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You are given n indepen- You are studying an asset whose price changes each month. dent, random observations of the percentage change of an asset over a month (for example, 1%, –2.4%,...). Call this data X1,..., Xn. You find it is Normally distributed, with some mean you call u and variance 0.1. Call X = !E, X;. n You are interested the average return after 2 independent months if someone invested 1000 dollars, or 0 = E(1000(1+ X;)(1+ X;)). Consider the estimate Ô = 1000(1 + X)². (a) Find the expected value of 1000(1 + X;)(1+X;) for any i # j in terms of µ. (b) Is ô an unbiased estimate of 0? What does this mean in practice? (c) What does 0 go to as n gets large using the law of large numbers and other results from class? What does this mean in practice?

You are given n indepen- You are studying an asset whose price changes each month. dent, random observations of the percentage change of an asset over a month (for example, 1%, –2.4%,...). Call this data X1,..., Xn. You find it is Normally distributed, with some mean you call u and variance 0.1. Call X = !E, X;. n You are interested the average return after 2 independent months if someone invested 1000 dollars, or 0 = E(1000(1+ X;)(1+ X;)). Consider the estimate Ô = 1000(1 + X)². (a) Find the expected value of 1000(1 + X;)(1+X;) for any i # j in terms of µ. (b) Is ô an unbiased estimate of 0? What does this mean in practice? (c) What does 0 go to as n gets large using the law of large numbers and other results from class? What does this mean in practice?

MATLAB: An Introduction with Applications
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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You are studying an asset whose price changes each month. You are given n indepen- dent, random observations of the percentage change of an asset over a month (for example, 1%, -2.4%,...). Call this data X1,. mean you call µ and variance 0.1. Call X =;E=1 X;. .., Xn. You find it is Normally distributed, with some n You are interested the average return after 2 independent months if someone invested 1000 dollars, or 0 = E(1000(1+ X;)(1+X;)). Consider the estimate ô = 1000(1+ X)². (a) Find the expected value of 1000(1+ X;)(1+ X;) for any i +j in terms of (b) Is ô an unbiased estimate of 0? What does this mean in practice? (c) What does 0 go to as n gets large using the law of large numbers and other results from class? What does this mean in practice?
Transcribed Image Text:You are studying an asset whose price changes each month. You are given n indepen- dent, random observations of the percentage change of an asset over a month (for example, 1%, -2.4%,...). Call this data X1,. mean you call µ and variance 0.1. Call X =;E=1 X;. .., Xn. You find it is Normally distributed, with some n You are interested the average return after 2 independent months if someone invested 1000 dollars, or 0 = E(1000(1+ X;)(1+X;)). Consider the estimate ô = 1000(1+ X)². (a) Find the expected value of 1000(1+ X;)(1+ X;) for any i +j in terms of (b) Is ô an unbiased estimate of 0? What does this mean in practice? (c) What does 0 go to as n gets large using the law of large numbers and other results from class? What does this mean in practice?
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