Task 2

[HD]

Discussions for task 2 of the CDEF scenario.

[Jared]

It would seem that most of the people that fail have task 2 included in their list of tasks to improve.

(8 out of the last 10 failures on the spreadsheet specified task 2)

I'm looking up information right now, but I might need some help seeing as I have not yet seen exactly what is asked in Task 2.

[Jared]

For anyone that hasn't noticed the Task 2 thread going on in the outpost, here's what started it all off:

https://www.casact.org/education/ratesem/2007/handouts/bingham2.ppt

This slideshow seems like a pretty useful resource. It covers the basics of risk/return.

[Jared]

Here's an introduction to some of the terminology that seems to be used in Task 2:

VaR (Value at Risk): This is basically a glorified percentile. VaR(90) refers to the 90th percentile.

Using exam P terminology:

F(x) = 0.9 when X = VaR(90)

CTE (Conditional Tail Expectation): This is the expected value above a certain percentile.

Using exam P terminology:

CTE(90) = E[X | x > VaR(90)]

*post above deleted due to typo*

[Austin]

Have a look at this post. We really need to understand the terminology of Risk/Return Metric and tackle Task 2 carefully in order to pass this.

Risk/Return Metric: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=330243

Anyone has extra idea on top of this?

[said.t...@gmail.com]

Task 2 _ Question 2

I am confused about using risk/return metric

- Risk     = Volatility (Standard Deviation) Or CTE (  Not VaR becasue it is just a quantile )
- Return = mean

Then metric can be either :
1)  Coefficient of Variation=standard deviation / mean    , Interpretation : minimize contribution amount with minium variability , is that right ?
Or 
2) CTE/ mean    Interpretation : I Don't know ! Anyone can give me a suggestion please !


Which risk/return metric should we use ?
We should recommend only 1 metric or 2 metrics ?

[DM]

The risk/return requirement is something everyone seems to fret about (including me).  I personally used Coefficient of Variation last time as a risk metric and got DNMMR.  That said, I don't necessarily think CV was a bad metric to use, and I'm not sure if I'm going to use it again or try something different.  People have passed with various use of metrics (1 metric from the model, 2 metrics from the model, a ratio of metrics from the model).

I'm going to focus this time through on a more qualitative discussion for question 2 of this task.  For me personally, I think I may have been two quantitative on my previous submission and my risk limit I placed on my metric felt ended up being quite arbitrary.  I think it is quite difficult (given the model and metrics available in it) to not be arbitrary in setting a numerical parameter for risk or return.  I think it is important to provide a discussion in question 2 that focuses heavily on the four bullet objectives of the CDEF, the general background information of the assignment about the fund/CDEF and the risks identified in task 1.  

[Tai duong dang]

To me, the risk/return metrics can be flexible per your adjustment and knowledge, however I think you should have the pros and cons of the metrics, how they fit the CDEF case. Or you even discuss ab the risk metric us till ok, I have some friends pass who only discussed ab tisk metric. Given said that, maybe it dont direct to the requirements of question 1-2. But I think it is more important on the question 3-4, how you give a recommendation and defend it.
Any thoughts ?

[DM]

*too quantitative not "two"...  sorry it really bothered me that I used the wrong one!

[said.t...@gmail.com]

Questions 1 and 2 are qualitative
Questions 3 and 4 are quantitative

[DM]

I agree with you, said.t...@gmail.com.  This thread (http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=330272#post9252393) phrases a question about if the response to question 2 should be "general/generic" or "more specific".  By "specific" they mean setting actual numerical values in question 2.  The few who did respond to the question all concurred that there should be a "specific" (i.e. numerical parameter set against some metric) answer in question 2.  I think this mindset previously led me too quickly to move into the quantitative part without a full qualitative discussion of question 2.  I think the risk/return requirements don't necessarily have to be numerical yet in addressing question 2, but certainly things turn quantitative as we move into question 3.

[Katherine Garner]

From that Sir Isaac AO post, it's suggested that the Sharpe ratio is used as the risk/return ratio. I understand the ratio in regards to rate of return but having some trouble applying it to our spreadsheet that uses "Cost per Employed Persons" rather than return on portfolio. 

[Jared]

Like Katherine, I'm having difficulty with that too.

I know that cost per person and rate of return are inversely related, but it's can't possibly be a Y = c/X type of deal, where Y is the sharpe ratio, X is cost per person, and c is some constant.

[Katherine Garner]

This post helped clarify!

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=330243&page=4

[3rdtimesacharm]

I failed this already, but here's my thought:

1) i used a metric by incorporating CTE and Mean together. I think this is fine, but...i didnt' discuss the cons of this risk metric, just the pros. I will now discuss the cons of it

2) The AO discussions made me think that I also should discuss the pros/cons other risk metrics such as CoV and sharpe ratio. I think choosing any risk/return metric is fine, but the discussion in that AO thread about using the sharpe ratio by solving the risk free rate i think is outside the scope of this problem.

3) One thing i'm still failing to understand is how to choose the a contribution amount after choosing an asset allocation. I just picked the mean. Anyone have thoughts on this???

