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  #121  
Old 02-15-2018, 09:29 AM
Actuary9914 Actuary9914 is offline
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For the INV track, can anyone explain the inflation duration/exposure of COLA/NONCOLA and by retired/Active?

How would a NON COLA plan for retirees have a higher inflation duration than COLA plan? If there is no cola, then wouldn't higher inflation reduce the liability?
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  #122  
Old 02-15-2018, 01:22 PM
CubsPhan CubsPhan is offline
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For the ILA extension reading Hedging for Liabilities in Life Insurance Companies (reading 413-17), there's an example of delta-hedging a liability using a 3-month futures contract. When calculating the futures price for both the base value and the 1% shock value, the authors determine the value as 10 * Stock Index * e^(rt) (well, 99% times that value for the 1% shock.)

I understand what they're doing except for the factor of 10. Can anyone explain why we need to multiply this value by 10. My only thought would be that maybe we're hedging 10 units of the underlying liability, but nowhere in the reading does it indicate that.

Last edited by CubsPhan; 02-15-2018 at 01:41 PM..
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  #123  
Old 02-15-2018, 03:32 PM
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Originally Posted by Actuary9914 View Post
For the INV track, can anyone explain the inflation duration/exposure of COLA/NONCOLA and by retired/Active?

How would a NON COLA plan for retirees have a higher inflation duration than COLA plan? If there is no cola, then wouldn't higher inflation reduce the liability?
I'll get back to you when I get that far... I would give it about a month tho.
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  #124  
Old 02-15-2018, 10:03 PM
ActurialMike ActurialMike is offline
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Does anyone have any experience with the PAK practice question sets? Thinking of purchasing to complement my studying leading up to the exam. There is a 900+ practice question set and a 110+ mock question set. Any idea what the difference is and if one is better than the other?
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  #125  
Old 02-15-2018, 11:07 PM
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Originally Posted by Actuary9914 View Post
For the INV track, can anyone explain the inflation duration/exposure of COLA/NONCOLA and by retired/Active?

How would a NON COLA plan for retirees have a higher inflation duration than COLA plan? If there is no cola, then wouldn't higher inflation reduce the liability?
Let's work through this a bit. First let's remember that normal duration means that higher interest rates => lower values. For example, when interest rates go up, bond values go down.

Inflation duration is the change in liability with respect to the change in inflation.

With COLA, our liability is something like...

Liability = (1+inflation)*CF / (1+r)

BUT, our interest rates are dependent on inflation. If inflation goes up, our discount rate goes up. We can rewrite (1+r) as (1+inflation)(1+real rates), where real rates won't change with inflation. So our formula becomes...

Liability = (1+inflation)*CF / [(1+inflation)(1+real rates)]
or...
Liability = CF / (1+real rates)

If inflation changes, how much does our liability change? Since inflation is no longer in the formula, the answer is 0! So, the liability isn't affected by inflation, because the increase in the numerator (payments) is offset by the increase in the denominator (discount). We'll call this, then, zero duration.

Without COLA we just take the inflation out of the numerator.

Liability = CF / [(1+inflation)(1+real rates)]

Now, if inflation goes up, our liability goes down, because the denominator is larger. And, just like we would see with bonds, when rates go up and values go down, we have positive duration. So, similarly in this situation, we have positive inflation duration.


Hopefully that helps! I'd be happy to put together an example if that would help.
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Last edited by PaulP; 02-16-2018 at 09:30 AM..
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  #126  
Old 02-15-2018, 11:16 PM
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Originally Posted by CubsPhan View Post
For the ILA extension reading Hedging for Liabilities in Life Insurance Companies (reading 413-17), there's an example of delta-hedging a liability using a 3-month futures contract. When calculating the futures price for both the base value and the 1% shock value, the authors determine the value as 10 * Stock Index * e^(rt) (well, 99% times that value for the 1% shock.)

I understand what they're doing except for the factor of 10. Can anyone explain why we need to multiply this value by 10. My only thought would be that maybe we're hedging 10 units of the underlying liability, but nowhere in the reading does it indicate that.
There's not a great reason here, to be honest. They just take the convention that a "standard" contract is 10 units. Other readings would say 100. If we assumed 1 unit, we'd just need 10x more futures contract.

This has come up on the exam before (where the SOA's solution assumed 100 units per contract). Since there is no fixed rule clearly laid out, they are pretty forgiving, as long as you show what you are assuming.
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  #127  
Old 02-16-2018, 09:08 AM
Actuary9914 Actuary9914 is offline
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Quote:
Originally Posted by PaulP View Post
Let's work through this a bit. First let's remember that normal duration means that higher interest rates => lower values. For example, when interest rates go up, bond values go down.

