2012-la-val-act-49

2012 Valuation Actuary Symposium

Sept. 10- 11, 2012

Session #49 PD: Introduction to

Asset Modeling Concepts

Yidong Liu, FSA, MAAA

Gregory J. Roemelt, FSA, MAAA

Moderator

Guillaume Briere-Giroux, FSA, MAAA

Primary Competency

Technical Skills & Analytical Problem Solving

Introduction to Asset Modeling 1

Tuesday, September 11, 2012Valuation Actuary Symposium

ASSET MODELING

1

Greg RoemeltWinter Liu

September 11, 2012

Need for Asset Models

§ Cash flow testing§ ALM work§ Financial plan§ Capital planning§ RBC calculations § SOP 03-1§ Principle based reserves

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Purpose of Session

§ Agendaú Building blocks of asset modelsú Common asset classes and modeling

considerationsú Reinvestment / disinvestment

§ Exclusionú Only focus on the general accountú Will not include a discussion of interest rate or

equity scenario generators

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Fundamental Asset Components

§ An asset model tracks three fundamental components of any underlying assets

ú Interest§ Coupon

frequency§ Coupon rate§ Reference

rate

ú Principal§ Scheduled

amortization§ Call / put /

prepayment§ Default§ Maturity§ Sales

ú Value§ Par§ Book§ Market

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Fundamental Asset Components

§ An asset model tracks three fundamental components of any underlying assets

ú Interest§ Coupon

frequency§ Coupon rate§ Reference

rate

ú Principal§ Scheduled

amortization§ Call / put /

prepayment§ Default§ Maturity§ Sales

ú Value§ Par§ Book§ Market

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Asset Class Yield Curves

§ Use of asset yield curvesú Calculate market valueú Determine yields on reinvestmentsú Basis for exercise of financial options

§ Model asset yield curvesú Treasury yield curve + asset spread

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Model Asset Yield Curve

§ Treasury yield curve § Published daily§ Can be modeled deterministically or stochastically

§ Asset spreads are the incremental amounts added to treasury rates to get the yields for risky assetú Readily available for frequently traded assetsú Vary by various risk factorsú Typically modeled deterministicallyú Typically use initial spreads based on market

conditions and grade to long term averages

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Asset Spreads Vs. Treasury

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BBB Bond

10yr Treasury



Asset Spreads Consideration

§ Credit rating§ Maturity§ Liquidity§ Embedded optionú May be more difficult to develop

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Sample Bond Credit Spreads

AA A BBB90-Day 95 125 1401-Yr 120 150 1602-Yr 130 160 1753-Yr 140 170 1905-Yr 150 180 21010-Yr 160 190 23030-Yr 190 220 260

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Asset Default

§ Vary by asset class and credit rating§ Level or by durationú Level: could vary by years to maturityú Duration: increasing rates with age

§ Probability times severity§ “Fallen Angels”

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Model Defaults

§ Modeled as a reduction in book valueú 20 bps annual default assumption translates to

a 0.2% annual reduction in book value

§ Modeled as a reduction to investment incomeú 5.25% coupon with a 20 bps annual default

assumption generates 5.05% income

§ Deterministic vs. Stochastic§ Linked to interest rate?

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Default Assumption

§ Default assumption – sources of dataú Moody'sú S&Pú Wall streetú Company experience/investment advisors

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Asset Classes

ú Non-callable bondsú Callable bondsú Inflation indexed bondsú Mortgages and mortgage pass-through'sú Collateralize mortgage obligations (CMOs)ú Asset Back Securities (ABS)ú Collateralize debt obligations (CDOs)ú Derivatives

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Non–Callable Bonds

§ Required dataú Book value (Stat, tax, GAAP)ú Par valueú Maturity dateú Coupon – rate and modeú Sinking fund schedule

§ Other useful dataú CUSIPú Market value

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Non–Callable Bonds – Cash Flows

§ Fairly simple to project§ Interest paymentú At coupon date: Cash Flow = Par x Coupon / Mode

§ Principal paymentú If sinking fund date, scheduled amountú At maturity, Par

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Non–Callable Bonds – Cash Flows

