Bk 2 Pg 41-42:Behavioural Portfolio Theory Example
- Thread starter Semacks
- Start date
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
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
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
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
- Thread starter
- #3
Perfect, i understand it now. My confusion in the first place was on why the 2nd layer was not used at all. Tracking back to the CFAI text on page 41, maybe the answer lies here…”As a result, the optimal portfolio of a BPT investor is a combination of bonds/riskless assets and ‘highly speculative’ assets”
second risky investment offers an “insurance policy” that covers losses above 3 percent while the investor can tolerate losses from 0 to 10% . And the lottery ticket in second risky investment has an 80% guarantee of only 5% gain when he desires 10% . So 2nd investment is not suitable anyway, even when 100% is invested in it ( neither insurance policy nor lottery ticket is suitable )
. That leaves only the third investment.
. That leaves only the third investment.
is this correct?
aspirational return :
(2100000-2000000)/2000000=5%
Layer 2 provides an expected return of (100% investment)
-0.03*0.1+0.05*0.8+0.09*0.1=4.6% which is less than aspirational return
Layer 3 provides an expected return of(100%investment)
-0.5*0.15+0.12*0.5+0.75*0.35=24.75% which is greater than aspirational return
…So we discard Layer 2 completely because a 100 % investment in it would yield less than the aspirational return ?
thx for any help
thx
aspirational return :
(2100000-2000000)/2000000=5%
Layer 2 provides an expected return of (100% investment)
-0.03*0.1+0.05*0.8+0.09*0.1=4.6% which is less than aspirational return
Layer 3 provides an expected return of(100%investment)
-0.5*0.15+0.12*0.5+0.75*0.35=24.75% which is greater than aspirational return
…So we discard Layer 2 completely because a 100 % investment in it would yield less than the aspirational return ?
thx for any help
thx
Janakisri and Alladin might be interested about the following email, that I just sent the CFA institute.
Subject: possible error in Behavioural Portfolio Theory - CFA level 3 2014, book 2, page 40, reading 7, example 3.
Good evening,
I was working out the example 3 in reading 7 of the CFA-level 3 course (page 40 in book2)
I happen to find a different result from the one suggested in the solution, and I thought you might want to investigate this.
The question is to calculate a portfolio as per Behavioural Portfolio Theory, along 3 layers.
As per the book, the answer for the investor 1 is “approximately 100 percent in the layer of riskless investment”. I agree with this, the exact answer is to allocate 1,960,784 euro in layer 1 (98.04%) and 39,216 euro in layer 3, for a total of 2 millions.
However, for the investor 2 the book suggests to allocate 78.43% in layer 1, 0% in layer 2 and 21.57% in layer 3. Additionally, says the book, “the safety objective is met, but the portfolio is short of the aspirational goal”.
My own calculation suggests that by allocating 612,500 euro in layer 1 (30.63%), 1,037,500 euro in layer 2 (51.88%) and 350,00 euros in layer 3 (17.50%), we get a portfolio allocation that fill both the safety objective and the aspirational goal. This portfolio is optimal and yields an expected return of 7.02%.
I can provide my calculation spreadsheet on request.
Best regards,
YAG
Subject: possible error in Behavioural Portfolio Theory - CFA level 3 2014, book 2, page 40, reading 7, example 3.
Good evening,
I was working out the example 3 in reading 7 of the CFA-level 3 course (page 40 in book2)
I happen to find a different result from the one suggested in the solution, and I thought you might want to investigate this.
The question is to calculate a portfolio as per Behavioural Portfolio Theory, along 3 layers.
As per the book, the answer for the investor 1 is “approximately 100 percent in the layer of riskless investment”. I agree with this, the exact answer is to allocate 1,960,784 euro in layer 1 (98.04%) and 39,216 euro in layer 3, for a total of 2 millions.
However, for the investor 2 the book suggests to allocate 78.43% in layer 1, 0% in layer 2 and 21.57% in layer 3. Additionally, says the book, “the safety objective is met, but the portfolio is short of the aspirational goal”.
My own calculation suggests that by allocating 612,500 euro in layer 1 (30.63%), 1,037,500 euro in layer 2 (51.88%) and 350,00 euros in layer 3 (17.50%), we get a portfolio allocation that fill both the safety objective and the aspirational goal. This portfolio is optimal and yields an expected return of 7.02%.
I can provide my calculation spreadsheet on request.
Best regards,
YAG
yag - point you forgot - he will never invest in Layer 2 - because it falls short of the aspirational goal of 5%. It earns only 4.6%. So while your calculation was fine, and possibly right - it DOES NOT MEET THE FIRST REQUIREMENT that the portfolio layer must be able to satisfy the requirements.
and this part
As per the book, the answer for the investor 1 is “approximately 100 percent in the layer of riskless investment”. I agree with this, the exact answer is to allocate 1,960,784 euro in layer 1 (98.04%) and 39,216 euro in layer 3, for a total of 2 millions.
is also incorrect. he will invest 100% in layer 1, period.
As per the book, the answer for the investor 1 is “approximately 100 percent in the layer of riskless investment”. I agree with this, the exact answer is to allocate 1,960,784 euro in layer 1 (98.04%) and 39,216 euro in layer 3, for a total of 2 millions.
is also incorrect. he will invest 100% in layer 1, period.
Hi cpk123
As regards your first comment, I’m not sure that I am right, but as regards your second comment, I am sure you’re wrong
The book itself says “approximately 100%”, and that is clearly different from “100% in layer 1, period”.
For the first point, the book does not exclude layers just because of the aspirational requirement. However, I reckon the book langage might suggest to use only 2 layers, see paragraph mentionned by Semacks above. This sounds to me inconsistent with the rest of theory and mathematically unreasonable (why disqualify a proven, mathematically-correct solution?). We’ll see. No big deal, it’s pretty unlikely the exam will ask for such a 3-layer optimisation.
As regards your first comment, I’m not sure that I am right, but as regards your second comment, I am sure you’re wrong
The book itself says “approximately 100%”, and that is clearly different from “100% in layer 1, period”.
For the first point, the book does not exclude layers just because of the aspirational requirement. However, I reckon the book langage might suggest to use only 2 layers, see paragraph mentionned by Semacks above. This sounds to me inconsistent with the rest of theory and mathematically unreasonable (why disqualify a proven, mathematically-correct solution?). We’ll see. No big deal, it’s pretty unlikely the exam will ask for such a 3-layer optimisation.