CIA.Discnt

There is overlap between this and the CSOP paper, but CIA.Discnt also addresses discounting of [1] ceded liabilities [2] premium liabilities   Forum

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What is the formula for CI (Comprehensive Income)? (See Calculating Equity from CCIR.ARinstr)

BattlePlan

Based on past exams, the main things you need to know (in rough order of importance) are:

• discount rate selection considerations [Hint: MARY(IE)-CapG]
• calculating the discount rate (easy - there is a practice template for this)
• a few miscellaneous facts:

- cash flow timing risk for asset cash flows & liability cash flows

- selection considerations for payment patterns

- basis for reserve analysis: (gross & net) OR (gross & ceded) [Hint: D.C.Re.D]

- definition of PYR (portfolio yield rate)

• Note: sub-parts of many of the exam questions are from other readings

Top Questions ← Questions you absolutely need to know!

reference	part (a)	part (b)	part (c)	part (d)
E (2017.Fall #27)	identify AA error 1: - see CIA.MfAD	identify AA error 2: - see CIA.MfAD	identify AA error 3: - ceded APV formula	identify AA error 4: - see OSFI.AA
E (2017.Spring #26)	discount rate: - selection considerations	cash flow timing risk: asset CFs v liability CFs
E (2016.Fall #26)	see CIA.CSOP	see CIA.CSOP	payment patterns: - selection considerations	see CIA.Disclosure
E (2016.Spring #13)	calculate: - discount rate 1	calculate APV(ClmLiabs): - see CIA.MfAD	calculate APV(PrLiabs): - see CIA.PrLiabs	calculate interest rate risk margin: see OSFI.MCT
E (2016.Spring #15)	see OSFI.MCT	discount rate: - selection considerations
E (2015.Fall #26)	basis for analysis: - gross/net/ceded	PV v APV: - see CIA.MfAD
E (2015.Spring #20)	calculate: - discount rate	SCENARIO: - evaluate discount rate	discount rate: - selection considerations
E (2014.Spring #33)	define: - PYR (portfolio yield rate)	discount rate: - selection considerations	PYR: for ceded liabilities
E (2013.Fall #36)	PV v APV: - see CIA.MfAD	discount rate: - selection considerations

¹ This problem contains an ambiguity. When calculating the weighted average of the yield rates, you should use the book value of HTM bonds, but the market value of HFT and AFS bonds. The problem doesn't specify they type of bond so you all you can do is use market value.

In Plain English!

Intro

This reading is just a long list of principles for selecting items like discount rates and payment patterns that are associated with discounting policy liabilities.

Section 1,2: Intro & Terms

As always, check the BattleCards for details. Here, I'd like to highlight what seems to be the main idea from this section:

Situation: You are doing a valuation of reserves for net, gross, and ceded business.

Observe: You only need to calculate two of these directly; the other is obtained by addition or subtraction.

• (If you calculate net and ceded directly then gross = net + ceded)
• (If you calculate net and gross directly then ceded = gross - net)
• (If you calculate ceded and gross directly then net = gross - ceded)

Question: how do you decide which two of these to calculate directly [Hint: D.C.Re.D]

Data - consider credibility of the data

→ if the ceded business is small, then the net and gross data would have the highest credibility

Cash flow - consider the volatility & duration of the cash flows

→ different LOBs may have different Cash Flows, so the choice may vary by LOB

Reinsurance - type of reinsurnace program and consistency from year to year

→ if net retention level has changed, then do NOT calc net losses directly (CALCULATE: net = gross - ceded)

Discount rate - if the discount rates for net and ceded are different, then calc net and ceded directly

Other noteworthy items in this section are the definitions of claim liability and premium liability, but those are covered in CIA.CSOP (and have been asked on a prior exam.)

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Section 3,4: P-Patt (Payment Pattern) & DiscRt (Discount Rate)

Here's a question that's been asked many times on recent exams...

Question: what are the considerations when selecting a discount rate (or expected investment return rate) [Hint: MARY-(IE)-CapG]

Methods - for asset valuation & reporting investment income

Allocation - of assets & investment income by LOB

Return - on assets @ B/S date

Yield - on assets acquired after B/S date

(IE) Investment Expenses - and losses from default

CapG Capital Gains/losses - on assets sold after B/S date

See the BattleCards for P-Patt (Payment Pattern) considerations and other facts you need to know.

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Calculating a Discount Rate

This is a calculational problem that has come up twice: (2016.Spring #13i), (2015.Spring #20a), sometimes as part of a larger problem. (It's actually pretty easy.)