Date Par – BOY Coupon Sinking Fund Total CF

12/31/2008 $10,000 $500 $2,000 $2,500

12/31/2009 $8,000 $400 $2,000 $2,400

12/31/2010 $6,000 $300 $2,000 $2,300

12/31/2011 $4,000 $200 $2,000 $2,200

12/30/2012 $2,000 $100 $2,000 $2,100

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Non–Callable Bonds –Investment Income§ Cash flow§ Change in investment income due & accrued§ Amortization of premium/accrual of discountú Yield is not equal to coupon if book not equal to

par

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Non-callable bonds – Investment Expenses§ Sources of assumption ú Annual Statement – Exhibit 2ú Investment advisors

§ May vary by asset categoryú Bondsú Mortgagesú Real estateú Policy loans

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Non-callable Bonds – Market Values§ Present value of future cash flows§ Based on assumed asset category yieldú Treasury yield + asset spreadú Yield and spread tied to average life

§ Market value calibrationú Calculated MV likely differs from reported MVú Additional spread calculated to calibrateú Ignore, maintain or grade additional spread

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Callable Bonds

§ Similar to non-callable, except issuer of the bond has the right (option) to call (pay off) the bond at some future date(s)§ May be callable at a point in time (European

option), or may be callable over a period of time (American option)§ May be a “call premium”

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Callable Bonds

§ Higher coupon than comparable non-callable bond§ Difference is price of call option§ Purchaser of bond has sold a call option to

issuer of the bond

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Callable Bonds – Cash Flows

§ If bond is not called, identical to non-callable§ Call behaviorú Driven by interest ratesú Present value of cash flows at current rates VS.

call price plus any refinancing costú The more “in the money” the call, the more likely

the bond will be calledú Easier (or cheaper) for high grade lenders to

refinance

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Callable Bonds – Market Values

§ Much more difficult to calculate§ Include the price of the call option§ No closed form solutions for American calls§ Multiple scenario / binomial lattice

methodology

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Treasury Inflation-Protected Securities (or TIPS)

§ Coupon is fixed§ Principal adjusted to the Consumer Price

Index

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Mortgages

§ Property typeú Commercialú Residential

§ Amortization Patternú Amortizingú Non-Amortizing (interest only)ú Balloon

§ Interest Rateú Fixedú Floating

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Quality of Underwriting –Residential Mortgages§ Conforming mortgage ú Strict standards Amount Down payment Income Credit history Property condition

§ Non – conforming loansú Alt-Aú Subprime

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Mortgages – Cash Flow

§ Interest only – identical to bullet bond§ Amortizing – Payment to amortize ú Loan period for non-balloonú “Amortization period” for balloonú Payment recalculated for ARM

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Outstanding Principal

0%10%20%30%40%50%60%70%80%90%

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Outstanding Principal

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Prepayments

§ Mortgagees frequently have the right to pay off or “prepay” mortgage§ Residential – usually no prepayment penalty§ Commercial – lock out period and “Make

Whole” provisions

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Factors Influencing Prepayments§ Refinancing incentiveú Current rate VS. market rate + refinancing cost

§ Age of the mortgage§ Seasonality§ Burnout

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Public Securities Assoc (PSA) Prepayment Model§ Increasing prepayment amounts for 30

months§ Constant thereafter at 6.0% per year§ Not based on hard data§ Used as industry standard pattern

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100% PSA

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Principal Payments – 100% PSA

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Mortgages – Market Value Calculations§ Can be pricing using a constant PSA§ Monte Carlo techniques more robust but

more time consuming§ “Model” similar mortgages to develop a

market to book ratios, apply to all modeled§ Outside systems

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Mortgage Passthrough Securities§ An asset-backed security whose cash flows

are backed by the principal and interest payments of a set (pool) of mortgage loans§ Holders of MBS share proportionally in the

cash flows of the mortgage pool

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Description of Pools

§ Type of collateralú Agencyú Whole loan

§ Weighted Average Coupon (WAC)ú Average of all the coupons in the mortgage pool,

weighted by principalú Will tend to decrease over timeú Always higher than the “passthrough rate”

§ Weighted Average Maturity (WAM)ú average of the maturities of the mortgages in the pool

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Modeling MBS

§ Similar to modeling regular mortgages§ Default assumptions different if agency

backed§ Careful to model prepayments based on the

weighted average coupon and not the passthrough rate

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Collateralize Mortgage Obligations (CMOs)§ A CMO is essentially a way to create many

different kinds of bonds from the same mortgage pool so as to please many different kinds of investors.§ CMO is a Special Purpose Entityú Legal owner of a set of mortgages, called a pool.ú Investors buy bonds (tranches) issued by the entityú Payments to the investors made based on a defined

set of rules, called the structure

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Types of CMO Tranches

§ Sequentials§ PACs/TACs§ Z tranche§ Principal Only§ Interest Only

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Sequential CMOs

§ First CMOs§ Pay principal sequential to tranches§ Purpose was to create short, medium and

long term out of a single mortgage pool

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Sequential CMOPrincipal Payments – 100% PSA

