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You own a stock portfolio invested 17 percent in Stock Q, 23 percent in Stock R, 37 percent in Stock S, and 23 percent in Stock T. The betas for these four stocks are .93, .99, 1.39, and 1.84, respectively.

Required:
a. What is the portfolio beta?

User Moeffju
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1 Answer

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Final answer:

To calculate the portfolio beta, multiply each stock's weight by its beta and sum the results. For a portfolio of investments, the portfolio beta is the weighted average of the beta coefficient of all individual securities in the portfolio.

Step-by-step explanation:

To calculate the portfolio beta, we need to multiply the weight of each stock by its corresponding beta and then sum up the results. We can use the formula:

Portfolio Beta = (Weight of Stock Q * Beta of Stock Q) + (Weight of Stock R * Beta of Stock R) + (Weight of Stock S * Beta of Stock S) + (Weight of Stock T * Beta of Stock T)

Plugging in the given values:

Portfolio Beta = (0.17 * 0.93) + (0.23 * 0.99) + (0.37 * 1.39) + (0.23 * 1.84)

Simplifying the equation:

Portfolio Beta = 0.1581 + 0.2277 + 0.5133 + 0.4232 = 1.3223

Therefore, the portfolio beta is 1.3223.

Conceptually, the portfolio beta is the expected volatility in returns relative to the market as a whole. Therefore, investors often analyze the portfolio beta to determine the expected return on their collection of investments to protect their returns against market risk.

User Rgaut
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