- CFA Exams
- CFA Level I Exam
- Study Session 3. Quantitative Methods (2)
- Reading 9. Common Probability Distributions
- Subject 9. Shortfall Risk and Roy's Safety-First Criterion

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**CFA Practice Question**

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 for her annual vacation. The investor is considering three alternative portfolios:

Portfolio 2: Expected Return: 10%, Standard Deviation of Returns: 13%

Portfolio 3: Expected Return: 14%, Standard Deviation of Returns: 22%

Portfolio 1: Expected Return: 8%, Standard Deviation of Returns: 10%

Portfolio 2: Expected Return: 10%, Standard Deviation of Returns: 13%

Portfolio 3: Expected Return: 14%, Standard Deviation of Returns: 22%

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

A. Portfolio 1

B. Portfolio 2

C. Portfolio 3

**Explanation:**The investor requires a minimum return of $40,000/$700,000 or 5.71 percent. 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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