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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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Introduction to Asset Modeling 2
Tuesday, September 11, 2012Valuation Actuary Symposium
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
3
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
4
Introduction to Asset Modeling 3
Tuesday, September 11, 2012Valuation Actuary Symposium
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
5
Asset Class Yield Curves
§ Use of asset yield curvesú Calculate market valueú Determine yields on reinvestmentsú Basis for exercise of financial options
Tuesday, September 11, 2012Valuation Actuary Symposium
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
Introduction to Asset Modeling 5
Tuesday, September 11, 2012Valuation Actuary Symposium
Asset Spreads Consideration
§ Credit rating§ Maturity§ Liquidity§ Embedded optionú May be more difficult to develop
Tuesday, September 11, 2012Valuation Actuary Symposium
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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Introduction to Asset Modeling 9
Tuesday, September 11, 2012Valuation Actuary Symposium
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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Tuesday, September 11, 2012Valuation Actuary Symposium
§ 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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Introduction to Asset Modeling 11
Tuesday, September 11, 2012Valuation Actuary Symposium
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
Tuesday, September 11, 2012Valuation Actuary Symposium
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%
100%
0 3 6 9 12 15 18 21 24 27 30
Period
Pri
ncip
al
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Outstanding Principal
Period
Cas
h Fl
ow
Interest Principal Total
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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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Introduction to Asset Modeling 17
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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
0%
1%
2%
3%
4%
5%
6%
7%
Months
Con
stan
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paym
ent Rat
e
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Principal Payments – 100% PSA
0.0
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ents
Month
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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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Introduction to Asset Modeling 21
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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
0.0
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Principal Payments 100% and 350% PSA
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PAC Schedule 100% PSA 350% PSA
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Introduction to Asset Modeling 23
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Principal Payments – 100 PSA
0.0
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PAC Support
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Principal Payments – 350 PSA
0.0
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PAC Support
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Introduction to Asset Modeling 24
Tuesday, September 11, 2012Valuation Actuary Symposium
Principal Payments – 600 PSA
0.0
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PAC Support PAC Schedule
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Principal Payments – 50 PSA
0.0
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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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Introduction to Asset Modeling 26
Tuesday, September 11, 2012Valuation Actuary Symposium
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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Introduction to Asset Modeling 27
Tuesday, September 11, 2012Valuation Actuary Symposium
§ 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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Tuesday, September 11, 2012Valuation Actuary Symposium
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