# CFAI Vol3 Page 287 Q 12

Re: Monte Carlo simulation related to asset allocation. In the question, why is the 10% line the relevant line and not the 90% line given the fact that the investor wants a 90% probability of achieving the goal. Any MC punters, who can shed some light? Thanks,

trying to remember this quesiton but i believe the 10% line represents the point that 90% of the returns will be better than. So the 10% line is relevant because you care about if its high enough to ensure the investor reaches their goals.

from my memory, it works somewhat like VAR, where it can mean min. loss or max. gain.

well, I agree with you sshank…what you mentioned is basically what the answer template said. But, the question is why do we care about the lowest line if the probability of this occuring (i.e allocation not meeting the reqd return) is only 10% when there is a 90% probability that the other four allocations handily meet the required return. The way, I’m thinking is - if there is a 90% probability that the required return will be met, why do I care so much about the 10% probability of not meeting the required return goal - this is a statistical outlier. But, careerchange you may be right - there is some sort of a VAR or frankly inverted thinking here…if anybody can shed some light it will be very helpful…thanks to both sshank and cchange for the post!!

BUT there isn’t a 90% probability of meeting his goal…if you look at exhibit P-8 the lines are wealth PERCENTILES not probability of achieving a certain portfolio value. Meaning that the 90% percentile is the 10% probability the portfolio will be worth at least \$2,067,044. Where as the 10% percentile is the 90% probability the portfolio will be worth at least \$0 (as they didn’t give a value for the terminal portfolio at the 10% percentile)

that seems to make sense…so the last line is the 10% percentile (what does this mean?) that will be achieved with a 90% probability… thanksmuch

the tenth percentile is the line where 90% of the outcomes are expected to be above that value and 10% are expected to be below the value (similar to VAR). So if someone wants a 90% probability of achieving a portfolio value of \$X, then you want that portfolio value to be above the 10th percentile.