CFA Problems

1. A portfolio of nondividend-paying stocks earned a geometric mean return of 5% between January 1, 2005, and December 31, 2011. The arithmetic mean return for the same period was 6%. If the market value of the portfolio at the beginning of 2005 was $100,000, what was the market value of the portfolio at the end of 2011? (LO 5-1)
2. Which of the following statements about the standard deviation is/are true? A standard deviation: (LO 5-2)
   a. Is the square root of the variance?
   b. Is denominated in the same units as the original data.
   c. Can be a positive or a negative number.
3. Which of the following statements reflects the importance of the asset allocation decision to the investment process? The asset allocation decision: (LO 5-3)
   a. Helps the investor decide on realistic investment goals.
   b. Identifies the specific securities to include in a portfolio.
   c. Determines most of the portfolio’s returns and volatility over time.
   d. Creates a standard by which to establish an appropriate investment time horizon.

Use the following data in answering CFA Questions 4–6.
Investment Expected Return, E(r) Standard Deviation, s
1 .12 .30
2 .15 .50
3 .21 .16
4 .24 .21
Investor “satisfaction” with portfolio increases with expected return and decreases with variance according to the “utility” formula: U = E(r) – ½ A σ2 where A = 4.

4. Based on the formula for investor satisfaction or “utility,” which investment would you select if you were risk averse with A = 4? (LO 5-4)
5. Based on the formula above, which investment would you select if you were risk neutral? (LO 5-4)
6. The variable (A) in the utility formula represents the: (LO 5-4)
   a. Investor’s return requirement.
   b. Investor’s aversion to risk.
   c. Certainty equivalent rate of the portfolio.
   d. Preference for one unit of return per four units of risk.

Use the following scenario analysis for stocks X and Y to answer CFA Questions 7 through 9.

Bear Market Normal Market   Bull Market

Probability .2 .5 .3
Stock X -20% 18% 50%
Stock Y -15% 20% 10%

7. What are the expected returns for stocks X and Y ? (LO 5-2)
8. What are the standard deviations of returns on stocks X and Y ? (LO 5-2)
9. Assume that of your $10,000 portfolio, you invest $9,000 in stock X and $1,000 in stock Y. What is the expected return on your portfolio? (LO 5-3)