Using Derivatives in Asset Allocation
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Candidates may remember their inferential statistics training from CFA Level I. This reading delves deeper into Type I and Type II errors within the context of hiring and firing investment managers. It's important to note that the null hypothesis presumes the manager lacks skill, doesn't meet expectations, or underperforms.
Null Hypothesis: Manager Underperforms
Therefore, the two potential errors are:
Another, perhaps simpler and less scientific way to think about these errors is:
Determining whether to avoid type I or type II errors in fund selection varies based on the fund sponsor's preferences. Many prefer steering clear of poor managers, in other words, avoiding type I errors. Here are a few reasons for this choice:
While most investors often focus on type I errors, type II errors are also significant. Monitoring managers who were fired or overlooked can help fund sponsors identify weaknesses in their selection process.
The impact of type I and type II errors is generally smaller in more efficient markets. Market efficiency, especially its tendency to mean-revert, influences the costs associated with these errors. For instance, in a mean-reverting market, firing an underperformer only to see them bounce back represents a Type I error. Conversely, a Type II error would involve retaining strong performers and avoiding managers with weaker short-term track records, which also incurs costs.
Question
Which of the following most accurately describes a type I error?
- Rejecting the null hypothesis when it is correct.
- Not rejecting the null hypothesis when it is incorrect.
- Not rejecting the null hypothesis with it is correct.
Solution
The correct answer is A.
It describes a Type I error accurately. It occurs when a researcher or analyst incorrectly rejects the null hypothesis, which essentially means they conclude that there is a significant effect or difference when, in reality, there isn't one. This is also known as a “false positive.”
B is incorrect. It describes the correct decision in hypothesis testing. When the null hypothesis is incorrect, you should indeed not reject it because you're essentially saying that the data doesn't provide enough evidence to support the alternative hypothesis. This is not a Type I error.
C is incorrect. It is describing the correct decision in hypothesis testing. When the null hypothesis is correct, you should not reject it because it means that the data doesn't provide enough evidence to support the alternative hypothesis. This is not a Type I error.
Remember:
The null hypothesis is that the manager has no skill.
Reading 13: Investment Manager Selection
Los 13 (b) Contrast Type I and Type II errors in manager hiring and continuation decisions