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Chapter 12: Problem 25

Last year you looked at all the financial firms that had stock growth funds. You picked the growth fund that had the best performance last year (ranking at the 99 th percentile on performance) and invested all your money in it this year. This year, with their new investments, they ranked only at the 65 th percentile on performance. Your friend suggests that their stock picker became complacent or was burned out. Can you give another explanation?

Short Answer

Expert verified
The change in performance can be explained by regression to the mean, where extreme performances are often followed by average ones, rather than complacency or burnout.

Step by step solution

01

Understanding Percentile Performance

Percentiles are used to compare the performance of a fund relative to its peers. Being in the 99th percentile means it outperformed 99% of all other funds. In this year, at the 65th percentile, the fund outperforms 65% of its peers but does not match last year's achievement.
02

Introducing Regression to the Mean

Regression to the mean is a statistical phenomenon where extreme performances tend to be followed by more average or typical performances. Last year's exceptional 99th percentile performance could have been influenced by unique or temporary factors, leading to an average performance the following year. This year's 65th percentile might be closer to the fund's typical capability.
03

Evaluating Other Potential Influences

Investment returns are affected by many factors, such as market conditions, economic trends, and management decisions. Any of these could have shifted from last year to this year, affecting the performance relative to their peers.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Percentiles
Percentiles play a crucial role in evaluating investments and understanding how a particular fund performs compared to others. Imagine percentiles as a sorting mechanism that organizes data points into 100 equal parts. When we say a fund is in the 99th percentile, it signifies that this fund has outperformed 99% of all other funds within the group.

This ranking provides a snapshot of relative performance at a given time. If a fund drops to the 65th percentile, it is still doing well, outperforming 65% of its peers, though not as well as before. However, it's important not to view percentile rankings in isolation as they can fluctuate due to numerous external factors.
Regression to the Mean
Regression to the mean is a fascinating concept in statistics, which can explain why extreme values tend to be followed by more average ones. This happens because extreme results can often arise due to chance or temporary conditions. For instance, when a fund performs spectacularly well, achieving results at the 99th percentile, such a high achievement might partly be due to unique factors like a booming sector or an excellent managerial decision that might not be replicable.

Over time, these special conditions can fade, and performances may "regress" or move closer to the average. So, if a fund that once held a position in the 99th percentile drops back to the 65th percentile, it might be an outcome of this natural statistical effect rather than a sign of complacency or burnout.
Investment Performance Analysis
Analyzing investment performance involves more than just looking at percentile ranks. Several elements can impact the performance of investments, such as:
  • Market conditions: Fluctuations in the market environment may positively or negatively influence fund performance.
  • Economic trends: Broader economic shifts like changes in interest rates, inflation, or geopolitical events can impact how funds are performing.
  • Management decisions: Strategic choices made by the fund鈥檚 management team can significantly influence performance outcomes.

It's important to consider these diverse factors for a holistic view of why performance might change. Understanding these dynamics helps investors make informed decisions, ultimately aiding in assessing risk and potential returns.

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Most popular questions from this chapter

Let \(x\) denote a person's age and let \(y\) be the death rate, measured as the number of deaths per thousand individuals of a fixed age within a period of a year. For men in the United States, these variables follow approximately the equation \(\hat{y}=0.32(1.078)^{x}\). a. Interpret 0.32 and 1.078 in this equation. b. Find the predicted death rate when age is (i) \(20,(\) ii \() 50,\) and (iii) 80 . c. In every how many years does the death rate double? (Hint: What is \(x\) such that \(\left.(1.078)^{x}=2 ?\right)\)

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If a slope is 1.50 when \(x=\) income in thousands of dollars, then what is the slope when \(x=\) income in dollars? (Hint: A \(\$ 1\) change has only \(1 / 1000\) of the impact of a \(\$ 1000\) change?)

All students who attend Lake Wobegon College must take the math and verbal SAT exams. Both exams have a mean of 500 and a standard deviation of 100 . The regression equation relating \(y=\) math SAT score and \(x=\) verbal SAT score is \(\hat{y}=250+0.5 x\) a. Find the predicted math SAT score for a student who has the mean verbal SAT score of \(500 .\) (Note: At the \(x\) value equal to \(\bar{x},\) the predicted value of \(y\) equals \(\bar{y} .)\) b. Show how to find the correlation. Interpret its value as a standardized slope. (Hint: Both standard deviations are equal.) c. Find \(r^{2}\) and interpret its value.
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