A Highly Risk-Averse Investor Is Considering Adding One Additional Stock

question 135

Multiple Choice

A highly risk-averse investor is considering adding one additional stock to a 3-stock portfolio,to form a 4-stock portfolio.The three stocks currently held all have b = 1.0,and they are perfectly positively correlated with the market.Potential new Stocks A and B both have expected returns of 15%,are in equilibrium,and are equally correlated with the market,with r = 0.75.However,Stock A's standard deviation of returns is 12% versus 8% for Stock B.Which stock should this investor add to his or her portfolio,or does the choice not matter?

• A) Either A or B,i.e. ,the investor should be indifferent between the two.
• B) Stock A.
• C) Stock B.
• D) Neither A nor B,as neither has a return sufficient to compensate for risk.
• E) Add A,since its beta must be lower.

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Definitions:

Variance

A measure of the dispersion of a set of data points in a population, showing how much the data diverge from the average value.

Degrees of Freedom

The number of independent values or quantities which can vary in the calculation of a statistic, typically in the context of hypothesis testing.

F Distribution

A continuous probability distribution that arises frequently as the null distribution of a test statistic, especially in the analysis of variance (ANOVA).

Numerator

The top number in a fraction, representing the part of the whole or the dividend in division.