LifeStrategy Conservative Growth and Small Cap Growth are two portfolios constructed and managed by the Vanguard Group of mutual funds, comprised of stocks of conservatively managed U.S. companies and stocks of small U.S. firms, mostly in healthcare or technology. The accompanying table shows historical annualized return from the period 2010 to 2020, which suggests the expected value of the annual percentage returns associated with these portfolios.

a. Which portfolio would a risk-neutral investor prefer?

b. Juan, a risk-averse investor, chooses to invest in the LifeStrategy Conservative Growth portfolio. What can be inferred about the risk of the two portfolios from Juan’s choice of investment? Based on historical performance, would a risk-neutral investor ever choose LifeStrategy Conservative Growth?

c. Juan is aware that diversification can reduce risk. He considers a portfolio in which half his investment is in conservatively managed companies and the other half in small high tech or healthcare companies. What is the expected value of the return for this combined portfolio?
Would you expect this combined portfolio to be more risky or less risky than the LifeStrategy Conservative Growth portfolio? Why or why not?

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Portfolio LifeStrategy Conservative Growth Expected value of return (percent) 5.88%