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Chapter 1: Problem 95

Comparing investments Should you put your money into a fund that buys stocks or a fund that invests in real estate? The boxplots compare the daily returns (in percent) on a 鈥渢otal stock market鈥� fund and a real estate fund over a year ending in November 2007.43 (a) Read the graph: about what were the highest and lowest daily returns on the stock fund? (b) Read the graph: the median return was about the same on both investments. About what was the median return? c) What is the most important difference betweenthe two distributions?

Short Answer

Expert verified
(a) Highest: around x%, Lowest: around y%. (b) Median return: around z%. (c) Check spread and outliers.

Step by step solution

01

Analyze Stock Fund Boxplot

First, examine the boxplot for the total stock market fund to identify the highest and lowest daily returns. The highest return is represented by the top whisker or the topmost point if there are outliers. Similarly, the lowest return is found at the bottom whisker or the lowest point if outliers are present.
02

Determine Real Estate Fund Range

Next, check the boxplot for the real estate fund. Identify the highest and lowest daily returns, much like you did for the stock fund, by looking at the position of the top and bottom whiskers, or any potential outliers.
03

Compare Median Returns

Find the median line within each box of the box plots for both the stock and real estate funds. The median line divides each dataset in half and represents the middle point where half of the values are above, and half are below. Note that the problem suggests these medians are approximately equal.
04

Identify Main Distribution Difference

The final step is to examine what distinguishes the two distributions represented by the boxplots. This involves looking at the spread of each boxplot's interquartile range, the presence of outliers, and the symmetry or skewness of data distribution in each plot.

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Key Concepts

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

Comparing Investments
When evaluating investments, two common choices are stock funds and real estate funds. Each has its distinct characteristics and risks, which can be visualized using boxplots that represent the distribution of their daily returns. By examining these plots, investors can make informed decisions about where to allocate their resources. Understanding the differences, such as variability and median returns, is essential for assessing which investment might better align with their risk tolerance and financial goals.
Stock Fund Returns
Stock funds typically invest in a wide range of equities across various sectors. The boxplot for a stock fund reveals how its daily returns are distributed over a set period. Key features to observe include:
  • Highest and lowest returns: Shown by the top and bottom whiskers.
  • Range: Difference between highest and lowest returns, indicating volatility.
  • Outliers: Individual points that fall significantly above or below the typical range, representing extreme returns.
Examining these elements helps investors understand the potential for high gains or losses in stock funds.
Real Estate Fund Returns
Real estate funds invest in property or real estate-related assets. The boxplot for real estate fund returns provides a visual representation of how these returns are spread out. Important aspects to examine include:
  • Highest and lowest returns: As shown by the whiskers on the boxplot.
  • Outliers: Points that are unusually high or low compared to the rest.
  • Frequency and consistency: Which are sometimes reflected in a narrower interquartile range.
These factors help indicate the stability or volatility of returns from real estate investments.
Distribution Difference
The main difference between stock and real estate fund distributions often lies in the spread and shape of the boxplots. The width of the box, or the interquartile range, shows variability. A larger box implies greater variability and risk.
  • Outliers: Indicate potential for extreme returns in either direction.
  • Symmetry vs. skewness: Symmetrical boxplots suggest balanced returns around the median, whereas skewed plots show a tendency towards higher or lower returns.
These attributes help investors understand potential risks and whether returns are consistently near the average or differ significantly.
Median Returns
The median return is a critical measure in boxplot analysis, representing the midpoint of the data. In investments, it is important because:
  • Equal medians across investment types suggest similar average performance.
  • Provides a central value that is unaffected by extreme returns.
  • Helps investors estimate average expected return.
In the given example, both stock and real estate funds had approximately equal medians, indicating comparable mid-term performance, even if variability and risk differ.

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