behavioral finance blue box question

[VR]

Rain01 wrote:
Hi this post is related to blue box question on page 39 of volume 2 of cfai 2013 book. (reading 7).
I think the asset allocation prescribed for the second investor is not optimal. I also do not understand the “thinking/reasonning” behind arriving at this allocation.
Instead of the solution given if the second investor puts all his money in the second layer. His minimum return would be .97(2000000)= 1940000. This is greater then the minimum amount required of “1800000”. Also he has a 80 percent chance of earnning a 5 percent return and hence have a final wealth of 1.05 (2000000) = 2100000 which is what is required.
Instead the answer given in the book does not even meet all requirements which is mentioned in the solution it self. Hence it is sub optimal in any case then why not go down the route as explained in my answer. can someone please explain

TO the original poster:
The point of this example is to illustrate why the BPT investor will not go for what you have explained as your solution: go for layer 2. Here’s my explanation:
Premise of BPT is that the BPT investor will always shoot for low risk in the safe layer and high risk assets in aspirational layer. The optimal portfolio of a BPT investor is a combination of “bonds or riskless assets” and highly speculative assets (this is described in the previous page in the curriculum before the example). Based on this here’s the math: L1 = investment in layer 1, L3 = investment in layer 3. Equation 1: L1 + L3 = 2 million, Equation 2: 1.01 L1 + (1-0.5) L3 = 1.8 million. Solve these two equations for L1 and L3 and you will get L1 = 1.568627 million L3 = 431,373.
The key to this is BPT investor will always go for L1 (and hence L3 as well) even though he could have just easily invested only in L2 and satisfied his objectives and constraints.
There’s no combination of L1 and L2 that satisfies the equations above (solve using L1 and L2 and you will see L2 weight goes negative).
Hope this helps.

 

[janakisri]

VR has the correct answer. BPT investor builds portfolios with lottery tickets and insurance policies , not a comprehensive constrained mean variance optimized portfolio.
He first builds the riskless layer by considering a mental account which never loses more than 200k at the most. This is the insurance layer . There are NO guarantees in layer 2 , which is a moderate risk layer . there is a guarantee of 1% in layer 1 , which is riskless. An insurance policy invokes a constraint of the wealth never falling below some aspirational level ( in this case 1.8 M). I think you have to read the layer 2 probability of loss carefully . -3% with 10% probability .So 10% loss with what probability ? Is it 0% probability? No. I bet there is some finite probability that it will lose 10% , i.e. wealth falls to below 1800000.
Mr. BPT Investor cannot tolerate this utility point of view . He needs to be sure in riskless layer and totally risky in risky layer
So he builds the risky layer where he aspires to gain 100k. This is the lottery ticket layer.
Here CPK is correct . Aspirationally layer 2 can never provide 5% return , while layer 3 can . BPT Investor has worked with first two of Shefrin/Statman’s 5 factors of BPT Portfolio construction:
1. Allocation to layers depends on goals.More important the goal more the allocation . Here layer 1 has greater allocation ( nearly 4 times layer 3 )
2. Allocation within layer depends on the aspiration for the layer . So the risky layer aspiration of loss is ( absolute maximum ) loss of 200 k , which is 50% of layer 3 allocation.
Allocation within risky layer tries for 5% gain . Layer 2 can only provide 4.6% . Layer 3 can do ~ 25% . Sounds like a lottery ticket

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