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  #1  
Old 03-27-2003, 03:06 PM
Milkman Milkman is offline
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Default Duration of Life Insurance Liability

The insurance company that I work for is looking to calculate the effective duration of our traditional life insurance liabilities (in order to match our asset duration to our liability duration).

In order to do this, we are using results from our in-force cash flow testing model. We are using results from the following scenarios: (1) level interest rate scenario, (2) Pop-up 1.00% immediately and remain level thereafter, and (3) Pop-down 1.00% immediately and remain level thereafter. In each of these scenarios, the model runs for 29.25 years. For the three scenarios, we wish to calculate the present value of liability cash flows (from those three numbers we can calculate effective duration and convexity). The problem we are having is deciding how to calculate this present value.

Here are some questions that we are encountering. If anyone could help with any question it would be greatly appreciated.

1. What are the liability cash flows? Some are obvious such as: death benefits, surrender and maturity benefits, acquisition expenses, commissions, maintenance expenses, premium taxes. Are there any others that I am missing?

2. Should the liability cash flows be net of premiums? For example if liability cash flows are 10 and premiums are 4, is the correct figure 6? I believe it is.

3. Should Federal Income Taxes be considered as a liability cash flow?

4. How should increase in reserves be handled? I think they should be ignored but I'm not positive.

5. Should After-tax statutory book profit be treated as a liability cash flow or should it be ignored?

6. How should we handle the ending liability (i.e. the liability at the end of 29.25 years)? I believe we should just treat it as a cash flow due at t=29.25 years.

7. Should target surplus enter the calculation? I don't believe so.

8. What should the discount rate be? The pre-tax asset rate? After-tax asset rate? Other?

I realize these are a lot of questions, but if you have insight to even just one of them it would be greatly appreciated.
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  #2  
Old 03-28-2003, 12:45 PM
actuari actuari is offline
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Have to run but just a quick comment on B/T - A/T. Be consistent in your CFs and discount rate if A/T CFs then use A/T rate. Use the spot rates for each CF. It's a controversial issue whether to account for the InsCo. Credit risk or not. There has been some discussion I’ll try to get some references later.
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  #3  
Old 03-28-2003, 05:35 PM
hactuary hactuary is offline
 
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This is a great question, and while I'm no expert, here's how I have looked at things in the past.

1. What are the liability cash flows? Some are obvious such as: death benefits, surrender and maturity benefits, acquisition expenses, commissions, maintenance expenses, premium taxes. Are there any others that I am missing? ANY CASH PAYMENTS SHOULD BE USED HERE.

2. Should the liability cash flows be net of premiums? For example if liability cash flows are 10 and premiums are 4, is the correct figure 6? I believe it is. PREMIUMS ARE PART OF THE CASH FLOWS.

3. Should Federal Income Taxes be considered as a liability cash flow? I WOULD SUSPECT YOU WOULD WANT TO MATCH ON A PRE-TAX BASIS. TAXES CAN CHANGE THE INTERACTIONS OF THE VARIOUS PIECES.

4. How should increase in reserves be handled? I think they should be ignored but I'm not positive. RESERVES ARE THE WHOLE POINT--THIS IS WHERE THE CASH FLOWS ARE INVESTED. DON'T INCLUDE RESERVES, JUST THE CASH INCOME AND PAYMENTS.

5. Should After-tax statutory book profit be treated as a liability cash flow or should it be ignored? THE OVERALL QUESTION YOU ARE ASKING IS ABOUT THE SENSITIVITY OF YOUR LIABILITY CASH FLOWS TO INTEREST RATE CHANGES. WITH UL, YOU EXPECT TO SEE LESS INCOME AND MORE SURRENDERS WITH INCREASING INTEREST RATES (UNTIL THE PORTFOLIO RATE CATCHES UP). NON-INTEREST-SENSITIVE LIFE WILL HAVE FEW CHALLENGES WITH INTEREST RATE CHANGES, SO YOU SHOULD BE ABLE TO LOCK IN AN INVESTMENT STRATEGY UP-FRONT.

