- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 2. Organizing, Visualizing, and Describing Data
- Subject 8. Measures of Dispersion

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**CFA Practice Question**

You have invested in a stock with an expected return of 14% and a standard deviation of 7%. Your target rate of return is 7%. What is the probability that you will not meet your objective, assuming stock returns are normally distributed?

A. 16%

B. 32%

C. 68%

**Explanation:**There is a 68% chance that the stock returns will be within one standard deviation of the mean (i.e., there is a 68% chance that the stock returns will be between 7% and 21%). Hence, the probability that stock returns will lie outside this range is 100% - 68% = 32%. Since the normal distribution is symmetrically distributed about the mean, the probability that the returns will be less than 7% equals 32/2 = 16%

You could also solve this problem using the z-score and the normal probability distribution table. You should, however, be aware of short-cuts like the one above.

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**User Contributed Comments**
2

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

Pooh |
using empirical rule: 68% within 1s, 95% within 2s, 99% within 3s |

edwardike |
68% is from 7% to 21%. 1-.68% = 32% but we only want the downside so divide by 2 to get the probability of only the downside. |