Question

You expect HGH stock have a 30% return next year and a 45% volatility. You have $50,000 to invest, but plan to invest a total of $75,000 in HGH, raising the additional $25,000 by shorting either KBH or LWI stock. Both KBH and LWI have an expected return of 5% and a volatility of 20%. If KBH has a correlation of +0.5 with HGH, and LWI has a correlation of −0.5 with HGH, which stock should you short? Which portfolio is superior? Why? (Select the best choice below.) A. Both portfolios have the same expected return, but shorting LWI is better because we should seek to hold stocks that are positively correlated to reduce volatility. B. Both portfolios have the same expected return, but shorting LWI is better because we should seek to hold stocks that are negatively correlated to reduce volatility. C. Both portfolios have the same expected return, but shorting KBH is better because we should seek to hold stocks that are positively correlated to reduce volatility. D. Both portfolios have the same expected return, but by shorting KBH, we achieve a lower volatility because it has a positive correlation with HGH. By shorting KBH, some of the common risk shared by the stocks is reduced.

Answer 1

B. Both portfolios have the same expected return, but shorting LWI is better because we should seek to hold stocks that are negatively correlated to reduce volatility.

Step-by-step explanation:

Calculate the expected return and volatility for each portfolio:

Portfolio with shorting KBH:

Expected return: HGH (30%), KBH (5%)

Volatility: HGH (45%), KBH (20%)

Portfolio with shorting LWI:

Expected return: HGH (30%), LWI (5%)

Volatility: HGH (45%), LWI (20%)

Consider the correlation between each stock and HGH:

KBH correlation with HGH: +0.5

LWI correlation with HGH: -0.5

Choose the portfolio that reduces volatility by shorting a stock that is negatively correlated with HGH:

Shorting LWI (negatively correlated) would be better to reduce volatility.