Reading 7: Example 3 pg 40 CFAI Curriculum

[samiah.khngamil.com]

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??

 

[cpk123]

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%

 

[samiah.khngamil.com]

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?

 

[cpk123]

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.

 

[samiah.khngamil.com]

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%?

 

[cpk123]

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.