Study Notes and Published Refences - Note 8I-306-00

Study Notes and Published Refences - Note 8I-306-00 - CASH FLOW ANALYSIS TECHNIQUES

Valuation Concepts

Forms of Risk
- Interest rate duration risk - C-3
  - insurance co can be selected against when int rates move
  - if rates increase - disintermediation risk
  - if rated decline - reinvestment risk
  - Valn Actuary's concern - how to make good and sufficient opinion w/r to reserves when faced w/ C-3 risk
- Credit (or default) Risk - C-1
  - real default in asset value or a mkt value change in the common stock
- Pricing Risk - C-2
  - ins co can suffer loss due to unforseen changes in experience levels w/r to mortality, morbidity, expenses, etc
Valuation Actuary's Job
- have skills and tools necessary to measure C1, C2 adn C3 risk
- understand and obey SOP established by profession adn regulations regarding messurement of risk
- recognize that need to rely on key indiv in co (COO, CEO, CIO (inv)) for continuation of stated policy and good business judgement in managing co's affairs
  - let them take responsibility for what is theirs
- render an opinion as to adequacy of reserves, taking into account nature of assets supporting the reserves
- NOT the Valn Actuary's job to guarantee solvency
Statement of Opinion
- two levels to the various opinions
  - reasonable reserves
  - reasonable reserve + designated surplus to cover plausible deviations
- current opinion
  - reasonable - probability of reserves being inadequate < x% where x% > 1
  - plausible - probability of reserves & designated surplus being inadequate < 1%
    - actually probability of ruin
Elements of Cash Flow
- insurance (liability) adn asset cash flows projected into future under various int rate scenarios
- some assumptions used in projection are dynamic (vary w/ int)
- main elements of cash flow
  - liab side
    - income components - premiums, policy loan repayments, policy loan interest
    - outflow - benfit payments, surr, divs, comm, expenses, taxes, policy loans
    - policy loans on liab side (asset on B/S) b/c investment people can't invest in policy loans
  - asset side
    - income - bond maturities, mort prin & int pmts, coupons, calls, prepayments, stock divs, real estate, rental income, liquidations adn borrowed money
    - outflow - repayment of borrowed money and capital losses

Cash Flow Analysis for Valuation

actuary must select: scenario set, lapse function, prepayment functions adn reinv function
information on assets more extensive than traditional valuation methods
Scenarios
- definitions
  - int rate scenario defined as sequence of yield curves
  - yield curves - function showing relationship of yield to duratino
  - scenario - sequence of yield curves - one for each period-end in teh future
- cash flow analysis requires choosing a scenario set
- can arbitrarily select a set of scenarios that seem to cover possibilities (NY7)
- drawbacks
  - # possible scenarios unlimited therefore no singel scenario likely to occur in real life
  - no unique way to make probability statement about outcome of testing
- advised (in absense of regulation) to use approach that attempts to capture statistical meaning
- common methods: transitional probability and successive ratios
Transitional Probability Approach
- begin by defining universe of std yield curves
  - one approach, 10yr and 1yr rates w/ intermediate rates set by fitting exponential curve
- define matrix of transitional probabilities
  - P(ij) -> prob c(j) follows c(i)
  - often set in consultation w/ investment officers
  - most of the time, probabilites equal and opposite moves set equal
- set c(0) to std yield curve most like current rates
- monte carlo simulation used to pick future yield curves
- repeat using same c(0) and transition matrix until adequate # scenarios choses
Successive Ratios Model
- stochastic model of ratios of successive interest rates
- y(1)...y(n)... sequence of historical int rates
  - ratio of y(n+1)/y(n) calculated for last 10 years for 1 long and 1 short dur
  - dist function determined which models frequency values appear
  - correlations between long and short rates studied historically
    - bivariate dist w/ proper correlation coefficient constructed
  - simulation performed on bivariate dist to get N pairs of rates for each scenario
- Morgan Stanley research shows promise using ln(y(n+1)/y(n))
  - distribution not precisely normal
  - close enough to justify simplifying assumption

