2008 CFA Level 1 － Sample 样题(3)－Q21 investor, objective, currently, class, face

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21、An investor currently has a portfolio valued at $700,000. The investor's objective is long-term growth, but the investor will need $30,000 by the end of the year to pay her son's college tuition and another $10,000 by year-end for her annual vacation. The investor is considering four alternative portfolios:

Portfolio Expected Return   Standard Deviation of Returns

1     8%  10%

2     10%       13%

3     14%       22%

4     18%       35%

Using Roy's safety-first criterion, which of the alternative portfolios minimizes the probability that the investor's portfolio will have a value lower than $700,000 at year-end?

A. Portfolio 1.

B. Portfolio 2.

C. Portfolio 3.

D. Portfolio 4.

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答案和详解如下：

21、Correct answer is C

"Common Probability Distributions," Richard A. Defusco, Dennis W. McLeavey, Jerald E. Pinto, and David E. Runkel

2008 Modular Level I, Vol. 1, pp. 397-400

Study Session 3-9-i

define shortfall risk, calculate the safety-first ratio, and select an optimal portfolio using Roy's safety-first criterion

The investor requires a minimum return of $40,000 / $700,000 or 5.71%. Roy's safety-first model uses the excess of each portfolio's expected return over the minimum return and divides that excess by the standard deviation for that portfolio. The highest safety-first ratio is associated with Portfolio 3:

(14% - 5.71%) / 22% = 0.3768.

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