# CFAI Book 2: Example 3 pg. 40 Behavioral Portfolio Theory

Hi All-

The Blue Box on page 40 on Behavioral Portfolio Theory - how are the 1,568,627 and 431,373 derived?

Someone else asked the same question but copied the whole thing from the CFA text so it got taken down by the moderator, but my explanation is below (if its a little confusing let me know… My lack of ability to explain things properly is probably one of the key reasons I am resitting level 3):

The first portfolio will need to be invested in 100% riskless assets as the client will not accept any loss.

For the second you need to work out the expected return for each level. Riskless is easy as it is 1%, when you calculate layer 2 (moderately risky investments) you will find the return is 4.6% (-.03*.1 + .05*.8 + .09*.1), which is below the return objective. Knowing that you need to achieve 5% you can eliminate this layer. Next you work out layer 3 return (the risky layer) which works out at 24.75% (same math as before).

With the above you know you can work this out from the riskless and risky layers. Remember that there is a possibility that you could lose 50% of the value with layer three so your split between layers 1 and 3 needs to work so that initial investment is (layer 1*1.01 + layer 3 *.5) = 1,800,000 remembering layer 3 will equal (2,000,000-layer 1). Once you have substituted this in you should get (layer 1*1.01)+((2,000,000-layer 1)*.5) = 1,800,000, which you can rearrange to get the amount required for layer 1 and then 2,000,000- layer 1 amount will give you layer 3.

(x*1.01)+((2,000,000-x)*.5)=1,800,000

(x*1.01)+(1,000,000-.5x)=1,800,000

x*1.01-.5x=800,000

.51x=800,000

x=1,568,627

Rob_84 - really appreciate the explanation. Thanks so much!

Rob_84 - I appreciate this as well. PLEASE tell me that the rest of the CFAI blue boxes will not be as short on explanation. Or is the Institute trying to convince me that I’m unworthy since I couldn’t figure it out? Maybe my brain is just slow to reboot after my CFA summer vacation.

I’m glad I passed this stuff

+1

Dear all

I got the numbers with the repartition of the layers,but I’m not sure I understand their probability calculation at the end.

Would it be safe to say that you weight the probabilies?

ie 0.76 x 100% plus 0.24 x 0.50 ??

They state that “portfolio will result in 1800000 euros with 15 pct probability, 2067451 euros with 50 percent probability…” … and then later they state

“The Portfolio will result in at least 2067451 euros with 85 percent probability…” how can this be ?

Pls ???

You need to look at it from cumulative prob perspective for this one.

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.

I am trying to understand this Example based on the explanation you have provided. And it is much better than the one in curriculam. Can you please explain why did you multiply 2M - x with 0.5? You have mentioned - Remember that there is a possibility that you could lose 50% of the value with layer three…

But, which part of the question states that you could loose 50%??