91Ó°ÊÓ

Returns on stocks. How well have stocks done over the past generation? The Wilshire 5000 index describes the average performance of all U.S. stocks. The average is weighted by the total market value of each company's stock, so think of the index as measuring the performance of the average investor. Here are the percent returns on the Wilshire 5000 index for the years from 19712015: 22 ? WILSHIRE $$ \begin{array}{lc|cc|cc} \hline \text { Year } & \text { Return } & \text { Year } & \text { Return } & \text { Year } & \text { Return } \\ \hline 1971 & 17.68 & 1986 & 16.09 & 2001 & -10.97 \\ \hline 1972 & 17.98 & 1987 & 2.27 & 2002 & -20.86 \\ \hline 1973 & -18.52 & 1988 & 17.94 & 2003 & 31.64 \\ \hline 1974 & -28.39 & 1989 & 29.17 & 2004 & 12.62 \\ \hline 1975 & 38.47 & 1990 & -6.18 & 2005 & 6.32 \\ \hline 1976 & 26.59 & 1991 & 34.20 & 2006 & 15.88 \\ \hline 1977 & -2.64 & 1992 & 8.97 & 2007 & 5.73 \\ \hline 1978 & 9.27 & 1993 & 11.28 & 2008 & -37.34 \\ \hline 1979 & 25.56 & 1994 & -0.06 & 2009 & 29.42 \\ \hline 1980 & 33.67 & 1995 & 36.45 & 2010 & 17.87 \\ \hline 1981 & -3.75 & 1996 & 21.21 & 2011 & 0.59 \\ \hline 1982 & 18.71 & 1997 & 31.29 & 2012 & 16.12 \\ \hline & & & & & \end{array} $$ $$ \begin{array}{lc|cc|ll} 1983 & 23.47 & 1998 & 23.43 & 2013 & 34.02 \\ \hline 1984 & 3.05 & 1999 & 23.56 & 2014 & 12.07 \\ \hline 1985 & 32.56 & 2000 & -10.89 & 2015 & -0.24 \\ \hline \end{array} $$ What can you say about the distribution of yearly returns on stocks?

Step by step solution

01

Organize the Data

We have a list of the Wilshire 5000 index annual returns from the year 1971 to 2015. These returns range from significant negative values, such as -37.34% in 2008, to high positive values, like 38.47% in 1975. First, ensure all years and their corresponding returns are noted for analysis.

02

Calculate Summary Statistics

To understand the distribution, compute key summary statistics: 1. **Mean (Average) Return:** Sum all yearly returns and divide by the number of years (45 years). 2. **Median Return:** Arrange returns in order and find the middle value. 3. **Range of Returns:** Calculate the difference between the maximum and minimum values. 4. **Standard Deviation:** Measure how much each year's return deviates from the mean, indicating variability.

03

Analyze the Distribution Shape

Examine the skewness and make note of any outlier years. Returns vary widely, suggesting a spread with both high peaks and deep troughs, indicating potential skewness. Determine if extreme values (outliers) like 2008 with -37.34% or 1975 with 38.47% significantly affect the distribution.

04

Characterize the Distribution

Given the summary statistics and observed distribution shape, describe the pattern: - **Mean Return:** An average positive value, indicating general growth over time. - **Variability:** With high standard deviation, the volatility was substantial, showing years with both gains and losses. - **Asymmetrical Shape:** The distribution may be slightly skewed to the negative due to years like 2008 but high gains also suggest notable positive peaks.

Unlock Step-by-Step Solutions & Ace Your Exams!

• Full Textbook Solutions

  Get detailed explanations and key concepts

• Unlimited Al creation

  Al flashcards, explanations, exams and more...

• Ads-free access

  To over 500 millions flashcards

• Money-back guarantee

  We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

Key Concepts

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

Wilshire 5000 Index

The Wilshire 5000 Index is a comprehensive barometer for the overall performance of the U.S. stock market. It includes all publicly traded U.S. stocks, providing a complete picture of the market's health. The index is weighted by each company's total market value. This means larger companies have a bigger impact on the index than smaller ones. It effectively reflects how the average investor might fare in the stock market because of its wide coverage.
A better understanding of the Wilshire 5000 Index helps investors see broad market trends rather than just focusing on individual stocks or sectors. It's like looking at the entire forest instead of just the trees.

Summary Statistics

Summary statistics are essential for a crisp grasp of stock returns. They simplify complex datasets into easier-to-understand metrics. When analyzing data like the Wilshire 5000 index returns, you should focus on key statistics such as the mean, median, range, and standard deviation.

• **Mean Return:** This is the average of all yearly returns. It provides a general sense of how the market performs over time.
• **Median Return:** This is the midpoint in a dataset, showing the middle value, which can sometimes present a more accurate picture than the mean, especially when data is skewed.
• **Range:** This illustrates the spread between the highest and lowest returns, giving us insight into the market's volatility.
• **Standard Deviation:** This measures the typical amount by which values differ from the mean, indicating overall volatility.

Utilizing these summary statistics provides a clear snapshot of trends and variations in stock market returns, helping investors make informed decisions.

Distribution Shape

Understanding the shape of the distribution of returns is crucial for grasping market dynamics. Essentially, the distribution shape tells us about the frequency and magnitude of stock returns variations over time. A look into the distribution of the Wilshire 5000 index returns can reveal skewness, whether left or right. This skewness indicates whether more returns were significantly lower or higher than the average.

• If the distribution is skewed negatively, there will be more occurrences of returns below the average, suggesting that certain events led to sharp downward trends.
• Conversely, a positive skew indicates more returns above average, reflecting periods of significant growth.

Years with extreme values, such as 2008 with -37.34% or 1975 with 38.47%, act as outliers. These can heavily influence the shape of the distribution, making it critical to consider them in any analysis. They show patterns of volatility and periods that defy average market behaviors.

Investing Trends

Examining investing trends over the years in the Wilshire 5000 index provides insight into how market conditions have developed and evolved. By understanding these trends, investors can make better-informed decisions about their future investment strategies.
Over decades, various trends emerge:

• **Bull Markets:** Prolonged periods where the stock returns were consistently positive, indicating economic growth and investor confidence.
• **Bear Markets:** Poor performance phases with negative returns, reflecting economic downturns or major financial crises.
• **Volatile Periods:** Times with significant return fluctuations, highlighting instability and risk in the market.

Recognizing these patterns is crucial. It allows for the anticipation of potential future movements based on past events, though it's important to remember that historical trends do not guarantee future performances. Observing how the Wilshire 5000 behaved in different economic scenarios helps to contextualize new market developments.