Jane holds a large diversified portfolio of 100 randomly selected stocks and the

Question

Jane holds a large diversified portfolio of 100 randomly selected stocks and the portfolio’s beta = 1.2. Each of the individual stocks in her portfolio has a standard deviation of 20 percent. Jack has the same amount of money invested in a single stock with a beta equal to 1.6 and a standard deviation of 20 percent. Which of the following statements is most correct?

a). Jane’s portfolio has a larger amount of company-specific risk since she is holding more stocks in her portfolio.

b). Jane has a higher required rate of return, since she is more diversified.

c). Jane’s portfolio has less market risk since it has a lower beta.

d). Statements b and c are correct.

e). None of the statements above is correct.

Explanation / Answer

Jane's company have large amount of shares in her portfolio which diversified the total risk on the stock. So the large amount of company risk or diversified risk has been reduced due to increase in number of stocks in the portfolio. So the statement (a) is not correct.

The expected rate of return is weighted average rate of return using the probability of each rate of return as the weight associated with the stock. If the single stock have same standard deviation on their return compare to the Jane's porfolio it shows both have same total required rate of return. And Jane's portfolio have same risk on their portfolio as single stock holder have on their stock. So the part (b) is not correct.

Total risk is divided on two part one is diversified risk and second one is non diversified risk that is also known as market risk. And this risk is measued by the beta cofficient. Jane's portfolio have low beta having low market risk. So the statement (c) is correct.

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