[rebec...@gmail.com]

I failed 2 as well but I think the idea is that your contribution amount needs to reflect your investment strategy. If you picked mean, why did you pick the mean and not some other value? If your investment strategy is more on the conservative side than you want your payroll tax to be something on the higher end to cover most scenarios. If your investment strategy is more balanced , taking on some risk to lessen the burden on the tax payer than your payroll tax can be lower. I don't think there is any right answer you just need to pick something and justify it so that it is in line with the key risks, objectives and your overall strategy. I used mean * 5% margin last time. This time i am using VaR (75) . It actually gets me to the same amount pretty much but I can justify VaR much more than some arbitrary 5%. I also mentioned why I didn't use VaR(90) to show that I considered something else and did not just pick a number.

[Zoo Keeper]

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=330243&page=4

I agree with Katherine. There's some quite helpful info in this post.

[Katherine Garner]

I decided to use the geometric mean of the mean and the CTE(95). 

[3rdtimesacharm]

Can I ask for your general logical behind using the geometric mean of CTE(95) and mean? seems a little arbitrary

[Katherine Garner]

I do think the relationship between CTE and Mean is significant but I didn't like how the AO suggested using Mean/CTE because dividing by a high CTE will actually lower that value which is not what I would want to do since you want to minimize both the Mean and the CTE. That is why that ratio still said that 100% equity is ideal. So I figured if I just took the average of the two, it wouldn't give that false minimization like the ratio did. My idea was right because the portfolio that ended up winning was 75/25 equity/bonds which is much more reasonable than 100% equity.

[Jared]

People kept bringing up the Sharpe Ratio, and it made me wonder if the SOA would accept it, because you can kinda-sorta derive it using the metrics given.

Sharpe Ratio = (alpha - r) / sigma

We are not given alpha, nor r, nor sigma.

However, we are given certain parameters:

-Mean cost of selected portfolio

-Mean cost of T-Note-based portfolio

-Standard deviation of cost

alpha is negatively correlated to mean cost of selected portfolio (in other words, alpha ~ -1 * cost_of_selected)

r is negatively correlated to the mean cost of the 100% t-note portfolio (r ~ -1 * cost_of_tnoteportfolio)

sigma is positively correlated to the standard deviation of the cost of the portfolio (sigma ~ -1 * stand_dev)

sub in the new parameters and you get the formula that Sir Isaac mentioned in the thread linked to above,

The Sharpe Ratio can more-or-less be represented using (Cost of T-Note portfolio - Cost of Selected Portfolio)/(Stand Dev. of Selected Portfolio).

-----------------------------------------------------------------------------------

If you feel uncomfortable doing this, I think the point is for you to use at least two metrics, one of them measuring risk and the other measuring return.

The whole point of step 1 in task 2 was for us to understand that NO SINGLE MEASURE WILL BE ADEQUATE.

Find one that measures risk, find another one that measures return, and figure out how the minimum/maximum of their product/divisor to determine the "best" portfolio. At this point, I'm 95% certain that's what the SOA wants us to do.

[Eduardo Sebayan]

Hi, I am a little late to the party, but I have a lingering question.

The first question asks about the pros/cons of the available risk/return metrics. It seems like most are saying we should discuss the ten in the excel worksheet. However, I am not sure Mean, Max, and Min are really measuring risk?  I think of them as statistics about the data. 

Can anyone indicate where in the FAP they discuss risk/return metrics? 

Thanks!

[Eduardo Sebayan]

Hi Jared, 

I was typing my question before I saw your comment, and I think you clarified my first question! Thanks!

Ed

[Katherine Garner]

Hi Jared, I used that same sharpe ratio formula before in my workbook but still had the issue of 100% Equity being superior to the other asset mixes. 

[HD]

Great clarification Jared, I think you narrowed down the main reason why people fail 2 most often.

Katherine, I think it's hard to pick any reasonable risk/return metric and not have a high equity allocation. That may be where the SOA wants us to pick a limit to how much equities the portfolio should have based on the investment goals of the investment committee (specifically, ensure CDEF meets daily financial obligations), and justify it.

[Jared]

I just noticed something GLARINGLY wrong with the results of the model.

I don't want to just give this away, but think:

1) Are any assets correlated to each other?

2) If so, is it a positive or negative correlation?
3) What's happening to the standard deviation when these assets are combined?

4) What should be happening to the standard deviation when these assets are combined, given the underlying correlation between the two (or lack thereof)?

[said.t...@gmail.com]

Jared,

1) For the Question 3 in the Task 2 , we should look for the ASSUMPTIONS that are interrelated and not for the ASSETS.

For example : to look if The assumption of the attrition rate is related to Unemployment or Employment population ?

Or something like that...

[said.t...@gmail.com]

DID the investment committee set a rate for their investment goals. For example , did they said that maximum of equities of 20 % ?
Because I don't see any informations avout their investment goals ! Only the sample Investment policy is available.

[HD]

No specific rates for investment goals, just a sample investment policy and a qualitative description of their objectives.