Functional Relationship: The Liab Side

significance of number 40 - can get 40-50 scenario results on a single sheet of paper
when testing stochastically generated scenarios, quite a few boring ones and on a few exciting ones
most extreme scenarios don't necessarily give most extreme results
function relationships - formerly known as setting assumptions
ways to choose assumptions
- dart board
- xerox - using someone else's assumptions
- rules of thumb - similar to Delphi technique
key element sto consider when choosing functional relationships
- relationships
- consistency
- validation
  - should validate reasonably to whatever experience is available
  - should validate reasonable results (sniff test)
Market Rate Assumption
- possibly most important functional relationship - between credited rates, mkt rates, and lapse rates
- mkt rate - rate PO can get by lapsing policy and buying comparable new policy
  - generally rate competing co offering on similar products
- when defining mkt rate, keep in mind what mkt rate used for
- if intest to set credited rate = mkt rate, mkt rate definition for model should match definition for way intend to credit
- sometimes results very sensitive to mkt rate definition and sometimes not
- relationship between earned rate adn mkt rate may not be rational, but there is a relationship
- when choosing mkt rate assumption, dont give too much weight to current situation
- mkt does not always react as quickly as scenario rates doo
- assumption should make sence for the long term
  - s/b consisten w/ historical past
  - apply common sense when looking forward
- mkt rate assumption typically based on current int and sometimes a rolling avg int rate (for cos crediting based on portfolio rate)
- common assumption - mkt rate = max(current, rolling avg)
Credited Rate Strategy
- not an assumption, but a strategy
- decide whether crediting strategy matches what in in CF projection
- strategies key off of one or more of 3 rates
  - fixed rate - initial guar rate, bailout rate, min guar rate
  - earned rate less spread
  - mkt rate
- SC may complicate matters - somewhat safer to have lower credited rate if SC is present
- consider increasing spread for higher int rates
  - applying relationship to mkt rate as well could produce some reasonable answers
- for UL, trend is credit current money rate for 3-5 years
  - then roll into new money rate at end of period
- special considerations for div scales on par policies
  - such as pegged divs
Lapse Rate Function
- largely based on intuition and judgement
  - littel experience available for many types of plans
- considerations
  - if product has SC, less sensitive to difference between credited and mkt
  - PO/Agent characteristics important (stockbroker sold -> higher lapses)
  - bailout
  - "hidden" interest (not obvious to PO like Par WL pols)
  - aging of business - possibility that excess lapses decrease over time
    - core group of PO not sensitive to int rates
- sample SPDA laspe formulas
  - 1982-C3 study - min(5%+ (M-C)^1.5,75%)
  - VA Handbook ex - 15% + 2*(M-C)^2 - 3*SC
  - Case Study - min(5%+2(M-C)^2, 50%)
- excess lapses increase dramatically as spread widens
  - exponential term seems to be fairly well accepted
Policy Loan Utilization
- policy loan environment changed a lot
  - direct recognition and tax law changes
- less likely to take loan and more likely to lapse
- sample utilization rate (mkt rate - loan rate)^1.8
  - function of % of unloaded values and % total avail CV
- SP policies w/ 0 net cost loans - loan assumption could be key assumption to CF analysis
Premium Suspension
- very littel experience available
- new money product premium suspensions should nto be greatly interest sensitive
  - lapses could be problem if PO looks at overall credited rate
- premium suspenstion can be very sensitive to credited rate of interest
Expense Inflation
- generally a valuation concern only for effect on maint expenses
- common assumption - inflation = gov't bond int rate - spread
- overhead might not get appropriate weight in high lapse scenarios
Mortality
- generally accepted - if extra lapses, future mortality will increase
- impaired lives more likely to keep life ins policy since unable to get equiv policy elsewhere
- several models available for calculating excess mortality due to excess lapse
after assumptoins created, run through scenarios
- look at results and see if reasonable

Functional Relationships: The Asset Side

Role of the actuary and the Investment Officer: A discussion
- no agreement on what exactly the Actuary's role s/b w/r to setting inv assumptions
- Larger role in determing investment philosophy
  - actuary determining for LOB responsible for
    - type of assets, type of maturities, type of risks willing to take
    - quality of assets and probability of net realizing expected returns
  - strong communications w/ investment dept a must
  - actuary shoudl decide if CF volatility for a type of asset is acceptable
- Reliance Role
  - one of jobs as Valn Actuary is to rely on other key people
  - rely - work with them, not tell them what to do
  - collaborative effort
  - let the investment people select teh assets they deem appropriate given some guidelines w/ explanations of ramifications of choosing certain types of assets, maturity, structures
  - investment people understand modeling, but modeling not "real world"
  - inv people look at what's happening in mktplace daily and try to take advantage of mkt conditions
- What is an Investment Philosophy?
  - used day-to-day basis by inv dept
  - need assumptions re: investment philosophy in the future
    - may not match what inv people doing today
  - future inv philosophy is an actuarial assumption - actuary responsible for it
    - ought to know current inv philosophy
    - think about possibility that other philosophies will be used in the future
  - inv philosophy may be different depending on purpose of projection
    - stat solvency - only need a 1 year projection
  - Valn Actuary's role is to evaluate effects of an investment philosophy
    - Sr Mgmt's role is to choose the inv philosophy
  - if not sure what your co is going to do in the future
    - run projections w/ different inv philosophies
  - one method - bring in Inv officer, show him the int scenarios and ask "How would you invest?"
    - inv officer will buy into projection and feel comfortable with results
- Reinvestment Function
  - Positive Cash Flows
    - 3 methods
      - continuatino of current strategy
      - follow stated policy (set of rules)
        
