# Reading 7: Example 3 pg 40 CFAI Curriculum

Can anyone please explain how the optimal portfolio for the second BPT investor is constructed? How do you arrive at values of 78.43% to Layer 1 and 21.57% to Layer 3??

For the 2nd investor, the Required return=2.1/2-1=5%

So Layer 2 may not be chosen, since its expected return = 4.6% < 5%. Its worst case is -3%. So it’s allocation between Layer 1 & 3.

1.8m=X*(1+1%) + (2m-X)*(1-50%)

X=1,568,627.

1,568,627/2,000,000=78.4%

Thanks!

Isn’t the expected return for Layer 3, 24.75% (-50%x0.15+12%x0.5+75%x0.35)? Why did you take -50% return for Layer 3?

that 24.75% return after accounting for all the probabilities - is the Expected Return on Layer 3.

However we are trying to find the portfolio that would be able to satisfy the condition -> be able to match the 1.8 Million \$ at the end of the period, at the worst case.

Worst case for Layer 3 - it loses 50%.

Layer 1 is risk free - so earns 1% no matter what.

Layer 2 cannot be select at all.

Thanks a lot cpk123! It’s clear to me now.

The solution has a statement: ‘The portfolio will result in atleast 2,067,451 euros with 85% probability rather then 2,100,000 euros with 80% probability’… Isn’t the probability for 2,067,451 euros 50%?

but look at it from a cumulative probability perspective:

15% -> 1.8 M

50 % = 2.067451

35 % = 2.339216 M

for 50 + 35% of the time = 85% of the time - he has at least 2.067451 M.

Thanks!