April 2011
Beginner
704 pages
21h 44m
English
book
The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition
by Frank J. Fabozzi, Harry M. Markowitz
Content preview from The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition
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ARITHMETIC RANDOM WALKS
Instead of assuming that at each step the asset price can only move up or down by a certain multiple with a given probability, we could assume that the price moves by an amount that follows a normal distribution with mean μ and standard deviation σ. In other words, the price for each period is determined from the price of the previous period by the equation
where 
is a normal random variable with mean 0 and standard deviation σ. We will also assume that the random variable 
, describing the change in the price in one time period is independent of the random variables describing the change in the price in any other time period.80 A sequence of independent and identically distributed (IID) random variables 
,... with zero mean and finite variance σ78 is sometimes referred to as white noise.
is a normal random variable with mean 0 and standard deviation σ. We will also assume that the random variable , describing the change in the price in one time period is independent of the random variables describing the change in the price in any other time period.80 A sequence of independent and identically distributed (IID) random variables ,... with zero mean and finite variance σ78 is sometimes referred to as white noise.
EXHIBIT 6.3 Binomial Distribution
EXHIBIT 6.4 Standard Normal Distribution
The movement of the price expressed through the equation above is called an arithmetic random ...
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