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Asset Modeling 1
Tuesday, September 11, 2012Consultant's Name
Virtual Session 49 PD:Introduction to
Asset Modeling Concepts
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Asset Modeling 2
Tuesday, September 11, 2012Consultant's Name
ASSET MODELING
3
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
4
Asset Modeling 3
Tuesday, September 11, 2012Consultant's Name
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
5
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
6
Asset Modeling 4
Tuesday, September 11, 2012Consultant's Name
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
7
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
8
Asset Modeling 5
Tuesday, September 11, 2012Consultant's Name
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
9
Asset Spreads Consideration
§ Credit rating§ Maturity§ Liquidity§ Embedded optionú May be more difficult to develop
10
Asset Modeling 6
Tuesday, September 11, 2012Consultant's Name
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
11
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”
12
Asset Modeling 7
Tuesday, September 11, 2012Consultant's Name
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?
13
Default Assumption
§ Default assumption – sources of dataú Moody'sú S&Pú Wall streetú Company experience/investment advisors
14
Asset Modeling 8
Tuesday, September 11, 2012Consultant's Name
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
15
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
16
Asset Modeling 9
Tuesday, September 11, 2012Consultant's Name
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
17
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
18
Asset Modeling 10
Tuesday, September 11, 2012Consultant's Name
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
19
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
20
Asset Modeling 11
Tuesday, September 11, 2012Consultant's Name
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
21
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”
22
Asset Modeling 12
Tuesday, September 11, 2012Consultant's Name
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
23
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
24
Asset Modeling 13
Tuesday, September 11, 2012Consultant's Name
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
25
Treasury Inflation-Protected Securities (or TIPS)
§ Coupon is fixed§ Principal adjusted to the Consumer Price
Index
26
Asset Modeling 14
Tuesday, September 11, 2012Consultant's Name
Mortgages
§ Property typeú Commercialú Residential
§ Amortization Patternú Amortizingú Non-Amortizing (interest only)ú Balloon
§ Interest Rateú Fixedú Floating
27
Quality of Underwriting –Residential Mortgages§ Conforming mortgage ú Strict standards Amount Down payment Income Credit history Property condition
§ Non – conforming loansú Alt-Aú Subprime
28
Asset Modeling 15
Tuesday, September 11, 2012Consultant's Name
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
29
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
30
Asset Modeling 16
Tuesday, September 11, 2012Consultant's Name
Outstanding Principal
Period
Cas
h Fl
ow
Interest Principal Total
31
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
32
Asset Modeling 17
Tuesday, September 11, 2012Consultant's Name
Factors Influencing Prepayments§ Refinancing incentiveú Current rate VS. market rate + refinancing cost
§ Age of the mortgage§ Seasonality§ Burnout
33
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
34
Asset Modeling 18
Tuesday, September 11, 2012Consultant's Name
100% PSA
0%
1%
2%
3%
4%
5%
6%
7%
Months
Con
stan
t Pre
paym
ent Rat
e
35
Principal Payments – 100% PSA
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Pri
ncip
al P
aym
ents
Month
36
Asset Modeling 19
Tuesday, September 11, 2012Consultant's Name
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
37
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
38
Asset Modeling 20
Tuesday, September 11, 2012Consultant's Name
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
39
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
40
Asset Modeling 21
Tuesday, September 11, 2012Consultant's Name
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
41
Types of CMO Tranches
§ Sequentials§ PACs/TACs§ Z tranche§ Principal Only§ Interest Only
42
Asset Modeling 22
Tuesday, September 11, 2012Consultant's Name
Sequential CMOs
§ First CMOs§ Pay principal sequential to tranches§ Purpose was to create short, medium and
long term out of a single mortgage pool
43
Sequential CMOPrincipal Payments – 100% PSA
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Pri
ncip
al P
aym
ents
Month
44
Asset Modeling 23
Tuesday, September 11, 2012Consultant's Name
Principal Payments 100% and 350% PSA
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Pri
ncip
al P
aym
ents
Month
PAC Schedule 100% PSA 350% PSA
45
Principal Payments – 100 PSA
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Pri
ncip
al P
aym
ents
Month
PAC Support
46
Asset Modeling 24
Tuesday, September 11, 2012Consultant's Name
Principal Payments – 350 PSA
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Pri
ncip
al P
aym
ents
Month
PAC Support
47
Principal Payments – 600 PSA
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Pri
ncip
al P
aym
ents
Month
PAC Support PAC Schedule
48
Asset Modeling 25
Tuesday, September 11, 2012Consultant's Name
Principal Payments – 50 PSA
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
Pri
ncip
al P
aym
ents
Month
PAC Support PAC Schedule
49
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
50
Asset Modeling 26
Tuesday, September 11, 2012Consultant's Name
Asset Backed Securities
§ Home Equity Loans§ Auto Loans§ Manufacture Housing§ Credit Cards§ Student Loans§ Equipment Leases§ Other Assets
51
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
52
Asset Modeling 27
Tuesday, September 11, 2012Consultant's Name
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
53
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
54
Asset Modeling 28
Tuesday, September 11, 2012Consultant's Name
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) ]
55
Equity Derivatives
§ Typically only modeled for specific products (e.g., FIA)§ Pricing difficult§ Options/derivatives as a reinvestment asset
56
Asset Modeling 29
Tuesday, September 11, 2012Consultant's Name
Validation of Asset Models
§ Starting valuesú Bookú Parú Market
§ Portfolio Yield§ Cash flow analysisú Principal paymentsú Interest paymentsú Calls/Prepaymentsú Defaults
§ Policy loans
57
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
58
Asset Modeling 30
Tuesday, September 11, 2012Consultant's Name
Asset/Liability Interaction
§ Reinvestment§ Disinvestment
59
Reinvestment Strategies -Basic§ Define asset mixú Asset classú Credit ratingú Maturity
§ Rebalanceú No - Cash methodú Yes - Book method
60
Asset Modeling 31
Tuesday, September 11, 2012Consultant's Name
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 duration61
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?
62
Asset Modeling 32
Tuesday, September 11, 2012Consultant's Name
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
63
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
64
Asset Modeling 33
Tuesday, September 11, 2012Consultant's Name
Questions?
65
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