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Basic Question 5 of 7
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%?
B. 58.51%
CD. 61.22%
A. 39.87%
B. 58.51%
CD. 61.22%
User Contributed Comments 17
| User | Comment |
|---|---|
| rockeR | P*100+(1-P)*0-45/45=30%=2.222p-1=0.3 2.222p=1.3 p=0.5851 |
| 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. |
I used your notes and passed ... highly recommended!
Lauren
Learning Outcome Statements
formulate an investment problem as a probability tree and explain the use of conditional expectations in investment application
CFA® 2024 Level I Curriculum, Volume 1, Module 4.