        keep dur matched and x% to type A assets etc
      - mkt timing - important to get investment person involved
        
        if mkt does A, invest in B
        inv officer will "do whatever is best"
  - Negative Cash Flows
    - borrow funds - reflect cost of borrowing in projections
    - liquidate assets - pro-rata across all assets or involve specific assets
- Activeness of Asset Portfolio
  - how will assets be managed
    - buy and hold
    - trading or purposeful disinvestment
- Valn Actuary needs ot deal w/ pos cash flows, neg cash flows and asset mgmt when doing cash flow analysis

Assets

which assets backing products valuing?
- s/b consistent w/ investment philosophy statement filed w/ state
if assets not segmented, either set up segmented pool or use pro-rata share of all assets
obtain listing of current assets from inv dept (hopefully inv database)
Treasuries
- 100% guar by govt adn non-callable
- perfect asset except don't earn enough interest to support credited rates
- amortization of prem or discount as CF item
  - Donna Claire would not use since not real cash
  - better to recognize prem/discount @ sale/maturity
Corp Bonds
- used to be most popular asset for ins co investments
- major problem - generally callable
- range where very few bonds called - generally 1% of original int environment
- fairly simple approx - 2% greater than current coupon rate - it gets called
- another approx: .25*(coupon rate - current coupon rate - .25*call prem) min 0, max 1.0
- also check other provisions, such as sinking fund provisions
Commercial Mortgages
- characteristics similar to bonds - take coupons and pay back principal at end
- some have sinking fund payments
- prepayment provision - some have very generous provisions
- current prepayment penalties - such that if investor took payment and invested it in T-bills for remaining period, still wind up w/ same amt int
- could be modeled as non-callable bonds since little reinvestment risk
- have a default risk
- depending on rating, C-1 default risk charge s/b subtracted (similar to corps)
Agricultural Mortgages
- generally short mortgages
- can be variable int - appear to be well suited for I/S products
- problem: many are defaulting - approx 25% industry wide
- C-1 charge s/b enough to cover this type of default (worse than junk)
- charge must be large enough to cover
  - int forfeited
  - opportunity loss when owning property
  - principal loss on sale of asset
- can be as high as 75bps
Gov't Backed Mortgages
- GNMA, FNMA, FHLMC - some of most popular inv for ins cos
- give fairly high int rate
- major problem is duration risk
- very important to model correctly in terms of effect of int scenarios on GNMAs
- sample prepayment equation: 5% + 3*S + 2*S^2 where S and 5 <= P <= 60
- # factors affecting prepayments
  - moving, years left on mort, general economy in area, employment stats
Junk Bonds
- begun to play important role in portfolio
- subtract approx 2.5% of principal to cover default in models
- check diversification - very important in junk
Real Estate
- becoming more popular in I/S portfolios b/c asset is inflation adaptive
- problems modeling real estate
  - need to check w/ inv dept as to expected cash flows, not just expected avg returns over expected holding period
  - when do you assume you sell property
  - what will price be when real estate is sold
    - good approx is that it appreciates at economic int rate + x% (typically around 3%)
Case Study Life
- additional reserve req'd to make probably of inadequacies < 1%
  - take PV of cashflows from each trian using that trials int rates
  - assuming results normally distributed, use std dev and mean to determine point probability that PV < 0 is <= 1%
- generation of scenarios - monte carlo & lognormal method
  - monte carlo - randomly generated using starting yield curve, yield curve universe and probability of movement matrix
  - lognormal - randomly generated using starting yield curve, volatility factor and lognormal dist function
  - differences between two not enough to say which is better
- reserves should cover reasonable deviations
- reserves and surplus should cover reasonable and plausible deviations

Copyright © 2004 Steve Welander.
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