# How do you calculate d (the downward movement factor) if a price is said to decrease by x%?

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asked May 29, 2018
edited May 29, 2018

There seems to be some inconsistency (or I am missing something) in how the downward factor d is calculated if the asset price is said to decrease by x%.

For example, in the Tutorial 4, question 3, the question states "In any unit of time the price of the stock either increases by 25% or decreases by 20%). In the memo, it then gives that d=0.8.

However, in the Q&A booklet, in section 3 (Binomial Model), question 13 states "Over each of the next two three-month periods it (the stock price) is expected to go up by 6% or down by 5% over each period." In the memo for that question, d is then given by d=1/1.05 which is not the same as d=0.95 as would be given in the method used in Tutorial 4.

What is the difference between these questions? Am I missing something in the wording?

Thanks a lot!

## 1 Answer

+1 vote
answered May 30, 2018 by (580 points)

The memo is wrong. You need to set d=0.95.

If something goes from x to x/1.05, it is incorrect to say that it has decreased by 5%.

Note that if u=1.05 (which does imply a 5% increase), and if one was using CRR, then d=1/1.05. But the question is not asking you to use CRR (there is no mention of volatility); instead it is describing the up and down movements directly. Perhaps this CRR form is how the error crept into the memo.