Answered: Standard and Poor 500 (S&P500) is an…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Standard and Poor 500 (S&P500) is an index of 500 large corporations capitalization on the NYSE. The annual rate of return of the index is approximately normal. From January 1, 1960 to December 31, 2019, the S&P 500 had an average annual return of 10.98%, with a deviation standard of approximately 17.46%. Consider this normal distribution to be the distribution of annual returns over a long period.

(a) In what mean interval do 95% of the annual returns fall? (95% center)
(b) Stock prices can go up or down. What are the yields of 2.5% lower?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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