In section 6.1 of reading 49, the CFA book says (if you hover on 21 in eBook or see footnote 21 in hardcopy) below whlle explaining why 1+r should be greater than d and less than u
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d is downward move i.e. say asset of $100 goes down to $98. d is 1 plus the rate of return on downside move. Rate of return on downside move will always be -ve i.e. in this case -2.0% and accordingly d will be 1 + (-0.02) i.e. 0.98. Now risk free rate is by and large +ve so d will naturally be always less than 1+r.
I didn’t get why CFA book is saying that 'To avoid an obvious arbitrage opportunity, we require that d < 1+r < u when d can never be greater that 1+r.
Can anyone explain the relevance of what CFA book is trying to say. I never found CFA saying useless things so must be something I am missing to understand.
Thanks,
Ca
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Not sure I fully understand your question, but if you’re asking why the down movement (d) must be less than 1 + r, you’ve actually already answered your own question.
If d was greater than 1 + r, we would say 1 + r < d < u and we are using these movements to determine price of the possible moves. If the equation above was true, no matter if the asset had a down movement or up movement, the value of the asset at the next time node would be greater than the cost of borrowing - asset price( 1 + r) - we would be able to buy the underlying asset by borrowing at the risk free rate and generate a return at the next node greater than the risk free rate itself.
I’m thinking you’re just over thinking this and the wording of the CFAI material isnt always crystal clear. It’s essentially stating the obvious, but in a manner that can cause some confusion.