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Question 3 (2 points)
Jane has a portfolio of 20 average stocks, and Dick has a portfolio of 2 average stocks. Assuming the market is in
equilibrium, which of the following statements is CORRECT?
Dick’s portfolio will have more diversifiable risk, the same market risk, and thus more total risk than Jane’s
portfolio, but the required (and expected) returns will be the same on both portfolios.
The required return on Jane’s portfolio will be lower than that on Dick’s portfolio because Jane’s portfolio will
have less total risk.
Jane’s portfolio will have less diversifiable risk and also less market risk than Dick’s portfolio.
If the two portfolios have the same beta, their required returns will be the same, but Jane’s portfolio will have
less market risk than Dick’s.

Ask by Dunn Ortega. in the United States
Mar 30,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Dick’s portfolio has more diversifiable risk and more total risk than Jane’s, but both have the same required return.

Solution

In equilibrium, the required (expected) return on a portfolio depends only on its market (systematic) risk, as measured by its beta. Unsystematic, or diversifiable risk, can be reduced (or nearly eliminated) by diversification. The average stock has a certain systematic risk (beta) and diversifiable risk. With more stocks in the portfolio, the diversifiable risk is reduced.
  • : Contains 20 average stocks. With 20 stocks, the unsystematic (diversifiable) risk is considerably reduced due to diversification. However, the market risk (systematic risk) remains, and it is embedded in the beta of the portfolio.
  • : Contains only 2 average stocks. With only 2 stocks, the portfolio is not well diversified. Thus, it retains a significant portion of the unsystematic risk while having the same systematic risk (if the stocks are average) as Jane’s portfolio.
Since the Capital Asset Pricing Model (CAPM) states that the required return depends on the beta (market risk), and assuming both portfolios consist of average stocks, the beta for each portfolio would be roughly the same. Therefore, the required (and expected) return on each portfolio should be the same.
However, because Dick’s portfolio has not diversified its unsystematic risk effectively, it carries more total risk even though the excess risk (diversifiable risk) does not require a higher expected return.
  • “Dick’s portfolio will have more diversifiable risk, the same market risk, and thus more total risk than Jane’s portfolio, but the required (and expected) returns will be the same on both portfolios.”
    • This statement correctly captures the situation: both portfolios have similar market risk (thus similar required returns), but Dick’s portfolio has higher diversifiable risk due to less diversification.
  • “The required return on Jane’s portfolio will be lower than that on Dick’s portfolio because Jane’s portfolio will have less total risk.”
    • This is incorrect because required return is a function of market risk (beta), not total risk.
  • “Jane’s portfolio will have less diversifiable risk and also less market risk than Dick’s portfolio.”
    • Incorrect, because both portfolios have similar market risk if they consist of average stocks; only the diversifiable risk differs.
  • “If the two portfolios have the same beta, their required returns will be the same, but Jane’s portfolio will have less market risk than Dick’s.”
    • Incorrect, because if the portfolios have the same beta, they have the same market risk; the diversification affects diversifiable risk, not systematic risk.
The correct statement is Option A.

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Bonus Knowledge

Diversification is key when it comes to investment portfolios! Jane, with her 20 stocks, is likely to experience less diversifiable risk because her holdings are spread out. This means that if one stock underperforms, it’s less likely to make a significant dent in her overall portfolio. On the other hand, Dick’s concentrated portfolio of just 2 stocks carries more risk because the performance of either stock can drastically impact his returns.
When it comes to required returns, as per the Capital Asset Pricing Model (CAPM), if both portfolios have the same beta, they will indeed have similar required returns. However, Jane’s diversified portfolio is inherently less risky overall. Thus, while their expected returns may align due to similar betas, Jane’s portfolio faces less overall risk than Dick’s concentrated holdings.

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