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Principal Payments 100% and 350% PSA

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Principal Payments – 100 PSA

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PAC Support

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PAC Support

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PAC Support PAC Schedule

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PAC Support PAC Schedule

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PACs – Cash Flow Priorities

§ Model cash flows of underlying mortgage pool§ Allocate principal payments to “Most Protected”

PAC§ Allocate principal payments to “Less Protected”

PAC § If principal remaining, allocate to support

tranches§ If principal remaining, allocate to “Less

Protected” PAC§ If principal remaining, allocate to “Most

Protected” PAC

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Asset Backed Securities

§ Home Equity Loans§ Auto Loans§ Manufacture Housing§ Credit Cards§ Student Loans§ Equipment Leases§ Other Assets

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Modeling CMO & ABS

§ Key considerationú CMOs tranche prepayment riskú ABS tranche default riskú Model underlying collateralú Allocate principal based on structure

§ Typically difficult to model in-house

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Collateralized Debt Obligations (CDOs)§ Similar to ABS, but collateral is a wide variety

of financial instruments§ Modeling strategy is the same:ú Project cash flows of underlying collateralú Use CDO structure to parse cash flows amongst

various classes within the CDO

§ Complexity Risk

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Types of CDOs

§ Structured finance securities (mortgage-backed securities, home equity asset-backed securities, commercial mortgage-backed securities)

§ Leveraged loans § Corporate bonds § Real estate investment trust (REIT) debt § Commercial real estate mortgage debt (including whole

loans, B notes, and Mezzanine debt) § Emerging-market sovereign debt § Project finance debt § Trust Preferred securities

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Interest Rate Derivatives

§ Notional amount applied to some combination of reference rates and strike rates§ Cap: Notional x max ( reference rate - strike

rate, 0 )§ Floor: Notional x max ( strike rate – reference

rate, 0 )§ Swap: Notional x [ reference rate(1) –

reference rate(2) ]

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Equity Derivatives

§ Typically only modeled for specific products (e.g., FIA)§ Pricing difficult§ Options/derivatives as a reinvestment asset

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Validation of Asset Models

§ Starting valuesú Bookú Parú Market

§ Portfolio Yield§ Cash flow analysisú Principal paymentsú Interest paymentsú Calls/Prepaymentsú Defaults

§ Policy loans

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Typical Modeling Approach by Asset Class§ Model seriatim in-houseú Bondsú Mortgages & mortgage pass-throughú Interest rate derivativesú Simple European equity options

§ Model via external vendors (EPA)ú CMOú MBSú CDO

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Asset/Liability Interaction

§ Reinvestment§ Disinvestment

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Reinvestment Strategies -Basic§ Define asset mixú Asset classú Credit ratingú Maturity

§ Rebalanceú No - Cash methodú Yes - Book method

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Reinvestment Strategies -Conditional§ Change over projection horizonú E.g., invest in longer average duration in first five

years, then shorter duration thereafter

§ Scenario drivenú E.g., invest in longer average duration when yield

curve is normal (i.e., upward sloping) and switch to shorter duration when yield curve is inversed

§ Duration matchú Keep average asset duration within tolerance level

to average liability duration60



Reinvestment Strategies –Duration Match§ Determine liability durationú Pre-specifiedú Dynamically calculated

§ Define tolerance & frequency§ Define “duration match” portfolioú Long vs. shortú Asset class (e.g., bonds, interest derivatives)

§ Allow rebalance?

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Reinvestment Strategies –Duration Match

Liability duration = Existing asset duration x Weight1 + “Match portfolio” duration x Weight2

§ No rebalance: 0 < Weight2 < cash available§ With rebalance: 0 < Weight2 < 1

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Disinvestment Strategies

§ Selling assetsú Market value calculationsú Order of sales Existing vs. reinvested (or “model purchased“) By asset class – e.g., sell easier-to-value assets Pro rata vs. single assets (e.g., maximize gain)

§ Buying negative assets (borrowing from another Line of business)§ Borrowing

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Questions?

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Documents

2012-la-val-act-49