Inflation duration is the change in liability with respect to the change in inflation.

With COLA, our liability is something like...

Liability = (1+inflation)*CF / (1+r)

BUT, our interest rates are dependent on inflation. If inflation goes up, our discount rate goes up. We can rewrite (1+r) as (1+inflation)(1+real rates), where real rates won't change with inflation. So our formula becomes...

Liability = (1+inflation)*CF / [(1+inflation)(1+real rates)]
or...
Liability = CF / (1+real rates)

If inflation changes, how much does our liability change? Since inflation is no longer in the formula, the answer is 0! So, the liability isn't affected by inflation, because the increase in the numerator (payments) is offset by the increase in the denominator (discount). We'll call this, then, zero duration.

Without COLA we just take the inflation out of the denominator.

Liability = CF / [(1+inflation)(1+real rates)]

Now, if inflation goes up, our liability goes down, because the denominator is larger. And, just like we would see with bonds, when rates go up and values go down, we have positive duration. So, similarly in this situation, we have positive inflation duration.


Hopefully that helps! I'd be happy to put together an example if that would help.
Thanks Paul! Very clear and easy to understand.
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  #128  
Old 02-18-2018, 04:22 PM
ActurialMike ActurialMike is offline
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Question on RAROC vs RARORAC.

ERM 119 defines RAROC as risk adjusted return / total capital and RARORAC as risk adjusted return / required capital.

However, in the linkage with strategic planning article, they define RAROC as (PV(underwriting) + PV (inv income)) / PV(required capital).

Is that not a contradiction?
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  #129  
Old 02-19-2018, 12:40 PM
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xpactuarial xpactuarial is offline
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ERM-119-14 is written by Milliman and the Risk Appetite article is written by Kailan Shang and Zhen Chen. Two different authors to begin with... so differences may arise.

Getting back to the concepts... there are 3 commonly used ratios that are related to each other. The two covered in the readings are RAROC and RARORAC. The 3rd is RORAC.

The RAROC attempts to adjust the numerator of the equation by accounting for risk. Here you should use Capital in the denominator as per Milliman.

RORAC stands for Return on Risk Adjusted Capital. This equation adjusts the denominator by accounting for risk. Here you would use Required Capital in the denominator (but this is not testable and is presented here for completeness).

The RARORAC formula adjusts both the numerator and denominator in the equation and gives us the Risk Adjusted Return on Risk Adjusted Capital. Here we would use Required Capital in the denominator.

The issue is that RAROC can also be defined as Expected Return over Economic Capital. Here you could argue (if your required capital components are set using economic capital methods), that the Risk Appetite formula is also correct.

With all this being said, I don't think that the graders could penalize you on a RAROC question if you argued to use Capital instead of Required Capital.

If the question gives you one set of capital figures, then assume that the capital given is the denominator. If the question gives you both Capital and Required capital, then it would likely be referring to the ERM-119 reading.
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  #130  
Old 02-19-2018, 02:08 PM
ActurialMike ActurialMike is offline
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Quote:
Originally Posted by xpactuarial View Post
ERM-119-14 is written by Milliman and the Risk Appetite article is written by Kailan Shang and Zhen Chen. Two different authors to begin with... so differences may arise.

Getting back to the concepts... there are 3 commonly used ratios that are related to each other. The two covered in the readings are RAROC and RARORAC. The 3rd is RORAC.

The RAROC attempts to adjust the numerator of the equation by accounting for risk. Here you should use Capital in the denominator as per Milliman.

RORAC stands for Return on Risk Adjusted Capital. This equation adjusts the denominator by accounting for risk. Here you would use Required Capital in the denominator (but this is not testable and is presented here for completeness).

The RARORAC formula adjusts both the numerator and denominator in the equation and gives us the Risk Adjusted Return on Risk Adjusted Capital. Here we would use Required Capital in the denominator.

The issue is that RAROC can also be defined as Expected Return over Economic Capital. Here you could argue (if your required capital components are set using economic capital methods), that the Risk Appetite formula is also correct.

With all this being said, I don't think that the graders could penalize you on a RAROC question if you argued to use Capital instead of Required Capital.

If the question gives you one set of capital figures, then assume that the capital given is the denominator. If the question gives you both Capital and Required capital, then it would likely be referring to the ERM-119 reading.
Thank you!!! Very helpful!
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