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  #21  
Old 03-09-2018, 04:04 PM
bannedpianoman bannedpianoman is offline
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Originally Posted by jxl886 View Post
Does anyone think mean*CTE95 as a risk/return metric makes sense? I think it makes sense because we want to minimize both mean and cte95, using this metric would not give you 100% equities as sharpe ratio does, since the cte95 is way higher for 100 equities, the idea behind this mean*cte95 is risk/return tradeoff value.
I originally had that thought process and wound up with something like 40% equities... but my coworkers who all passed on the first try ripped that strategy apart when I was discussing my approach with them. "Non-intuitive" was the message I got from them, and the grader might feel the same way.

I then decided to use mean+(c*s.d.), "c" being a constant. Obviously, lowest metric would be best. The portfolio with the lowest metric wound up having bonds take up a bulk of the portfolio with treasuries and equities evenly splitting the remaining portion.

My coworkers were more accepting of this strategy, and said I should be able to pass Task 2 assuming I explain it effectively.

We'll see if I pass; I'm still waiting on my result. Hopefully this can be a one-and-done thing (this is my first attempt).
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  #22  
Old 03-09-2018, 04:17 PM
arto83 arto83 is offline
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Originally Posted by bannedpianoman View Post
I originally had that thought process and wound up with something like 40% equities... but my coworkers who all passed on the first try ripped that strategy apart when I was discussing my approach with them. "Non-intuitive" was the message I got from them, and the grader might feel the same way.

I then decided to use mean+(c*s.d.), "c" being a constant. Obviously, lowest metric would be best. The portfolio with the lowest metric wound up having bonds take up a bulk of the portfolio with treasuries and equities evenly splitting the remaining portion.

My coworkers were more accepting of this strategy, and said I should be able to pass Task 2 assuming I explain it effectively.

We'll see if I pass; I'm still waiting on my result. Hopefully this can be a one-and-done thing (this is my first attempt).
How did you pick your constant? Was it arbitrary?
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  #23  
Old 03-10-2018, 06:36 PM
rjhav1025 rjhav1025 is offline
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Did anyone set the price as the CTE value, but set the requirements as mean<x and standard deviation <y? My reasoning for this is that the CTE value will be likelier to pay for the costs if the assumptions are not correct.
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  #24  
Old 03-10-2018, 11:21 PM
actuary1122 actuary1122 is offline
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Originally Posted by rjhav1025 View Post
Did anyone set the price as the CTE value, but set the requirements as mean<x and standard deviation <y? My reasoning for this is that the CTE value will be likelier to pay for the costs if the assumptions are not correct.
I'd personally choose to set the tax amount at Var rather than CTE. Var gives you the exact % of scenarios for which the tax contribution amount is sufficient. However, as CTE measures the average tax amount for the worst X% of scenarios, the amount of scenarios that CTE is sufficient for would vary based on the shape of the distribution.

For example, let's assume you set the price at CTE (90). If in the worst 100 scenarios, one scenario has a tax amount of 1000 and the other 99 scenarios have a tax amount of 2000, CTE(90) would be 1990. However, setting the tax at 1990 would mean that CTE(90) would only be sufficient for 90.1% of scenarios. On the other hand, if 99 scenarios have a tax amount of 1000 and 1 scenario has a tax amount of 2000, CTE(90) is 1010. Setting tax at CTE(90) in this case would be sufficient for 99.9% of scenarios. Obviously, these two examples are pretty extreme but it illustrates the point that setting the tax at CTE would lead to a degree of confidence that can't be quantified.

CTE is still useful though and should probably be one of your risk/return requirements (ex: CTE is within X% of the Var to prove that the portfolio does not have a huge tail risk).
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  #25  
Old 03-10-2018, 11:30 PM
rjhav1025 rjhav1025 is offline
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Originally Posted by actuary1122 View Post
I'd personally choose to set the tax amount at Var rather than CTE. Var gives you the exact % of scenarios for which the tax contribution amount is sufficient. However, as CTE measures the average tax amount for the worst X% of scenarios, the amount of scenarios that CTE is sufficient for would vary based on the shape of the distribution.

For example, let's assume you set the price at CTE (90). If in the worst 100 scenarios, one scenario has a tax amount of 1000 and the other 99 scenarios have a tax amount of 2000, CTE(90) would be 1990. However, setting the tax at 1990 would mean that CTE(90) would only be sufficient for 90.1% of scenarios. On the other hand, if 99 scenarios have a tax amount of 1000 and 1 scenario has a tax amount of 2000, CTE(90) is 1010. Setting tax at CTE(90) in this case would be sufficient for 99.9% of scenarios. Obviously, these two examples are pretty extreme but it illustrates the point that setting the tax at CTE would lead to a degree of confidence that can't be quantified.

CTE is still useful though and should probably be one of your risk/return requirements (ex: CTE is within X% of the Var to prove that the portfolio does not have a huge tail risk).
I agree with your premise that the degree of confidence can not be quantified, but the reason for using CTE as the tax amount is so that there is a margin, in the event assumptions are understated. In your example, CTE(90) will cover atleast 90.1% of scenarios, while VaR(90) will cover exactly 90% of scenarios. I'm not sure if the degree of confidence actually matters.
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  #26  
Old 03-10-2018, 11:38 PM
actuary1122 actuary1122 is offline
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Originally Posted by rjhav1025 View Post
I agree with your premise that the degree of confidence can not be quantified, but the reason for using CTE as the tax amount is so that there is a margin, in the event assumptions are understated. In your example, CTE(90) will cover atleast 90.1% of scenarios, while VaR(90) will cover exactly 90% of scenarios. I'm not sure if the degree of confidence actually matters.
Personal preference I guess. By pricing the tax at one of the Var metrics, I am already applying a margin for adverse deviation, and I know exactly what my margin is. With CTE(90), I would be alright if it covers 90.1%, but what about the case where it covers 99.9%? At that point, that would be way too conservative (if it covers 99.9% of the scenarios then that's almost the same as pricing the tax at the max).

A fixed margin also helps in justifying why I chose to use one of 75, 90, or 95 over the other two. I would be able to explain that the percentile I chose gave me a known degree of confidence which provides a sufficient margin for adverse deviation without being overly conservative. With CTE, since the margin can vary, I personally believe it is harder to justify my choice between the 75th, 90th and 95th percentiles. Just my two cents, so if you personally feel more confident with setting the price at CTE then that is what you should do.
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  #27  
Old 03-11-2018, 09:00 AM
rocketprius92 rocketprius92 is offline
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Quote:
Originally Posted by jxl886 View Post
Does anyone think mean*CTE95 as a risk/return metric makes sense? I think it makes sense because we want to minimize both mean and cte95, using this metric would not give you 100% equities as sharpe ratio does, since the cte95 is way higher for 100 equities, the idea behind this mean*cte95 is risk/return tradeoff value.
My only concern is the units. What does squared dollars tell us? I've heard of people using the geometric mean of mean*CTE95, but I think that may be getting too complicated. Not sure.
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