Answered: A European growth mutual fund…

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

A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 500 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean ? = 1.5% and standard deviation ? = 1.3%.

(a) Let's consider the monthly return of the stocks in the fund to be a sample from the population of monthly returns of all European stocks. Is it reasonable to assume that x (the average monthly return on the 500 stocks in the fund) has a distribution that is approximately normal? Explain.

, x is a mean of a sample of n = 500 stocks. By the , the x distribution approximately normal.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

(d) Compare your answers to parts (b) and (c). Did the probability increase as n (number of months) increased? Why would this happen?

No, the probability stayed the same.Yes, probability increases as the mean increases. Yes, probability increases as the standard deviation increases.Yes, probability increases as the standard deviation decreases.

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that ? = 1.5%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) =

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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