behavioral finance blue box question

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Rain01

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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
 
Can you post the whole question, so that we know what we are talking about?
 
well investors can allocate his assets between three “layers”.
The return/probabillity values for each layer is as follows:
Layer 1: 1% return riskless
Layer 2: -3% (10 percent probabillity), 5% (80 percent probabillity), 9% (10 percent probabillity).
Layer 3: -50% (15% probility), 12% (50% probability), 75% (35% probability)
Investor has 2000000 dollars. Has aspiration of 2100000 with 80% probability. Investor cannot tolerate total portfolio declining below 1800000.
solution says. invest 78.43 in layer 1 and the rest in layer 3. The answer itself says this meets the safety objective (minimum wealth objective) but does not meet 2100000 with 80 percent probability objective. But this is apprantely propsed as “best possiblle” answer and the investor needs to lower his safety objective if he is lookin for a better outcome.
I say just put all money in layer 2 and all requirements are met.. So i do not understand why above answer is given.
 
all requirements are NOT Met by layer 2.
E(R) = Sum(Prob*E(R)) = 4.6% which is less than 5% required.
 
Layer 1 is riskless - so it meets the requirements.
Layer 3 - provides with an E(R) of 24.75% which meets the requirements.
 
there is no requirement anywhere which says that expected return should be 5%. Requirements are:
1) Portfolio should not fall below 1800000
2) Aspiration of 2100000 with 80% probability
There is no other requirement. and these requirements are delivered by layer 2. and not by the suggested portfolio of layer 1 and layer 3
 
5% required comes from (2100-2000)/2000 - the aspiration level that you are talking about.
go from there first… so on a minimum level the portfolio must satisfy the 5% return - which Layer 2 does not.
Layer 1 is riskless - so it can be used all the time even if the return is only 1%.
Layer 3 is Risky - but meets the Return requirement.
So Layer 1 and 3 will comprise the BPT Investor 2’s needs. Layer 2 will not.
 
“so on a minimum level the portfolio must satisfy the 5% return - which Layer 2 does not.” there is no such statement in the question.
i know where 5% comes from. IF you want to talk in % return terms, the question statement in the book implies:
“there should be atleast 80% probability of a 5% return”. it does not NOT say “so on a minimum level the portfolio must satisfy the 5% return”.
If there any such statement in the book, it will be really helpful if you can quote that line from the question statement.
 
his aspiration levels is 2.1 Mill$ - so he requires a 5% return at 80% probability.
Given the -3% at 10% probability - the layer 2 would not meet that requirement. The other two probabilities 5% (80 percent probabillity), 9% (10 percent probabillity) only provide him with 4.9% at 90% probability. Now do you get it?
 
his aspiration levels is 2.1 Mill$ - so he requires a 5% return at 80% probability.
I agree with this statement
If he selects layer 2. there are 3 states of the world only and for our purpose they can be converted into 2 states of the world.
So lets says he selects layer 2.
1) The other two probabilities 5% (80 percent probabillity), 9% (10 percent probabillity) only provide him with 4.9% at 90% probability. That is not correct:There is a 90 percent chance that he will earn atleast 5%. (80 percent chance of 5% return and 10% chance of 9% return). FIRST CONDITION SATISFIED.
2) There is a 10 percent chance that he will earn -3%. So his minimum porfolio value is .97 * 2000000 = 1940000. 1940000 > 1800000 so SECOND CONDITION OF MINIMUM PORTFOLIO RETRUN OF 1800000 IS ALSO SATISFIED.
I dont know why you keeep giving me expected return calculations. who said anything about expected return or requiring a expected return. all that was said was that the portfolio should not fall below amount 1800000 and there should be atleast 80 percent chance of earning 21 mil.
Forget about the suggested answer in the book. just read the question and figure out what it is asking for and then see which answer is correct
 
It is not suggested answer in the book I am going by. He is a BPT Investor. Read the first para on Pg 38. BPT uses a Probability weighting function. In BPT Investors construct a portfolio in layers and expectation of returns and attitudes toward risk vary between the layers.
So Given statement 1 - probability weighted expected return (For entire layer) is what he will use. So 4.9% is the number and not the minimum probability and return that you have shown above. An Entire layer would either be selected or rejected based on the E(R) seen (which is Prob * return in the particular level within the layer).
And last line in Pg 38 Risk Aversion of investor is taken into account by constraint that limits risk of failing to achieve the aspirational level of wealth. At 80% probability - he will not achieve the 5% aspirational return.
He needs to be able to select Layer 2 first to go by whatever else you are saying above.
 
