Behavioral Portfolio Theory

Does anyone know how the numbers from the second BPT portfolio are derived in Example 3 page 41 of Volume 2? (Reading 7)

it seems as though the resulting layer allocations are pulled from thin air (i.e 78.43%, 0%, and 21.57%).

never mind, got it

Care to share? I can see how the allocations are determined “given” 6.123% but, don’t we want a 5% return?

I did nto understand this eg. How are the allocations (78.43%, 0%, and 21.57%) deterimed? why layer 2 was not selected? Thanks

This was posted on the old forum… see if it helps you. 1. Assume the second investor puts X amount into Layer 3 and the rest in Layer 1 (2000000 - X). You can find X using the following equation : (2M - X)(1 + 0.01) + X (1 - 0.5) = 1.8M Note that Layer 1 is expected to yield 1% and Layer 3 -50% with 15% prob. Since the first Layer is risk-free, the above allocation should result in 1.8M, which happens to be his safety level, with 15% probability. 2. Solve the equaton for X: X = 431,373 (21.57%) (2M - X) = 1,568,627 (78.43%) - The 2nd investor would get 2,067,451 with 50% prob: 1,568,627 (1 + 0.01) + 431,373 (1+0.12) = 2,067,451 (12% of return given in the vignette) - He’d get 2,339,216 with 35% prob: 1,568,627 (1 + 0.01) + 431,373 (1+0.75) = 2,339,216 (75% of return given in the vignette) You might wonder why the 2nd layer is not being used at all. I bet CFAI won’t draw up a question with more than one unknown :slight_smile: I guess that given the low return on Portfolio 2 - with 4.6% - a better return is obtained with the portfolios layers 1 and 3.

Thanks CP

I think it can be argued that any combination of Layer 2 and Layer 3 is not tractable since we cannot calculate the worst-case scenario with the data given. That leaves us with either Layer 1+2 , Or Layer 1+3.

Since aspirational return is 5%, given 1% return in layer 1 + 4,6% return in Layer 2, this is not attainable.

Then we only have Layer 1 and 3 to work with. But then even with this combination, the answer shows that the aspirational level is not entirely met.

What do you think?

Can you please let me know why would combination of Layer 2 and Layer 3 isn’t tractable. How did you infer that we cannot calculate the worst case scenario with the given data?

Your argument about ignoring the combination of Layer 1 and Layer 3 makes sense to me but not your first statement.

“Since the first Layer is risk-free, the above allocation should result in 1.8M, which happens to be his safety level, with 15% probability”. I don’t understand this part. Why do you equate it to 1.8M? Shouldn’t it be 2.1M which is the aspiration level of second investor?

Also, how is ‘safety objective met’? as it is stated in the solution to vignette in the book?

please read the print before the table drawn on the page… and you see the 12% there on Layer 3 with 50% probability

Layer 1: 1568627

Layer 3: 431373

at a 15% probability: 1568627*1.01+431373*(1-0.5) = 1799999.77 (1800000)

at 50% probability: 1568627*1.01+431373*(1+0.12) = 2067451 (he falls short of the 2100000 aspiration level).

Now your other question: Why use 1800000 -> since he does not want to fall below that level. His maximum level he wants to attain is 2.1 Mill - but he uses his portfolio so as NOT TO FALL below the min level required.

Why can’t they just invest in Layer 2 alone? This way they’d limit loss to $2,037,000 and achieve the 5% return with 80% probability. CFAI doesn’t explain this well.

bcos the return on layer 2 just is not enough…

Portfolio 2 - with 4.6% - is lower than the aspiration level.