 # Up and down move calculation

I am confused with the CFA Institute method of calculating up and down moves for binomial probabilities. The Up move here given is 15%, and down move is 10%. I calculated the down move as .8697 which is 1/U, but the answer key uses .9 as the down move. The P(up-move) = [(1+r) - d] / [u - d] is therefore different from what I calculated based on the Schweser method. Does anyone know which method to use, or am i interpreting one of the methods incorrectly?

The right way to calculate this is actually to have absolute values at the nodes (in \$)

Then we find u = S+/So = 1,15 let’s say => up move is 15% (more = relative)

Then we find d = S-/So = 0,9 let’s say => down move is 10% (less = relative).

Do you have S, S+, S- values in the example ?

I am note sure, but I think the key here is that u = 1/d if the probability at each node for the next one (going up or down, not the risk-neutral probability) is 50%, then we can assume that u = 1/d.

Yeah I’ve come across these two methods also, CFAI treats a 10% down move as 1 - 0.1 = 0.9 and in fact I haven’t come across a CFAI question yet where they don’t explicitly give both the up and down moves in percentage terms.

I have only seen this 1/U calculation in Schweser.

Im confident that the CFAI will explicitly give both up and down moves.

A down move has to be 1/U as a down move followed by an up move or visa versa has to take you back to where you started.

I would suggest the down move you’ve seen is just slightly dubious rounding.

Unfortunately, this isn’t true.

The up move can be anything and the down move can be anything.

Often people will set the down factor to the reciprocal of the up factor (so that an up movement followed by a down movement returns you to the original price), but that is not necessary. The formulae work correctly no matter what the up and down factors are.

Does this mean that only when one side is provided, we should calculate the other side using d=1/u? Otherwise, we use the percentage up and down moves provided in the question?

If they gave only one of up and down I guess I’d have to assume that the up and down factors are reciprocals of each other. But that’s a stupid way to pose the question.