ok cpk. i understand what you are saying here but i feel there is a contradiction here. let me give you a small example:
lets assume layer 1: 95% probability of 4% return and 5% probability of 50% return.
The Exepcted return is: .95*4 + .05*50 = 3.8 + 2.5 = 9.5% return.
In this layer the expected return is greater than 5% but the “probabillity of of the return being greater or equal to 5% is only 5%”.
So if this was one of the layers in the question and you went by expeceted return calculation then you would have the wrong answer because the probability of a return being greater 5% HAS to be atleast 80% as explicitly stated in the investor preference and here it is only 5%.
Moreover given your arguement about investor looks at ER AND RISK. In this specific question he has NOT expressed his preference in terms of EXPECTED RETURN AND RISK. The only 2 things he has said i have already stated in previous post. So we cant enforce something which he did not say. How can you convert:
1) Portfolio should not fall below 1800000
2) Aspiration of 2100000 with 80% probability
How can you magically CONVERT the above two statements into saying that he wants expeceted return of 5%. HE did not say that!. The two things are not the same and there is no law which can make them equivalent. If he did express his preference in Er and risk we could have taken that into account but he simply did not say that regardless of what he should or should not have done according to theory.
 
Rain01 wrote:
…..
Moreover given your arguement about investor looks at ER AND RISK. In this specific question he has NOT expressed his preference in terms of EXPECTED RETURN AND RISK. The only 2 things he has said i have already stated in previous post. So we cant enforce something which he did not say. How can you convert:
…..
Click to expand...
[1] the investor is a BPT investor, so looking at returtns/risk is not surprising
[2] the layers are defined in terms of risk/return/probabilities, so you need to convert money terms into returns
[3] there is nothing magical about converting nominal prices into returns
 
please reread my post.
1) the investor is a BPT investor, so looking at returtns/risk is not surprising:
I did not argue with what should be looked at. I only stated looking at the information given and taking it for what it is.
2) the layers are defined in terms of risk/return/probabilities, so you need to convert money terms into returns
I did not argue with how layers are defined. I argued with how preferences were defined in this specific/particular case. and they are not defined in terms of expected return and cannot be converted into expected return, given the information given.
3) there is nothing magical about converting nominal prices into returns
I have no idea where this came from. What i said was it is not possible to convert the expressed preference of investor into an equivalent expected return requirement. In other words two statements below cannot be converetd into an equivalent expected return requirement. If yes, i would be most interested to know how.
1) Portfolio should not fall below 1800000
2) Aspiration of 2100000 with 80% probability
4) lastly there is a contradiction in using expected return metric in this specific case:
example:
lets assume layer 1: 95% probability of 4% return and 5% probability of 50% return.
The Exepcted return is: .95*4 + .05*50 = 3.8 + 2.5 = 9.5% return.
In this layer the expected return is greater than 5% but the “probabillity of of the return being greater or equal to 5% is only 5%”.
So if this was one of the layers in the question and you went by expeceted return calculation then you would have the wrong answer because the probability of a return being greater 5% HAS to be atleast 80% as explicitly stated in the investor preference and here it is only 5%.
 
somehow…i think you are overthinking this…keep it simple mate,cpk has answered all there is
 
Rain01 wrote:
lets assume layer 1: 95% probability of 4% return and 5% probability of 50% return.
The Exepcted return is: .95*4 + .05*50 = 3.8 + 2.5 = 9.5% return.
Click to expand...
I thought 3.8 + 2.5 was 6.3… but I might be wrong.
 
lol yes you are right cirkon. my mistake. But the point is still valid.
 
Rain01 wrote:
lets assume layer 1: 95% probability of 4% return and 5% probability of 50% return.
The Exepcted return is: .95*4 + .05*50 = 3.8 + 2.5 = 9.5% return.
In this layer the expected return is greater than 5% but the “probabillity of of the return being greater or equal to 5% is only 5%”.
So if this was one of the layers in the question and you went by expeceted return calculation then you would have the wrong answer because the probability of a return being greater 5% HAS to be atleast 80% as explicitly stated in the investor preference and here it is only 5%.
Click to expand...
I might be completely wrong, but I’d look at it another way:
You have a portfolio where you invest $100. The portfolio comprises 2 assets - one yields 4% and the other yields 50%. You have $95 invested in the first one and $5 in the second one respectively. You CANNOT rebalance or choose only one asset to invest - you have to take the whole portfolio with its weights and returns. Your aspiration is $105 after a year. Does this portfolio meet your requirements (based on expectations, of course..). What is your expected return? The answer is $6.3 (or 6.3%). So the answer is YES. It meets your requirements as you get $106.3 after one year, and you wished for $105. Hope it helps you.
 
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