Stock Selection for Portfolio Optimization

Which Stock Should You Add to Your Portfolio?

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Question

Juliet Kaufman manages a large portfolio of risky assets for a family of investors- The portfolio consists primarily of stocks but also includes a small allocation of fixed-income investments. Currently, the expected return and standard deviation of the portfolio are 14.0% and 12.0%, respectively. Kaufman is considering adding one of three stocks to the portfolio. Data on each stock's expected return, beta, standard deviation, and covariance with the existing portfolio are presented below. Which stock should Kaufman add to the portfolio?

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Explanations

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A. B. C.

A

To determine which stock Juliet Kaufman should add to her portfolio, we need to analyze the expected return, risk (standard deviation), and the stock's relationship with the existing portfolio.

Let's review the provided data:

Existing Portfolio: Expected return (Rp) = 14.0% Standard deviation (σp) = 12.0%

Stock A: Expected return (Ra) = 12.0% Beta (βa) = 1.2 Standard deviation (σa) = 10.0% Covariance with the existing portfolio (Cov(a,p)) = 0.08

Stock B: Expected return (Rb) = 15.0% Beta (βb) = 1.5 Standard deviation (σb) = 18.0% Covariance with the existing portfolio (Cov(b,p)) = 0.12

Stock C: Expected return (Rc) = 17.0% Beta (βc) = 0.8 Standard deviation (σc) = 6.0% Covariance with the existing portfolio (Cov(c,p)) = -0.04

Now, let's analyze each stock's potential contribution to the portfolio.

  1. Stock A: Stock A has an expected return of 12.0% and a standard deviation of 10.0%. Comparing the expected return of Stock A to the existing portfolio's expected return (14.0%), Stock A has a lower expected return. However, Stock A has a lower standard deviation (less risk) compared to the existing portfolio.

  2. Stock B: Stock B has an expected return of 15.0% and a standard deviation of 18.0%. Comparing the expected return of Stock B to the existing portfolio's expected return, Stock B offers a higher expected return. However, Stock B has a higher standard deviation (more risk) compared to the existing portfolio.

  3. Stock C: Stock C has an expected return of 17.0% and a standard deviation of 6.0%. Comparing the expected return of Stock C to the existing portfolio's expected return, Stock C offers the highest expected return. Additionally, Stock C has a lower standard deviation (less risk) compared to the existing portfolio.

Now, let's consider each stock's covariance with the existing portfolio. The covariance measures the relationship between the returns of the stock and the portfolio. A positive covariance indicates that the stock's returns tend to move in the same direction as the portfolio, while a negative covariance indicates the opposite.

The covariance values are as follows:

Cov(a,p) = 0.08 Cov(b,p) = 0.12 Cov(c,p) = -0.04

Based on the provided covariance values, Stock A and Stock B have positive covariance with the existing portfolio, while Stock C has a negative covariance.

Considering all the factors, it is generally desirable to add a stock to a portfolio if it has a higher expected return and a lower risk (standard deviation). In this case, Stock C has the highest expected return and the lowest standard deviation, making it an attractive choice. Additionally, the negative covariance of Stock C indicates that it has a potential diversification benefit for the existing portfolio.

Therefore, based on the analysis, Juliet Kaufman should add Stock C to the portfolio. Hence, the correct answer is C. Stock C.

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