6. How should we handle the ending liability (i.e. the liability at the end of 29.25 years)? I believe we should just treat it as a cash flow due at t=29.25 years. I AGREE WITH YOUR THOUGHT HERE.

7. Should target surplus enter the calculation? I don't believe so. TS IS NOT REALLY THE POINT; RSVS ARE. YOU WANT TO HAVE INVESTMENTS FOR RSVS MATCH THE DURATION (INTEREST SENSITIVITY) OF THE LIABILITIES. THAT SAID, TS IS SOMETHING YOU NEED AND IF IT NEEDS TO BE IMMUNIZED, IT SHOULD BE CONSIDERED.

8. What should the discount rate be? The pre-tax asset rate? After-tax asset rate? Other? IF THIS IS DONE PRE-TAX AS SUGGESETED ABOVE, THEN YOU SHOULD DISCOUNT AT THE ASSET RATE. I'D USE THE PORTFOLIO RATE, THEN DROP IT BY 1 BP OR 1%, THEN RAISE IT SIMILARLY--THESE GIVE THE SENSITIVITIES.

THAT'S MY UNDERSTANDING. I'D BE INTERESTED IF OTHERS SEE THINGS DIFFERENTLY.
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Old 04-11-2003, 09:37 AM
papercut papercut is offline
 
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My 2 cents.

I generally agree with the above except for the discounting. Since you're trying to value the liabilities to compute duration you should be discounting at spot rates that are in line when the cashflow is paid. When you value a bond, you discount at the then current spot rate (forward rate) + risk spread. Same methodology should be used for the Liab. As you should be using stochastic arbitrage free interest rate sets to value liab (not CFT scenarios), discounting at the rolling 90 day along each scenario should suffice since the forward 90 day rates are in line with the current spot rates. The difficulty comes up on the spread above the 90 day Treas to use... that's debatable. Sorry if this is clear as mud.

Note that when value-ing liab with premiums, you could get very strange values and duration numbers. I highly encourage you to explore dollar duration and dollar surplus duration analysis.
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  #5  
Old 04-01-2010, 05:31 AM
Jason Jason is offline
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This was a very good discussion and helped me a lot. I have a further question to this, would appreciate if anybody could give any thoughts on this. When including premiums in the liability cash flows, for certain lines of business, i end up with negative duration for liabilities. How should I interpret this with regard to matching asset and liability durations?
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  #6  
Old 04-01-2010, 08:34 AM
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JMO JMO is offline
Carol Marler
 
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A couple of items:
First, http://www.soa.org/files/pdf/2010-ny-dicke.pdf
This presentation discusses the implications of RBC calculations for Asset management. One of the points made is that the "Greatest Present Value of Accumulated Deficiencies" adds a new wrinkle to duration management. In the past it was sufficient for weighted duration of assets to match overall the weighted duration of liabilities. However, looking at the accumulated deficiencies year by year may require finer granularity in analyzing duration mix of assets.

Second, a few words about duration. For simple bonds, the sensitivity of price to interest rate changes turns out to be equal to the average (interest weighted) duration of the payments. This rule is useful if you want to be sure your asset portfolio responds to interest rate changes in the same way your liabilities do. However, insurance cash flows have some features that are a bit different than a simple bond. As Jason notes, the average duration of insurance liabilities can indeed be negative. The makes it a trickier proposition to match asset duration to liability duration. However, remember the way we originally came up with "duration" as our metric. In fact, insurance cash flows themselves can change if the interest rate environment does. (On the asset side, mortgage cash flows can also change when interest rates go up or down.) To perform the immunization step, we need to calculate the change in liabilities when interest rates change, NOT just a weighted duration of deterministic cash flows.

I hope that helps.
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Carol Marler, FSA, MAAA, A Former Actuary
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  #7  
Old 04-01-2010, 06:58 PM
Jason Jason is offline
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Thanks, JMO for your reply. I managed to also find results of research commissioned by the SOA in 2004 on the subject. Incredibly helpful. I'm just realisiing how extensive SOA's research database is on the SOA website.
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