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Old 02-23-2018, 06:06 PM
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Default FA CDEF Task 2: Risk/Return Metrics Helpful Info

I told myself that if I pass the FA I am going to provide useful info that I learned about task 2 risk/return metrics. Basically it's info I wish I had available when I started doing the task to better understand what the question is asking. I do not believe the module readings provide adequate information regarding what risk/return metrics are and how to use them.

Disclaimer: All of the information I am about to provide are from my own research. If you believe that anything I have said is wrong or not entirely correct, please provide a comment to correct it.

What exactly is a risk/return metric? I believe this is the question that confuses a lot of people taking the task (including me at first).

Please refer to the following powerpoint presentation from CAS:

https://www.casact.org/education/rat...s/bingham2.ppt

Slide 12 mentions that metrics such as VaR and CTE are only expression of risk. So it would be technically incorrect to state that VaR or CTE is your risk/return metric. I believe that the same concept applies for the mean and standard deviation. On their own they are not a risk/return metric.

A risk/return metric should be able to measure some kind of trade-off between risk and return. (I will give an example of this)

Examples of risk/return metrics in real life:

An example of a risk/return metric in real life is Sharpe Ratio:

Sharpe Ratio = (Average Return on Portfolio - Risk Free Rate) / Standard deviation of returns. The higher the Sharpe Ratio the better the risk/return trade-off.

So why is Sharpe Ratio a risk/return metric? Well, it's because it evaluates some kind of trade-off between risk and return. Basically the Sharpe ratio attempts to find the highest return above the risk free rate with the lowest volatility.

Example with numbers:
  • Risk Free Rate = 3%
    Average Return on Portfolio A: 10%
    Standard Deviation on Portfolio A: 8%
    Average Return on Portfolio B: 7%
    Standard Deviation on Portfolio B: 4%

    Portfolio A Sharpe Ratio: (10 - 3) / 8 = 0.875
    Portfolio B Sharpe Ratio: (7 - 3 ) / 4 = 1

Therefore, while the average return on Portfolio A was 3% higher than Portfolio B, the risk/return trade-off of Portfolio B is better since the volatility is much lower. This is according to the Sharpe Ratio risk/return metric. Notice how this metric can assess some kind of risk/return trade-off. While the average return on portfolio A was higher than B's, this metric suggested that the extra risk from the volatility is not worth the return, so portfolio B is better. Notice how this metric incorporates both RISK and RETURN

Another example of risk/reutrn metric in real life is coefficient of variation. See https://www.investopedia.com/terms/c...fvariation.asp for more explanation.

Quote:
In the investing world, the coefficient of variation allows you to determine how much volatility, or risk, you are assuming in comparison to the amount of return you can expect from your investment. In simple language, the lower the ratio of standard deviation to mean return, the better your risk-return tradeoff.
Again, notice how this metric measures a risk/return tradeoff

I hope this gave you a better understanding of the concept behind risk/return metrics. Note that in the CDEF example, you are provided the cost per employee as the result of each portfolio mix NOT the return on the portfolio. Therefore you need to come up with an appropriate risk/return metric that uses the cost per employee as opposed to the return on the investment.

JUST MAKE SURE THAT YOUR METRIC IS ABLE TO MEASURE SOME KIND OF RISK/RETURN TRADE-OFF. It doesn't have to be a metric that is used in real life. The CDEF task uses cost per employee not actual returns, so you need to think how to incorporate risk and return based on that.

I hope this helps!!

FAQ:

Q. Some risk/return metrics seem to suggest 100 percent equities.

My Answer:

Quote:
All risk/return metrics that I personally tried perform the best with 100 equities. Try thinking of it as follows (IMO):

Portfolio theory says that you can maximize returns for a certain level of risk taken (you will use the metric for this)

Now what level of risk you think is adequate for the CDEF? 100% equities? Probably not. 100% equities may generate big returns in the long term but can have large short-term losses and the CDEF cannot afford that.

Therefore you should set a requirement for how much equities you want the CDEF to take under each market scanario then use the metric to to determine the best one given that restriction.
2. Should I use sharpe ratio as a risk/return metric?

Quote:
The sharpe ratio is not some golden metric that will get you a pass. Some people passed with it, others failed. I provided the sharpe ratio example above to simply show an example of risk/return tradeoff based on a risk/return metric. If you feel like you can’t justify why you’re using the sharpe ratio, you shouldn’t use it.
3. also see this http://www.actuarialoutpost.com/actu...&postcount=230

Last edited by Sir Issac; 03-21-2019 at 05:06 PM..
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Old 02-23-2018, 06:15 PM
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this is good stuff
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Old 02-23-2018, 09:11 PM
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The Loss Model textbook (it s so thick and heavy that I can use it as door holder) has a couple pages on comparing CTE, VaR, Stdev. It also has a paragraph on why choose different number (degree of certainty for VaR). This material is the most useful I found so far. I stumbled upon this material by looking up CTE and VaR under index page. I was looking for CTE and VaR under index page from every textbook I got an hold of. But none were as useful as the one in Loss Model.
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Old 02-23-2018, 10:10 PM
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The prompt specifically says to use "available risk/return metrics". I'm glad but kind of surprised introducing a metric other than what was listed/available worked.

I failed though.
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Old 02-23-2018, 10:15 PM
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Quote:
Originally Posted by LunchBox View Post
The prompt specifically says to use "available risk/return metrics". I'm glad but kind of surprised introducing a metric other than what was listed/available worked.

I failed though.
But the Sharpe ratio uses a combination of the metrics listed. I intepretet that as a way to use the metrics given and not as introducing a new metric and would therefore be okay.
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Old 02-23-2018, 10:29 PM
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Quote:
Originally Posted by ao fan View Post
But the Sharpe ratio uses a combination of the metrics listed. I intepretet that as a way to use the metrics given and not as introducing a new metric and would therefore be okay.
I'm probably wrong, since I failed this task. I thought I read most people were passing just picking a metric or two of the 10 listed rather than using a ratio.

I actually did use a ratio and failed. I thought that might have been why. Maybe not. Who knows. Maybe I'll guess right on what they want next submission.

I used a ratio in addition to a requirement on mean.
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Old 02-23-2018, 11:34 PM
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Quote:
Originally Posted by LunchBox View Post
I'm probably wrong, since I failed this task. I thought I read most people were passing just picking a metric or two of the 10 listed rather than using a ratio.

I actually did use a ratio and failed. I thought that might have been why. Maybe not. Who knows. Maybe I'll guess right on what they want next submission.

I used a ratio in addition to a requirement on mean.
just because i passed doesn't mean i'm right. i'm guessing that someone can pass even if some portion of it isn't perfect. my task 2 might have been subpar and maybe my other tasks were okay. i was least confident in my task 2.
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Old 02-23-2018, 11:36 PM
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sir issac's links make a strong argument for using a ratio, but who knows what the soa is looking for. someone posted that they heard of feedback said not to use a ratio. that makes no sense to me though.
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Old 02-23-2018, 11:37 PM
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If I were to use the sharpe ratio or coefficient of variation, I'm confused about how I would go about figuring out the pros and cons of it...
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Old 02-24-2018, 01:22 AM
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Funny, I used the loss models text and I talked about the sharpe ratio. Hopefully you can figure out some pros...as far as cons, let's say you calculate the ratio, what can you do with it? You can use it to compare two scenarios. Is the number useful otherwise? What can't you do with it?
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