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%?

A. 39.87%
B. 58.51%
CD. 61.22%
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

User Comment
rockeR P*100+(1-P)*0-45/45=30%=2.222p-1=0.3


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[100] + [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.
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