1.You have $10,000 to invest. You decide to invest $20,000 in Google and short sell $10,000 worth of Yahoo! Google’s expected return is 15% with a volatility of 30% and Yahoo!’s expected return is 12% with a volatility of 25%. The stocks have a correlation of 0.9. What is the expected return and volatility of the portfolio?
2.You expect HGH stock to have a 20% return next year and a 30% volatility. You have $25,000 to invest, but plan to invest a total of $50,000 in HGH, raising the additional $25,000 by shorting either KBH or LWI stock. Both KBH and LWI have an expected return of 10% and a volatility of 20%. If KBH has a correlation of +0.5 with HGH, and LWI has a correlation of −0.50 with HGH, which stock should you short?
3.Suppose you have $100,000 in cash, and you decide to borrow another $15,000 at a 4% interest rate to invest in the stock market. You invest the entire $115,000 in a portfolio J with a 15% expected return and a 25% volatility.
a. What is the expected return and volatility (standard deviation) of your investment?
b. What is your realized return if J goes up 25% over the year?
c. What return do you realize if J falls by 20% over the year?
4.You have $100,000 to invest. You choose to put $150,000 into the market by borrowing $50,000.
a. If the risk-free interest rate is 5% and the market expected return is 10%, what is the expected return of your investment?
b. If the market volatility is 15%, what is the volatility of your investment?
5.You currently have $100,000 invested in a portfolio that has an expected return of 12% and a volatility of 8%. Suppose the risk-free rate is 5%, and there is another portfolio that has an expected return of 20% and a volatility of 12%.
a. What portfolio has a higher expected return than your portfolio but with the same volatility?
b. What portfolio has a lower volatility than your portfolio but with the same expected return?