- 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

###
**CFA Practice Question**

A portfolio manager gathers the following information about three possible asset allocations:

I | 13% | 6%

II | 26% | 14%

III | 32% | 20%

Allocation | Expected annual return | Standard deviation of return

I | 13% | 6%

II | 26% | 14%

III | 32% | 20%

The manager's client has stated that her minimum acceptable return is 8 percent. Based on Roy's safety-first criterion, the most appropriate allocation is ______.

A. I

B. II

C. III

**Explanation:**Roy's safety-first ratio = [E(R

_{P}) - R

_{L}] / σ

_{P}with the optimal portfolio having the highest ratio. The safety-first ratios for the three allocations are:

I : 0.83; II: 1.29; III: 1.20

###
**User Contributed Comments**
2

User |
Comment |
---|---|

GBolt93 |
Does this have any real world use? Seems like it mores sense logically to choose the portfolio with the highest sharp ratio and an expected return above 8% |

edrei7 |
It does. Roy's safety-first ratio ((Portfolio return - Benchmark return)/Sigma) can be reconstructed as: (Benchmark return - Portfolio return)/Sigma This can be interpreted as a z-statistic with the true mean at portfolio return and the sample mean at benchmark return. Thereafter, we can estimate the probability that the return will fall equal to or less than the benchmark return. |