Let's look at the 2016.Spring problem. It's a long, LONG problem, but the first step is to calculate the discount rate. For this, we need the last 3 rows of the 2nd table, the table on page 14. Assume the bonds are HTM. (If the were HFT or AFS, we would use market value instead of book value in the weighted average.)

Description	Bond #1	Bond #2
annual effective yield	2.31%	3.23%
modified duration	0.972	1.888
book value	$10,030	$10,060

Calculate the discount rate as follows:

discount rate = a weighted average of the annual effective yields with weights = (duration) x (value)

→ weight for Bond #1 = 0.972 x 10,030 = 9,749

→ weight for Bond #2 = 1.888 x 10,060 = 18,993

discount rate = [ (2.31% x 9,749) + (3.23% x 18,993) ] / ( 9,749 + 18,993) = 2.92%

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Section 5: MfADs

This is just a rehash of stuff you already know from CIA.MfAD.

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Appendices: Cash-Flow Matching Model

The syllabus says you're responsible for the information in the appendices, and there is a link to an Excel file in the syllabus.

• This model is a more sophisticated version of the CF (cash flow) example on page 12.
• The page 12 table is pretty simple to understand:
  • net CF = (asset CF) - (liability CF)
  • (The key is to make sure that cumulative CF is positive.)
• The cash flow model goes further in that it shows how/when to:

reinvest excess CFs in 1 period to offset negative CFs in other periods

Appendix A is a summary of exhibits B, C, and D. Appendices B, C, and D have the same format, just with different numbers and assumptions. (Appendix C seems to be missing sheet 4, however.) Let's focus on appendix B. It has 4 sheets:

Sheet 1: Information about the assets (bonds) that support the liabilities

Sheet 2: Claim liability and premium liability payment patterns for 5 LOBs, and cash in-flows from the bonds described on sheet 1

Sheet 3: Cash out-flows from liabilities, cash in-flows from bonds and incremental & cumulative cash flow excess & deficiency by year.

Sheet 4: Summary of out-flows, in-flows, and reinvested funds. The goal is to have a closing balance of 0 in the final year, 2026. (That means that assets and liabilities are perfectly matched.)

Things to understand from this model:

• The goal is to somehow match the in-flows from the assets with the out-flows from the claim & premium liabilities.
• You can't control the liability cash flows - you can only give your best estimate of what you think they will be.
• You can control cash flows of the assets simply by purchasing assets that generate the cash flows you need.
• Excess cash flows from one year are reinvested at the start of the following year.

Question 1: Given liability cash flows, what combination of assets (bonds) would you purchase to achieve a closing balance of 0 at the end of a given future year?

• This is not something you can calculate directly. You could, however, use trial and error: Enter a combination of bonds on sheet 1, then check the closing balance on sheet 4. If it isn't equal to 0, go back to sheet 1 and try a different combination.
• Once you have a combination of bonds that gives a closing balance of 0, you can calculate the IRR (Internal Rate of Return) with a computer. The IRR gives you some sense of the level of risk you have assumed in your book of business. If find you need an IRR of 20% to support your liabilities, then you have assumed WAY TOO MUCH risk!!!

Question 2: Given liability cash flows, and specific assumptions for a set of bonds, will these bonds be sufficient to support the liabilities?

• This could be answered by constructing a table similar to sheet 4. But this would still be a lot of work, even for a small example!
• If this question were asked on an exam, they would probably give you some of the pieces. You would then just have to know how to put them together.

There are currently no BattleCards for the cash flow matching model. After you've read this section of the wiki article, take a look at the exhibits in the original paper. I think a calculation problem on this model is a low-probability question. Cash-flow is more of an accounting concept, so this is an area where the actuary (as an enquiring professional) can reasonably rely on the work of the accountant (who would be the responding professional.)

BattleCodes

• Memorize:
  • 4 considerations for deciding which two quantities to calculate directly: net / gross / ceded
  • 6 considerations for selecting a discount rate
  • 3 broad considerations and 5 detailed considerations for selecting P-Patt for claims liabilities
  • 2 additional considerations for selecting P-Patt (Payment Pattern) for premium liabilities

• Conceptual:
  • You should know the fundamental elements of discounting PolLiabs (Policy Liabilities):
    • discount rate
    • P-Patt (Payment Pattern)
    • MfADs
  • In particular, how do you select each of these items. (Recall that the discount rate considerations has been asked on 5 prior exams. Maybe it's time for the CAS to ask about P-Patt or MfAD)

• Calculational:
  • Assessing whether assets are sufficient to support liabilities (easy - see table on page 12, and the explanation underneath.)
  • Calculating a discount rate given (yield, duration, market value) for various assets.

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POP QUIZ ANSWERS

CI = NI + OCI

where

NI = Net Income

OCI = Other Comprehensive Income