[Jared]

Dang... I was going to try to record a macro to have the spreadsheet iterate through a ton of asset mixes and record the results but VBA is password-protected. That's really unfortunate.

[Katherine Garner]

Yeah lol I tried doing that too. They def setup these files so that you only see what they want you to see.

[HD]

I added 20 extra run numbers so I can enter 30 different asset mixes to see the effects on the results at the same time.

[Eduardo Sebayan]

I am also thinking that the best course of action is to minimize the CTE(95) (since I believe the main goal is to be solvent, in that they want to be able to provide for all students going to college) and also minimize the mean (you want to be able to pay the least given a minimum CTE)

However, not sure how to combine those. I do tend to agree an average seems to make more sense then a ratio, but I am still unsure. I might just go with an average, and come back to this if I have second thoughts. I need to move on to the next task, I feel like I'm falling behind! 

[JL]

just run several scenarios, you will see a pattern, the CTE95 wont change much but the Mean would, among those scenarios, pick something you find reasonable.

[JL]

I have a question regarding the part 2, asking for the risk/return requirements. I am thinking to run couple senarios and then get the numbers from CTE/VaR, and Mean, then just BS a range based on these numbers? like CTE +-30 will be the requirement, something like that? wouldnt that be just couple sentences for this part? am i missing something here? 

[Andrew Taggart]

In response to the comment that involved this thread: 

http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=330272#post9252393

In that thread they talk about how you can't calculate a needed return rate but I don't think that is true.  The return rates and cost per employed person are indeed from the last of 1000 scenarios run but you can easily just change the cost per employed person number and then set all of the returns to the same number and adjust the return amounts until the ending balance is as close to 0 as possible to find the return needed to keep the fund solvent.  Does this make sense?  As long as you have your final asset mix and proposed cost per employed person numbers input into the model page correctly I think it should work.

[JL]

I think you are over thinking it. my understanding is that the cost per employed person is solved by goal seek, which already makes sure the fund is solvent. in other words, the returned tax amount is the minimum amount the keeps the fund solvent. 

[Andrew Taggart]

Yes, I understand that.  I'm saying you can solve for the required return amount based on your proposed cost per employee by plugging that in with the correct asset allocation and then guess and checking the return on assets until the ending balance is as close to $0 as possible.

[DM]

I've had the same thought, Andrew.  I do ultimately think you may be able to use it that way to solve for a return amount, but I haven't attempted it because I think is going well beyond what the graders are looking for.  I think one of the best pieces of advice I've heard thus far regarding the FA is essentially "answer the questions directly and provide nothing more and nothing less"  That seems like really simple advice, but is actually quite challenging to do...  I've struggled with finding that balance for sure.  I think in this case, the suggestion of using the model to back into a required return is beyond what they want to see when grading and won't help much for getting a passing grade.

[Tai duong dang]

How do you guys think about risk coverage ratio. This can incorporate the CTE and present the tail risk.

[Katherine Garner]

What portfolio performs best under the rcr?

[Andrew Taggart]

I agree with you not to add to much beyond what is asked but I had initially used this as part of my answer to question 2 under the task rather than some arbitrary amount for my metric.  How did you all set a requirement for your metric (Sharpe ratio, CoV, etc.)?  I instead set out a return requirement with a range of what the return can be, setting one higher than the minimum required so they can have some off years.

[Jared]

I've come to the conclusion that it's not *what* we decide to use as a metric, but rather:

1) Does it account for both risk and return?

2) Did you explain how it accounts for both risk and return?

Convince the grader that you evaluated both risk and return, not that you thought of "the best risk measure ever thought of on the FA". Your goal is not to impress them with ingenuity. Just convince them that you appropriately considered what the question asks, recommend a portfolio, and back it up.

I got a bit hung up on this earlier on, and it's not worth your time.

[3rdtimesacharm]

This probably was discussed at some point in Sir Isaac's AO thread, but what do you guys think about discussing pros/cons of multiple risk return metrics. So i first discussed the pros/cons of mean/min/max/std/var/cte. After that I discussed the pros/cons of CV, Sharpe ratio, and then i ended up choosing my own risk/return ratio. Do you guys think discussing the sharpe ratio and CV are superfluous considering i don't use them and that they're technically not "available metrics"?

[Jason]

Im personally discussing pros/cons of each of the metrics in the <Results> tab as well as my risk/reward metric. Sir Issac said he only discussed the metrics in <Results> tab here: http://www.actuarialoutpost.com/actuarial_discussion_forum/showthread.php?t=330243&page=3

How technical are you guys being with the pros and cons? I know this memo is to an actuary so it can be somewhat technical but I don't think it's justified to get too statistical proof-y. 

[Anika]

I'm only discussing the pros/cons of the individual metrics in the <Results> tab. Not being too technical. In each one of the cons I'm saying something like: risk/reward cannot be measured accurately with this metric alone because it's only a measure of reward and not risk (or vice versa). And for my chosen metric (I chose to do the Sharpe-like ratio) I'm pretty much just saying it covers both risk and reward, so it's what we want to do instead of using one of the metrics from #1 alone.