximately $2,949.85 in Stock B to achieve a portfolio with a beta of zero.