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Kelly Johnson is the owner of a portfolio that is invested 14 percent in Stock A, 50 percent in Stock B, and 36 percent in Stock C. The betas of her stocks are .81, 1.36, and 1.65, respectively. What is the beta of Kelly's portfolio?

User Simon Bull
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Final answer:

To find the beta of Kelly's portfolio, we need to calculate a weighted average of the betas of the individual stocks, using the proportions of the investments as weights. The beta of a portfolio is a measure of its systematic risk or the risk that cannot be diversified away.

Step-by-step explanation:

To find the beta of Kelly's portfolio, we need to calculate a weighted average of the betas of the individual stocks, using the proportions of the investments as weights.

The formula to calculate the beta of a portfolio is:

Betaportfolio = (ProportionA * BetaA) + (ProportionB * BetaB) + (ProportionC * BetaC)

Given that the proportions of Kelly's investments in Stock A, B, and C are 14%, 50%, and 36% respectively, and the betas of the stocks are 0.81, 1.36, and 1.65 respectively, we can substitute these values into the formula:

Betaportfolio = (0.14 * 0.81) + (0.50 * 1.36) + (0.36 * 1.65)

Simplifying the equation,

Betaportfolio = 0.1134 + 0.68 + 0.594

Betaportfolio = 1.3874

The beta of a portfolio is a measure of its systematic risk or the risk that cannot be diversified away. To calculate the beta of a portfolio, you use a weighted average of the individual stock betas, where the weights represent the proportion of the portfolio invested in each stock. So, the beta of Kelly Johnson's portfolio is approximately 1.3874. This means that the portfolio's systematic risk is 1.3874 times that of the overall market.

User Giorgionocera
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