The table below shows the forecasted return on Portfolio A and Portfolio B with their respective probabilities:Economic Cycle Probabilty Portfolio A Portfolio BBoom 0.1 Increase 15% Increase 12%Normal 0.6 Increase 10% Increase 9%Recession 0.3 Decrease 5% Decrease 2%Which of the following statements are true? Both the mean and the variance of Portfolio A are greater than that of Portfolio B. Both the mean and the variance of Portfolio B are greater than that of Portfolio A. Portfolio A has a greater variance than Portfolio B but they have the same mean. Portfolio B has a greater variance than Portfolio A but they have the same mean. Both Portfolio A and Portfolio B have the same mean and same variance.

For Portfolio A x P(X=x) x P(X=x) x^2 P(X=x) 0.15 0.1 0.015 0.0025 0.1 0.6 0.06 0.006 0.05…

Answered: The table below shows the forecasted…

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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The table below shows the forecasted return on Portfolio A and Portfolio B with their respective probabilities:

Economic Cycle Probabilty Portfolio A Portfolio B

Boom 0.1 Increase 15% Increase 12%

Normal 0.6 Increase 10% Increase 9%

Recession 0.3 Decrease 5% Decrease 2%

Which of the following statements are true?

Both the mean and the variance of Portfolio A are greater than that of Portfolio B.
Both the mean and the variance of Portfolio B are greater than that of Portfolio A.
Portfolio A has a greater variance than Portfolio B but they have the same mean.
Portfolio B has a greater variance than Portfolio A but they have the same mean.
Both Portfolio A and Portfolio B have the same mean and same variance.

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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