CFA Practice Question
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CFA Practice Question
A derivative security pays $100 if the Dow Jones Industrial Average shows a 15% return over the next year and does not pay anything if the return is lower. If the security costs $45 and its expected return is 30%, what's the probability that the Dow Jones return will exceed 15%?
Correct Answer: B
If p is the probability of the Dow Jones return exceeding 15%, then the expected total return on the derivative security is (p * 100 + (1 - p)*0)/45 = 2.222p. Since the expected return is given as 30%, we get 2.22p = 1.3. Therefore, p = 1.3/2.222 = 58.51%.
User Contributed Comments 17
|katybo||($45*1.3)/100 = 58.5% ??|
|stefdunk||either calculation is correct. Note that in answer B, 0.001% is due to rounding|
|sunilcfa||If the second formula is correct then it means that 15% DJIA return has no relevance. I dont think the second formula is correct.|
|surob||I think both of them are correct approaches.|
|mirfanrana||there is no relevence of 15% in 1st formula also|
|quantwannabe||15% is just a condition that is given for whether derivative pays $100 or not.
|soarer1||Can someone please explain steps and where 2.222p came from?|
|StanleyMo||here is what i think:
Your expected retun of cost = expected money earn
so, 45 * 1.3 = P + [1-P]0
Where P = probability DJ > 15%
P = 58.5/100 = 0.585 = 58.5%
If you expected return has increase to let say 60%, then you should also expect the probability of DJ > 15% increase as well. Hope this help.
|dobrekone||the future value of the security:
FV = 45*(1+0.3)
the expected payoff (PO) has to be equal to the FV:
PO = 100*p - 0*(1-p) = 100*p
FV = PO i,e:
45*1.3 = 100*p
p = 58.5/100 = 0.585
|mountaingoat||if p = probability rtn > 15% and pays $100
and (1-p) = probability rtn < or = 15% and pays $0.
isn't this inconsistent with the question? I thought it stated that if the rtn > or = 15% it paid $100 and ONLY paid $0 if the rtn < 15%. therefore shouldn't we have 3 probabilities. 1st for rtn > 15%, 2nd for rtn = 15%, and a 3rd for rtn < 15%?
|k1731477||you can do it backwards too if you just use the multiple choice answers.
if you plug in 100(.5851)+0(.4149) / (1 + .3) = 45. since you get the price given in the question it is the right probability. Kind of cheap way to do it but it solves the problem.
|dealer80||thx stanleyMo good explanation|
|elmagico10||thanks StanleyMo, good explanation|
|dbedford||How are we going from expected return is .3 to 1.3|
|dbedford||Nm it's a FV = PV(1+r)^n|
|REllis||So to solve this, I did PV = -45 I/Y = 30 N=1 PMT = 0 then CPT FV= 58.5. Didnt even use probability.|